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This is an AI modernization of Dialogue Concerning the Two Chief World Systems into contemporary English. The original is available from Wikisource (Italian). Also available as an epub.
Galileo Galilei was sixty-eight when this book was printed in Florence in 1632, and the most famous scientist in Europe. Twenty-two years earlier he had pointed a telescope at the sky and reported mountains on the moon, four moons going round Jupiter and phases on Venus. In 1616 the church had declared the claim that the Earth moves around the sun to be contrary to Scripture, and Galileo had been told not to hold or defend it. The Dialogue was licensed on the understanding that it laid out the arguments on both sides and reached no verdict.
It is a conversation over four days in a palace in Venice between three men. Salviati puts the Copernican case. Sagredo is the host, quick and amused, an intelligent amateur who asks the questions a reader would ask. Simplicio defends Aristotle and Ptolemy, and he loses. Galileo named the first two after real friends of his who were dead by 1632; the third name is his own invention and it is not flattering.
He wrote it in Italian rather than Latin, deliberately. Latin was the language of the universities and of the men who had ruled against him. Italian was the language of everybody else, and the book is written for them: arguments built out of ships and cannon and birds and dropped stones, geometry explained in words, and long stretches that are funny on purpose. It is also rude. Simplicio quotes authorities, gets tied in knots, and is teased for it, and that tone is part of what made the book dangerous.
Day One takes apart the old division between a corruptible Earth and a perfect unchanging sky. Day Two argues that the Earth turns daily, and contains the passage everyone remembers: shut yourself in the cabin below the deck of a ship with some flies and a bowl of water, and nothing you can do in there will tell you whether the ship is moving. Day Three argues the yearly orbit. Day Four explains the tides as a result of the Earth's two motions sloshing the seas about, which was the argument Galileo was proudest of and is wrong. It is translated here straight, with full conviction and no correction, because that is how he wrote it.
The book sold out. Within months it was stopped, and in 1633 Galileo was summoned to Rome, tried by the Inquisition, made to kneel and abjure, and sentenced to house arrest. He spent his last nine years confined to his villa outside Florence, going blind, and died there in 1642. The Dialogue stayed on the church's list of forbidden books for two hundred years.
This translation is from Galileo's own Italian.
A Dialogue by Galileo Galilei, member of the Lincean Academy, Extraordinary Mathematician of the University of Pisa, and Chief Philosopher and Mathematician to the Most Serene Grand Duke of Tuscany.
In which, over the course of four days of conversation, the two chief systems of the world — the Ptolemaic and the Copernican — are discussed, and the philosophical and natural arguments for each side are set out without a verdict.
With privileges. Printed in Florence by Giovanni Battista Landini, 1632. With the license of the authorities.
Let it be printed, if it so appears to the Most Reverend Father, Master of the Sacred Apostolic Palace. A., Bishop of Bellicastro, Vicegerent.
Let it be printed. Fra Niccolò Riccardi, Master of the Sacred Apostolic Palace.
Let it be printed in Florence, the customary requirements being observed. September 11, 1630. Pietro Niccolini, Vicar General of Florence.
Let it be printed. September 11, 1630. Fra Clemente Egidi, Inquisitor General of Florence.
Let it be printed. September 12, 1630. Niccolò dell'Antella.
The difference between human beings and the other animals is enormous; and yet anyone who claimed that a difference nearly as great exists among human beings themselves would not be talking nonsense. What is the ratio of one to a thousand? And still the proverb is on everyone's lips: one man may be worth a thousand, where a thousand are not worth one. A difference like that comes down to the varying powers of our minds, and for me it reduces to this — being or not being a philosopher. For philosophy is the proper food of such minds, and whoever can feed on it is set apart, in fact, from the common run of humanity, to a greater or lesser degree of worth depending on how rich that nourishment is. Whoever looks higher stands out more highly; and turning to the great book of nature — which is the true object of philosophy — is the way to lift one's eyes. In that book, everything we read, being the work of an all-powerful Craftsman, is for that reason perfectly proportioned; but the reading is swiftest and worthiest where the work and the artistry appear, to our sight, the greatest. Among all the natural things our minds can grasp, the constitution of the universe deserves, I believe, first place: for as it contains everything and surpasses everything else in size, so, as the rule and sustainer of everything, it must surpass everything else in nobility as well. Therefore, if it ever fell to any men to stand out in intellect above the rest of humanity, it was Ptolemy and Copernicus, who read so loftily in the constitution of the world, fixed their gaze on it, and philosophized about it. Since these Dialogues of mine turn chiefly on the works of those two, it seemed they should be dedicated to no one but Your Highness; for their doctrine rests on those two men, whom I judge the greatest minds ever to have left us their works on such speculations, and so, to spare them any loss of rank, I had to place them under the favor of the one who is, in my eyes, greatest of all, from whom they may receive both glory and protection. And if those two have brought so much light to my understanding that this work of mine may largely be called theirs, it may just as well be called Your Highness's; for by your generous magnificence I was given not only the leisure and peace to write it, but also, through your effective help — never weary of honoring me — it has at last been brought into the light. Accept it, then, Your Highness, with your customary kindness; and if lovers of truth find in it anything that yields them fuller knowledge or real benefit, count it as your very own, accustomed as you are to doing good — so much so that in your happy dominion no one feels any of the universal hardships of this world troubling him. Praying for your prosperity, and that you may grow ever greater in this pious and magnanimous habit, I offer you my most humble reverence.
Your most humble and most devoted servant and vassal, Galileo Galilei.
Some years ago a salutary edict was issued in Rome which, to head off the dangerous scandals of the present age, imposed a timely silence on the Pythagorean opinion that the Earth moves. There was no shortage of people who rashly asserted that this decree was the offspring not of judicious examination but of poorly informed passion; and complaints were heard that consultants wholly inexperienced in astronomical observation ought not, with a sudden prohibition, to clip the wings of speculative minds. My zeal could not keep silent when I heard the recklessness of such complaints. Being fully informed about that most prudent determination, I judged it right to appear publicly on the stage of the world as a witness of the honest truth. I happened to be in Rome at the time; I received not only audiences but applause from the most eminent prelates of that court; nor was the decree published without my having had some advance notice of it. Therefore it is my purpose in the present work to show foreign nations that as much is known of this matter in Italy — and particularly in Rome — as ultramontane diligence could ever have imagined; and, by gathering together all my own speculations on the Copernican system, to make it known that awareness of every one of them preceded the Roman censure, and that from this climate come not only dogmas for the salvation of the soul, but ingenious discoveries for the delight of the mind as well.
To this end I have taken the Copernican side in the discussion, proceeding upon a pure mathematical hypothesis, and striving by every artful means to present it as superior — not to the doctrine of the Earth's stillness absolutely, but to that doctrine as it is defended by certain men who profess to be Peripatetics yet keep only the name, content, without ever taking a walk, to worship shadows, philosophizing not with due attention but from the mere memory of four ill-understood principles.
Three main topics will be treated. First, I shall try to show that all experiments that can be performed on the Earth are insufficient means for proving its mobility, since they can be fitted indifferently to a moving Earth or to one at rest; and I hope that in this connection many observations unknown to the ancients will come to light. Second, the celestial phenomena will be examined, reinforcing the Copernican hypothesis as if it must emerge absolutely victorious, and adding new speculations — which, however, serve for convenience in astronomy, not as necessities of nature. In the third place I shall propose an ingenious fancy. I found myself saying, many years ago, that the unsolved problem of the tides might receive some light if the Earth's motion were granted. This remark of mine, flying from mouth to mouth, had found charitable fathers ready to adopt it as the child of their own wit. Now, so that no foreigner may ever appear who, arming himself with our own weapons, reproaches us for inattention to so important a matter, I have judged it best to set out the probable arguments that would make it persuasive, granted that the Earth moves. I hope that from these considerations the world will learn that if other nations have navigated more, we have speculated no less; and that to submit to asserting the Earth's stillness, and to take the contrary as nothing more than a mathematical caprice, comes not from ignorance of what others have thought about it, but — if from nothing else — from those reasons supplied by piety, by religion, by the knowledge of divine omnipotence, and by the consciousness of the weakness of the human mind.
I have thought it fitting, moreover, to unfold these ideas in the form of a dialogue, which, not being bound to the rigorous observance of mathematical laws, leaves room for digressions too — at times no less interesting than the main argument.
Many years ago I often found myself in the marvelous city of Venice in conversation with Signor Giovan Francesco Sagredo, a man of most illustrious birth and most penetrating mind. From Florence came Signor Filippo Salviati, the least of whose splendors were the purity of his blood and the magnificence of his wealth: a sublime intellect that fed on no delicacy more avidly than on exquisite speculations. With these two I often found myself discussing these matters, in the presence of a Peripatetic philosopher — one for whom nothing seemed to stand more in the way of understanding the truth than the fame he had acquired as an interpreter of Aristotle.
Now, since a most bitter death has, in the very prime of their years, deprived Venice and Florence of those two great lights, I have resolved to prolong their fame, as far as my feeble powers allow, upon these pages of mine, by bringing them in as speakers in the present controversy. Nor will the good Peripatetic lack his place: because of his excessive fondness for the commentaries of Simplicius, it seemed fitting, without revealing his name, to leave him the name of that revered author. May those two great souls, forever venerable to my heart, receive this public monument of my undying love; and may the memory of their eloquence help me to set forth to posterity the speculations here promised.
It happened (as it will) that various scattered discussions had arisen among these gentlemen, which had inflamed rather than quenched the thirst for learning in their minds; so they made the wise resolution to spend a few days together in which, with every other business set aside, they would devote themselves to contemplating, in more orderly speculations, the wonders of God in the heavens and on the earth. They gathered in the palace of the most illustrious Sagredo; and there, after the customary but brief compliments, Signor Salviati began as follows.
Salviati: Yesterday we ended with an agreement: today we would discuss, as clearly and in as much detail as we can manage, the natural arguments — and their real strength — that have so far been offered on either side, by the champions of the Aristotelian and Ptolemaic position and by the followers of the Copernican system. And since Copernicus, by placing the Earth among the moving bodies of the heavens, makes it a globe like a planet, the right place to begin our considerations is by examining just what force and energy there is in the arguments of the Peripatetics — the Aristotelian school — when they set out to demonstrate that this assumption is flatly impossible; given that, on their view, nature requires two substances utterly different from each other, the celestial and the elemental, the one impervious to change and immortal, the other alterable and perishable. Aristotle handles this argument in his books On the Heavens, first working up to it through reasoning that depends on certain general assumptions, and then confirming it with experience and with particular demonstrations. I'll follow his same order: I'll lay the case out, and then say freely what I think of it — submitting myself to your judgment, and especially to that of Simplicio, so vigorous a champion and defender of the Aristotelian doctrine.
The first step in the Peripatetic case is the one where Aristotle proves the completeness and perfection of the world by pointing out that it is not a mere line, nor a bare surface, but a body furnished with length, breadth, and depth; and since there are no dimensions beyond these three, in having them the world has them all, and having all, it is perfect. Now, that from simple length there is constituted the magnitude we call a line; that adding breadth gives us a surface; that adding height or depth on top of that yields a body; and that after these three dimensions there is no passing on to any other, so that in these three alone completeness — totality, so to speak — is exhausted: all this I could well have wished Aristotle had proved to me by strict necessity, above all since it can be done quite clearly and quickly.
Simplicio: What about the beautiful demonstrations in the second, third, and fourth texts, right after the definition of the continuum? Don't you have it there, first of all, that there is no dimension beyond the three because three is everything — three is in every direction? And isn't this confirmed by the authority and doctrine of the Pythagoreans, who say that all things are determined by three — beginning, middle, and end — which is the number of the whole? And where do you leave the other argument: that this number is used, as if by a law of nature, in the sacrifices to the gods? And that nature herself dictates that we give the title "all" to things that come in threes, and to nothing fewer? Of two things we say "both," not "all" — but of three we say it readily. All this doctrine you have in the second text. Then in the third, ad pleniorem scientiam — for fuller understanding — we read that "everything," "the whole," and "the perfect" are formally one and the same; and that this is why, among magnitudes, only body is perfect, because only body is determined by three, which is the whole, and being divisible in three ways, it is divisible in every direction — whereas of the others, one is divisible in one way and another in two, since each has its division and its continuity according to the number allotted to it: one is continuous in one direction, another in two, but body alone in all of them. What's more, in the fourth text, after some further doctrines, doesn't he prove the same point with yet another demonstration — namely, that a transition is made only where something is lacking (thus we pass from the line to the surface, because the line lacks breadth), but it is impossible for the perfect to lack anything, since it is complete in every direction, and therefore there is no passing from body to any further magnitude? Now from all these places, doesn't it seem to you sufficiently proved that beyond the three dimensions — length, breadth, and depth — there is no passage to any other, and that body, which has all three, is therefore perfect?
Salviati: To tell you the truth, in all these discourses the only thing I've felt compelled to concede is that whatever has a beginning, a middle, and an end may and should be called perfect. But that because beginning, middle, and end make three, the number three is therefore a perfect number, with the power to confer perfection on whatever possesses it — there I feel nothing that moves me to agree. I don't understand, and don't believe, that where legs are concerned, for example, the number three is any more perfect than four or two; nor am I aware that the number four does the elements any disservice, or that they'd be more perfect if there were three of them. Better, then, to have left these pretty conceits to the orators, and to have proved his point by necessary demonstration — for that is how one is to proceed in the demonstrative sciences.
Simplicio: You seem to treat these arguments as a joke. Yet all of this is the doctrine of the Pythagoreans, who attributed so much to numbers; and you, who are a mathematician — and, I believe, a Pythagorean philosopher in many of your opinions — now appear to scorn their mysteries.
Salviati: That the Pythagoreans held the science of numbers in the highest esteem, and that Plato himself admired the human intellect and thought it shared in divinity simply because it could understand the nature of numbers — this I know very well, and I'd be inclined to make the same judgment myself. But that the mysteries which led Pythagoras and his sect to hold the science of numbers in such veneration are the silly stuff that circulates in the mouths and on the pages of the crowd — that I don't believe for a moment. On the contrary: I know that they, so that marvelous things would not be exposed to the sneers and contempt of the mob, condemned as sacrilege the publishing of the most hidden properties of numbers, and of the incommensurable and irrational quantities they had investigated, and preached that whoever revealed them would be tormented in the next world. So I think one of them, to throw the crowd a scrap and buy himself free of its questions, told them that their numerical mysteries were precisely those trifles which afterwards spread among the common people — a piece of cunning and shrewdness much like that of the clever young man who, to rid himself of the pestering of his mother, or his inquisitive wife, I forget which, who besieged him to share the secrets of the senate, made up that famous tale which left her, and many other women with her, thoroughly mocked — to the great laughter of that same senate.
Simplicio: I have no wish to be counted among those too curious about the mysteries of the Pythagoreans. But to keep to our subject: I reply that the arguments Aristotle produces to prove that the dimensions are not, and cannot be, more than three seem conclusive to me; and I believe that if a more rigorous demonstration had existed, Aristotle would not have left it out.
Sagredo: Add at least: if he had known it, or if it had occurred to him. But Salviati, you'd be doing me a great kindness by giving me some clear argument of your own — if you have one plain enough for me to grasp.
Salviati: Not only for you, but for Simplicio too; and not merely one you can grasp, but one you already know — though perhaps without ever having noticed it. And to make it easier to follow, let's take paper and pen, which I see lying ready here for just such occasions, and draw ourselves a little figure. First we'll mark these two points, A and B, and draw from one to the other the curved lines ACB and ADB, and the straight line AB. Now I ask you: which of these, in your mind, is the one that determines the distance between the endpoints A and B — and why?
Sagredo: I'd say the straight line, and not the curves. Partly because the straight one is the shortest; partly because it is one — single and definite — while the others are infinitely many, unequal, and longer; and it seems to me the determination ought to be taken from what is one and certain.
Salviati: So we have the straight line, then, as the determiner of length between two endpoints. Now let's add another straight line, parallel to AB — call it CD — so that a surface lies enclosed between them; and I'd like you to assign me that surface's breadth. So, starting from the endpoint A, tell me where and by what route you'd go to land on the line CD, so as to assign me the breadth contained between the two lines. Will you determine it by the length of the curve AE, or by the straight line AF, or...
Simplicio: By the straight line AF, and not by the curve — curves having already been ruled out for such a use.
Sagredo: But I wouldn't use either of them, seeing that the straight line AF runs at a slant. I'd draw a line square to CD, because that one, it seems to me, would be the shortest — and the single one among the infinitely many longer, mutually unequal lines that can be drawn from the endpoint A to one point after another of the opposite line CD.
Salviati: Your choice, and the reason you give for it, strike me as perfect. So far, then, we have this: the first dimension is determined by a straight line; the second — breadth — by another line, also straight, and not merely straight, but at right angles to the one that determined length. And with that we have defined the two dimensions of a surface: length and breadth. But suppose you had to determine a height — say, how high this ceiling stands above the floor we have beneath our feet. From any point on the ceiling one can draw infinitely many lines, curved and straight, all of different lengths, to infinitely many points on the floor below. Which of all those lines would you use?
Sagredo: I'd fasten a string to the ceiling with a lead plumb hanging from it, and let it pay out freely until it came down almost to the floor. The length of that string — being the straight line, and the shortest of all the lines that could be drawn from that same point to the floor — I'd say is the true height of this room.
Salviati: Excellent. And if from the point marked on the floor by this hanging string (taking the floor to be level, not sloping) you set two more straight lines running, one along the length and the other along the breadth of the floor's surface, what angles would they make with the string?
Sagredo: Right angles, certainly — since the string falls plumb and the floor is good and flat and level.
Salviati: Then if you fix some point as the origin and starting place of your measurements, and from it draw one straight line as the determiner of the first measure, namely the length, then of necessity the line that is to define the breadth must set out at a right angle to the first; and the line that is to mark the height, the third dimension, setting out from that same point, must form with the other two angles that are not oblique but right. And so from the three perpendiculars — as from three lines that are each single, certain, and shortest — you'll have the three dimensions determined: AB length, AC breadth, AD height. And since it is clear that no further line can meet at that same point so as to make right angles with these, and since the dimensions must be determined by straight lines alone that make right angles with one another, it follows that the dimensions are no more than three. And whatever has the three has them all; and whatever has them all is divisible in every direction; and whatever is that, is perfect — and so on.
Simplicio: And who says other lines can't be drawn? Why can't I bring another line up from below to the point A, square to all the others?
Salviati: You most certainly cannot make more than three straight lines meet at one and the same point so as to form right angles with one another.
Sagredo: Yes — because the line Simplicio means would be, it seems to me, simply DA itself extended downward. In that fashion one could draw two more; but they would be the same first three lines, differing only in this: where they now merely touch at the point, they would then cut through it. They'd bring in no new dimensions.
Simplicio: I won't say this argument of yours can't be conclusive. But I will say, with Aristotle, that in the things of nature one need not always demand the necessity of mathematical demonstration.
Sagredo: Perhaps not — where it can't be had. But if here it can, why don't you want it used? Still, we'd best not spend more words on this point, because I believe Salviati would have granted Aristotle — and you — without any further demonstrations, that the world is a body, and perfect, and supremely perfect, as the greatest work of God.
Salviati: So he would, truly. So let's leave the general contemplation of the whole and come to the consideration of the parts, which Aristotle in his first division makes two, very different from each other and in a certain way contrary: the celestial and the elemental. The celestial: ingenerable, incorruptible, inalterable, impervious to change, and so on. The elemental: exposed to continual alteration, mutation, and the rest. This difference he derives, as from its original principle, from the diversity of local motions, and he proceeds along this path.
Leaving the world of the senses, so to speak, and withdrawing into the ideal world, he begins, architect-fashion, by considering that since nature is the principle of motion, it is fitting that natural bodies be movable with local motion. He then declares that local motions come in three kinds: circular, straight, and a mixture of straight and circular. The first two he calls simple, because of all lines only the circular and the straight are simple. Narrowing things down a bit, he then defines afresh: of the simple motions, one is the circular — that made around the center — and the straight is upward and downward; upward being the motion that departs from the center, downward the motion that goes toward the center. From this he infers that of necessity all simple motions are confined to these three kinds: toward the center, away from the center, and around the center. And this, he says, answers with a certain lovely proportion to what was said above about body — that it too is perfected in three things, and so likewise is its motion. With these motions established, he goes on to say that since some natural bodies are simple and others are compounds of them (and he calls simple those bodies that have from nature a principle of motion, like fire and earth), it is fitting that the simple motions belong to the simple bodies, and the mixed motions to the compounds — with this proviso, that the compounds follow the motion of whichever part predominates in their composition.
Sagredo: Please, Salviati, stop there a moment, because in this progression I feel doubts sprouting up on so many sides that I must either speak them now, if I'm to listen attentively to what you'll add next, or else withdraw my attention from what's to be said, if I'm to hold the doubts in memory.
Salviati: I'll stop very gladly, because I'm running the same risk myself, and at every step I'm on the point of losing my way — having to sail among reefs and waters so broken that they make me, as the saying goes, lose my compass. So before the pile grows any higher, set out your difficulties.
Sagredo: You began, together with Aristotle, by drawing me a little way out of the sensible world, to show me the architecture by which it must have been built; and, to my pleasure, you started by telling me that a natural body is by nature movable — nature having been defined elsewhere as the principle of motion. But here a small doubt was born in me: why didn't Aristotle say that some natural bodies are movable by nature and others immobile? For in the definition, nature is said to be the principle of motion and of rest. If natural bodies all have a principle of movement, then either there was no need to put rest into the definition of nature, or no need to bring such a definition in at this point.
Next, as to his explaining what he understands by simple motions, and how he determines them from the spaces they cover — calling simple those made along simple lines, which are only the circular and the straight — I accept that quietly enough; nor do I care to press the fine-grained objection of the helix wound around a cylinder, which, being in every part similar to itself, could seemingly be counted among the simple lines. But I do bristle a little at hearing him narrow this down — while seeming, in other words, merely to repeat the same definitions — to calling the one "motion around the center," and the other sursum et deorsum, that is, up and down: terms that have no use outside the built world, and that suppose it not only built but already inhabited by us. Now, if straight motion is simple by the simplicity of the straight line, and if simple motion is natural, then let it be made in any direction whatever — I mean up, down, forward, backward, to the right, to the left, and any other way you can imagine — so long as it's straight, it ought to belong to some simple natural body; or, if not, Aristotle's supposition is defective. One sees, moreover, that Aristotle hints there is only one circular motion in the world, and consequently only one center, to which alone the straight motions up and down refer — every sign that he means to switch the cards in our hand, and to fit the architecture to the building rather than build the building according to the precepts of architecture. For if I say that in the universe of nature there can be a thousand circular motions, and consequently a thousand centers, there will then also be a thousand motions up and a thousand motions down.
Moreover, he posits, as I said, simple motions and mixed motion — calling the circular and the straight simple, and the compound of the two mixed. Of natural bodies he calls some simple (namely, those that have a natural principle of simple motion) and others compound; and the simple motions he assigns to the simple bodies, and the compound motion to the compounds. But by compound motion he no longer means the mixture of straight and circular — which can exist in the world; he brings in a mixed motion as impossible as it is impossible to mix opposite motions along one and the same straight line, so as to produce from them a motion that is partly upward and partly downward. And to soften so great an awkwardness and impossibility, he falls back on saying that such mixed bodies move according to the simple part that predominates — which in the end forces one to say that even motion made along the same straight line is sometimes simple and sometimes compound; so that the simplicity of a motion no longer depends solely on the simplicity of its line.
Simplicio: Oh, doesn't it seem to you difference enough, if the simple and absolute motion is a great deal swifter than the motion that comes from predominance? How much faster does a piece of pure earth fall than a scrap of wood?
Sagredo: Fine, Simplicio. But if simplicity has to change on that account, then besides there being a hundred thousand mixed motions, you'll never be able to point out the simple one for me. Worse: if greater and lesser speed can alter the simplicity of a motion, then no simple body will ever move with simple motion — since in all natural straight motions the speed keeps forever increasing, and so keeps forever changing the simplicity, which, to be simplicity, must be unchangeable. And, what matters more, you'll be charging Aristotle with a fresh fault: in his definition of compound motion he made no mention of slowness or of speed, which you now lay down as a necessary and essential condition. Besides, you'll harvest no fruit at all from such a rule; for there will be mixed bodies, and not a few, of which some move more slowly and others more swiftly than the simple one — lead and wood, for example, compared with earth. So among these motions, which will you call the simple, and which the compound?
Simplicio: The simple motion will be the one performed by a simple body, and the mixed motion the one performed by a compound body.
Sagredo: Very fine indeed. But what's this, Simplicio? A moment ago you wanted simple and mixed motion to teach me which bodies are simple and which are compound; and now you want me to learn, from the simple bodies and the compound ones, which motion is simple and which is mixed. An excellent rule for never coming to know either the motions or the bodies. And besides, you're now declaring that greater speed no longer satisfies you either — you're after a third condition for defining simple motion, where Aristotle contented himself with just one, namely the simplicity of the path. But now, on your account, the simple motion will be the one performed along a simple line, at a certain determinate speed, by a simple movable body. Well, have it however you like, and let's get back to Aristotle — who defined mixed motion for me as the one compounded of the straight and the circular, but then never found me a single body that naturally moves with such a motion.
Salviati: Then I return to Aristotle. He began his discourse very well and methodically; but since his eye was fixed more on reaching and striking a target he had set up in his mind beforehand than on where the argument was straightforwardly leading him, he breaks the thread and comes at us sideways, offering as a known and obvious fact that as for the straight motions up and down, these naturally belong to fire and to earth — and that therefore, besides these bodies here around us, there must be another body in nature to which circular motion belongs, a body all the more excellent as circular motion is more perfect than straight motion. And just how much more perfect the one is than the other, he determines from the perfection of the circular line over the straight one, calling the circle perfect and the straight line imperfect: imperfect because, if it is infinite, it lacks an end and a boundary; and if it is finite, there is something outside it into which it can be extended.
This is the first stone — the base and foundation of the entire fabric of the Aristotelian world — on which all the other properties lean: neither heavy nor light, ingenerable, incorruptible, exempt from every change except change of place, and so on. All these attributes, he asserts, are proper to the simple body that moves with circular motion; and the contrary conditions — heaviness, lightness, corruptibility, and the rest — he assigns to the bodies naturally movable with straight motions. So whenever a flaw turns up in what has been established this far, we may reasonably doubt everything else that gets built on top of it. I don't deny that what Aristotle has introduced so far by a general discourse, resting on universal first principles, is later reconfirmed as he goes along with particular reasons and with experiences — all of which will have to be considered and weighed one by one. But since what has been said so far already presents many difficulties, and not small ones (and first principles and foundations really ought to be secure, firm, and stable, so that one can build on them with full confidence), it may be no bad idea, before we pile the doubts any higher, to see whether by chance — as I suspect — striking out along another road might set us on a straighter and surer path, and whether, with better-considered rules of architecture, we might lay the first foundations properly. So, suspending Aristotle's line of argument for now — we'll take it up again in due course and examine it point by point — I say that of the things he has said so far, I agree with him, and I grant that the world is a body endowed with all the dimensions, and therefore most perfect. And I add that as such it is necessarily supremely ordered — that is, made of parts arranged among themselves in the highest and most perfect order. This assumption I don't believe will be denied by you or by anyone else.
Simplicio: And who would you expect to deny it? First of all, it is Aristotle's own; and besides, the world's very name — cosmos — seems to be drawn from nothing else than the order it so perfectly contains.
Salviati: With that principle established, then, we can immediately conclude that if the integral bodies of the world are to be by nature movable, it is impossible for their motions to be straight, or anything other than circular. The reason is easy and plain enough. Whatever moves with straight motion changes place; and as it keeps moving, it gets farther and farther from the point it started from and from every place it successively passes through. Now if that motion belongs to it naturally, then at the beginning it was not in its natural place — and so the parts of the world were not arranged in perfect order. But we are supposing them to be perfectly ordered; as such, then, it is impossible that they should have from nature a tendency to change place, and consequently impossible that they move with straight motion.
Moreover, since straight motion is by its nature infinite — because the straight line is infinite and indeterminate — it is impossible for any movable body to have from nature a principle of moving along a straight line, that is, toward a place it is impossible to reach, there being no fixed end to arrive at; and nature, as Aristotle himself rightly says, does not undertake to do what cannot be done, nor undertake to move toward a place it is impossible to arrive at. And if someone objects that although the straight line, and consequently motion along it, can be extended to infinity — has no built-in end — nature has nevertheless, so to speak, arbitrarily assigned certain end-points to it, and given her natural bodies natural instincts to move toward them, I will answer that this might perhaps be told as a fable of the first chaos, where indistinct materials wandered about confusedly and in disorder. To set them in order, nature might very suitably have used straight motions — for just as such motions disorder well-arranged bodies when they move them, so they are suited to putting badly arranged ones into order. But after the best possible distribution and placement, it is impossible that any natural inclination to keep moving in a straight line should remain in those bodies; because from straight motion, now, nothing would follow but their removal from their own natural place — that is, their disordering. We can say, then, that straight motion serves to carry the materials for building the work; but once the work is built, it either stays motionless or, if it moves at all, moves only circularly.
Unless we would rather say, with Plato, that the world's bodies too, after they were made and fully established, were moved by their Maker for some time in straight motion, and that afterwards, on arriving at certain determinate places, they were turned one by one into circuits, passing from straight motion to circular — in which they have been maintained ever since, and are preserved still. A lofty thought, and truly worthy of Plato; and I remember hearing our mutual friend, the Academician, discourse on it. If I remember rightly, his discourse went like this. Every body constituted, for whatever cause, in a state of rest, but movable by its nature, will move when set at liberty — provided, that is, that it has by nature an inclination toward some particular place; for if it were indifferent to every place, it would stay at rest, having no more reason to move this way than that. And from its having such an inclination, it necessarily follows that in its motion it will keep continually accelerating. Beginning with the slowest possible motion, it will not acquire any degree of speed without first passing through all the lesser degrees of speed — or, if you prefer, the greater degrees of slowness. For setting out from the state of rest — which is the degree of infinite slowness of motion — there is no reason whatever why it should enter into one particular degree of speed before entering into a smaller one, and into another still smaller before that. On the contrary, it seems entirely reasonable that it should pass first through the degrees nearest to the one it starts from, and from those to the more remote; and the degree from which the body takes up its motion is that of extreme slowness, namely rest. Now, this acceleration of motion happens only as the moving body gains something by its moving; and its gain is nothing other than drawing nearer to the place it desires — the place its natural inclination pulls it toward; and it will make its way there by the shortest route, that is, by the straight line. So we may reasonably say that nature, in order to confer some determinate speed on a movable body first constituted at rest, makes use of having it move, for some time and through some space, with straight motion.
Granting this discourse, let us imagine that God created the body of, say, Jupiter, and had determined to confer on it a certain speed, which it must then keep perpetually uniform. We can say with Plato that He gave it at the beginning a straight and accelerated motion, and then, once it had reached that particular degree of speed, converted its straight motion into circular motion — whose speed is then naturally suited to remain uniform.
Sagredo: I hear this discourse with great pleasure, and I believe the pleasure will be greater still once you've removed one difficulty for me. It is this: I can't quite see how it must necessarily be that a movable body, setting out from rest and entering a motion toward which it has a natural inclination, passes through all the prior degrees of slowness lying between any assigned degree of speed and the state of rest — and those degrees are infinite. Couldn't nature, then, have given the body of Jupiter its circular motion, at just such-and-such a speed, the instant it was created?
Salviati: I did not say, nor would I dare to say, that it was impossible for nature or for God to confer that speed you speak of immediately. But I will say this: de facto — in actual fact — nature does not do it; so that doing it would be an operation outside the natural course of things, and therefore miraculous.
Sagredo: Then you believe that a stone, leaving rest and entering into its natural motion toward the center of the Earth, passes through every degree of slowness below any given degree of speed?
Salviati: I believe it — no, I am sure of it, and sure with such certainty that I can make you sure of it too.
Sagredo: If in the whole of today's reasoning I gained nothing but that one piece of knowledge, I'd count it a handsome return.
Salviati: As far as I can gather from the way you talk, a great part of your difficulty lies in this: that the body has to pass, in some stretch of time — even a very short one — through those infinite degrees of slowness that come before whatever speed it acquires in that time. So before going any further, I'll try to remove that scruple; and it should be an easy job, once I reply that the body does pass through all those degrees, but the passage is made without dwelling in any of them. Since the passage requires no more than a single instant of time, and any little stretch of time whatever contains infinite instants, we will never run short of instants to assign one to each of the infinite degrees of slowness — however brief the time may be.
Sagredo: So far I follow. Still, it seems an astonishing thing to me that a cannonball — for that's how I picture the falling body — which we see come down so headlong that in less than ten pulse-beats it will pass more than two hundred braccia — arm-lengths — of height, should at some point in its motion have been at so small a degree of speed that, had it kept moving at that rate without accelerating any further, it would not have covered that distance in a whole day.
Salviati: Say rather in a whole year — or in ten, or in a thousand; as I will try to persuade you, and perhaps even without your objecting, by a few quite simple questions I'll put to you. So tell me whether you have any difficulty granting that the ball, in coming down, keeps acquiring greater impetus — greater built-up drive — and greater speed.
Sagredo: Of that I am completely sure.
Salviati: And if I say that the impetus acquired at any point whatever of its motion is enough to carry it back up to the height it started from — would you grant me that?
Sagredo: I'd grant it without objection, provided the ball could apply its whole impetus, unimpeded, to that single operation of carrying itself, or another ball equal to it, back to that same height. So, for example, if the Earth were bored through the center, and the ball were let fall from a hundred or a thousand braccia above it, I firmly believe it would pass beyond the center, rising as far as it had fallen. And experience shows me the same thing happening with a weight hanging from a cord: pulled away from the vertical — which is its state of rest — and then set free, it swings down to that vertical and passes beyond it by just as much space, or falls short only by as much as the resistance of the air and the cord and other such accidents impede it. Water shows me the same: descending through a siphon, it climbs back up as far as it came down.
Salviati: You reason perfectly. And since I know you have no doubt about granting that the gaining of impetus comes from moving away from the point where the body starts and drawing nearer to the center toward which its motion tends — will you have any difficulty in granting that two equal movable bodies, even though they descend along different lines, acquire equal impetus, so long as their approach to the center is equal and nothing at all impedes them?
Sagredo: I don't quite understand the question.
Salviati: I'll explain it better by drawing a little figure. So: I'll mark this line AB, parallel to the horizon; on the point B I'll raise the perpendicular BC; and then I'll join the two with the slanting line CA. Now, take the line CA to be an inclined plane, exquisitely polished and hard, down which a perfectly round ball of the hardest material rolls, and let a similar ball fall freely down the perpendicular CB. I ask whether you would grant that the impetus of the one descending along the plane CA, once it has reached the endpoint A, could be equal to the impetus acquired by the other at the point B after its fall down the perpendicular CB.
Sagredo: I resolutely believe it could; because in fact both have approached the center equally, and, by what I granted just now, their impetuses would be equally sufficient to carry them back up to the same height.
Salviati: Now tell me what you believe that same ball would do if it were set on the horizontal plane AB.
Sagredo: It would stay still, that plane having no slope at all.
Salviati: But on the inclined plane CA it would descend — though with a slower motion than down the perpendicular CB.
Sagredo: I was about to answer a flat yes, since it seems necessary to me that the motion along the perpendicular CB must be faster than along the incline CA. And yet, if that's so, how can the body falling along the incline, when it reaches the point A, have as much impetus — that is, as great a degree of speed — as the body falling along the perpendicular has at the point B? These two propositions seem to contradict each other.
Salviati: Then it will seem far more false to you if I say that, taken absolutely, the speeds of the bodies falling along the perpendicular and along the incline are equal. And yet this is a perfectly true proposition — just as it is also true to say that the falling body moves faster along the perpendicular than along the incline.
Sagredo: To my ear those sound like contradictory propositions. And to yours, Simplicio?
Simplicio: They seem the same to me.
Salviati: I think you're teasing me, pretending not to grasp what you understand better than I do. So tell me, Simplicio: when you imagine one movable body being faster than another, what concept do you picture in your mind?
Simplicio: I picture one of them passing a greater space than the other in the same time — or else passing an equal space, but in less time.
Salviati: Very good. And for bodies that are equally fast, what concept do you picture?
Simplicio: I picture them passing equal spaces in equal times.
Salviati: And no other concept than that?
Simplicio: That, it seems to me, is the proper definition of equal motions.
Sagredo: Let's add one more to it, though: let the speeds also be called equal when the spaces passed have the same proportion as the times in which they are passed. That will be a more universal definition.
Salviati: So it is; because it covers equal spaces passed in equal times, and also unequal spaces passed in unequal times — provided those times are proportional to the spaces. Now take up the same figure again, and applying the concept you've formed of the faster motion, tell me why it seems to you that the speed of the body falling along CB is greater than the speed of the one descending along CA.
Simplicio: It seems so to me because, in the time the falling body passes the whole of CB, the descending one will pass, on CA, a part smaller than CB.
Salviati: Just so; and that is how it's verified that the body moves faster along the perpendicular than along the incline. Now consider whether, in this same figure, the other concept might be verified in some way — whether we might find the moving bodies to be equally fast along both the lines CA and CB.
Simplicio: I can see no such thing; in fact it seems to me a contradiction of what's just been said.
Salviati: And what do you say, Sagredo? I certainly wouldn't want to teach you what you already know — the very thing you brought me a moment ago as a definition.
Sagredo: The definition I offered was that movable bodies may be called equally fast when the spaces they pass have the same proportion as the times in which they pass them. So for the definition to apply in the present case, the time of the descent along CA would have to bear the same proportion to the time of the fall along CB as the line CA itself bears to the line CB; but I cannot understand how that can be, given that the motion along CB is faster than along CA.
Salviati: And yet you must understand it. Tell me now: don't these motions keep continually accelerating?
Sagredo: They do — but more in the perpendicular than in the incline.
Salviati: But is this acceleration in the perpendicular such, compared with the acceleration in the incline, that if we took two equal stretches anywhere at all on those two lines, the perpendicular and the incline, the motion in the stretch of the perpendicular would always be faster than in the stretch of the incline?
Sagredo: No indeed. On the contrary, I could take a stretch on the incline in which the speed is far greater than in an equal stretch taken on the perpendicular — and this will happen if the stretch on the perpendicular is taken near the end C, and the one on the incline far away from it.
Salviati: You see, then, that the proposition "motion along the perpendicular is faster than along the incline" does not hold universally, except for motions that begin from the first endpoint — that is, from rest. Without that condition, the proposition would be so defective that even its flat contradictory could be true: namely, that motion on the incline is faster than on the perpendicular; for it is true that on the incline we can take a stretch which the body passes in less time than it takes to pass an equal stretch on the perpendicular. Now, since motion on the incline is in some places faster, and in others slower, than on the perpendicular, it follows that along some places of the incline, the time of the body's motion will bear a greater proportion to the time of the body's motion along certain places of the perpendicular than the space passed bears to the space passed; and in other places, the proportion of time to time will be smaller than the proportion of space to space. For example: let two bodies set out from rest — that is, from the point C — one along the perpendicular CB and the other along the incline CA. In the time in which the body on the perpendicular will have passed the whole of CB, the other will have passed CT, which is smaller. And therefore the time along CT will bear a greater proportion to the time along CB — the two times being equal — than the line TC bears to the line CB, since the same magnitude bears a greater proportion to a smaller one than to a larger. And conversely: if on CA, prolonged as far as need be, we took a stretch equal to CB, but passed in a shorter time, then the time on the incline would bear a smaller proportion to the time on the perpendicular than the space bears to the space. If, then, on the incline and on the perpendicular we can conceive of spaces and speeds such that the proportions between the spaces come out both smaller and greater than the proportions between the times, we may very reasonably grant that there are also spaces along which the times of the motions retain the same proportion as the spaces.
Sagredo: That takes care of my biggest scruple: I now see that what looked to me like a contradiction is not only possible but — I'll go further — necessary. What I still don't see, though, is that one of these possible or necessary cases is the one we actually need right now. Is it really true that the time of descent along CA stands to the time of fall along CB in the same proportion as the line CA stands to the line CB, so that we can say, without contradiction, that the speeds along the incline CA and along the vertical CB are equal?
Salviati: Be content, for now, that I've cleared away your disbelief; the science itself you must wait for until another occasion — namely, when you see what our Academician has demonstrated about local motions. There you'll find it proved that in the time the falling body drops through the whole of CB, the other body descends along CA only as far as the point T, where the perpendicular drawn down from B cuts it. And to find where the body falling down the vertical would be at the moment the other one reaches A, draw the perpendicular to CA from A itself, extending it and CB until they meet: that intersection is the point you're looking for. In the meantime, notice how this shows that the motion along CB really is faster than along the incline CA (taking C as the starting point of the two motions we're comparing): the line CB is longer than CT, and the line from C down to where CB's extension meets the perpendicular drawn from A is longer than CA, and so the motion along it is faster than along CA. But when we compare the motion through the whole of CA not with the whole motion made in that same time along the extended vertical, but with the motion made in a part of that time through the part CB alone, then there's nothing absurd in this: the body on CA, continuing its descent past T, can reach A in a time that stands to the other time in exactly the proportion the line CA has to the line CB.
Now let's take up our original point again, which was to show that a heavy body, starting from rest, passes in its descent through every degree of slowness before reaching any degree of speed it acquires. Going back to the same figure, remember what we had agreed: that the body falling down the vertical CB and the one descending along the incline CA arrive at B and A having acquired equal degrees of speed. Moving on from there, I don't think you'll have the least difficulty granting that on another plane tilted less steeply than AC — say, DA — the descending motion would be slower still than on the plane CA. So there's no doubt whatever that planes can be marked out so slightly raised above the horizontal AB that the moving body — our same ball — would take as long as you please to reach the point A; after all, to get there along the plane BA itself, even infinite time isn't enough, and the motion grows ever slower as the slope grows smaller. So you must necessarily admit that we can take a point above B, so close to B, that if we drew a plane from it to A, the ball wouldn't cross it even in a year.
Now here is what you need to know: the impetus — that is, the degree of speed — that the ball has acquired by the time it arrives at point A is such that, if it kept moving at that same degree uniformly, neither speeding up nor slowing down, then in a second interval equal to the time of its descent it would cover a distance twice the length of the inclined plane. For example: if the ball had taken an hour to travel the plane DA, then, continuing uniformly at the speed it had on reaching A, it would in one hour cover a distance twice the length of DA. And since (as we were saying) the degrees of speed acquired at B and at A — by bodies that set out from any point you please on the vertical CB, one descending along the inclined plane and the other straight down the vertical — are always equal, it follows that the falling body can start from a point so close to B that the degree of speed acquired at B would not be enough (kept forever constant) to carry it through a distance twice the length of the inclined plane in a year, or in ten years, or in a hundred.
So we can conclude as follows. Suppose it's true that, in the ordinary course of nature, a body — with all external and accidental hindrances removed — moves down inclined planes more and more slowly as the tilt gets smaller, until finally the slowness becomes infinite, which happens when the tilt runs out altogether and we arrive at the horizontal plane. And suppose it's equally true that the degree of speed acquired at some point on the inclined plane is equal to the degree of speed of the body falling down the vertical, at the point cut off by a horizontal line drawn through that same point of the incline. Then we are forced to admit that a falling body, starting from rest, passes through all the infinite degrees of slowness; and consequently, that to acquire any given degree of speed it must first move in a straight line, descending through a short or a long distance according as the speed to be acquired is smaller or greater, and according as the plane of descent is gently or steeply tilted. So there can be a plane with so little tilt that, to acquire a given degree of speed on it, the body would first have to move through an immense distance, over an immense time. On the horizontal plane, then, no speed at all will ever be acquired naturally, since there the body will never move in the first place. But motion along a horizontal line, which slopes neither down nor up, is circular motion around the center. Therefore circular motion is never acquired naturally without straight motion coming first; but once it has been acquired, it will continue perpetually at uniform speed.
I could explain these same truths to you, and even demonstrate them, by other lines of argument; but I don't want to interrupt our main discussion with such long digressions. I'll come back to them on some other occasion — all the more since we got onto this point not to use it as a necessary demonstration, but to dress up a Platonic conceit. And to that conceit I want to add one further particular observation, again our Academician's, and it has something marvelous about it. Let's imagine that among the decrees of the divine Architect was the thought of creating in the world these globes we see continually moving in circles; of establishing the center of their revolutions, and placing there the Sun, immovable; and then of fashioning all those globes in one and the same place, and giving them from there an inclination to move, descending toward the center, until they had acquired those degrees of speed that seemed right to the divine Mind itself — whereupon, the speeds acquired, they were turned into circulation, each in its own circle, keeping the speed it had already gained. The question is: at what height, at what distance from the Sun, was the place where those globes were first created — and could they all have been created in the same place? To carry out the investigation, you take from the most expert astronomers the sizes of the circles in which the planets revolve, and likewise the times of their revolutions. From those two pieces of knowledge you work out how much faster, say, Jupiter's motion is than Saturn's; and having found (as is in fact the case) that Jupiter moves faster, it must be that, both having set out from the same height, Jupiter descended farther than Saturn — as we know is really true, his orbit lying below Saturn's. But pressing further: from the proportion between the speeds of Jupiter and Saturn, from the distance between their orbits, and from the ratio of acceleration in natural motion, one can work out at what height, at what distance from the center of their revolutions, lay the place they set out from. Once that's found and fixed, we ask whether Mars, descending from there down to his own orbit, checks out — and we find that the size of his orbit and the speed of his motion agree with what the calculation gives us. The same is done for the Earth, for Venus, and for Mercury; and the sizes of their circles and the speeds of their motions come so close to what the computations yield that it is a thing of wonder.
Sagredo: I've listened to this idea with the keenest pleasure; and if I didn't think that carrying out those calculations precisely would be a long and laborious undertaking — and perhaps too hard for me to follow — I'd insist you do it here and now.
Salviati: The operation really is long and difficult, and besides, I wouldn't trust myself to reconstruct it on the spot; so we'll save it for another time. For now let's return to our original subject, picking up right where we digressed. If I remember correctly, we were in the middle of establishing that motion in a straight line can be of no use whatever among the parts of a world in good order. And we were going on to say that it's just the opposite with circular motions: the one a body makes turning on itself keeps it always in the same place, while the one that carries a body around the circumference of a circle, about its own stable and fixed center, puts neither the body nor its neighbors into any disorder. For such motion, in the first place, is finite and bounded — indeed, not just finite and bounded, but there is no point on the circumference that isn't at once the first and the last terminus of the circuit; and continuing around its assigned circumference, the body leaves everything else, inside that circle and out, free for the needs of others, without ever hindering or disturbing them. Now, this being a motion in which the moving body is forever departing from its terminus and forever arriving at it, circular motion alone, in the first place, can be uniform. For acceleration happens in a body when it's moving toward a terminus it feels an inclination for, and slowing happens through its reluctance to leave that terminus and move away; and since in circular motion the body is always departing from its natural terminus and always moving toward that very same terminus, the reluctance and the inclination in it are always of equal strength. From that equality comes a speed neither slowed nor quickened — that is, uniform motion. And from this uniformity, and from the motion's being bounded, perpetual continuation can follow, the circuits repeating forever — which can never be found naturally on an unbounded line, or in a motion that is continually slowing or accelerating. And I say naturally, because straight motion that slows down is violent motion — forced motion — which cannot be perpetual; and accelerated straight motion necessarily arrives at its terminus, if there is one; and if there isn't one, there can't be any motion toward it either, for nature does not set out for a place it is impossible to reach. I conclude, therefore, that circular motion alone can naturally suit the natural bodies that make up the universe and stand in their best arrangement; and that straight motion, at the very most, is assigned by nature to bodies and their parts only when they find themselves outside their proper places, stuck in a bad arrangement, and therefore in need of getting back to their natural state by the shortest road. From this it seems to me we can quite reasonably conclude that, to maintain perfect order among the parts of the world, the movable ones must be movable only in circles; and if there are any that do not move circularly, they must of necessity be immovable — for nothing except rest and circular motion is fit for the preservation of order. And I'm more than a little surprised that Aristotle, who after all held that the terrestrial globe is located at the center of the world and stays there immovably, didn't say that among natural bodies some are movable by nature and others immovable — especially since he had already defined nature as the principle of motion and of rest.
Simplicio: Aristotle, being a man who never promised himself more from his own genius — piercing as it was — than is fitting, held in his philosophizing that the experiences of the senses must be set above any argument fabricated by human ingenuity; and he said that those who would deny the senses deserved to be punished by being deprived of the sense in question. Now, who is so blind that he cannot see the parts of earth and of water moving, as heavy things do, naturally downward — that is, toward the center of the universe, appointed by nature herself as the goal and terminus of straight motion deorsum — downward? And who cannot see, just as plainly, fire and air moving straight up toward the concave arch of the lunar orb, as toward the natural terminus of motion sursum — upward? And this being so manifestly seen, and since we are certain that eadem est ratio totius et partium — the same reasoning holds for the whole as for its parts — why shouldn't we call it a true and manifest proposition that the natural motion of earth is straight motion ad medium — toward the center — and that of fire, straight motion a medio — away from it?
Salviati: On the strength of this argument of yours, the very most you could claim to have won is this: that just as the parts of the earth, when removed from their whole — that is, from the place where they naturally reside, and so, in the end, put into a bad and disordered arrangement — return to their place spontaneously, and therefore naturally, in straight motion, so (granting that eadem sit ratio totius et partium — that whole and parts follow the same rule) one might infer that if the terrestrial globe were forcibly removed from the place nature assigned it, it would go back there in a straight line. That, as I say, is the most that could be conceded to you, and only after granting you every sort of accommodation along the way. But anyone who wanted to audit these accounts rigorously would first deny that the parts of the earth, in returning to their whole, move in a straight line at all, rather than in a circular one, or in some mixture of the two; and you would certainly have your work cut out demonstrating the contrary, as you'll see clearly in the replies to the particular reasons and experiments brought forward by Ptolemy and Aristotle. Secondly, if someone told you that the parts of the earth move not in order to go to the center of the world but to go and reunite with their whole, and that this is why their natural inclination is toward the center of the terrestrial globe — an inclination by which they conspire to form it and preserve it — then what other whole, what other center, would you find in the world for the entire terrestrial globe to seek to return to, if it were removed, so that the reasoning about the whole would still match the reasoning about the parts? Add to this that neither Aristotle nor you will ever prove that the Earth is de facto — in actual fact — at the center of the universe; if any center can be assigned to the universe at all, we shall find it is rather the Sun that sits there, as you'll come to understand as we proceed.
Now, just as from the concordant conspiring of all the parts of the earth to form their whole it follows that they converge on it from every side with equal inclination, and, to unite as closely as possible, fit themselves together into a sphere — why shouldn't we believe that the Moon, the Sun, and the other bodies of the world are likewise round for no other reason than the concordant instinct and natural convergence of all their component parts? And if at some time one of those parts were separated from its whole by some violence, isn't it reasonable to believe it would return there spontaneously, by natural instinct? And in this way to conclude that straight motion belongs equally to all the bodies of the world?
Simplicio: There isn't the least doubt that if you're prepared to deny not only the first principles of the sciences but manifest experience and the senses themselves, you can never be convinced or budged from any opinion you've conceived; and I will hold my peace, rather because contra negantes principia non est disputandum — with those who deny first principles there is no arguing — than because your reasons have persuaded me. But staying with what you've just now pronounced — since you throw doubt on whether even the motion of heavy bodies is straight — how can you ever reasonably deny that the parts of earth, that is, the heaviest of materials, descend toward the center in straight motion? When they're dropped from a very tall tower, with walls dead straight and built plumb, they come down grazing the wall, so to speak, and strike the ground at exactly — to a hair — the point where a plumb bob would land, hung from a cord fixed above at the very spot the stone was released. Isn't that a more than evident argument that this motion is straight, and toward the center? In the second place, you call into doubt whether the parts of the earth move, as Aristotle affirms, toward the center of the world — as though he hadn't demonstrated it conclusively from contrary motions, arguing like this: the motion of heavy things is contrary to that of light things; but the motion of light things is seen to be straight upward, that is, toward the circumference of the world; therefore the motion of heavy things is straight toward the center of the world, and it happens per accidens — merely incidentally — that it is toward the center of the Earth, since the one center happens to coincide with the other. As for asking what a piece of the lunar globe or of the Sun would do if it were separated from its whole — that's an idle question, because it asks what would follow from an impossibility; for, as Aristotle also demonstrates, celestial bodies are impervious to change, impenetrable, and unbreakable, so the case can never arise. And even if it did arise, and the separated piece returned to its whole, it wouldn't return as a heavy body or a light one — for the same Aristotle proves that celestial bodies are neither heavy nor light.
Salviati: How reasonable my doubt is, about whether heavy bodies move in a straight and plumb line, you'll hear when I come to examine that particular argument, as I said just now. As for the second point, I'm amazed you should need Aristotle's paralogism — his flawed reasoning — exposed for you, when it's so obvious on its face, and that you don't notice Aristotle is assuming the very thing in question. So observe...
Simplicio: Please, Salviati — speak of Aristotle with more respect. To whom could you ever sell the idea that a man who was the first, the only, the admirable expounder of the syllogistic form, of demonstration, of refutations, of the ways of detecting sophisms and paralogisms — in short, of the whole of logic — should then blunder so gravely as to assume as known the very thing in question? Gentlemen, first understand him perfectly; then try your hand at refuting him.
Salviati: Simplicio, we're here talking among ourselves, familiarly, to investigate some truth. I'll never take it badly that you point out my errors; and whenever I've failed to grasp Aristotle's meaning, correct me freely — I'll thank you for it. In the meantime, allow me to lay out my difficulties, and to answer a word or two of what you just said. Logic, as you know perfectly well, is the organ with which we philosophize — the instrument of the trade. But just as a craftsman can be excellent at building organs and yet untrained in playing them, so a man can be a great logician and yet little practiced in actually using logic — just as there are many who know the whole art of poetry by heart and then are hopeless at composing four lines of verse, and others who possess every one of Leonardo's precepts and couldn't paint a footstool. Playing the organ isn't learned from those who know how to build organs, but from those who know how to play them; poetry is learned from constant reading of the poets; painting is picked up by constant drawing and painting; and demonstration is learned from reading books full of demonstrations — and those are the books of the mathematicians alone, not of the logicians. Now, back to our subject. What Aristotle sees, concerning the motion of light bodies, is fire departing from any point on the surface of the terrestrial globe and moving straight away from it, rising upward. That truly is moving toward a circumference larger than the Earth's — indeed, Aristotle himself has it move up to the concave arch of the Moon's orb. But that this larger circumference is the circumference of the world, or concentric with it, so that moving toward the one is also moving toward the other — that cannot be affirmed unless you first suppose that the center of the Earth, the point we watch ascending light bodies move away from, is the same as the center of the world. And that is as much as to say that the terrestrial globe sits at the center of the world — which is precisely what we are doubting, and precisely what Aristotle set out to prove. And will you tell me this isn't a manifest paralogism?
Sagredo: This argument of Aristotle's had struck me as deficient and inconclusive in another respect as well, even if we grant him that the circumference toward which fire moves in a straight line is the one that encloses the world. For take, inside a circle, not just the center but any other point you please: every moving body that sets out from it along a straight line, in any direction whatever, will without any doubt be heading toward the circumference, and if it keeps moving it will get there too — so it's perfectly true to say that it moves toward the circumference. But it will not be true that a body moving along those same lines with the contrary motion is heading toward the center — not unless the point we chose was the center itself, or the motion ran along that one single line which, drawn from the chosen point, passes through the center. So the argument "Fire, moving in a straight line, goes toward the circumference of the world; therefore the parts of earth, which move along the same lines with the contrary motion, go toward the center of the world" concludes nothing at all — unless we first assume that fire's lines, extended, pass through the center of the world. And since we know for certain that those lines pass through the center of the terrestrial globe (being perpendicular to its surface, not slanted), then to make the conclusion work we must assume that the center of the Earth is the same as the center of the world — or at least that the parts of fire and earth rise and fall only along a single line that passes through the center of the world. And that is false, and it contradicts experience, which shows us that the parts of fire ascend not along one single line but along the infinitely many lines drawn from the center of the Earth toward every part of the world — always rising perpendicular to the surface of the terrestrial globe.
Salviati: Sagredo, you very ingeniously drive Aristotle into the same difficulty by exposing the obvious equivocation; but add one more awkwardness to it. We see that the Earth is spherical, so we're certain it has a center. We see that all its parts move toward that center — we're forced to say so, since their motions are all perpendicular to the Earth's surface. We understand that in moving toward the center of the Earth, they move toward their whole, toward their universal mother. And then we're so obliging that we let ourselves be talked into believing their natural instinct is not to head for the center of the Earth but for the center of the universe — which we don't know where it is, or whether it exists at all; and which, even if it does exist, is nothing but an imaginary point, a nothing, with no power to do anything.
As for Simplicio's last remark — that debating whether parts of the Sun or the Moon or some other celestial body, if separated from their whole, would naturally return to it is a waste of breath, because the case is impossible, it being evident from Aristotle's demonstrations that celestial bodies are impervious to change, impenetrable, indivisible, and so on — I answer this: not one of the conditions by which Aristotle makes celestial bodies differ from elemental ones has any footing except what he deduces from the difference between their natural motions. So that once we deny that circular motion belongs to celestial bodies alone, and affirm that it suits all naturally movable bodies, one of two conclusions necessarily follows: either the attributes of generable or ingenerable, alterable or inalterable, divisible or indivisible, and so on, belong equally and in common to all the bodies of the universe — celestial and elemental alike — or else Aristotle went badly and mistakenly wrong in deducing from circular motion the attributes he assigned to celestial bodies.
Simplicio: This way of philosophizing tends toward the subversion of all natural philosophy — toward throwing heaven and Earth and the whole universe into disorder and wreckage. But I believe the foundations of the Peripatetics are solid enough that there's no fear of new sciences being built on their ruins.
Salviati: Don't worry yourself about heaven or the Earth, and don't fear their subversion — nor philosophy's either. As for heaven, it's pointless for you to fear for the very thing you yourself hold to be inalterable and impervious to change. As for the Earth, we're trying to ennoble and perfect it: we're working to make it like the celestial bodies and, in a certain way, to set it almost in heaven — the place your philosophers banished it from. And philosophy itself can only profit from our disputes: if our thoughts turn out to be true, new ground will have been gained; if false, then in refuting them the original doctrines will stand all the more firmly confirmed. Worry instead about certain philosophers, and see how you might help them and prop them up — because the science itself cannot help but advance. And now, back to our subject: bring forward freely whatever occurs to you in support of the total difference Aristotle sets up between celestial bodies and the elemental region, making the former ingenerable, incorruptible, inalterable, and so on, and the latter corruptible, alterable, and the rest.
Simplicio: I don't yet see that Aristotle needs any rescuing. He is still on his feet, firm and strong — indeed, he hasn't yet even been attacked by you, let alone knocked down. And what will your shield be against this first assault? Aristotle writes: What is generated comes to be from a contrary, in some subject; and likewise it is corrupted, in some subject, from a contrary into a contrary — so that (mark this well) corruption and generation occur only among contraries. But the motions of contraries are contrary to each other; so if no contrary can be assigned to the celestial body — since no other motion is contrary to circular motion — then nature did very well indeed to exempt from contraries the thing that was meant to be ingenerable and incorruptible. With this first foundation laid, it follows immediately that the celestial body cannot grow, cannot alter, is impervious to change, and finally is eternal — a dwelling fit for the immortal gods, in agreement with the opinion of every person who has any conception of the gods at all. He then confirms the same thing by the senses: in all past time, according to tradition and record, nothing is seen to have changed, either in the whole of the outermost heaven or in any one of its proper parts. And that no other motion is contrary to circular motion, Aristotle proves in many ways; but without rehearsing them all, it stands demonstrated plainly enough by this: the simple motions are only three — toward the center, away from the center, and around the center; of these, the two straight ones, sursum et deorsum — upward and downward — are manifestly contrary; and since one thing has only one contrary, there remains no other motion that could be contrary to the circular. There you have Aristotle's argument, as sharp and as conclusive as could be, by which the incorruptibility of heaven is proved.
Salviati: That is nothing more than the bare course of Aristotle's argument, which I sketched for you already — and the moment I deny that the motion you attribute to celestial bodies is off-limits to the Earth, his inference comes to nothing. So I tell you plainly: that circular motion you assign to celestial bodies suits the Earth as well. From which — granting that the rest of your argument is conclusive — one of three things will follow, as I said a little while ago and now repeat: either the Earth is itself ingenerable and incorruptible, just like the celestial bodies; or the celestial bodies are, like the elemental ones, generable, alterable, and so on; or else this difference of motions has nothing to do with generation and corruption.
Aristotle's argument — and yours — contains many propositions that shouldn't be granted lightly, and to examine it better it will be worth reducing it to as clean and distinct a form as possible. Sagredo will forgive me if he finds it tedious to hear the same things said over more than once — let him imagine he's listening to the arguments being rehearsed again in a public disputation. You say: "Generation and corruption occur only where there are contraries; contraries exist only among simple natural bodies, movable with contrary motions; contrary motions are only those made along straight lines between contrary endpoints; and of these there are only two, namely away from the center and toward the center; and such motions belong to no natural bodies except earth, fire, and the other two elements. Therefore generation and corruption exist only among the elements. And since the third simple motion — the circular motion around the center — has no contrary (for the other two are each other's contraries, and one thing has only one contrary), the natural body to which that motion belongs lacks a contrary; and having no contrary, it remains ingenerable and incorruptible, and so on, because where there is no contrariety there is no generation or corruption. But that motion belongs only to celestial bodies; therefore they alone are ingenerable, incorruptible, and so forth."
Now, first of all: it strikes me as a far easier thing to make sure whether the Earth — a vast body, and, being so near us, by far the easiest to handle — moves with an enormous motion, such as turning on itself once every twenty-four hours, than it is to understand and make sure whether generation and corruption arise from contraries — indeed, whether corruption and generation and contraries exist in nature at all. And if you, Simplicio, could tell me nature's method of operation when she generates, in the briefest time, a hundred thousand gnats out of a little vapor rising off fermenting grape must — showing me what the contraries are in that case, what thing is corrupted, and how — I would think even more highly of you than I already do, because I understand none of it. Furthermore, I would dearly love to know how and why these corrupting contraries are so gentle with crows and so fierce with doves, so tolerant of stags and so impatient with horses, granting the former more years of life — which is to say, of incorruptibility — than they grant the latter weeks. Peach trees and olive trees put their roots into the same soils; they stand exposed to the same cold spells, the same heat, the same rains and winds — in short, to the same contrarieties — and yet the one is destroyed in a short time while the other lives many hundreds of years. What's more, I have never managed to feel at ease with this substantial transmutation (keeping strictly within purely natural terms) by which a piece of matter is supposed to be so transformed that we must say it has been utterly destroyed, with nothing of its first being remaining in it, and that another body, completely different from it, has been produced out of it. When a body presents itself to me under one aspect and, a little later, under another very different one, I don't consider it impossible that this comes about by a simple rearrangement of parts, without anything being corrupted or anything new generated — we see metamorphoses of that kind every day of our lives. So I say it once more: if you mean to persuade me that the Earth cannot move in a circle by way of an argument from corruptibility and generability, you will have far more work on your hands than I will — for I'll prove you the contrary with arguments a good deal harder, but no less conclusive.
Sagredo: Salviati, forgive me for interrupting your reasoning. It delights me greatly — I find myself tangled in these same difficulties — but I suspect there's no getting to the bottom of it without abandoning our principal subject altogether. So if the original discussion can be carried forward, I'd judge it best to set this question of generation and corruption aside for a separate, complete conversation of its own — and the same, if it suits you and Simplicio, for the other particular questions the course of our talks brings up. I'll keep a separate note of them, so we can raise them another day and examine them in detail. As for the present one: since you say that once Aristotle is denied the claim that circular motion belongs to the celestial bodies but not to the Earth, it follows that whatever holds of the Earth — being generable, alterable, and so on — holds of the heavens too, let's leave aside whether generation and corruption exist in nature or not, and get back to investigating what the terrestrial globe actually does.
Simplicio: I cannot bring my ears to listen to anyone doubting whether generation and corruption exist in nature — a thing we have continually before our eyes, and about which Aristotle wrote two entire books. Once you start denying the principles of the sciences and casting doubt on the most manifest things, who doesn't know that you can prove whatever you please and defend any paradox whatsoever? If you don't see grasses, plants, and animals generated and corrupted every day, then what do you see? How can you fail to see the contrarieties perpetually jousting against one another — earth changing into water, water converting into air, air into fire, and air again condensing into clouds, rains, hail, and storms?
Sagredo: Of course we see all these things; and so, as far as this part goes — generation and corruption produced by contraries — we're happy to grant you Aristotle's argument. But if, using those very propositions you've granted to Aristotle, I prove to you that the celestial bodies are themselves every bit as generable and corruptible as the elemental ones, what will you say then?
Simplicio: I'll say you've done the impossible.
Sagredo: Tell me something, Simplicio: aren't these properties contrary to one another?
Simplicio: Which ones?
Sagredo: These: alterable and inalterable, subject to change and impervious to change, generable and ingenerable, corruptible and incorruptible?
Simplicio: As contrary as can be.
Sagredo: Well then — if that's so, and if it's also true that celestial bodies are ingenerable and incorruptible, I'll prove to you that of necessity the celestial bodies must be generable and corruptible.
Simplicio: That can only be a sophism.
Sagredo: Hear the argument first; then give it its name and refute it. The celestial bodies, because they are ingenerable and incorruptible, have contraries in nature — namely, the generable and corruptible bodies. But where there is contrariety, there is generation and corruption. Therefore the celestial bodies are generable and corruptible.
Simplicio: Didn't I tell you it could be nothing but a sophism? This is one of those horned arguments they call sorites — like the one about the Cretan who said that all Cretans were liars. Being a Cretan, he was telling a lie when he said Cretans were liars; therefore Cretans must be truthful, and consequently he, being a Cretan, was truthful; and so, in saying Cretans were liars, he spoke the truth; and since he was included among the Cretans, he must have been a liar after all. With sophisms of this sort you could keep spinning in circles for all eternity without ever concluding anything.
Sagredo: So far you've only given it its name. It remains for you to solve it — to show where the fallacy lies.
Simplicio: As for solving it and exposing its fallacy — don't you see, first of all, the open contradiction? The celestial bodies are ingenerable and incorruptible; therefore the celestial bodies are generable and corruptible? And besides, the contrariety isn't among the celestial bodies at all; it's among the elements, which have the contrariety of the motions sursum et deorsum and of lightness and heaviness. But the heavens, which move circularly — a motion to which no other is contrary — lack all contrariety, and are therefore incorruptible, and so on.
Sagredo: Gently, Simplicio. This contrariety, by which you say certain simple bodies are corruptible — does it reside in the very body that gets corrupted, or does it stand in relation to some other body? I mean: the moisture, say, by which a portion of earth is corrupted — does it reside in that earth itself, or in another body, such as the air or the water? I believe you'll say that just as the motions up and down, and heaviness and lightness — which you make the primary contraries — cannot exist in one and the same subject, so neither can wet and dry, or hot and cold. So you're forced to say that when a body is corrupted, this happens through a quality residing in another body, contrary to its own. Therefore, to make the celestial body corruptible, it's enough that there exist in nature bodies that have a contrariety to the celestial body — and the elements are exactly such bodies, if it's true that corruptibility is contrary to incorruptibility.
Simplicio: That is not enough, my dear sir. The elements alter and corrupt because they touch and mingle with one another, and so can bring their contrarieties to bear; but the celestial bodies are separate from the elements — the elements don't even touch them, though they touch the elements. If you want to prove generation and corruption in the celestial bodies, you must show that the contrarieties reside among those bodies themselves.
Sagredo: Then watch me find them there. The first source from which you draw the contrarieties of the elements is the contrariety of their motions up and down; therefore the principles those motions depend on must be contraries as well. And since one body moves upward by lightness and the other downward by heaviness, lightness and heaviness must be contrary to each other; and no less must we believe that those further principles are contraries which cause one body to be heavy and another light. But by your own account, lightness and heaviness follow from rarity and density; therefore density and rarity are contraries. And these conditions are found so abundantly in the celestial bodies that you yourselves hold the stars to be nothing but denser parts of their own heaven; and if that's so, the density of the stars must exceed the density of the rest of heaven by an almost infinite margin — which is obvious from heaven's being supremely transparent and the stars supremely opaque, and from the fact that up there no other qualities are to be found, beyond the more and less dense or rare, that could serve as principles of greater and lesser transparency. Since such contrarieties exist among the celestial bodies, then, it necessarily follows either that they too are generable and corruptible in the very same way the elemental bodies are — or else that contrariety is not the cause of corruptibility, and so on.
Simplicio: Neither one is necessary — because density and rarity in the celestial bodies are not contraries to each other the way they are in elemental bodies. They don't depend on the primary qualities, hot and cold, which are contraries, but on there being much or little matter in proportion to the bulk. Now "much" and "little" express only a relative opposition — the weakest kind of opposition there is — and that has nothing to do with generation and corruption.
Sagredo: So then: for density and rarity to do their job among the elements — to be the cause of heaviness and lightness, which in turn can be causes of the contrary motions sursum et deorsum, on which in turn the contrarieties for generation and corruption depend — it isn't enough for them to be the kind of dense and rare that contain much or little matter under the same bulk; they must be dense and rare thanks to the primary qualities, cold and hot. Otherwise nothing gets accomplished. But if that's so, Aristotle has cheated us: he should have said so from the start, and left it in writing, that the generable and corruptible bodies are those simple bodies which are movable with the simple motions up and down, depending on lightness and heaviness, caused by rarity and density, made by much or little matter, by virtue of heat and cold — and not have stopped at simple upward and downward motion. Because I assure you that as far as making bodies heavy or light — so that they can then move with contrary motions — any density and rarity whatever will do the job, whether it comes from hot and cold or from anything else you please; hot and cold have nothing to do with the operation. You can see for yourself that a piece of iron glowing red — which surely may be called hot — weighs just the same, and moves in just the same way, as when it's cold. But leaving even that aside: how do you know that celestial density and rarity don't depend on cold and heat?
Simplicio: I do know: it's because such qualities have no place among the celestial bodies, which are neither hot nor cold.
Salviati: I can see we're about to plunge back into a boundless sea with no way out — because this is sailing without a compass, without stars, without oars, without a rudder, so that we'd be forced to grope from reef to reef, or run aground, or sail on forever lost. So if we mean to press ahead toward our main subject, as you advise, we must for now set aside this general question of whether straight-line motion is necessary in nature and belongs to certain bodies, and come down to the particular demonstrations, observations, and experiments. First we'll lay out everything that Aristotle, Ptolemy, and others have offered up to now as proof of the Earth's stability; second, we'll try to answer it; and last, we'll bring forward the arguments by which a person might be persuaded that the Earth, no less than the Moon or any other planet, deserves to be counted among the natural bodies that move in circles.
Sagredo: I'll hold to that plan all the more gladly because your grand architectural argument satisfies me far more than Aristotle's does. Yours puts my mind at rest without a single snag, while the other trips me over some stumbling block at every step. And I don't see how Simplicio wasn't instantly persuaded by the reason you gave to prove that straight-line motion can have no place in nature — provided we assume the parts of the universe are arranged in their best constitution and perfectly ordered.
Salviati: One moment, please, Sagredo — for it has just occurred to me how I might satisfy Simplicio too, so long as he isn't so bound to Aristotle's every word that he counts it sacrilege to depart from any of them. There's no doubt that, to maintain the perfect arrangement and order of the universe's parts as far as position is concerned, nothing will serve but circular motion and rest. As for motion in a straight line, I don't see that it can be good for anything except restoring to its natural constitution some particle of one of the integral world-bodies that had been separated from its whole by some accident, as we said earlier. Now let's consider the whole terrestrial globe, and see what can become of it, given that it and the other world-bodies must keep themselves in their best and natural arrangement. One of three things must be said: either it remains and keeps itself perpetually motionless in its place; or, staying always in the same place, it spins upon itself; or it goes around a center, traveling along the circumference of a circle. Of these possibilities, Aristotle and Ptolemy and all their followers say that it has always observed, and will maintain forever, the first — perpetual rest in the same place. Well then, why in heaven's name shouldn't they say that its natural tendency is to remain motionless, rather than making its nature the motion downward — a motion it has never once moved with, and never will? As for straight-line motion, let nature use it to restore to their wholes those particles of earth, of water, of air, of fire, and of every other integral world-body, whenever one of them happens to find itself separated, and so transported to a place out of order — unless it should turn out that even for making this restitution some circular motion is better suited. This primary position, it seems to me, answers all the other consequences far better — even keeping to Aristotle's own way of thinking — than attributing straight-line motions to the elements as an intrinsic and natural principle. And that's plain to see. For if I ask the Peripatetic whether, holding as he does that the celestial bodies are incorruptible and eternal, he believes the terrestrial globe is not so — believes it corruptible and mortal, so that a time must come when, while the Sun and the Moon and the other stars carry on their existence and their operations, the Earth is no longer to be found in the world but has been destroyed along with the rest of the elements and gone to nothing — I'm certain he will answer no. Therefore generation and corruption belong to the parts, not to the whole — and to the very smallest and most superficial parts at that, which are as good as imperceptible compared with the whole mass. And since Aristotle infers generation and corruption from the contrariety of straight-line motions, let's leave such motions to the parts, which alone alter and decay, and assign to the whole globe and the whole sphere of the elements either circular motion or a perpetual staying in their own place — the only conditions fit for perpetuation and for keeping the perfect order. What we say here of earth can be said with the same reasoning of fire and of the greater part of the air: the Peripatetics have been reduced to assigning those elements, as their intrinsic and natural motion, one with which they have never moved and never will, and to calling foreign to their nature the very motion with which they move now, have always moved, and will move perpetually. I say this because they assign to air and fire the motion upward, with which neither of those elements as a whole has ever moved — only some particle of them, and that for no other purpose than to return to its perfect constitution after finding itself outside its natural place. And on the other hand they call contrary to their nature the circular motion with which they move incessantly — forgetting, it would seem, what Aristotle has said again and again: that nothing violent can last for long.
Simplicio: To all of this we have the most fitting replies, which I'll set aside for now in order to come to the more particular reasons and to the evidence of the senses — which in the end must be given precedence, as Aristotle rightly says, over anything human reasoning can supply.
Sagredo: Then let everything said so far serve to help us weigh which of the two general accounts is the more probable. I mean Aristotle's, which would persuade us that the sublunar bodies — everything below the Moon — are by nature generable and corruptible and so on, and therefore utterly different in essence from the celestial bodies, those being impervious to change, ingenerable, incorruptible, and the rest, a conclusion drawn from the difference of their simple motions; or this account of Salviati's, which, supposing the integral parts of the world to be arranged in their best constitution, necessarily excludes straight-line motions from the simple natural bodies as being of no use in nature, and takes the Earth to be itself one of the celestial bodies, adorned with every privilege that belongs to them. So far his account rings far truer to me than the other. So let Simplicio be good enough to produce all the particular reasons, experiments, and observations, natural and astronomical alike, by which one might be persuaded that the Earth is different from the celestial bodies, motionless, and set at the center of the world — and whatever else there is that would rule out its moving like a planet, like Jupiter or the Moon and so on. And Salviati, out of his courtesy, will kindly answer them point by point.
Simplicio: Here you are, then, to begin with: two very powerful demonstrations proving that the Earth is completely different from the celestial bodies. First: bodies that are generable, corruptible, alterable, and so on are utterly different from bodies that are ingenerable, incorruptible, inalterable, and so on. The Earth is generable, corruptible, alterable, and so on; the celestial bodies are ingenerable, incorruptible, inalterable, and so on. Therefore the Earth is utterly different from the celestial bodies.
Sagredo: For your first argument, you're bringing back to the table the same dish that has been sitting on it all day and was only just now cleared away.
Simplicio: Gently, sir; hear the rest, and you'll see how different it is. Before, the minor premise was proved a priori — from first principles; now I want to prove it to you a posteriori — from experience. Judge for yourself whether that's the same thing. I prove the minor premise, then, since the major is perfectly obvious. The experience of the senses shows us that on Earth continual generations, corruptions, alterations, and so on take place — and not one of these, whether by our own senses or by the traditions and records of our ancestors, has ever been seen in heaven. Therefore heaven is inalterable and so on, and the Earth alterable and so on, and therefore different from heaven. The second argument I take from a principal and essential attribute, and it's this: a body that is by nature dark and devoid of light is different from bodies that are luminous and shining. The Earth is dark and without light; the celestial bodies are splendid and full of light; therefore, and so on. Answer these first, so we don't pile up too great a heap, and then I'll bring out others.
Salviati: As for the first, whose force you draw from experience, I'd like you to set out for me more precisely the alterations you see happening on Earth and not in heaven, on account of which you call the Earth alterable and heaven not.
Simplicio: On Earth I see grasses, plants, and animals continually generated and decaying; winds, rains, tempests, and storms stirred up; in short, this face of the Earth in perpetual metamorphosis. And not one of these changes can be made out in the celestial bodies, whose constitution and configuration agree to the letter with every record we possess — with nothing new ever generated there, and nothing old destroyed.
Salviati: But if you're going to rest your case on these visible — or rather, these actually seen — experiences, then you must count China and America as celestial bodies, because you've certainly never seen in them the alterations you see here in Italy; so as far as your own perception goes, they are inalterable.
Simplicio: Even if I haven't witnessed those alterations in those places with my own senses, there are reliable reports of them; besides which, cum eadem sit ratio totius et partium — the same reasoning holding for whole and parts — those countries, being parts of the Earth just like ours, must be alterable just as ours are.
Salviati: And why haven't you observed and seen these things for yourself, with your own eyes, instead of having to fall back on other people's reports?
Simplicio: Because those countries, besides not being exposed to our eyes, are so remote that our sight could never reach far enough to make out such changes.
Salviati: Now see how you have stumbled, all on your own, onto the flaw in your argument. If you say that the alterations seen on Earth near at hand couldn't be made out in America because of the great distance, much less could you see them on the Moon, hundreds of times farther away. And if you believe in the changes in Mexico on the strength of news arriving from there, what dispatches have reached you from the Moon to inform you that there is no alteration in it? So from your not seeing alterations in heaven — where, even if there were any, you couldn't see them for the distance, and from which no news is to be had — you cannot conclude that there are none, the way you rightly conclude, from seeing and hearing of them, that there are alterations on Earth.
Simplicio: Then I'll find you changes that have taken place on Earth so vast that, if any such had happened on the Moon, they could perfectly well have been observed from down here. We have it from the most ancient records that once, at the strait of Gibraltar, the headlands Abila and Calpe were joined together, along with lesser mountains that held the Ocean back; but when those mountains were parted — whatever the cause — and the opening let in the waters of the sea, the flood ran so far inland that it formed the whole Mediterranean Sea. If we consider its vastness, and the difference in appearance that the surface of water and the surface of land must present when seen from far away, there's no doubt that such a change could easily have been made out by anyone standing on the Moon — just as we inhabitants of the Earth would be able to make out alterations of that size on the Moon. But there is no record that any such thing was ever seen. So there's no foothold left for saying that any of the celestial bodies is alterable, and so forth.
Salviati: That changes so vast have taken place on the Moon, I wouldn't dare to say; but neither am I at all certain that they couldn't have. And since a change of that kind could show itself to us only as some variation between the brighter and the darker regions of the Moon, I don't know that we have had, here on Earth, any curious selenographers — Moon-mappers — who over a long run of years have kept us supplied with lunar maps so exact that we could be sure no such change has ever taken place in the face of the Moon. For a detailed description of its features, I find nothing more precise than one person saying it looks like a human face, another that it's like a lion's muzzle, and another that it's Cain with a bundle of thorns on his back. So to say "Heaven is inalterable, because on the Moon or in some other celestial body we don't see the alterations we make out on Earth" has no force to conclude anything at all.
Sagredo: And for my part there's another scruple still nagging me about this first argument of Simplicio's, which I'd like removed. So I ask him: was the Earth generable and corruptible before the Mediterranean flood, or did it only begin to be so then?
Simplicio: It was without doubt generable and corruptible before as well; but that was a change so vast that it could have been observed even from the Moon.
Sagredo: Well then: if the Earth was generable and corruptible even before that flood, why can't the Moon be so equally, without any such change? Why is something required of the Moon that counted for nothing in the case of the Earth?
Salviati: A very sharp thrust. But I begin to suspect that Simplicio is bending a little the meaning of the texts of Aristotle and the other Peripatetics. They say they hold heaven inalterable because no star has ever been seen generated or destroyed in it — and a star is perhaps a smaller part of heaven than a city is of the Earth; yet countless cities have been destroyed so thoroughly that not even their traces remain.
Sagredo: I truly thought otherwise: I believed Simplicio was keeping quiet about this reading of the text to spare the Master and his disciples a charge even uglier than the first. What foolishness it is to say "the celestial region is inalterable because stars are not generated and destroyed in it"! Is there anyone who has seen one terrestrial globe decay and another regenerated in its place? And isn't it accepted by all philosophers that very few stars in heaven are smaller than the Earth, while a very great many are much, much bigger? So for a star in heaven to decay is no smaller a thing than for the whole terrestrial globe to be destroyed. If, then, in order to introduce generation and corruption into the universe with any truth, it's required that bodies as vast as a star be destroyed and regenerated, you may as well strike the whole idea out — for I assure you that no one will ever see the terrestrial globe, or any other integral body of the world, decay in such a way that, after standing in view for centuries past, it dissolves without leaving a trace of itself behind.
Salviati: But to give Simplicio satisfaction in overflowing measure, and to free him from error if that can be done, I say that in our own age we have new events and observations of such a kind that, if Aristotle were alive today, I have no doubt at all he would change his opinion. That follows plainly from his own way of philosophizing. When he writes that he considers the heavens inalterable and so on because nothing new has been seen generated there and nothing old dissolved, he implicitly lets us understand that if he had seen any such event, he would have judged the contrary — and would have put the experience of the senses ahead of natural reasoning, as is proper. For if he had meant to give no weight to the senses, he would not have argued immutability from the fact that no change was ever sensibly seen.
Simplicio: Aristotle laid his principal foundation on a priori reasoning, showing the necessity of the heavens' inalterability by his natural principles, manifest and clear; and he then established the same conclusion a posteriori, by the senses and by the traditions of the ancients.
Salviati: What you describe is the method by which he wrote out his doctrine, but I don't believe it's the method by which he investigated it. I take it as certain that he first worked to assure himself of the conclusion as far as possible by way of the senses, experiments, and observations, and afterward went hunting for the means to demonstrate it — because that's how things are mostly done in the demonstrative sciences. And the reason is this: when the conclusion is true, then working backward from it — the method of resolution — you readily come upon some proposition already demonstrated, or arrive at some principle known in its own right; but if the conclusion is false, you can go on forever without ever meeting a single known truth — unless you happen to run into some impossibility or manifest absurdity along the way. And have no doubt that Pythagoras, long before he found the demonstration for which he offered the hecatomb — that sacrifice of a hundred oxen — had already made sure that in a right triangle the square on the side opposite the right angle is equal to the squares on the other two sides; and certainty about the conclusion helps not a little in the search for the demonstration — speaking always of the demonstrative sciences. But however Aristotle actually proceeded, whether the a priori reasoning came before the a posteriori evidence of the senses or the other way around, it's enough that this same Aristotle puts sensory experience ahead of all reasonings, as has been said more than once; and besides, as for the a priori arguments, we've already examined how much force they carry. Now, coming back to our subject, I say that what has been discovered in the heavens in our own times is such, and has been such, as can give complete satisfaction to all philosophers. In particular bodies and in the universal expanse of heaven alike, phenomena have been seen — and are being seen still — exactly like those we call generations and corruptions here among ourselves. Excellent astronomers have observed many comets generated and dissolved in regions higher than the Moon's orbit, besides the two new stars of 1572 and 1604, indisputably far above all the planets; and on the face of the Sun itself, thanks to the telescope, dense dark materials are seen being produced and dissolved, looking very like the clouds that surround the Earth — and many of them are so vast that they far exceed not only the Mediterranean basin but all of Africa and Asia besides. Now, if Aristotle saw these things, what do you think he would say and do, Simplicio?
Simplicio: I don't know what Aristotle would do or say, for he was the master of the sciences; but I know in part what his followers do and say — and what they must do and say, if they're not to be left without a guide, without an escort, and without a chief in philosophy. As for the comets: weren't those modern astronomers who wanted to make them celestial defeated by the Anti-Tycho, the book written against Tycho — and defeated with their own weapons, I mean by way of parallaxes — those apparent shifts in position — and calculations turned round and round in a hundred ways, concluding at last, in Aristotle's favor, that the comets are all elemental? And with that torn up — and it was the whole foundation the lovers of novelty had — what do they have left to stand on?
Salviati: Gently, Simplicio. What does this modern author of yours say about the new stars of 1572 and 1604, and about the sunspots? As for the comets, I myself would make little difficulty about placing their birth below the Moon or above it; I've never put much stock in Tycho's long-windedness, and I feel no reluctance at all about believing their matter is elemental stuff, free to rise as high as it pleases without meeting any obstacle in the impenetrability of the Peripatetic heaven — which I take to be far thinner, more yielding, and more subtle than our own air. As for the parallax calculations, there is first the doubt whether comets are even subject to that effect, and then the inconstancy of the observations the computations are built on; together these make me equally suspicious of the one set of opinions and the other — all the more because it seems to me the Anti-Tycho sometimes bends the observations to fit his own design, or writes off as faulty the ones that stand against it.
Simplicio: As for the new stars, the Anti-Tycho makes short work of them in four words: such modern new stars, he says, are no certain parts of the celestial bodies, and if his adversaries want to prove that there is alteration and generation up there, they must demonstrate changes in the stars that were charted ages ago — the ones nobody doubts are celestial things — and that they can never do by any means. As for the matter some claim is generated and dissolved on the face of the Sun, he makes no mention of it at all; from which I gather he takes it for a fable, or for illusions of the telescope, or at most for little effects produced in the air — in short, for anything in the world except celestial matter.
Salviati: But you, Simplicio — what answer have you worked out to the objection of these troublesome spots that have come along to muddy the heavens, and worse still, the Peripatetic philosophy? As that philosophy's intrepid defender, you must have found some remedy, some solution — and you mustn't cheat us out of it.
Simplicio: I have heard various opinions on this particular point. "Some say they are stars which, like Venus and Mercury, revolve around the Sun in orbits of their own, and show themselves dark to us when they pass beneath it; and since they are very numerous, it often happens that some of them cluster together and afterwards separate again. Others believe them to be impressions formed in the air; others, illusions of the lenses; and others, other things still. But I lean strongly toward believing — indeed I hold it for certain — that they are an aggregate of many and various opaque bodies, running together almost at random: which is why we often see, within a single spot, ten or more of these tiny bodies that can be counted, irregular in shape, looking to us like flakes of snow, or tufts of wool, or hovering flies. They shift position among themselves, now scattering, now clustering, and above all beneath the Sun, around which, as around their center, they keep moving. But it does not therefore follow that they are generated and corrupted; rather, at times they hide behind the body of the Sun, and at other times, though well clear of it, they cannot be seen because of the nearness of its overwhelming light. For within the Sun's eccentric orb there is built up a kind of onion, composed of many layers one inside another, each of them studded with certain small spots, and each in motion; and although their movement at first seemed inconstant and irregular, nevertheless it is said to have been observed lately that within fixed periods the very same spots return exactly." This seems to me the most serviceable remedy found so far for accounting for the appearance while still preserving the incorruptibility and ingenerability of the heavens; and if it should fall short, there will be no lack of loftier minds to find better ones.
Salviati: If what we are disputing were some point of law, or one of the other human studies, where there is neither truth nor falsehood, then one could rely a great deal on subtlety of wit, fluency of speech, and wider reading in the authors, and hope that whoever excelled in those things would make his case appear, and be judged, the stronger. But in the natural sciences, whose conclusions are true and necessary and where human preference counts for nothing, a man had better take care not to plant himself in defense of the false — because a thousand Demostheneses and a thousand Aristotles will be left unhorsed by any average mind that has had the luck to seize on the truth. So, Simplicio, put out of your head this thought and this hope of yours, that there could ever be men so much more learned, well-read, and steeped in books than the rest of us that they can make the false become true in defiance of nature. And since, of all the opinions produced so far about the essence of these sunspots, the one you have just laid out strikes you as the true one, it follows — if that is so — that all the others are false. And to free you from this one as well, which is an utterly false chimera, I will pass over the thousand other improbabilities in it and bring you just two observations against it. The first is that many of these spots are seen to be born in the middle of the solar disk, and many likewise to dissolve and vanish far from the Sun's edge — a necessary argument that they are generated and dissolved; for if they appeared there by mere local motion, without generation and corruption, they would all be seen to enter and exit across the outermost rim. The other observation, for anyone not stuck in the lowest grade of ignorance about perspective: from the change in their apparent shapes, and the apparent change in their speed of motion, it follows necessarily that the spots lie right against the body of the Sun — that they touch its surface and move with it or upon it, and in no way circle around it in orbits at a distance. The motion proves it: toward the rim of the solar disk it appears extremely slow, and toward the middle, faster. The shapes prove it too: toward the rim they appear extremely narrow compared with how they show in the middle regions, and this is because in the middle they are seen full-face, as they really are, while toward the rim, where the globe's surface curves away, they show foreshortened. And both diminutions, of shape and of motion, for anyone who has known how to observe and calculate them carefully, answer precisely to what ought to appear if the spots lie against the Sun — and clash inexcusably with their moving in circles at any distance from the solar body, however small — as our mutual friend has demonstrated at length in his Letters on Sunspots, addressed to Mark Welser. From the same change of shape it also follows that none of them is a star, or any other body of spherical shape; for among all shapes the sphere alone is never seen foreshortened, and can never present itself as anything but perfectly round. So if any single spot were a round body, as all stars are held to be, it would show the same roundness in the middle of the solar disk as near the edge; whereas their foreshortening so much, showing so slender near the rim and broad and spacious toward the middle, makes us certain that they are flakes of little depth or thickness compared with their length and breadth. And as for its having "lately been observed" that the spots come back exactly the same after their fixed periods — don't you believe it, Simplicio; whoever told you that means to deceive you. Notice that he kept quiet about the ones that are generated and dissolved on the face of the Sun far from the rim; nor did he say a word about that foreshortening, which is a necessary argument that they lie against the Sun. What truth there is about the same spots returning is nothing more than what may already be read in the Letters I mentioned: namely, that some of them may last so long that they do not break up within a single revolution around the Sun — a circuit that is completed in less than a month.
Simplicio: To tell the truth, I have not made observations long or careful enough to make me master of the quod est — the plain fact — of this matter. But I certainly mean to make them, and then to try for myself whether I can bring what experience offers us into accord with what Aristotle demonstrates — for it is obvious that two truths cannot contradict each other.
Salviati: Whenever you want to square what your senses show you with the soundest doctrines of Aristotle, you'll have no trouble at all. Doesn't Aristotle say that, because of their great distance, the things of the heavens cannot be treated with much certainty?
Simplicio: He says so plainly.
Salviati: And doesn't he likewise affirm that what experience and the senses show us must be preferred to any argument, however well-founded it may seem? And doesn't he say this flatly, without the least hesitation?
Simplicio: He does.
Salviati: Then of these two propositions, both of them Aristotle's own doctrine, the second — that the senses must be put before argument — is a much firmer and more resolute doctrine than the other, which holds the heavens unalterable. And so you will be philosophizing more Aristotelianly if you say, "The heavens are alterable, because my senses tell me so," than if you say, "The heavens are unalterable, because reasoning persuaded Aristotle it was so." Add to this that we can reason about the things of the heavens far better than Aristotle could; for in confessing that such knowledge was difficult for him because of their distance from the senses, he concedes that anyone to whom the senses could present those things better would be able to philosophize about them with greater assurance. Now we, thanks to the telescope, have brought the heavens thirty and forty times closer than they were to Aristotle, so that we can make out a hundred things in them that he could not see — among others, these spots on the Sun, which were absolutely invisible to him. Therefore we can treat of the heavens and the Sun with more assurance than Aristotle.
Sagredo: I can see straight into Simplicio's heart, and I can tell he is deeply shaken by the force of these all-too-conclusive arguments. But on the other side, when he sees the great authority Aristotle has won with the whole world, considers the number of famous interpreters who have labored to explain his meaning, and sees the other sciences, so useful and so necessary to the public, resting a great part of their esteem and reputation on Aristotle's credit — all this confounds him and frightens him badly. I can almost hear him saying: "Once Aristotle is pulled down from his seat, who is to settle our controversies? What other author are we to follow in the schools, the academies, the universities? What philosopher has written out every part of natural philosophy, and so methodically, without leaving behind even a single particular conclusion? Must we lay waste the great building that shelters so many travelers? Must we destroy that refuge, that Prytaneum — that civic hall — where so many students find such comfortable lodging, where, without ever exposing yourself to the weather, merely by turning a few pages you acquire complete knowledge of nature? Must we flatten the very fortress in which we live secure against every enemy assault?" I pity him — no less than I would pity some lord who, over long years, at immense expense, with the labor of hundreds upon hundreds of craftsmen, built himself a most noble palace, and then sees it threatening to collapse because the foundations were badly laid; and who, rather than watch, heartbroken, while the walls hung with so many beautiful paintings are pulled down, the columns that hold up the splendid galleries topple, the gilded ceilings fall, and the doorframes, the pediments, the marble cornices installed at such cost all come to ruin — tries to stave off the collapse with chains, props, braces, buttresses, and shores.
Salviati: Oh, Simplicio needn't fear any such collapse just yet; I would undertake to insure him against the damage at far smaller expense. There is no danger that so great a multitude of clever, sharp-eyed philosophers will let themselves be overrun by one or two men making a bit of noise; without so much as turning the points of their pens against them, by silence alone they will sink them into contempt and derision with the whole world. It is a perfectly idle notion to think anyone could establish a new philosophy just by refuting this author or that one. One would first have to learn how to remake men's brains — to render them fit to tell the true from the false — and that is something only God can do. But from one line of talk to the next, where have we wandered off to? I couldn't find my way back to the trail without your memory as my guide.
Simplicio: I remember it perfectly well. We were on the Anti-Tycho's answers to the objections against the immutability of the heavens; among those objections you inserted this one about the sunspots, which he never touches, and I believe you meant to consider his answer to the challenge of the new stars.
Salviati: Now the rest of it comes back to me. To carry on with the matter: it seems to me the Anti-Tycho's answer contains several things that deserve to be called out. First of all, if the two new stars — which he cannot avoid placing in the highest parts of the heavens, and which lasted a long while and finally vanished — give him no trouble in maintaining the inalterability of the heavens, simply because they were not certain parts of it, nor changes in the ancient stars, then what is the point of campaigning with so much anxiety and sweat against the comets, to banish them from the celestial regions at any cost? Wasn't it enough to say of them exactly what he said of the new stars — that since they are not certain parts of the heavens, nor alterations in any of its stars, they do no damage either to the heavens or to the doctrine of Aristotle? Second, I cannot quite make out what is really going on in his mind. He grants that alterations in the stars would be destructive of the heavens' prerogatives — their incorruptibility and the rest — and this because the stars are celestial things, as everyone unanimously agrees; and yet it does not disturb him in the least if those same alterations take place elsewhere, outside the stars, in the rest of the celestial expanse. Does he perhaps think the heavens are not a celestial thing? For my part, I always supposed the stars were called celestial things because they are in the heavens, or made of the heavens' own matter — so that the heavens should be more celestial than the stars, just as nothing can be said to be more earthly than earth itself, or more fiery than fire. And then his making no mention at all of the sunspots — which have been conclusively demonstrated to be produced and dissolved, to lie next to the body of the Sun, and to turn with it or around it — gives me a strong hint that this author may be writing more to please others than to satisfy himself. I say this because he shows himself competent in mathematics, and it is impossible that a competent man should not be persuaded by the demonstrations that these materials are necessarily in contact with the body of the Sun, and that they are generations and corruptions so vast that nothing so great ever happens on Earth. And if changes of such size, in such numbers, and so frequent take place on the very globe of the Sun — which may reasonably be reckoned among the noblest parts of the heavens — what argument is left strong enough to persuade us that others cannot take place on the other globes?
Sagredo: I cannot hear it without great astonishment — I will say more, without great resistance from my own intellect — when this quality of being impervious to change, immutable, unalterable, and so on, is held up as a great nobility and perfection in the natural bodies that make up the universe, while conversely being alterable, generable, mutable is counted a great imperfection. For my part, I hold the Earth most noble and admirable precisely because of the many and diverse alterations, mutations, and generations that go on in it without pause. If it were not subject to any change at all — if it were one vast solitude of sand, or a mass of jasper, or if at the time of the Flood the waters covering it had frozen and it had remained one immense globe of crystal, where nothing was ever born or altered or changed — I would count it a great useless carcass in the world, idle through and through, and, in a word, superfluous, as if it did not exist in nature at all; and I would draw the same distinction for it that there is between a living animal and a dead one. And I say the very same of the Moon, of Jupiter, and of all the other globes of the world. The deeper I go into the vanity of popular reasoning on this point, the more shallow and foolish I find it. What greater silliness can be imagined than to call gems, silver, and gold precious, and earth and mud worthless? Doesn't it occur to these people that if earth were as scarce as jewels or the most prized metals, there is not a prince alive who wouldn't gladly pay a load of diamonds and rubies and four cartloads of gold just to have enough earth to plant a jasmine in a little pot, or to sow a China orange and watch it sprout, grow, and put out such lovely leaves, such fragrant flowers, such delicate fruit? So it is scarcity and plenty that raise or sink the price of things with the crowd — the same crowd that will call a diamond magnificent because it resembles pure water, and then would not trade it for ten barrels of the real thing. These people who so exalt incorruptibility, inalterability, and the rest are driven to say such things, I believe, by their great longing to keep on living and by the terror they have of death; and they fail to consider that if men were immortal, their own turn to come into the world would never have arrived. They deserve to run into a Medusa's head and be transmuted into statues of jasper or diamond, so as to become more perfect than they are.
Salviati: And perhaps such a metamorphosis would even work to their advantage; for it is better, I think, not to reason at all than to reason backwards.
Simplicio: There is no doubt whatever that the Earth is far more perfect being, as it is, alterable, mutable, and so on, than it would be as a mass of stone — even if it were one whole diamond, supremely hard and impervious to change. But however much nobility these conditions confer on the Earth, they would make the celestial bodies just that much more imperfect, since in them such qualities would be superfluous: the celestial bodies — that is, the Sun, the Moon, and the other stars, which are ordered to no other use than the service of the Earth — need nothing beyond motion and light to achieve their end.
Sagredo: So nature has produced and set in order all those vast, consummate, most noble celestial bodies — impervious to change, immortal, divine — for no other use than the service of the Earth: a thing changeable, transient, and mortal? For the service of what you yourselves call the dregs of the world, the sink of every filth? To what purpose make the celestial bodies immortal and all the rest, in order to serve something perishable and all the rest? Take away this one use, the service of the Earth, and the innumerable host of celestial bodies is left entirely useless and superfluous, since they have not, and cannot have, any mutual interaction among themselves — all of them being unalterable, immutable, impervious to change. If the Moon, for example, is impervious to change, what do you expect the Sun or any other star to work upon her? The effect would surely be far feebler than that of a man trying to melt down a great mass of gold with a glance or a thought. Besides, it seems to me that if the celestial bodies really do cooperate in the generations and alterations on Earth, then they themselves must be alterable too; otherwise I cannot see how the Moon's or the Sun's being brought to bear upon the Earth to produce generation would be anything more than laying a marble statue beside the bride and expecting children from that union.
Simplicio: Corruptibility, alteration, change, and the rest are not in the terrestrial globe as a whole. As far as its integrity goes, the Earth is no less eternal than the Sun or the Moon; it is generable and corruptible only in its outer parts. But it's quite true that in those parts generation and corruption are perpetual, and as perpetual they require the eternal operations of the heavens; and therefore the celestial bodies must be eternal.
Sagredo: That all runs along nicely. But if the corruptibility of the surface parts does no harm whatever to the eternity of the whole terrestrial globe — if, in fact, being generable, corruptible, alterable, and the rest brings it great ornament and perfection — then why can't you, why shouldn't you, admit alterations, generations, and so on in the outer parts of the celestial globes as well? They would add ornament without diminishing perfection or robbing those globes of their actions; rather they'd increase them, by having them all act not only upon the Earth but mutually upon one another, and the Earth upon them in turn.
Simplicio: That cannot be, because the generations, changes, and so forth that took place, say, on the Moon would be useless and vain, and natura nihil frustra facit — nature does nothing in vain.
Sagredo: And why would they be useless and vain?
Simplicio: Because we plainly see, and touch with our own hands, that all the generations, changes, and so on that occur on Earth are directed — all of them, directly or indirectly — to the use, the convenience, and the benefit of man. Horses are born for men's convenience; for the horses' nourishment the Earth produces hay, and the clouds water it. For men's convenience and nourishment grow the herbs, the grains, the fruits, the beasts, the birds, the fish; in short, if we go through all these things and examine them carefully, we'll find that the end to which they are all directed is the need, the use, the convenience, and the delight of men. Now of what possible use to the human race could generations taking place on the Moon or on some other planet ever be? Unless you meant to say that there are men on the Moon as well, enjoying its fruits — a notion either fabulous or impious.
Sagredo: Whether on the Moon or on any other planet there grow herbs or plants or animals like ours, whether rains and winds and thunderstorms occur there as they do around the Earth — I don't know it and I don't believe it, and still less that the Moon is inhabited by men. But I don't at all see how it follows that, because nothing like our things is generated there, no alteration can take place there at all — that there can be no other things there that change, come to be, and dissolve: things not merely different from ours, but utterly remote from our imagination, and in a word wholly beyond our power to conceive. I am certain that a man born and raised in some immense forest, among beasts and birds, with no knowledge whatever of the element of water, could never so much as imagine that there exists in nature another world quite unlike the land, full of animals that travel swiftly without legs and without wings — and not only along the surface, as beasts do on land, but through the whole depth of it; and that they not only travel, but stop motionless wherever they please, which the birds cannot do in the air; and that men live there too, and build palaces and cities there, and find travel so convenient that without any effort at all they go off to the most distant countries with their whole family, house and all — with entire cities, even. As I say, I'm certain that such a man, however keen his imagination, could never picture to himself the fish, the ocean, the ships, the fleets, the navies. So too, and much more easily, it may be that on the Moon — removed from us by so vast an interval, and made, perhaps, of material very different from the Earth's — there are substances, and operations going on, that are not merely remote from all our imaginings but entirely outside them: things bearing no resemblance whatever to ours, and for that reason wholly inconceivable to us. For whatever we imagine has to be either something already seen, or a composite of things, or of parts of things, seen at some other time — which is exactly what sphinxes, sirens, chimeras, centaurs, and the rest are.
Salviati: I've often let my fancy roam over these matters, and in the end I think I can indeed pick out some of the things that are not and cannot be on the Moon — but none of the things that I believe are and can be there, except in the very broadest generality: things that adorn her, acting and moving and living, and perhaps — in a manner utterly different from ours — beholding and admiring the greatness and beauty of the world and of its Maker and Ruler, and singing His glory with continual praise; doing, in short (and this is my whole meaning), what the sacred writers so often affirm: all creatures perpetually occupied in praising God.
Sagredo: Those are among the things that, speaking in the most general terms, may well be there. But I'd gladly hear you name the ones you believe are not and cannot be there — those, surely, can be named more particularly.
Salviati: Take note, Sagredo: this will be the third time that, step by step and without noticing it, we've drifted away from our main plan; and at this rate of digression we'll be a long while getting to the end of our reasonings. So perhaps it would be well to defer this discussion, along with the others we've agreed to save for a session of their own.
Sagredo: Please — since we're on the Moon, let's finish the business that belongs to her, so that we don't have to make such a long journey a second time.
Salviati: As you like. And to begin with the most general points: I believe the lunar globe is very different from the terrestrial, though in some respects certain resemblances can be seen. I'll give the resemblances first, and then the differences. The Moon certainly conforms to the Earth in shape, which is beyond doubt spherical, as follows necessarily from our seeing her disk as a perfect circle, and from the way she receives the light of the Sun. If her surface were flat, the whole of it would be clothed in light at one and the same instant, and then likewise stripped of light all at once in a single moment — not the parts facing the Sun first and the following parts in succession, so that only when she reaches opposition — the point directly opposite the Sun — and not before, does the whole apparent disk stand illuminated. And the exact contrary would happen if her visible surface were concave: the illumination would begin from the parts turned away from the Sun. Second, she is, like the Earth, dark and opaque in herself, and it is this opacity that fits her to receive and throw back the Sun's light — which she could not do if she were otherwise. Third, I hold her material to be every bit as dense and solid as the Earth's; my clearest evidence for this is that her surface is for the most part uneven, full of the many prominences and hollows that the telescope reveals. Of these prominences many are in every respect like our most rugged and precipitous mountains, and some can be seen stretched out in continuous chains hundreds of miles long; others come in more compact clusters; and there are also many detached, solitary crags, very steep and sheer. But what occurs most frequently of all are certain raised banks (I'll use that word, since no other comes to mind that pictures them better), quite elevated, which enclose and encircle plains of various sizes, forming various figures, though most of them circular; many of these have a considerably raised mountain in the middle, and a few are filled with somewhat dark material — like that of the great spots seen with the naked eye — and these are the largest of the enclosures; of the smaller and smaller ones the number is enormous, and still almost all of them circular. Fourth, just as the surface of our globe is divided into two chief parts, the land and the water, so in the lunar disk we see a grand distinction between certain great fields that shine more brightly and others less. And I believe the Earth would present much the same appearance to anyone who could see her lit by the Sun from the Moon, or from some similar distance: the surface of the sea would appear darker, and that of the land brighter. Fifth, just as from the Earth we see the Moon now all luminous, now half, now more, now less, sometimes a sickle, and sometimes wholly invisible — namely when she lies beneath the Sun's rays, so that the part facing the Earth is left in darkness — just so, from the Moon, one would see the Sun's illumination of the face of the Earth, with precisely the same period, to the letter, and under the same changes of shape. Sixth —
Sagredo: Gently a moment, Salviati. That the illumination of the Earth, as far as the variety of shapes goes, would look to someone on the Moon exactly like what we observe in the Moon — that I understand perfectly well. But I don't yet see how it would show itself with the same period, seeing that what the Sun's illumination does upon the lunar surface in a month, it does upon the terrestrial in twenty-four hours.
Salviati: It's true that the Sun's effect, so far as lighting these two bodies and sweeping their entire surfaces with its splendor, is accomplished on the Earth in one natural day and on the Moon in a month. But the variation of the shapes under which the illuminated parts of the terrestrial surface would be seen from the Moon doesn't depend on that alone; it depends on the changing aspects the Moon keeps taking up with respect to the Sun. So that if, for example, the Moon followed the Sun's motion exactly and happened to stand always directly in line between it and the Earth — in the aspect we call conjunction — then, since she would always be seeing the same hemisphere of the Earth that the Sun sees, she would see it perpetually all bright. If, on the contrary, she stood always at opposition to the Sun, she would never see the Earth at all, since the Earth's dark part would be continuously turned toward the Moon, and therefore invisible. But when the Moon is at quadrature with the Sun — a quarter-circle away from it — then, of the terrestrial hemisphere exposed to the Moon's view, the half toward the Sun is luminous and the other half, turned away from the Sun, is dark; and so the illuminated part of the Earth would present itself to the Moon in the shape of a half circle.
Sagredo: I'm entirely satisfied; and now I understand it perfectly. As the Moon departs from opposition to the Sun, where she saw nothing of the illuminated part of the terrestrial surface, and comes day by day toward the Sun, she begins little by little to uncover some small portion of the Earth's illuminated face, and she sees it in the shape of a thin sickle, the Earth being round; and as her motion brings her day by day closer to the Sun, she keeps uncovering more and more of the illuminated terrestrial hemisphere, so that at quadrature she uncovers exactly half of it, just as we see the same amount of her; then, continuing on toward conjunction, she uncovers successively more of the lit surface, and finally, at conjunction, sees the entire hemisphere all luminous. In short, I understand very well that what happens to the inhabitants of the Earth in watching the Moon's changes would happen to anyone on the Moon watching the Earth, but in the reverse order: when the Moon is full for us, at opposition to the Sun, for them the Earth would be at conjunction with the Sun, wholly dark and invisible; and conversely, the configuration that for us is conjunction of Moon with Sun — the Moon silent, as they say, and unseen — would there be opposition of Earth to Sun: a full Earth, so to speak, all luminous. And finally, however much of the illuminated lunar surface shows itself to us at a given time, just so much of the Earth, at that same time, would be seen from the Moon to be dark; and however much of the Moon is left without light for us, just so much of the Earth is illuminated for the Moon. Only at the quadratures, then, do we see a half circle of the Moon luminous, and they just as much of the Earth. In one thing, though, these reciprocal operations seem to me to differ: granting, for argument's sake and not conceding it, that there were someone on the Moon who could gaze at the Earth from up there, he would see the whole terrestrial surface every single day, thanks to the Moon's motion around the Earth in twenty-four or twenty-five hours; whereas we never see anything but half of the Moon, since she does not revolve upon herself, as she would have to do to be able to show us all of her.
Salviati: Provided it isn't the other way around — that it's precisely her turning upon herself that keeps us from ever seeing the other half; for that is how it would have to be, if she rode on the epicycle — that small secondary circle the astronomers assign her. But you're leaving out another difference, to set against the one you've just pointed out.
Sagredo: And which is that? No other comes to my mind at the moment.
Salviati: It's this: if the Earth (as you've rightly noted) sees no more than half of the Moon, while from the Moon the whole Earth is seen, then, on the other hand, all the Earth sees the Moon, but only half the Moon sees the Earth. For the inhabitants, so to speak, of the upper hemisphere of the Moon — the one invisible to us — are deprived of the sight of the Earth; and these, perhaps, are the antichthones, the "counter-dwellers" the ancients talked of. But here I'm reminded of a particular phenomenon, newly observed in the Moon by our mutual friend, the Academician, from which two necessary consequences follow: one, that we actually see somewhat more than half of the Moon; the other, that the Moon's motion is related exactly to the center of the Earth. And the phenomenon and the observation are these. If the Moon has a correspondence and a natural sympathy with the Earth, toward which she keeps a certain fixed part of herself turned, then the straight line joining their two centers must always pass through the same point of the Moon's surface — so that anyone gazing at her from the center of the Earth would always see the same lunar disk, bounded precisely by one and the same circumference. But for someone stationed on the Earth's surface, the ray running from his eye to the center of the lunar globe would not pass through that same point of her surface through which the line drawn from the Earth's center to the Moon's passes — except when she stood directly overhead. With the Moon placed in the east or in the west, however, the point where the visual ray strikes lies above the point of the line joining the centers; and so some part of the lunar hemisphere toward the upper circumference comes into view, and just as much is hidden on the lower side — comes into view and is hidden, I mean, with respect to the hemisphere that would be seen from the Earth's true center. And since the part of the Moon's circumference that is uppermost at her rising is lowermost at her setting, the difference in the appearance of those upper and lower parts should be quite noticeable, with spots or other marked features in those regions now showing themselves, now hiding. A similar variation should also be seen toward the northern and southern edges of the same disk, according as the Moon stands in one or the other belly of her "dragon" — the old astronomers' name for the two arcs of her path that swing north and south: when she is to the north, some of her northern parts are hidden from us and some southern parts come into view, and the reverse when she is to the south. Now, that these consequences are in fact borne out, the telescope makes us certain. For there are on the Moon two particular spots, one of which, when the Moon is on the meridian, faces toward the northwest, while the other lies almost diametrically opposite; and the first is visible even without the telescope, but not the second. The northwesterly one is a small oval spot, separate from the other very large ones; the opposite one is smaller, likewise detached from the great spots, and set in a quite bright field. In both of these the variations I've described are observed very plainly: they are seen — each moving contrary to the other — now near the rim of the lunar disk, now drawn back from it, and with such a difference that the interval between the northwesterly spot and the circumference of the disk is at one time more than double what it is at another; and as for the other spot, since it lies closer to the circumference, its shift amounts to more than triple from one time to the next. From all this it is plain that the Moon, as if drawn by a magnetic power, constantly faces the terrestrial globe with one and the same face, and never turns away from it.
Sagredo: And when will there be an end to the new observations and discoveries of this admirable instrument?
Salviati: If its progress follows the course of other great inventions, we may hope that with the passage of time we'll come to see things we can't now so much as imagine. But to return to our original discussion: I say, as the sixth point of resemblance between the Moon and the Earth, that just as the Moon, a great part of the time, makes up for the absence of the Sun's light and renders our nights quite bright by the reflection of her own, so the Earth repays her in kind when her need is greatest, reflecting the solar rays back at her with a very vigorous illumination — greater, in my judgment, than the light that comes to us from her, in the same proportion as the Earth's surface is greater than the Moon's.
Sagredo: No more, no more, Salviati! Leave me the pleasure of showing you how, at this first hint, I've penetrated the cause of a phenomenon I've thought about a thousand times without ever getting to the bottom of it. You mean that a certain pale glow we see in the Moon, above all when she's a sickle, comes from the reflection of the Sun's light off the surface of the land and the sea; and that this light shows the more clearly, the thinner the crescent is — because then the luminous part of the Earth seen from the Moon is larger, in keeping with what we concluded a moment ago: that the luminous part of the Earth showing itself to the Moon is always exactly as large as the dark part of the Moon that faces the Earth. So when the Moon is a thin sickle, and her dark portion consequently great, great too is the illuminated part of the Earth as seen from the Moon, and so much the more powerful its reflection of light.
Salviati: That is exactly what I meant to say. Truly, it's a great sweetness to talk with people of judgment and quick understanding — above all when one is strolling and discoursing among truths. I've run into brains so thick that, though I repeated to them a thousand times this very thing you've just penetrated on your own, they never once managed to grasp it.
Simplicio: If you mean that you couldn't persuade them to the point of understanding it, I'm greatly amazed, and I'm confident that if they didn't understand it from your explanation, they'll hardly understand it from anyone else's — your way of putting it seems very clear to me. But if you mean you didn't persuade them to the point of believing it, that doesn't amaze me in the least; for I confess that I myself am one of those who understand your discourses without being set at rest by them. Indeed, on this and on parts of the other six points of resemblance, many difficulties remain with me — and I'll bring them forward once you've finished recounting them all.
Salviati: My desire to get at some truth — a pursuit in which the objections of intelligent men like you two can help me a great deal — will make me very brief in dispatching what's left. Let the seventh point of resemblance, then, be this: that the Earth and the Moon answer each other in injuries no less than in favors. The Moon, quite often at the very peak of her illumination, is robbed of light and eclipsed when the Earth steps between her and the Sun; and she in her turn, by way of payback, places herself between the Earth and the Sun, and with her shadow darkens the Earth. True, the revenge doesn't measure up to the offense: the Moon often remains plunged entirely in the Earth's shadow, and for a good long while, whereas the whole Earth is never darkened by the Moon, nor for any long stretch of time. Still, considering how small her body is compared to the size of the Earth's, you can only say that her fighting spirit, in a certain way, is very great. So much for the resemblances. What would come next is a discussion of the disparities; but since Simplicio means to favor us with his doubts about the resemblances, we'd better hear them and weigh them before moving on.
Sagredo: Yes — since it's a fair bet that Simplicio will have no objections to the disparities and differences between the Earth and the Moon, seeing that he holds their substances to be utterly different.
Simplicio: Of the resemblances you recited in drawing your parallel between the Earth and the Moon, I find I can admit without objection only the first and two others. I admit the first — the spherical shape — though even there there's a catch, since I take the Moon's sphere to be highly polished and smooth as a mirror, whereas this Earth of ours we can touch with our own hands and feel how rough and rugged it is. But that point, concerning the unevenness of the surface, belongs under another of the resemblances you brought forward, so I'll save what I have to say about it for the consideration of that one.
That the Moon is, as you claim in your second resemblance, opaque and dark in herself like the Earth — of that I admit only the first attribute, the opacity, of which solar eclipses assure me: for if the Moon were transparent, the air during a total eclipse of the Sun would not go as dark as it does; a refracted light would come through the transparency of the lunar body, as we see happen through the densest clouds. But as for the darkness, I don't believe the Moon is wholly without light of her own, as the Earth is. On the contrary, that faint brightness we see across the rest of her disc, beyond the slender horns lit by the Sun, I take to be her own proper and natural light, and not a reflection from the Earth — which I judge incapable, by its extreme roughness and darkness, of reflecting the Sun's rays.
In the third parallel I agree with you in one part and dissent in the other. I agree in judging the body of the Moon utterly solid and hard, like the Earth — indeed much more so; for if we take from Aristotle that the heavens are of impenetrable hardness, and the stars are the denser parts of the heavens, then they must necessarily be perfectly firm and perfectly impenetrable.
Sagredo: What beautiful material the stuff of the heavens would be for building palaces, if only one could get hold of it — so hard, and so transparent!
Salviati: Terrible material, rather: being, by its utter transparency, completely invisible, you couldn't walk through the rooms without grave danger of banging into the doorposts and cracking your head.
Sagredo: There'd be no such danger, if it's true, as some Peripatetics say, that the stuff is intangible; and if it can't be touched, still less can it be bumped into.
Salviati: That would be no comfort at all. For even if celestial matter can't be touched, since it lacks the tangible qualities, it can perfectly well touch elemental bodies; and as far as hurting us goes, it comes to the same thing whether it crashes into us — or worse — or we crash into it. But let's leave these palaces, or better, these castles in the air, and not hold up Simplicio.
Simplicio: The question you've raised in passing is one of the hard ones treated in philosophy, and I have some very fine thoughts on it from a great professor who held a chair at Padua; but this isn't the moment to go into them. So, returning to our subject: I say again that I take the Moon to be far more solid than the Earth — but I argue it not, as you do, from the roughness and ruggedness of her surface, but from the opposite: from her being fit to take (as we see among ourselves in the hardest gems) a polish and luster beyond that of the smoothest mirror; for her surface must be like that, to send us so vivid a reflection of the Sun's rays. As for those appearances you speak of — mountains, crags, ridges, valleys, and so on — they're all illusions. I've been present at public disputations where it was stoutly maintained, against these introducers of novelties, that such appearances come from nothing but parts unequally opaque and transparent, of which the Moon is composed inside and out — the kind of thing we often see happen in crystal, in amber, and in many perfectly polished precious stones, where, from the opacity of some parts and the transparency of others, all sorts of hollows and bulges seem to appear in them.
In the fourth resemblance I concede that the surface of the terrestrial globe, seen from far away, would present two different appearances, one brighter and one darker; but I think those differences would fall out the reverse of what you say. That is, I believe the surface of the water would appear bright, because it's smooth and transparent, and the surface of the land would stay dark, because of its opacity and roughness, poorly suited to throwing back the light of the Sun.
On the fifth comparison I admit everything, and I'm satisfied that if the Earth shone as the Moon does, it would show itself, to anyone gazing at it from up there, in shapes matching the phases we see in the Moon. I understand, too, how the period of its illumination and its change of shapes would be a month, even though the Sun sweeps over the whole of it in twenty-four hours; and finally I have no difficulty admitting that only half the Moon sees all the Earth, and all the Earth sees only half the Moon.
The sixth I hold to be utterly false — that the Moon could receive light from the Earth, which is pitch-dark, opaque, and thoroughly unfit to reflect the Sun's light the way the Moon reflects it to us. As I've said, I hold that the light we see on the rest of the Moon's face, beyond the horns blazing with the Sun's illumination, is the Moon's own proper and natural light — and it would take a great deal to make me believe otherwise.
The seventh, on the mutual eclipses, can also be admitted — though what you insist on calling an eclipse of the Earth is properly and customarily called an eclipse of the Sun. And that is all I need say to you for now in contradiction of the seven resemblances. If you'd like to reply to any of these objections, I'll listen gladly.
Salviati: If I've rightly taken in what you've answered, it seems to me that certain conditions I had made common to the Moon and the Earth still remain in dispute between you and us — and they are these. You take the Moon to be smooth and polished like a mirror, and as such fit to reflect the Sun's light to us, and the Earth, on the contrary, too rough to make any such reflection. You grant that the Moon is solid and hard, and you argue this from her being polished and smooth, not from her being mountainous; and for her mountainous appearance you assign as the cause her being made of parts more and less opaque and transparent. And finally, you hold that secondary light to be the Moon's own, and not a reflection from the Earth — though you don't seem to deny the sea some reflection, its surface being smooth. As for undeceiving you on this error — that the Moon's reflection cannot work as from a mirror — I have little hope, when I see that what's written on exactly this subject in The Assayer and in the Letters on Sunspots of our mutual friend has gained no ground at all in your mind — if, that is, you've read attentively what's written there on the matter.
Simplicio: I've skimmed them, only superficially, in what little idle time my more solid studies leave me. So if, by repeating some of those arguments or bringing up others, you think you can resolve my difficulties, I'll listen more attentively.
Salviati: I'll say what comes to mind at the moment, and it may well be a mixture of my own thoughts and what I once read in those books — from which, I remember well, I came away entirely persuaded, though at first sight the conclusions struck me as great paradoxes. What we're asking, Simplicio, is whether, to make a reflection of light like the one that comes to us from the Moon, it's necessary that the surface it comes from be as smooth and polished as a mirror, or whether a surface that is not smooth and not polished — rough and badly finished — is better suited to it. Now, suppose two reflections reached us, one brighter and one less so, from two surfaces facing us. I ask you: which of the two surfaces do you think would appear brighter to our eyes, and which darker?
Simplicio: I believe, without any doubt, that the one reflecting the light to me more vividly would show itself brighter in appearance, and the other darker.
Salviati: Now be so kind as to take that mirror hanging on the wall there, and let's step out into the courtyard. Come, Sagredo. Hang the mirror there, on that wall where the sun strikes; now let's move away and pull back here into the shade. There you have two surfaces struck by the sun — the wall and the mirror. Tell me now: which looks brighter to you, the wall's surface or the mirror's? You don't answer?
Sagredo: I leave the answering to Simplicio; the difficulty is his. As for me, this little beginning of an experiment has already persuaded me that the Moon must, of necessity, have a very badly polished surface.
Salviati: Tell me, Simplicio: if you had to paint a picture of that wall with the mirror hanging on it, where would you use the darker colors — in painting the wall, or in painting the mirror?
Simplicio: Much darker in painting the mirror.
Salviati: Then if the more powerful reflection of light comes from the surface that appears brighter, the wall will reflect the Sun's rays to us more vividly than the mirror.
Simplicio: Very good, my dear sir — is that the best experiment you have? You've stationed us where the mirror's reverberation doesn't strike. But come with me a little this way. No — come along.
Sagredo: Are you looking for the spot where the mirror throws its reflection?
Simplicio: I am.
Sagredo: Well, there it is — on the opposite wall, exactly as big as the mirror, and hardly less bright than if the Sun were striking there directly.
Simplicio: Come over here, then, and look from this spot at the surface of the mirror, and tell me whether it looks darker than the wall's.
Sagredo: Look at it yourself; I'm not ready to blind myself just yet. I know perfectly well, without looking, that it shows as vivid and bright as the Sun itself, or very little less.
Simplicio: So what do you say now — that the reflection of a mirror is less powerful than that of a wall? I see that on this opposite wall, where the reflection from the other sunlit wall arrives together with the one from the mirror, the mirror's is far brighter; and I see likewise that from here the mirror itself looks much brighter than the wall.
Salviati: You've gotten ahead of me with your sharpness, because this is exactly the observation I needed in order to explain the rest. You see, then, the difference between the two reflections made by the two surfaces of the wall and the mirror, struck in precisely the same way by the Sun's rays. And you see how the reflection coming from the wall spreads out toward all the parts facing it, while the mirror's goes toward one single place, not a bit bigger than the mirror itself. You see likewise how the surface of the wall, looked at from any spot whatever, always shows equally bright, and everywhere much brighter than the mirror's — except for that one small place alone where the mirror's reflection strikes, for from there the mirror appears much brighter than the wall. From these experiences, which we can see and all but touch, it seems to me we can very quickly come to know whether the reflection that reaches us from the Moon comes as from a mirror or as from a wall — that is, from a smooth surface or a rough one.
Sagredo: If I were standing on the Moon herself, I don't believe I could touch the roughness of her surface with my hand more plainly than I grasp it right now by following the argument. The Moon, seen in any position whatever with respect to the Sun and to us, shows us the surface the Sun touches as always equally bright — an effect that matches the wall's to a hair, since the wall, viewed from anywhere, appears equally bright; and it clashes with the mirror, which shows luminous from one spot only and dark from all the others. What's more, the light that reaches me from the wall's reflection is bearable and weak compared with the mirror's, which is ferociously strong, and hardly less punishing to the eyes than the primary, direct light of the Sun. And that's why we can gaze comfortably at the face of the Moon: if she were like a mirror — showing herself, because she's so near, as large as the Sun itself — her blaze would be absolutely unbearable, and it would seem to us that we were staring at almost a second Sun.
Salviati: Please, Sagredo, don't credit my demonstration with more than it's worth. Let me raise a counter-objection against you, and I'm not sure it's an easy knot to untie. You count it a great difference between the Moon and the mirror that she sends her reflection toward all parts equally, as the wall does, while the mirror sends it to one single determinate place; and from this you conclude that the Moon is like the wall, and not like the mirror. But I tell you: that mirror sends its reflection to one place alone because its surface is flat, and since reflected rays must leave at angles equal to those of the incoming rays, rays leaving a flat surface must depart together toward the same place. But the Moon's surface is not flat — it's spherical; and rays falling on such a surface find slopes from which to reflect, at angles equal to their angles of incidence, toward every direction, thanks to the infinity of inclinations that make up a spherical surface. So the Moon can send her reflection everywhere, and isn't forced to send it to one place alone, like that mirror, which is flat.
Simplicio: That is precisely one of the objections I wanted to raise against him.
Sagredo: If that's one, you must have others; so out with them — though as for this first one, I think it's going to turn out to count against you rather than in your favor.
Simplicio: You pronounced it as an obvious thing that the reflection from that wall is as bright and illuminating as the one that comes to us from the Moon, and I count it as nothing by comparison. For "in this business of illumination one must pay attention to, and distinguish, the sphere of activity — the reach of a body's power; and who doubts that celestial bodies have a greater sphere of activity than these elemental, frail, and mortal things of ours? And that wall, when all is said — what is it but a bit of earth, dark and unfit to give light?"
Sagredo: Here too, I believe, you're very much deceived. But let me come to the first objection raised by Salviati. I observe that for an object to appear luminous to us, it isn't enough that the rays of the illuminating body fall upon it; the reflected rays have to come to our eye. That's plain in the example of that mirror: no doubt the Sun's luminous rays are landing on it, and yet it doesn't show itself bright and lit up except when we put our eye in that one particular place where the reflection goes. Now let's consider what would happen if the mirror's surface were spherical. We'd find, without question, that of the reflection made by the whole illuminated surface, only the tiniest part reaches the eye of any one particular observer — because the portion of the whole spherical surface whose inclination bounces the ray to the particular spot where the eye is, is a most minute particle. So only the smallest part of the spherical surface can show itself shining to the eye, and all the rest appears dark. If the Moon, then, were polished like a mirror, only the tiniest part of her would show itself to any one person's eyes as lit by the Sun, even though a whole hemisphere lay exposed to the Sun's rays; all the rest would remain, to the observer's eye, as if unilluminated, and therefore invisible — and finally the Moon herself would be entirely invisible, since that little particle sending the reflection would be lost through its smallness and its great distance. And just as she would remain invisible to the eye, so her illumination would amount to nothing; for it's simply impossible that a luminous body should drive away our darkness with its splendor while we fail to see it.
Salviati: Hold on a moment, please, Sagredo, for I see certain movements in Simplicio's face and bearing that tell me he isn't fully convinced or satisfied by what you've said with such complete clarity and absolute truth. And it's just occurred to me that I can remove his every scruple with another experiment. I've seen, in a room upstairs, a large spherical mirror: let's have it brought down here; and while it's on its way, let Simplicio go back and consider how great the brightness is that the flat mirror's reflection throws on the wall here under the loggia.
Simplicio: I see that it's hardly less bright than if the Sun were striking it directly.
Salviati: So it is. Now tell me: if we take away that little flat mirror and set the big spherical one in the same place, what effect do you think its reflection will have on that same wall?
Simplicio: I believe it will throw a much greater and much broader light onto it.
Salviati: But if the illumination turns out to be nothing, or so small you can barely make it out — what will you say then?
Simplicio: When I've seen the effect, I'll think about my answer.
Salviati: Here's the mirror, and I want it set right next to the other one. But first let's go over there, near the reflection thrown by the flat one, and look closely at its brightness. See how bright it is here where it strikes, and how distinctly you can make out all these little details of the wall.
Simplicio: I've looked and observed it perfectly well. Have the other mirror set beside the first.
Salviati: There it is. It was put there the moment you started studying the little details, and you never noticed — that's how great an increase of light it made on the rest of the wall. Now let the flat mirror be taken away. Look: every reflection is gone, even though the big convex mirror is still there. Take that one away too, and put it back as many times as you please — you'll see no change of light at all across the whole wall. So there you have it, shown to your very senses: the reflection of the Sun made in a spherical convex mirror does not perceptibly light up the places around it. Now — what do you answer to this experiment?
Simplicio: I'm afraid there's some sleight of hand at work here. I do see, when I look at that mirror, a great blaze of light coming off it that nearly blinds me; and — what matters more — I see it from every spot I look at it from, and I see it shift position across the mirror's surface as I move to view it from this place or that. Which is a conclusive sign that the light is reflected vividly toward every side, and so strikes that whole wall as powerfully as it strikes my eye.
Salviati: Now you see how careful and reserved we need to be about granting our assent to what reasoning alone sets before us. No doubt what you say has plenty of surface plausibility; and yet you can see how the experience of the senses shows the contrary.
Simplicio: Then how does this business work?
Salviati: I'll tell you what I make of it, though I don't know how far it will satisfy you. First: that brilliant splash of light you see on the mirror, which seems to you to take up a good part of it, isn't anywhere near that large — in fact it's very, very small. But its intensity produces in your eye — by way of the reflection made in the moisture at the rims of your eyelids, which spreads across the pupil — a borrowed radiance, like the fringe of fine hairs we seem to see around the flame of a candle set some distance away; or, if you prefer, compare it to the adventitious sparkle of a star. If you set the tiny little body of, say, the Dog Star, seen by day through the telescope, when it shows without any radiance, beside the same star seen at night by the naked eye, you'll grasp beyond any doubt that with its rays it looks more than a thousand times bigger than the bare, real little body. And the Sun's image that you see in that mirror undergoes a similar enlargement, or a greater one — greater, I say, because it's more vivid than the star, as is obvious from the fact that you can stare at the star with far less injury to your eyes than at this reflection from the mirror. So the reverberation that has to be shared out over this whole wall comes from a small part of that mirror; whereas a moment ago, what came from the whole flat mirror was delivered to — and confined within — a very small part of the same wall. What wonder, then, that the first reflection illuminates very vividly, while this other remains almost imperceptible?
Simplicio: I find myself more tangled up than ever, and now the other difficulty comes over me: how can it be that that wall, made of such dark material, with a surface so badly polished, throws back light more powerful and vivid than a mirror that's been beautifully smoothed and cleaned?
Salviati: More vivid, no — but more universal, yes. As for intensity, you can see for yourself: the reflection from that little flat mirror, where it strikes over there under the loggia, illuminates powerfully; and the rest of the wall, which receives the reflection from the wall the mirror hangs on, is nowhere near as brightly lit as the small patch the mirror's reflection lands on. And if you want to understand the whole of this business, consider that the roughness of that wall's surface amounts to the same thing as its being composed of countless tiny little surfaces, set at countless different inclinations — among which, of necessity, many happen to be placed so as to send the rays they reflect to one particular spot, and many others to another; in short, there is no place that doesn't receive a great many rays, reflected from a great many little surfaces scattered over the entire face of the rough body the luminous rays fall on. From which it necessarily follows that reflected rays — and with them illumination — reach every part of any surface whatever that faces the one receiving the primary incident rays. It follows, too, that the body the illuminating rays fall on shows itself wholly lit and bright when viewed from anywhere at all. And that is why the Moon, having a rough rather than a polished surface, sends the Sun's light back in every direction and shows equally bright to every observer. Whereas if its surface, being spherical, were also as smooth as a mirror, it would be completely invisible — since that very tiny part of it that could reflect the Sun's image to the eye of any one person would, across so great a distance, remain invisible, as we've already said.
Simplicio: I follow your reasoning quite well; still, I think I can dispose of it with very little effort, and maintain perfectly well that the Moon is round and highly polished and reflects the Sun's light to us the way a mirror does — nor does it follow that the Sun's image must be seen in the middle of it. For "it is not by the image of the Sun itself that the Sun's small figure can be made out at so great a distance; rather, what we perceive is the illumination of the whole lunar body, produced by the Sun's light. We may see the like in a gilded and well-burnished plate, which, when struck by a luminous body, shows itself all resplendent to one who views it from afar; only from close up does one make out, at its center, the small image of the luminous body."
Salviati: Frankly confessing my own incapacity, I'll say that of this speech of yours I understand nothing except the part about the gilded plate. And if you'll permit me to speak freely, I strongly suspect you don't understand it either, but memorized those words — written by somebody out of the itch to contradict and to show himself cleverer than his opponent; to show himself, that is, to the sort of people who, wanting to look clever themselves, applaud what they don't understand, and think the more highly of a writer the less they understand him. Provided the writer himself isn't (as many are) one of those who write what they themselves don't understand — which is why what they write is understood by nobody. So, leaving the rest aside, here is my answer about the gilded plate. If it's flat and not very large, it can indeed appear all ablaze from a distance while a strong light strikes it — but only when the eye lies on one determinate line, namely the line of the reflected rays; and it will look more fiery than if it were, say, silver, because it's colored, and because the extreme density of the metal lets it take an absolutely perfect polish. And if its surface, though beautifully polished, were not exactly flat but carried various inclinations, then its blaze would be visible from more positions — from as many, that is, as the different reflections made by the different surfaces reached. That's why diamonds are cut with many facets: so their delightful sparkle can be seen from many places. But if the plate were very large, it would not show all ablaze from a distance even if it were perfectly flat. Let me put it more precisely: imagine a huge flat gilded plate set out in the Sun. To a distant eye, the Sun's image will appear to occupy only one part of that plate — the part the reflection of the incident solar rays comes from. It's true that, because of the light's intensity, the image will appear garlanded with a great many rays, and so will seem to occupy a considerably larger portion of the plate than it really does. And to test that this is true: note the particular spot on the plate the reflection comes from, mark out likewise how large the blazing patch looks to you, then cover the greater part of that space, leaving only the region around its middle exposed. The apparent blaze won't shrink one bit for the distant viewer — on the contrary, you'll see it spread wide over the cloth or whatever else you covered it with. So if anyone, from seeing a small gilded plate all ablaze from a distance, has convinced himself the same must happen with plates as big as the Moon, he has fooled himself no less than if he believed the Moon to be no bigger than the bottom of a wine vat. And if the plate's surface were spherical, the powerful reflection would be seen in only a single small patch of it — though, thanks to its intensity, that patch would indeed show wreathed in many quivering rays; the rest of the ball would appear merely tinted, and even that only if it were not polished to the highest degree — for if it were perfectly burnished, it would appear dark. We have an example of this before our eyes every day in silver vessels: so long as they've only been boiled in the whitening bath, they're all white as snow and return no images at all; but burnish any part of them, and that part immediately turns dark, and from it images come back as from a mirror. That darkening comes from nothing else than the flattening of the very fine grain that made the silver's surface rough — rough in just the way that reflected light toward every side, so that from every position it showed equally illuminated. When burnishing then planes those minute inequalities exquisitely smooth, so that the reflection of the incident rays is all directed to one determinate place, the burnished part shows, from that place, far brighter and shinier than the rest, which is merely whitened; but from every other position it looks quite dark. And it's well known that the change of viewpoint in looking at burnished surfaces produces such differences of appearance that painters, to imitate a burnished breastplate, say, have to set pure blacks and pure whites side by side on parts of the armor where the light falls equally.
Sagredo: So then: if these philosopher gentlemen would content themselves with granting that the Moon, Venus, and the other planets have surfaces not quite so glossy and polished as a mirror — a hair's-breadth less, that is: like a silver plate that has been whitened but not burnished — would that be enough to make it visible, and fit to bounce the Sun's light back to us?
Salviati: It would be enough in part; but it wouldn't give a light as powerful as it does by being mountainous — full, in short, of great heights and hollows. But these philosopher gentlemen will never grant it to be less polished than a mirror; they'll have it far more so, if more can be imagined, because, holding that the most perfect shapes belong to the most perfect bodies, they need the sphericity of those celestial globes to be absolute. Besides, if they granted me any unevenness at all, however tiny, I'd help myself without the least scruple to a much bigger one — for since a perfection of that kind consists in indivisibles, a hair spoils it as thoroughly as a mountain does.
Sagredo: Here two questions occur to me: one is to understand why a greater unevenness of surface should make a more powerful reflection of light; the other, why these Peripatetic gentlemen insist on this exactness of shape.
Salviati: I'll answer the first, and leave to Simplicio the job of answering the second. You should note, then, that the same surfaces are more or less illuminated by the same light according as the illuminating rays fall on them more or less obliquely; the greatest illumination is where the rays are perpendicular. And look — I'll show it to your senses. I bend this sheet of paper so that one part makes an angle with the other; and holding it up to the light reflected from that wall opposite, you see how this face, which receives the rays obliquely, is less bright than this other, where the reflection arrives at right angles; and notice how, as I turn it to catch them more and more obliquely, the illumination grows weaker.
Sagredo: I see the effect, but I don't grasp the cause.
Salviati: If you thought about it for a hundredth of an hour, you'd find it; but so as not to waste time, here's a quick demonstration of it in this figure.
Sagredo: The mere sight of the figure has cleared the whole thing up for me — go on.
Simplicio: Kindly spell out the rest for me; I'm not so quick on the uptake.
Salviati: Take all the parallel lines you see setting out from the points A and B to be the rays that arrive at the line CD at right angles. Now tilt CD so that it leans like DO: don't you see that a good number of the rays that were striking CD now pass by without touching DO? So if DO is lit by fewer rays, it stands to reason that the light it receives is weaker. Now back to the Moon. Being spherical in shape, if its surface were as smooth as this paper, the parts of its Sun-lit hemisphere toward the rim would receive vastly less light than the parts in the middle, since the rays fall on the former at the most extreme slant and on the latter at right angles. So at full Moon, when we see nearly the whole hemisphere illuminated, the parts toward the middle ought to show more brilliant to us than the parts toward the circumference — which is not what we see. Now picture the Moon's face full of good high mountains: don't you see how their slopes and ridges, rising above the curve of the perfect spherical surface, stand exposed to the Sun's view, placed to receive its rays far less obliquely — and so to show as brightly lit as the rest?
Sagredo: All well and good. But if such mountains are there, then it's true the Sun will strike them far more squarely than it would the slant of a smooth surface; but it's also true that all the valleys between those mountains would stay dark, because of the enormous shadows the mountains would cast at that time; whereas the middle regions, though full of valleys and mountains, would be free of shadow, the Sun standing high above them — and so a great deal brighter than the outer parts, which would be sown with as much shadow as light. And yet we see no such difference.
Simplicio: A similar difficulty was winding its way through my own imagination.
Salviati: How much readier Simplicio is at penetrating the difficulties that favor Aristotle's opinions than at penetrating their solutions! And I have a suspicion that at times he deliberately keeps quiet about those, too; in the present case, since he was able to spot the objection on his own — and it's a genuinely ingenious one — I can't believe he hasn't also noticed the answer. So I'll try to draw it out of his mouth, as they say. Tell me, then, Simplicio: do you believe there can be shadow anywhere the Sun's rays strike?
Simplicio: I believe — no, I'm certain — that there cannot; because the Sun, being the greatest of luminaries, driving out the darkness with its rays, it's impossible that any place it reaches should stay dark. Besides, we have the definition: tenebrae sunt privatio luminis — darkness is the absence of light.
Salviati: So the Sun, gazing at the Earth or the Moon or any other opaque body, never sees any of their shadowed parts — since it has no other eyes to see with than its own rays, the bearers of light. And consequently someone standing on the Sun would never see anything in shadow at all, because his visual rays would always travel in company with the Sun's illuminating rays.
Simplicio: Perfectly true — no contradiction possible.
Salviati: Now: when the Moon stands at opposition to the Sun, what difference is there between the path traveled by the rays of your sight and the path traveled by the rays of the Sun?
Simplicio: Now I've got it. You mean that since the rays of sight and the rays of the Sun travel along the same lines, we can't make out any of the Moon's shadowed valleys. And please — rid yourself of this notion that I'm a faker or a dissembler. I swear to you on my honor as a gentleman that I had not penetrated to that answer, and might never have found it without your help, or without long thinking.
Sagredo: The solution the two of you have produced between you for this last difficulty has genuinely satisfied me as well. But at the same time, this point about the rays of sight traveling with the rays of the Sun has stirred up another scruple in me about the earlier part — though I don't know whether I'll manage to explain it, because it's only just been born and I haven't yet got it into order to my own liking. But let's see, among us, if we can bring it into the clear. There's no doubt at all that the parts toward the rim of a smooth but unburnished hemisphere lit by the Sun, receiving the rays obliquely, receive far fewer of them than the middle parts, which receive them head-on. It may well be that a band, say, twenty degrees wide out toward the edge of the hemisphere receives no more rays than another band toward the middle only four degrees wide; so the first will certainly be much darker than the second, and will look so to anyone who views them both face-on — full-face, as we say. But if the observer's eye were positioned so that the twenty-degree width of the dark band presented itself looking no longer than a four-degree band set at the middle of the hemisphere, then I don't hold it impossible that it might show him just as bright and luminous as the other — because, in the end, within two equal angles of four degrees each, the eye receives the reflections of two equal multitudes of rays: those reflected from the middle band four degrees wide, and those reflected from the other band of twenty degrees but seen foreshortened, compressed into the span of four. And the eye will get itself such a position when it stands between that hemisphere and the body illuminating it, because then the sight and the rays travel along the same lines. So it doesn't seem impossible that the Moon should have a perfectly even surface and nonetheless, at full Moon, show itself no less luminous at the rim than in the middle.
Salviati: The doubt is an ingenious one and deserves consideration; and since it came to you just now, unrehearsed, I'll likewise answer with whatever falls into my mind unrehearsed — and it may well be that with more thought a better answer would occur to me. But before I bring anything else into it, we'd do well to make sure by experiment that your objection holds up in fact the way it seems to conclude in appearance. So, taking the same sheet of paper again and bending a small part of it so that it tilts against the rest, let's test whether, when we hold it to the light so that the rays fall directly on the smaller part and obliquely on the other, the part receiving the direct rays shows brighter. And there — the experiment already settles it: it's noticeably more luminous. Now, if your objection is conclusive, then when we lower the eye far enough that, viewing that other, larger, less illuminated part foreshortened, it appears no wider than the brighter part — so that we see it under no greater an angle — then, I say, its light will have to increase enough to look as brilliant to us as the other. There: I'm looking at it, viewing it so obliquely that it appears narrower than the other; and yet its darkness doesn't lighten for me in the least. See now whether the same happens for you.
Sagredo: I've looked; and however far I lower my eye, I don't see that surface pick up any light or brighten in the slightest — if anything, it seems to me to darken.
Salviati: So far, then, we can be sure the objection has no force. As for the solution: I believe that since this paper's surface falls only a little short of smooth, very few rays get reflected back toward the incident ones, compared with the multitude reflected toward the opposite side; and of those few, more and more are lost the closer the visual rays draw to the incident luminous rays. And since it's not the incident rays but the rays reflected to the eye that make an object look luminous, in lowering the eye you lose more than you gain — just as you said yourself, seeing the sheet grow darker.
Sagredo: Experience and reason are enough for me. It now remains for Simplicio to answer my other question, and tell me what it is that moves the Peripatetics to insist on this roundness in the celestial bodies being so exact.
Simplicio: The celestial bodies' being ingenerable, incorruptible, inalterable, impervious to change, immortal, and so on, makes them absolutely perfect; and their being absolutely perfect carries the consequence that every kind of perfection is in them — and therefore that their shape, too, is perfect: that is, spherical, and absolutely and perfectly spherical, not rough and irregular.
Salviati: And this incorruptibility — from what do you derive it?
Simplicio: Immediately, from their having no contraries; mediately, from their simple circular motion.
Salviati: So then, as far as I gather from your account, in constituting the essence of the celestial bodies as incorruptible, inalterable, and the rest, roundness doesn't enter into it as a cause or a necessary requirement. For if roundness were what produced inalterability, then we could make wood, wax, and other elemental materials incorruptible whenever we pleased, simply by working them into a spherical shape.
Simplicio: And isn't it obvious that a wooden ball will keep better and longer than a spire, or any other angular shape, made from the same amount of the same wood?
Salviati: That is perfectly true; but it won't thereby pass from corruptible to incorruptible. It stays corruptible — merely longer-lasting. Note this, then: the corruptible admits of more and less. We can say, "This is less corruptible than that" — jasper, for instance, is less corruptible than soft gray sandstone. But the incorruptible admits no more and no less; you cannot say, "This is more incorruptible than that other," if both are incorruptible and eternal. Difference of shape, therefore, can operate only on materials capable of lasting a longer or a shorter time; but in eternal things, which can only be equally eternal, the operation of shape ceases. And so, since celestial matter is incorruptible not through its shape but through something else, there is no need to be so anxious about this perfect sphericity; for once the matter is incorruptible, let it have whatever shape you like — it will always remain so.
Sagredo: But I'm turning over something further, and I say this: grant that the spherical shape had the power to confer incorruptibility, and then all bodies, of whatever shape, would be eternal and incorruptible. For since the round body is incorruptible, corruptibility would have to reside in those parts that spoil the perfect roundness. Take a die, for example: inside it there is a perfectly round ball, and as such incorruptible; so what remains corruptible must be those corners that cover and hide the roundness. The very most that could happen, then, is that those corners — those excrescences, so to speak — should decay. But if we look deeper still, within those parts toward the corners there lie other, smaller balls of the same material, and they too, being round, are incorruptible; and in the remnants surrounding these eight smaller little spheres one can conceive still others; so that at last, resolving the whole die into innumerable balls, you will have to confess it incorruptible. And this same argument, with a similar resolution, can be run on every other shape.
Salviati: The argument runs beautifully. So that if, say, a sphere of crystal owed its incorruptibility to its shape — that is, the power to resist every internal and external alteration — then it's hard to see why adding more crystal to it and reworking it into, say, a cube should alter it within or without, or leave it less able to resist a new surrounding made of its very own material than it was against a former one of different material. Especially if it's true that corruption is worked by contraries, as Aristotle says: for what can you wrap around that ball of crystal that is less contrary to it than crystal itself? But we're not noticing how the hours are slipping away, and we'll come late to the end of our discussions if we make such long speeches over every particular; besides which, my memory gets so tangled in the multitude of things that I can barely recall the propositions Simplicio laid out for us, in order, to be considered.
Simplicio: I remember them very well. And on this particular point of the Moon's mountainousness, the cause I brought forward for that appearance still stands: it can perfectly well be accounted for by saying it is an illusion arising from the parts of the Moon being unequally opaque and transparent.
Sagredo: A little while ago, when Simplicio was attributing the Moon's apparent unevenness — following the opinion of a certain Peripatetic friend of his — to its parts being variously opaque and transparent, on the model of the similar illusions one sees in crystals and gems of many kinds, I thought of a material far better suited to produce such effects, one I feel certain that philosopher would pay any price for: mother-of-pearl. It is worked into various shapes, and even when brought to an extreme polish it looks to the eye so variously hollowed and swelling from place to place that the touch itself can scarcely be trusted to vouch for its smoothness.
Salviati: A truly beautiful thought; and what hasn't been done yet may well be done another time — if other gems and crystals have been brought forward that have nothing to do with the illusions of mother-of-pearl, these will surely be brought forward too. In the meantime, so as not to cut off anyone's opportunity, I'll keep quiet about the answer that would meet it, and for now try only to satisfy the objections Simplicio has raised. I say, then, that this reason of yours is far too general; and unless you apply it, one by one, to all the appearances that are seen in the Moon — the ones that have moved me and others to hold it mountainous — I don't believe you'll find anyone content with such a doctrine. Nor do I believe that you yourself, or the author himself, find any more rest in it than in anything else remote from the point. Of the many, many varied appearances that are seen evening after evening through one lunar month, you could not imitate so much as one by building a ball to your own specification out of parts more and less opaque and transparent, with a polished surface. Whereas, on the other side, from any solid, non-transparent material whatever, one can make balls which — by nothing but ridges and hollows, and by catching the light in different ways — will reproduce exactly, to a hair, the same sights and changes that are seen in the Moon from hour to hour. On them you will see the crests of the ridges facing the Sun's light show quite bright, and behind them the cast shadows lying very dark; you will see those shadows greater and smaller, according as the ridges stand nearer to or farther from the boundary dividing the lit part of the Moon from the dark; you will see that same dividing line drawn not evenly, as it would be if the ball were smooth, but winding and notched like battlements; you will see, beyond that line, in the dark part, many illuminated summits standing detached from the region already luminous; you will see the shadows I've described shrink as the illumination climbs, until they vanish altogether, not one of them left once the whole hemisphere is lit; and then, as the light passes over toward the other lunar hemisphere, you will recognize the same ridges you observed before, and see the projections of their shadows thrown the opposite way and growing. Of all these things — I say it again — you cannot show me even one with your opaque-and-transparent.
Sagredo: One of them, in fact, will be imitated: the full moon, when everything is lit and no shadow is seen any longer, nor anything else that takes any variation from ridges and hollows. But please, Salviati, lose no more time on this particular; for anyone who had the patience to make the observations through one or two lunations and still could not take in this truth that the senses themselves deliver might fairly be sentenced as wholly devoid of judgment — and with such people, why spend time and words for nothing?
Simplicio: I honestly haven't made such observations, because I've never had that curiosity, nor an instrument fit to make them with; but I fully mean to. And meanwhile we can leave this question hanging and pass to the point that follows: your producing the grounds on which you hold that the Earth can reflect the Sun's light no less vigorously than the Moon. For to me it looks so dark and opaque that such an effect strikes me as utterly impossible.
Salviati: The cause that makes you consider the Earth unfit for illumination is not at all what you think, Simplicio. And wouldn't it be a fine thing if I understood your own reasoning better than you do yourself?
Simplicio: Whether I reason well or badly, you may perhaps know better than I do; but that you can see into my reasoning better than I can myself — that I will never believe.
Salviati: Then I'll make you believe it right now. Tell me a little: when the Moon is nearly full, so that it can be seen by day and at midnight too, when does it look more brilliant to you — by day, or at night?
Simplicio: At night, beyond all comparison. It seems to me the Moon is like that pillar of cloud and fire that went before the children of Israel: in the Sun's presence it showed like a little cloud, but at night it was most splendid. So I have sometimes observed the Moon by day among small clouds, looking exactly like one of them, whitish; but then at night it shines magnificently.
Salviati: So that if you had never happened to see the Moon except by day, you would never have judged it brighter than one of those little clouds.
Simplicio: I firmly believe I wouldn't have.
Salviati: Now tell me: do you believe the Moon is really more luminous at night than by day, or does it only show that way through some accident?
Simplicio: I believe it shines in itself just as much by day as by night, but that its light looks greater at night because we see it against the dark field of the sky; whereas by day, the whole surrounding air being quite bright, the Moon exceeds it in light by only a little, and so appears to us much less luminous.
Salviati: Now tell me this: have you ever, at midnight, seen the terrestrial globe illuminated by the Sun?
Simplicio: That strikes me as a question to be asked only as a joke — or else of someone known to be an outright fool.
Salviati: No, no: I hold you a most sensible man, and I ask the question in earnest. So answer anyway; and then, if my talk seems beside the point, I'm content to be the fool myself — for the one who asks foolishly is a bigger fool than the one who's asked.
Simplicio: If, then, you don't take me for a complete simpleton, consider that I've answered you, and said this: it is impossible for anyone standing on the Earth, as we do, to see by night that part of the Earth where it is day — the part the Sun is striking.
Salviati: So it has never fallen to you to see the Earth illuminated except by day; whereas the Moon you see shining in the sky even in the deepest night. And that, Simplicio, is the reason you believe the Earth doesn't shine like the Moon. If you could see the Earth illuminated while you stood in a place as dark as our night is, you would see it more resplendent than the Moon. Now, if the comparison is to be run fairly, we must set the Earth's light against the light of the Moon seen by day — not against the nighttime Moon — since we never get to see the Earth illuminated except by day. Isn't that so?
Simplicio: So it must be.
Salviati: And since you yourself have already confessed to having seen the Moon by day among whitish little clouds, looking in appearance exactly like one of them, you have thereby already granted, to begin with, that those little clouds — which after all are elemental matter — are as fit to receive illumination as the Moon is; more fit, in fact, if you will call back to mind having sometimes seen certain enormous clouds white as snow. And there can be no doubt that if such a cloud could stay that luminous through the deepest night, it would light the surrounding country more than a hundred Moons. If we were certain, then, that the Earth is lit by the Sun as much as one of those clouds, no doubt would remain that it shines no less than the Moon. And on this point every doubt vanishes when we see those same clouds, in the Sun's absence, stay as dark by night as the Earth does; and — what's more — there is not one of us who hasn't many times seen certain low, distant clouds and stood in doubt whether they were clouds or mountains: clear evidence that mountains are no less luminous than those clouds.
Sagredo: But why go on arguing? Look — there's the Moon up there, more than half full; and there's that high wall the Sun is beating on. Step back this way, so the Moon shows beside the wall. Now look: which seems brighter to you? Don't you see that if either has the advantage, it's the wall? The Sun strikes that wall; from there the light bounces onto the walls of the hall; from those it is reflected into that room beyond, so that it arrives there at the third reflection — and even so, I am certain there is more light in that room than if the Moon's light reached it directly.
Simplicio: Oh, that I don't believe. The Moon's light — above all when it's full — is a great illumination.
Sagredo: It seems great because of the darkness of the shadowy places around it, but in absolute terms it isn't much; it's less than the twilight half an hour after sunset. That's plain, because it's only around then that the shadows of bodies lit by the Moon begin to be distinguishable on the ground. As for whether that third reflection lights that room better than the Moon's first — that can be settled by going in there and reading a book, and then trying again tonight, by moonlight, whether it reads more easily or less. Less, I have no doubt at all.
Salviati: Now, Simplicio — if you are satisfied, that is — you can see how you yourself truly knew all along that the Earth shines no less than the Moon, and that merely being reminded of things you knew on your own, and were never taught by me, is what has made you certain of it. For I did not teach you that the Moon shows more resplendent by night than by day — you knew it yourself; just as you knew on your own that a little cloud shows as bright as the Moon. You knew likewise that the Earth's illumination cannot be seen at night; in short, you knew everything, without knowing that you knew it. From here, then, it should not reasonably be hard for you to grant that the Earth's reflection can light the dark part of the Moon with a light no weaker than that with which the Moon lights the darkness of our night — indeed, so much the stronger, inasmuch as the Earth is forty times larger than the Moon.
Simplicio: Truly, I believed that secondary light — that dim glow on the dark part — was the Moon's own.
Salviati: And this too you know on your own, and don't notice that you know it. Tell me: haven't you known, all by yourself, that the Moon shows far more luminous by night than by day, on account of the darkness of the surrounding field? And consequently, don't you know in general that every shining body shows brighter, the darker its surroundings?
Simplicio: That I know perfectly well.
Salviati: When the Moon is a thin crescent and shows you that secondary light quite plainly, isn't it always near the Sun, and consequently in the glow of twilight?
Simplicio: It is; and many times I've wished the air would grow darker so I could see that light more clearly — but the Moon always set before full dark.
Salviati: So you know very well that in deep night that light would show more?
Simplicio: Yes indeed — and more still, if one could take away the great light of the horns the Sun touches, whose presence badly dims the other, lesser light.
Salviati: Well then — doesn't it sometimes happen that one can see the Moon's whole disk on the darkest of nights, without its being lit by the Sun at all?
Simplicio: I don't know that that ever happens, except in total eclipses of the Moon.
Salviati: Then at those moments this light of its own ought to show at its most vivid, standing as it does in a pitch-dark field, undimmed by the brightness of the luminous horns. In that state, how bright have you seen it?
Simplicio: I've seen it sometimes the color of copper, faintly whitish; but at other times it has stayed so dark that I lost sight of it entirely.
Salviati: How, then, can that light be the Moon's own — this light you see so clearly in the pale of twilight, despite the interference of the great splendor of the horns right beside it, and which then, in the darkest night, with every other light removed, doesn't appear at all?
Simplicio: I understand there have been some who believed such light comes to the Moon as a share from the other stars, and in particular from Venus, its neighbor.
Salviati: And that likewise is an empty notion; because at the time of its total darkening it ought then to show more brilliant than ever — for no one can say the Earth's shadow blocks its view of Venus or of the other stars. But in fact the Moon is then wholly deprived of that light, because the terrestrial hemisphere facing the Moon at that time is the one where it is night — that is, a total privation of the Sun's light. And if you go observing carefully, you will see with your own senses that just as the Moon, when it is a thin crescent, gives very little light to the Earth, and as the Sun-lit part of it grows, the splendor reflected down to us grows along with it — so too the Moon, while it is a thin crescent and, standing between the Sun and the Earth, looks out over a very great part of the illuminated terrestrial hemisphere, shows quite bright; and as it draws away from the Sun toward quadrature — the half-moon position — that light is seen to languish; and past quadrature it shows quite feeble, because it keeps losing more and more of its view of the luminous part of the Earth. Yet exactly the contrary ought to happen if that light were its own, or lent to it by the stars — for then we could see it in deep night, against very dark surroundings.
Simplicio: Stop, please — for just now I remember reading, in a recent little book of theses, one full of novelties, "that this secondary light is not caused by the stars, nor is it the Moon's own, and least of all is it lent to her by the Earth; rather it derives from the Sun's own illumination, which — the substance of the lunar globe being somewhat transparent — penetrates through the whole of its body; but it lights most vividly the surface of the hemisphere exposed to the Sun's rays, while the depths beneath, drinking in that light and, so to speak, soaking themselves with it after the manner of a cloud or a crystal, transmit it and become visibly luminous." And this (if I remember rightly) he proves by authority, by experience, and by reason, citing Cleomedes, Witelo, Macrobius, and some other modern author; and he adds that experience shows the Moon very bright in the days near conjunction — that is, when it is a crescent — and shining above all around its rim; and further, he writes that in solar eclipses, when the Moon stands beneath the Sun's disk, it can be seen glowing through, especially around its outermost circle. As for the reasons, I think he says that since this light can come neither from the Earth nor from the stars nor from the Moon itself, it necessarily remains that it comes from the Sun; and besides, once this supposition is granted, tidy explanations can be given for every particular that arises. That the secondary light shows livelier around the outer rim has for its cause the shortness of the space the Sun's rays have to penetrate there — since, of the lines crossing a circle, the greatest is the one through the center, and of the others, those farther from it are always shorter than those nearer. From the same principle, he says, it follows that this light diminishes very little. And finally, on this account one can assign the cause of why that brighter circle around the Moon's outer margin is seen, in a solar eclipse, in the part standing under the Sun's disk, but not in the part outside it; this comes about because the Sun's rays pass straight through the parts of the Moon lying under the disk and on to our eye, while from the parts outside the disk they fall wide of the eye.
Salviati: If this philosopher had been the first author of that opinion, I wouldn't be surprised that he was so fond of it he took it for true. But since he received it from others, I can't find any excuse good enough for his failure to see through its fallacies — above all after he had heard the true cause of the effect, and could have assured himself, by a thousand trials and plain confirmations, that it comes from the reflection of the Earth and from nothing else. And as much as that knowledge makes us wish for a little more discernment in this author, and in everyone else who withholds assent, so much does the fact that it was never understood — never even occurred to them — excuse the older writers, who, I'm quite certain, would admit it now without the slightest resistance if they understood it. And if I'm to tell you my honest thought: I can't believe this modern author doesn't privately accept it. I suspect, rather, that not being able to claim it as his own invention goads him a little into trying to suppress it, or at least to discredit it in the eyes of the simple — whose numbers, we know, are enormous. And there are plenty of men who enjoy the loud applause of the crowd far more than the assent of the discerning few.
Sagredo: Hold on a moment, Salviati — I don't think you're going straight to the real point. These men who spread their nets for the public also know how to pass themselves off as the authors of other people's inventions, provided the inventions aren't so old, so broadcast from the lecture halls and the piazzas, that everyone already knows them by heart.
Salviati: Oh, I'm more wicked than you are. Why talk about "public" or "well known"? Isn't it all the same whether the opinions and inventions are new to the men, or the men are new to them? If you'd settle for the admiration of beginners in the sciences — and a fresh crop comes up every season — you could set yourself up as the inventor of the alphabet itself and be their marvel. And if in time your little game were discovered, it would hardly hurt your purpose, since new recruits step in to keep the ranks of your admirers full.
But let's get back to showing Simplicio how feeble his modern author's arguments are — arguments containing falsehoods, non-sequiturs, and sheer implausibilities. First of all, it is false that this secondary light is brighter around the outer rim than in the middle, forming a sort of ring or circle more brilliant than the rest of the field. It's true that when you look at the Moon in the twilight, at its first appearance, such a circle does show — but it's an illusion, born of the different borders that bound the lunar disc bathed in this secondary light. On the side toward the Sun, it borders the dazzling horns of the Moon; on the other side, its neighbor is the dark field of the twilight sky, and by that contrast the pale glow of the lunar disc looks brighter to us, while on the opposite side the same glow is drowned out by the greater splendor of the horns. If our modern author had tried placing an obstacle between his eye and the primary brilliance — the roof of some house, or any other screen — so that only the stretch of the Moon outside the horns stayed visible, he would have seen it all equally luminous.
Simplicio: I do seem to remember that he writes of having used exactly that kind of trick to hide the bright sickle from himself.
Salviati: Oh — then what I was charitably calling an oversight becomes a lie, and a reckless one at that, since anyone can repeat the test as often as he likes. As for seeing the Moon's disc during an eclipse of the Sun in any way except as a dark absence, I doubt it very much — especially when the eclipse isn't total, as the ones this author observed must necessarily have been. But even if the disc did show as luminous then, that wouldn't contradict our opinion; it would favor it, because at that moment the entire terrestrial hemisphere lit by the Sun is facing the Moon, and though the Moon's shadow darkens a part of it, that part is tiny compared with what stays illuminated.
What he adds — that in this case the part of the rim lying under the Sun shows quite bright, but not the part outside it, because the Sun's rays reach our eye directly through the one part and not the other — is truly one of those fables that give away all the teller's other fictions. If the Sun's rays have to come straight to our eye for the lunar disc to be visible by secondary light, doesn't the poor man see that we would then never see that secondary light except during a solar eclipse? And if a part of the Moon standing less than half a degree away from the Sun's disc can deflect the solar rays enough to keep them from our eye, what happens when the Moon stands twenty or thirty degrees away, as it does at its first appearance? How are the Sun's rays, which are supposed to pass clean through the body of the Moon, going to find our eye then?
This man goes along, step by step, imagining things as they would need to be to serve his purpose, instead of adjusting his purpose, step by step, to things as they are. Watch: to let the Sun's splendor penetrate the Moon's substance, he makes that substance partly transparent — transparent, say, the way a cloud or a crystal is. But I don't know what he'd make of that transparency once the Sun's rays had to penetrate a depth of cloud more than two thousand miles thick. Suppose he answers boldly that this can perfectly well happen in celestial bodies, which are quite another affair from these impure and dreggy elemental bodies of ours; then let's convict him of his error by means that admit no reply — or rather, no subterfuge. If he wants to maintain that the Moon's substance is transparent, he'll have to say it is transparent when the Sun's rays must pass through its whole depth — more than two thousand miles of it — and yet, when faced with barely a single mile, it blocks them as stubbornly as one of our mountains would.
Sagredo: You remind me of a man who wanted to sell me a secret: how to speak with someone two or three thousand miles away, by means of a certain sympathy between magnetized needles. I told him I'd gladly buy it, but that I wanted to see a trial first, and that it would satisfy me to make it with me standing in one room of my house and him in another. He answered that at so short a distance the operation couldn't be seen properly. So I showed him the door, telling him I didn't feel like traveling to Cairo or to Muscovy just then to watch the demonstration — but if he wanted to go himself, I would hold up the other end from Venice. But let's hear where the author's own logic lands him, and how he's forced to admit that the Moon's material is supremely permeable to the Sun's rays through a depth of two thousand miles, yet more opaque than one of our mountains across the thickness of a single mile.
Salviati: The Moon's own mountains are the witnesses. Struck by the Sun on one side, they cast pitch-black shadows on the other — sharper-edged and more cleanly cut, by far, than the shadows of ours. If they were transparent, we could never have detected the least roughness in the Moon's surface, nor seen those luminous peaks standing detached beyond the line that divides the lit part from the dark. Still less would we see that line itself so distinctly, if it were true that the Sun's light sank deep into the Moon. On the author's own account, in fact, the passage and border between the part the Sun sees and the part it doesn't would have to look thoroughly blurred, a muddle of light and darkness — because material that lets the Sun's rays through two thousand miles of depth must be so transparent that it would scarcely resist them across a hundredth of that thickness or less. Yet the line separating the illuminated part from the dark one is as clean and distinct as the line between white and black — above all where the cut crosses the naturally brighter and rougher part of the Moon. Where it slices across the ancient spots, which are plains, the edge isn't so sharp — those plains curve away with the sphere, so they catch the Sun's rays very obliquely, and the fainter illumination softens the line.
Finally, what he says about the secondary light neither shrinking nor dimming as the Moon waxes, but keeping the same strength throughout, is utterly false. It's barely visible at quadrature — the half-Moon — precisely when it ought to show at its liveliest, since it can then be seen clear of twilight, in the dead of night. Let us conclude, therefore, that the Earth's reflection is very powerful upon the Moon. And — this is what you should prize most — draw from it one more beautiful correspondence: if it's true that the planets act upon the Earth by their motion and their light, then perhaps the Earth is no less able to act back upon them with the same light, and, for all we know, with motion too. And even if the Earth didn't move, the same action could remain; for, as we've seen, the action of the light is exactly the same — reflected sunlight — and motion does nothing but vary the aspects, which change in exactly the same way whether you make the Earth move and the Sun stand still, or the other way around.
Simplicio: You will find no philosopher who has said that these lower bodies act on the celestial ones — and Aristotle says plainly the contrary.
Salviati: Aristotle and the others who didn't know that the Earth and the Moon light each other in turn deserve to be excused. But they would richly deserve blame if, while demanding that we grant and believe on their word that the Moon acts on the Earth by its light, they then turned around and denied — to us, who have taught them that the Earth illuminates the Moon — any action of the Earth upon the Moon.
Simplicio: The plain truth is, I feel an extreme reluctance in myself to admit this fellowship you want to talk me into between the Earth and the Moon — enrolling the Earth, as the saying goes, in the company of the stars. If nothing else, the sheer separation and distance between it and the celestial bodies seems to me to force the conclusion that their natures are enormously dissimilar.
Salviati: See, Simplicio, what an inveterate attachment and a deep-rooted opinion can do. It is strong enough to make the very things you produce against yourself look like points in your favor. For if separation and distance are valid grounds for persuading you of a great diversity of natures, then nearness and contact must, by the same token, imply similarity — and how much nearer is the Moon to the Earth than to any other celestial globe? Confess, then, by your own concession — and you'll have other philosophers for company — that there is a very great affinity between the Earth and the Moon. Now let's push on: tell us whether anything remains to consider among the difficulties you raised against the correspondences between these two bodies.
Simplicio: There would remain something about the solidity of the Moon — which I argued from its being supremely polished and smooth, and you from its being mountainous. And another difficulty occurred to me, from my belief that the sea's reflection ought to be stronger than the land's, because of the evenness of its surface, while the land's surface is so rough and dull.
Salviati: As to the first doubt: just as among the parts of the Earth — all of which, by their heaviness, conspire to press as close as they can to the center — some nonetheless remain farther out than others, the mountains more than the plains, and this because of their solidity and hardness (if they were made of fluid matter, they would level out); so, in the same way, seeing some parts of the Moon standing raised above the sphere of the lower parts tells us they are hard. For it's credible that the Moon's material gathers itself into a spherical shape by the concordant conspiring of all its parts toward the same center.
As for the other doubt: from what we've already observed happening with mirrors, we can understand perfectly well that the reflection of light coming from the sea is far weaker than the one coming from land — speaking, that is, of the universal reflection. As for the particular reflection that a surface of calm water sends toward one determinate place, there's no doubt that whoever stands in that place will see a very powerful reflection in the water; but from every other spot the water's surface will look darker than the land's. And to show it to your senses, let's step into the hall here and pour a little water on the floor. Now tell me: doesn't this wet brick show much darker than the dry ones? Certainly it does — and it will look that way from any point you view it, with one single exception: the spot where the reflection of the light coming in at that window lands. So back away, slowly.
Simplicio: From here I see the wet part brighter than the rest of the floor, and I see that it happens because the reflection of the light coming in at the window is heading toward me.
Salviati: All the wetting has done is fill in the little hollows in the brick and reduce its surface to an exquisite flatness, so that the reflected rays leave it united, all toward the same place. The rest of the floor, dry, keeps its roughness — an innumerable variety of tilts among its tiniest particles — so the reflections of the light go off in every direction, but weaker than if they all traveled united together. That's why its look changes little or nothing as you view it from different sides; it shows the same from everywhere, but far less bright than the reflection from the wet part. I conclude, therefore, that the surface of the sea, seen from the Moon, would look extremely even — islands and reefs aside — but less bright than the surface of the land, mountainous and uneven as it is.
And if I weren't afraid of seeming, as they say, to want too much, I'd tell you that I have observed that secondary light on the Moon — the light I say comes to it from the reflection of the terrestrial globe — to be noticeably brighter two or three days before conjunction than after it: that is, brighter when we see the Moon in the east before dawn than when it shows in the west in the evening, after sunset. The cause of the difference is that the terrestrial hemisphere facing the eastern Moon has little sea and a very great deal of land — all of Asia — whereas when the Moon is in the west, it looks down on immense seas: the whole Atlantic Ocean, clear to the Americas. A rather probable argument that the surface of water shows itself less splendid than the surface of land.
Simplicio: But do you actually believe, then, that those great spots we see in the face of the Moon are seas, and the brighter remainder land, or something of that sort?
Salviati: What you're asking is the beginning of the disparities that I hold to exist between the Moon and the Earth — and it's time we worked our way through those, for we have lingered on this Moon quite long enough. I say, then, that if nature had only one way of making two sunlit surfaces appear one brighter than the other — namely, by one being land and the other water — then we would necessarily have to say the Moon's surface is part earthy and part watery. But because we know of several ways to produce the same effect, and there may be still others unknown to us, I would not dare affirm that this one rather than that exists on the Moon.
We saw above how a plate of whitened silver, touched with the burnisher, goes from bright white to dark. The wet part of the Earth shows darker than the dry. On mountain ridges, the wooded stretches appear much duskier than the bare and barren ones, because among the trees a great quantity of shadow falls, while the open ground lies fully lit by the Sun. And this mingling of shadows works so strongly that in figured velvet the cut silk shows much darker than the uncut, thanks to the shadows scattered between thread and thread — and plain velvet, likewise, much darker than a smooth taffeta made of the very same silk. So if there were things on the Moon that resembled immense forests, their aspect could well present us with the spots we see; the spots would show a like difference if they were seas; and, finally, nothing rules out those spots really being of a darker color than the rest — after all, that is how snow makes mountains look brighter.
What is plainly seen on the Moon is this: the darker parts are all plains, with few reefs and ridges inside them, though there are some; the brighter remainder is all full of reefs, mountains, little rounded ridges, and other shapes; and in particular, around the spots run enormous chains of mountains. That the spots are flat surfaces we can be sure of, from seeing that the line dividing the lit part from the dark cuts evenly where it crosses the spots, while in the bright parts it shows jagged and toothed everywhere. But whether that evenness of surface is enough, by itself, to account for the darkness — that I don't know; I rather think not.
Beyond all this, I judge the Moon to be profoundly different from the Earth. Though I imagine those regions are not idle and dead, I still would not assert that motion and life exist there — much less that plants, animals, or other things like ours are generated there; and if anything is, it would be utterly different, remote from everything we can imagine. I'm moved to think so, first, because I judge that the material of the lunar globe is not earth and water, and that alone is enough to rule out generations and alterations like ours. But even granting that there were water and earth up there, plants and animals like ours still would not arise, and for two principal reasons.
The first is that the varying aspects of the Sun are so necessary to our generations that without them everything would fail — and the Sun's dispositions toward the Earth are very different from its dispositions toward the Moon. As for daily illumination, we, over most of the Earth, get part day and part night in every twenty-four hours; on the Moon, that effect takes a month. And the yearly dipping and climbing by which the Sun brings us the changing seasons and the inequality of days and nights is likewise finished, on the Moon, in a month. And whereas for us the Sun rises and sinks so far that between its greatest and least altitude there runs a difference of about forty-seven degrees — the distance from one tropic to the other — on the Moon it comes to no more than ten degrees or a little over, which is as far as the greatest latitudes of the dragon, the Moon's tilted path, stray on either side of the ecliptic. Now consider what the Sun's action would be within the torrid zone if it went on striking it with its rays for fifteen days without a break: you will grasp at once that all the plants and grasses and animals would be destroyed; and if generations did occur there, they would be of grasses, plants, and animals utterly different from the present ones.
Second, I hold it for certain that there are no rains on the Moon; because if clouds gathered anywhere on it, as they do around the Earth, they would hide from us some of the things we see on the Moon with the telescope — in short, they would change the view in one particular or another. And that is an effect I have never once seen in long and careful observation: I have always found there a uniform, perfectly pure serenity.
Sagredo: To that one might answer either that there are enormous dews there, or that it rains during their night — that is, when the Sun isn't shining on it.
Salviati: If other evidence gave us signs that things are generated there the way they are here, and rain were the only ingredient missing, we could come up with this or some other arrangement to stand in for it — the way the flooding of the Nile stands in for rain in Egypt. But since we haven't found one single feature that matches ours, out of the many that would be needed to produce similar effects up there, there's no point straining to introduce even one — and that one not because we have any solid observation of it, but merely because nothing rules it out. Besides, if I were asked what my first impression and plain natural reasoning tell me about whether the things produced there are like ours or different, I would always answer: utterly different, and entirely beyond our imagining — for that, it seems to me, is what the richness of nature and the omnipotence of her Creator and Governor demand.
Sagredo: It has always seemed to me the height of rashness when people make human capacity the measure of what nature can do and knows how to do — when in fact the opposite is true: there is not a single effect in nature, however small, that the most speculative minds can ever completely understand. That vain presumption of understanding everything can have no other root than never having understood anything at all; for anyone who had experienced, even once, the perfect understanding of one single thing, and had truly tasted what knowledge is made of, would recognize that of the infinity of other conclusions he understands nothing.
Salviati: Your argument is airtight. And confirming it we have the experience of those who understand something, or once did: the wiser they are, the more clearly they recognize — and the more freely they confess — how little they know. And the wisest man in Greece, pronounced so by the oracles themselves, said openly that he knew he knew nothing.
Simplicio: Then we'd have to say that either the oracle or Socrates himself was lying — the one proclaiming him the wisest of men, the other declaring that he knew himself to be utterly ignorant.
Salviati: Neither follows, because both pronouncements can be true. The oracle judges Socrates wisest above other men, whose wisdom is limited; Socrates knows that he knows nothing when measured against absolute wisdom, which is infinite. And since, against infinity, much is just as small a portion as little, or as nothing — to reach an infinite number, piling up thousands gets you no closer than piling up tens, or zeros — Socrates saw very well that his finite wisdom was nothing next to the infinite wisdom he lacked. But since there is nonetheless some knowledge to be found among men, and it isn't shared out equally to all, Socrates could hold a larger portion of it than anyone else — and so the oracle's answer came true.
Sagredo: I think I understand this point very well. Among men, Simplicio, there is the power to act, but not shared equally by all: no one doubts that an emperor's power is far greater than a private person's, yet both are nothing compared with divine omnipotence. Among men there are some who understand farming better than many others; but what does knowing how to plant a vine cutting in a trench have to do with knowing how to make it take root, draw in nourishment, and sort out from that nourishment the part that's good for making leaves, this other part for the tendrils, that one for the clusters, another for the grapes, still another for the skins — all of which are the works of supremely wise nature? This is one single, particular operation among the countless ones nature performs, and in it alone we recognize an infinite wisdom; so we may conclude that divine knowledge is infinitely infinite.
Salviati: Here's another example. Wouldn't we say that the power to discover a beautiful statue inside a block of marble lifted Michelangelo's genius far, far above the ordinary minds of other men? And yet that work is nothing but the imitation of a single posture — one outward, surface arrangement of the limbs of a motionless man. What is it compared to a man made by nature, composed of so many parts outside and in, so many muscles, tendons, nerves, and bones, serving so many different movements? And what shall we say of the senses, of the powers of the soul, and finally of understanding itself? Can't we say, with good reason, that the making of a statue falls infinitely short of the forming of a living man — indeed, of the forming of the lowliest worm?
Sagredo: And what difference do we suppose there was between Archytas' dove — that ancient mechanical bird — and one of nature's own?
Simplicio: Either I'm not one of these men who understand, or there is an open contradiction in this talk of yours. Among the greatest tributes you pay to man, made by nature — indeed as the greatest of them all — you count this power of understanding; and a moment ago you were saying, with Socrates, that his understanding was nothing. So it would follow that not even nature has understood how to make an intellect that understands.
Salviati: A very sharp objection. To answer it, we have to fall back on a philosophical distinction, and say that understanding can be taken in two ways: intensive — in depth — or extensive — in range. Taken extensive, that is, with respect to the multitude of things there are to be understood, which are infinite, human understanding is as nothing, even if it understood a thousand propositions — because a thousand, next to infinity, is like zero. But taking understanding intensive — insofar as that term means grasping some proposition intensively, that is, perfectly — I say that the human intellect does understand some propositions as perfectly, and holds them with as absolute a certainty, as nature herself has. Such are the pure mathematical sciences, geometry and arithmetic. Of these the divine intellect knows infinitely more propositions, to be sure, since it knows them all; but of those few the human intellect does grasp, I believe its knowledge equals the divine in objective certainty — for it reaches the point of comprehending their necessity, and beyond necessity there does not seem to be any greater sureness.
Simplicio: This strikes me as very bold and daring talk.
Salviati: These are commonplace propositions, far from any shadow of rashness or daring, and they take nothing away from the majesty of divine wisdom — just as saying that God cannot make what has been done be undone diminishes His omnipotence not at all. But I suspect, Simplicio, that you've taken alarm because my words reached you with a certain ambiguity in them. So, to explain myself better: as for the truth that mathematical demonstrations give us knowledge of, it is the same truth that divine wisdom knows. But I will gladly grant you that the way God knows the infinitely many propositions, of which we know a few, is supremely more excellent than ours. Ours proceeds by reasoning, by passages from one conclusion to the next; His is a single, simple intuition. Where we, for example, to win the knowledge of a few of the properties of the circle — which has infinitely many — begin from one of the simplest, take it as the definition, and pass by reasoning to a second, and from that to a third, then a fourth, and so on, the divine intellect, by the simple apprehension of the circle's essence, comprehends the whole infinity of its properties without any reasoning through time. And in fact all those properties are virtually contained in the definitions of all things anyway — and being infinite, perhaps they are, in their essence and in the divine Mind, one single property. Nor is any of this entirely unknown to the human intellect either; it is only veiled by a deep, dense fog, which thins and clears in part whenever we have made ourselves masters of some conclusions firmly demonstrated and possessed so readily that we can run swiftly among them. For, in the end, what is it for the square on the side opposite the right angle of a triangle to be equal to the squares on the other two sides, if not for parallelograms on a common base between parallel lines to be equal to each other? And isn't that, finally, the same as two surfaces being equal that, when fitted together, do not spill over each other but close within the same boundary? Now these passages, which our intellect makes in time, moving step by step, the divine intellect runs through in an instant, like light — which is the same as saying that they are all always present to it. So I conclude that our understanding — both in the manner and in the number of things understood — is surpassed by the divine at an infinite distance. But I do not for all that debase it so far as to count it absolutely nothing. No: when I go considering how many and how marvelous are the things men have understood, investigated, and accomplished, I recognize and understand all too clearly that the human mind is a work of God, and one of the most excellent.
Sagredo: Many times, along the lines of what you're saying now, I have turned over in my own mind how great the sharpness of human ingenuity is. And when I run through the many marvelous inventions men have found, in the arts as in letters, and then reflect on my own knowledge — so far from promising me the discovery of anything new that I can hardly hope even to learn what has already been found — I am confounded with wonder and afflicted with despair, and count myself little short of miserable. If I look at one of the excellent statues, I say to myself: "And when would you know how to strip the excess away from a block of marble, and uncover so beautiful a figure hidden inside it? When would you know how to mix and spread different colors over a canvas or a wall, and with them represent every visible object, like a Michelangelo, a Raphael, a Titian?" If I look at what men have discovered in dividing up the musical intervals, in laying down precepts and rules for handling them to the marvelous delight of the ear — when will I ever be done being amazed? What shall I say of all the many, and so different, instruments? What wonder does the reading of the excellent poets fill us with, for anyone who attends closely to the invention of their ideas and the unfolding of them? What shall we say of architecture? What of the art of navigation? But above all stupendous inventions, what towering mind was his who imagined finding a way to communicate his most hidden thoughts to any other person whatsoever, however distant in place and in time? To speak with those who are in the Indies; to speak to those who are not yet born, and will not be born for a thousand or ten thousand years? And with what ease? — with the various arrangements of twenty little characters on a page. Let this be the seal of all humanity's admirable inventions, and the close of our reasonings for today. And now that the hottest hours are past, I think Salviati will enjoy going out to taste the cool of the evening on our boat; and tomorrow I shall be expecting you both, to carry on with the discussions we have begun.
Salviati: Yesterday's digressions, which pulled us off the straight thread of our main discussions, were so many and so varied that I don't know whether I can find the trail again without your help, so as to move forward.
Sagredo: I'm not surprised that you, with your imagination filled and cluttered both with what's been said and with what remains to be said, should find yourself in some confusion. But I, being a simple listener, carry nothing in my head but the things I've heard; so perhaps, by recalling them in summary, I can set the reasoning back on its thread. As far as my memory serves, then, the sum of yesterday's discussions was an examination, from their very foundations, of which of two opinions is the more probable and reasonable: the one which holds that the substance of the celestial bodies is ingenerable, incorruptible, inalterable, impervious to change — in short, exempt from every kind of alteration except change of place, and therefore a fifth essence utterly different from this substance of our elemental bodies, which are generable, corruptible, alterable, and so on; or else the other opinion, which strips this lopsidedness out of the world and holds that the Earth enjoys the very same perfections as the other integral bodies of the universe — that it is, in short, a globe that moves and wanders no less than the Moon, Jupiter, Venus, or any other planet. In the end many particular parallels were drawn between this Earth of ours and the Moon — more with the Moon than with any other planet, perhaps because we have greater and more solid knowledge of her, thanks to her lesser distance. And having finally concluded that this second opinion has more of the likely about it than the first, it seems to me the natural next step was to begin examining whether the Earth should be judged immobile, as most people have believed up to now, or mobile, as certain ancient philosophers believed and as others have come to think in more recent times — and, if mobile, what its motion might be.
Salviati: I already recognize the landmarks of our road. But before we set out any further, I have to say a word about those last remarks of yours — that we concluded the opinion which grants the Earth the same conditions as the celestial bodies to be more likely than its contrary. I concluded no such thing, just as I don't intend to reach a verdict on any other of the disputed propositions. My intention was only to produce, for each side equally, the reasons and replies, the objections and solutions, that others have thought of up to now, along with a few more that have dropped into my mind after long thinking about it — and then to leave the decision to the judgment of others.
Sagredo: I let myself be carried away by my own feeling; and believing that what I felt in myself must be what others felt too, I made universal a conclusion I should have kept particular. I truly was wrong, especially since I didn't know the view of Simplicio, here present.
Simplicio: I'll confess to you that all last night I was ruminating over yesterday's matters, and truly I find many fine, new, and vigorous considerations in them. All the same, I feel myself gripped far more strongly by the authority of so many great writers, and in particular... You're shaking your head, Sagredo, and smirking, as though I'd said something wildly out of line.
Sagredo: I'm only smirking — but believe me, I'm about to burst with the effort of holding back a much bigger laugh. You've reminded me of a wonderful incident I witnessed not many years ago, together with some noble friends of mine whom I could still name for you.
Salviati: Then you'd better tell it, so that Simplicio doesn't go on believing it was he who set you laughing.
Sagredo: Gladly. One day I was at the house of a highly esteemed physician in Venice, where people gathered from time to time — some for their studies, others out of curiosity — to watch a dissection at the hands of an anatomist who was truly as learned as he was careful and skilled. It happened that day that the search was on for the origin and root of the nerves, the subject of a famous controversy between the Galenist physicians and the Peripatetics. The anatomist showed how the great trunk of nerves sets out from the brain, passes through the nape of the neck, then stretches down along the spine and branches out through the whole body, while only a single strand, fine as sewing thread, arrives at the heart. Then he turned to a gentleman he knew to be a Peripatetic philosopher — for whose benefit he had uncovered and demonstrated the whole thing with extraordinary care — and asked whether he was now satisfied and certain that the nerves originate in the brain and not in the heart. And the philosopher, after standing lost in thought for a while, answered: "You have made me see this matter so plainly and palpably that if Aristotle's text did not stand against it — for it says openly that the nerves are born in the heart — I would be forced to confess it true."
Simplicio: Gentlemen, I want you to know that this dispute over the origin of the nerves is by no means as digested and settled as some people may persuade themselves.
Sagredo: Nor will it ever be, safe to say, so long as it has opponents of that sort. But what you say doesn't shave one bit off the extravagance of the Peripatetic's reply: against such palpable evidence of the senses he produced no other experiments or arguments of Aristotle's — only bare authority, the pure Ipse dixit: he himself said it.
Simplicio: Aristotle did not acquire so great an authority except by the force of his demonstrations and the depth of his reasoning. But you have to understand him — and not merely understand him, but have such long practice in his books that you've formed a complete and perfect idea of them, so that every saying of his is always present to your mind. He did not write for the crowd, nor did he bind himself to string out his syllogisms in the ordinary schoolroom order. Instead, using a scattered method, he sometimes placed the proof of a proposition among texts that seem to deal with anything but. So you must hold that whole grand scheme in your head, and know how to combine this passage with that one, to piece this text together with another far removed from it. There's no doubt that whoever has this practice will be able to draw from his books the demonstrations of everything that can be known — because everything is in them.
Sagredo: My dear Simplicio: since having things scattered here and there doesn't bother you, and since you believe that by piecing together and combining various little scraps you can squeeze out their juice — well, what you and the other brave philosophers do with the texts of Aristotle, I will do with the verses of Virgil or Ovid, stitching them into centos — patchwork poems — and using them to explain all the affairs of men and the secrets of nature. But why do I even mention Virgil, or any other poet? I have a little book much shorter than Aristotle or Ovid, which contains all the sciences, and with very little study anyone can form a most perfect idea of it: the alphabet. There's no doubt that whoever knows how to couple and arrange this vowel and that one with those consonants or these others will draw from them the truest answers to every doubt, and the teachings of every science and every art — in exactly the way a painter, from simple colors laid out separately on his palette, goes about combining a little of this with a little of that and a little of the other, and shapes men, plants, buildings, birds, fish; in short, imitates every visible object, though there are no eyes on his palette, no feathers, no scales, no leaves, no stones. In fact it's necessary that none of the things to be imitated, nor any part of them, be actually present among the colors, if you want those colors to be capable of representing everything; if there were feathers among them, say, they'd serve to paint nothing but birds and plumes.
Salviati: There are gentlemen still alive and well who were present when a doctor lecturing in a famous university, hearing the telescope described — he hadn't yet seen it — announced that the invention was lifted from Aristotle. He had a text brought to him, found a certain passage where Aristotle gives the reason why, from the bottom of a very deep well, one can see stars in the sky during the day, and said to the company: "Here you have the well, which stands for the tube; here the thick vapors, from which the invention of the lenses was taken; and here, finally, the strengthening of vision as the rays pass through a transparent medium that is denser and darker."
Sagredo: That's a way of containing everything knowable which is very like the way a block of marble contains within itself one beautiful statue — no, a thousand beautiful statues; the trick is knowing how to uncover them. Or we might say it's like the prophecies of Abbot Joachim, or the answers of the pagan oracles, which are understood only after the prophesied events have happened.
Salviati: And where do you leave the predictions of the horoscope-casters, which after the outcome can be seen so clearly in the birth-chart — or, as they say, the celestial figure?
Sagredo: It's in just this fashion that the alchemists, led on by their melancholy humor, discover that all the loftiest geniuses of the world never really wrote about anything except how to make gold — only, so as to say it without revealing it to the crowd, each went fancifully hiding it under a different cover. And it's the most delightful thing to hear their commentaries on the ancient poets, uncovering the weighty mysteries concealed under the fables: what the loves of the Moon really mean, and her coming down to Earth for Endymion, and her fury at Actaeon; and when Jupiter turns himself into a shower of gold, and when into burning flames; and what great secrets of the art lie in that Mercury the interpreter, in those abductions by Pluto, in those golden boughs.
Simplicio: I believe — indeed in part I know — that the world doesn't lack for thoroughly extravagant brains; but their follies shouldn't redound to the discredit of Aristotle, of whom it seems to me you sometimes speak with too little respect. His antiquity alone, and the great name he has won in the minds of so many distinguished men, should be enough to make him honorable in the eyes of all the learned.
Salviati: That's not how the matter runs, Simplicio. It is certain of his followers, too fainthearted by half, who give occasion — or rather, who would give occasion — for thinking less of him, if we chose to applaud their frivolities. Tell me, honestly: are you really so naive that you don't see that if Aristotle had been there to hear the doctor who wanted to make him the inventor of the telescope, he'd have been far angrier with him than with the people laughing at the doctor and his interpretations? Do you have any doubt that if Aristotle could see the new discoveries in the heavens, he would change his opinion, amend his books, move toward the doctrines that agree with the senses, and drive away from himself those pitifully small brains who too timidly let themselves be drawn into defending his every word — never grasping that if Aristotle were the man they imagine, he'd be an intractable brain, an obstinate mind, a spirit full of barbarity, a tyrant's will, someone who reckoned everyone else to be witless sheep and wanted his own decrees set above the senses, above experience, above nature herself? It is his followers who have given Aristotle his authority; he never usurped it or took it for himself. And since it's easier to hide behind another man's shield than to show one's own face in the open, they're afraid — they don't dare step one single pace away from him; and rather than admit any alteration in Aristotle's heaven, they insolently deny the alterations they can see with their own eyes in nature's heaven.
Sagredo: These people put me in mind of that sculptor who carved a great block of marble into the image of — Hercules, I think it was, or a thundering Jupiter — and gave it, by his marvelous craft, such vividness and ferocity that it frightened everyone who looked at it; and then he began to be afraid of it himself, though all its spirit and menace was the work of his own hands. The terror got such a grip on him that he no longer dared face it with his chisels and mallet.
Salviati: I have often marveled at how these strict upholders of Aristotle's every word can fail to notice what damage they do to his reputation and credit — how much, in trying to swell his authority, they diminish it. When I see them obstinately defending propositions that I can touch with my hand to be manifestly false, and trying to persuade me that this is what a true philosopher does, and that Aristotle himself would do the same, my confidence sinks that he reasoned rightly about the other conclusions that lie beyond my reach. Whereas if I saw them yield and change their minds before manifest truths, I'd be ready to believe that where they held firm, they might have solid demonstrations I hadn't understood or hadn't heard.
Sagredo: Or else — if they felt they'd be staking too much of their own reputation, and Aristotle's, by confessing they hadn't known some conclusion discovered by someone else — wouldn't it be the lesser evil to go find it among his texts, by piecing several of them together, according to the practice Simplicio has described to us? For if everything knowable is in there, then it must follow that everything can be found in there.
Salviati: Sagredo, don't make fun of this stratagem — I can see you propose it as a joke, but it's no laughing matter. Not long ago a philosopher of great name composed a book on the soul, in which, reporting Aristotle's opinion on whether or not it is immortal, he adduced many texts — not the ones cited by Alexander, because in those, he said, Aristotle wasn't even treating that subject, let alone settling anything about it — but others he had dug up himself in various out-of-the-way places, which leaned toward the dangerous reading. Warned that he'd have trouble getting the book licensed, he wrote back to his friend not to let that stop the approval going forward: if no other obstacle turned up, he'd have no difficulty at all in changing Aristotle's doctrine, and with different expositions and different texts he'd defend the contrary opinion — and it would still agree with the mind of Aristotle.
Sagredo: Oh, now this doctor can give me orders any day! He won't let Aristotle bamboozle him — he means to lead Aristotle by the nose and make him talk to order! See how much it matters to know how to seize the right moment. You don't go negotiating with Hercules while he's raging and in a fury, but while he's spinning tales among the Maeonian serving-girls. Ah, the unheard-of cowardice of servile minds! To make yourself a slave of your own free will; to accept another man's decrees as inviolable; to bind yourself to declare yourself persuaded and convinced by arguments so effective, so clearly conclusive, that the defenders themselves cannot decide whether they were even written on that subject, or whether they prove that conclusion at all! And here is the greater madness still: among themselves they are still in doubt whether the author himself held the affirmative side or the negative. What is this but making a wooden statue their oracle — running to it for answers, fearing it, revering it, adoring it?
Simplicio: But if we abandon Aristotle, who is to be our escort in philosophy? Name some author, if you can.
Salviati: You need an escort in unknown and savage country; in open, level places only the blind need a guide. Whoever is blind would do best to stay home; but whoever has eyes in his head and in his mind — those are the escort he should use. Not that I'm saying we shouldn't listen to Aristotle; on the contrary, I applaud reading him and studying him diligently. What I blame is handing yourself over to him as his property, so that you blindly countersign his every word and, without looking for any further reason, are bound to hold it as an inviolable decree. That is an abuse, and it drags another extreme disorder behind it: people stop trying to understand the force of his demonstrations at all. And what is more shameful than to hear, in public disputations about demonstrable conclusions, someone cut in from the sidelines with a text — often written on some entirely different subject — and shut his opponent's mouth with it? If you insist on going on studying this way, then put down the name of philosophers and call yourselves historians, or doctors of memory; for it isn't right that people who never philosophize should usurp the honorable title of philosopher. But we'd better pull back to shore, or we'll drift into an endless sea we couldn't get out of all day. So, Simplicio: come forward, please, with reasons and demonstrations — your own or Aristotle's — and not with texts and bare authorities, because our discussions are to be about the sensible world, and not about a world on paper. Yesterday's discourse hauled the Earth up out of the darkness and set it out under the open sky, showing that the wish to count it among what we call the celestial bodies is not a proposition so beaten and flattened that no breath of life is left in it. It follows, then, that we go on to examine how much probability there is in holding the Earth fixed and wholly immobile — I mean as to its entire globe — and how much likelihood in making it mobile with some motion, and of what kind. And since I'm undecided on this question, while Simplicio, along with Aristotle, stands resolute on the side of immobility, he shall bring out, step by step, the motives for their opinion; I'll bring the replies and the arguments for the contrary side; and Sagredo shall tell us the motions of his own mind, and which way he feels himself pulled.
Sagredo: That suits me very well — provided I also keep the freedom to bring up whatever plain natural common sense may dictate to me now and then.
Salviati: Indeed, that's the very thing I beg of you in particular. For of the easier — the material, so to speak — considerations, I think few have been left out by the writers on the subject, so that only some of the subtler and more remote ones can still be wanting or missing; and for hunting those down, what subtlety could be better suited than the wit of Sagredo, sharp and penetrating as it is?
Sagredo: I am whatever Salviati pleases. But please, let's not slide into yet another kind of digression — the ceremonial kind — because right now I'm a philosopher, and in the schoolroom, not at the Broglio, trading compliments.
Salviati: Then let our contemplation begin with this consideration: whatever motion may be attributed to the Earth, it is necessary that for us — as inhabitants of the Earth and therefore sharers in that motion — it remain completely imperceptible, as if it didn't exist, so long as we look only at terrestrial things; but on the other hand, it is just as necessary that this same motion appear to us as a motion shared in common by all the other bodies and visible objects which, being separated from the Earth, lack it. So the true method for investigating whether any motion can be attributed to the Earth, and if so, what it is, is to consider and observe whether in the bodies separated from the Earth we can detect some appearance of motion that belongs equally to all of them. Because a motion that showed up only in the Moon, say, and had nothing to do with Venus or Jupiter or the other stars, could not possibly belong to the Earth — or to anything but the Moon itself. Now, there is one motion that is the most general and the greatest of all: the one by which the Sun, the Moon, the other planets, and the fixed stars — in short, the whole universe, the Earth alone excepted — appear to us to move together from east to west in the space of twenty-four hours. And this motion, as far as this first appearance goes, might just as well belong to the Earth alone as to all the rest of the world with the Earth left out; for the same appearances would be seen in the one arrangement as in the other. That's why Aristotle and Ptolemy, who had grasped this point thoroughly, argue against no other motion than this daily one when they set out to prove the Earth immobile — except that Aristotle does touch briefly on a certain something against another motion attributed to the Earth by one of the ancients, which we'll speak of in its proper place.
Sagredo: I'm fully persuaded by the necessity with which your argument reaches its conclusion, but a doubt is stirring in me that I can't shake off. It's this: Copernicus assigns the Earth another motion besides the daily one. By the rule you've just laid down, that motion ought to be imperceptible to us here on the Earth, as far as appearances go, but visible in all the rest of the world. So it seems to me I can draw one necessary conclusion or the other: either Copernicus plainly blundered in assigning the Earth a motion whose general correspondence doesn't show up anywhere in the sky, or else, if the correspondence is there, then Ptolemy was just as much at fault for failing to refute this motion the way he refuted the other.
Salviati: A very reasonable doubt; and when we come to deal with that other motion, you'll see by how wide a margin Copernicus outstripped Ptolemy in sharpness and penetration of mind — for he saw what Ptolemy did not see, I mean the marvelous correspondence with which that motion is reflected in all the rest of the celestial bodies. But for now let's set that part aside and come back to our first consideration. Beginning with the most general points, I'll go on proposing the reasons that seem to favor the Earth's mobility, and then we'll hear the contrary ones from Simplicio. First: if we consider nothing but the immense bulk of the starry sphere, compared with the smallness of the terrestrial globe — which it contains many millions of times over — and then think of the speed of a motion that has to complete one entire revolution in a day and a night, I can't persuade myself that anyone could be found who thought it the more reasonable and credible thing that it's the celestial sphere doing the turning while the terrestrial globe stands still.
Sagredo: If, for the whole universe of effects that can depend in nature on motions like these, all the very same consequences followed, to a hair, from the one arrangement as from the other, then — as my first, general impression — I'd judge that anyone who considered it more reasonable to set the entire universe moving in order to keep the Earth still is more unreasonable than a man who climbed to the top of your great dome for no other purpose than to take in a view of the city and the countryside around it, and then demanded that the whole landscape be spun around him so he could be spared the trouble of turning his head. The conveniences to be drawn from that arrangement and not from this one would have to be many and great indeed to balance out, in my mind, and outweigh this absurdity, and so make the first more believable to me than the second. But perhaps Aristotle, Ptolemy, and Simplicio must find some advantages in it — and if there are any, it would be well to have them laid before us too; or else let it be shown to me how and why there are none, and can be none.
Salviati: For all the thought I've given it, I haven't been able to find any difference; and what's more, I think I've found that no difference can exist — so that I judge any further search for one to be in vain. So mark this: motion is motion, and does its work as motion, only in relation to things that lack it; among things that all share it equally, it does nothing — it's as if it weren't there at all. The goods a ship is loaded with move in the sense that, leaving Venice, they pass by Corfu, by Candia, by Cyprus, and go on to Aleppo — Venice, Corfu, Candia, and the rest staying behind, not moving with the ship. But for the bales, the crates, and the other bundles the ship is loaded and stowed with, and with respect to the ship itself, the motion from Venice to Syria is as good as nothing: it doesn't alter the relation among them in the least. And that's because the motion is common to them all, and shared equally by all. If, of all the cargo aboard, one bale should shift a single finger's breadth away from a crate, that alone would be, for the bale, a greater motion in relation to the crate than the two-thousand-mile voyage they made together.
Simplicio: That is good, solid doctrine, and Peripatetic through and through.
Salviati: I take it to be older than that; and I suspect that Aristotle, in taking it over from some good school, didn't penetrate it fully, and that having written it down in altered form, he became a source of confusion — thanks to those who insist on defending his every word. When he wrote that everything that moves, moves upon something immobile, I suspect he was garbling the statement that everything that moves, moves with respect to something immobile. That proposition suffers no difficulty at all; the other suffers many.
Sagredo: Please, let's not break the thread — carry on with the argument you began.
Salviati: It's clear, then, that a motion common to many moving bodies is idle, as good as null, with respect to the relation of those bodies among themselves, since among them nothing changes; it does its work only in the relation those bodies have with others that lack the motion — for with those, their arrangement does change. Now, we've divided the universe into two parts, one of which is necessarily movable and the other motionless. So as far as anything that can depend on such a motion is concerned, moving the Earth alone comes to exactly the same as moving all the rest of the world, since the whole operation of the motion lies in nothing but the relation between the celestial bodies and the Earth — and that relation alone is what changes. Now, if to obtain the very same effect ad unguem — to the last detail — it makes no difference whether the Earth alone moves while all the rest of the universe stays still, or the Earth alone stays still while the whole universe moves with one and the same motion, who is going to believe that nature — which, by common consent, does not employ many things to bring about what can be managed with few — chose to set an immense number of enormous bodies moving, at an inestimable speed, to achieve what could be had by the moderate motion of one single body turning around its own center?
Simplicio: I don't quite see how this vast motion can count as nothing for the Sun, for the Moon, for the other planets, and for the innumerable host of the fixed stars. How can you call it nothing that the Sun passes from one meridian to the next, climbs above this horizon, sinks below that one, brings now the day and now the night — and that the Moon, the other planets, and the fixed stars too go through the same variations?
Salviati: All these variations you list are nothing except in relation to the Earth. To see that this is true, just remove the Earth in your imagination: there is no longer any rising or setting of Sun or Moon left in the world, no horizons, no meridians, no days, no nights — in short, from that motion there never arises any change at all between the Moon and the Sun or any other stars you please, fixed or wandering. All the changes are relative to the Earth; and all of them, when you come down to it, amount to nothing more than the Sun showing itself first to China, then to Persia, afterwards to Egypt, to Greece, to France, to Spain, to America, and so on — with the Moon and the rest of the celestial bodies doing the same. And it all comes out in exactly the same way if, without dragging in so great a part of the universe, you simply let the terrestrial globe turn in place. But let's double the difficulty with another, enormous one. If you attribute this great motion to the heavens, you're forced of necessity to make it contrary to the particular motions of all the planetary orbs — each of which, beyond any dispute, has its own proper motion from west to east, and a gentle, moderate motion at that — and then to have them swept off the opposite way, from east to west, by this furiously rapid daily motion. Whereas if the Earth is made to turn on itself, the contrariety of motions vanishes, and the single motion from west to east accommodates every appearance and satisfies them all completely.
Simplicio: As for the contrariety of motions, that would matter little, because Aristotle demonstrates that circular motions are not contrary to one another, and that theirs cannot be called true contrariety.
Salviati: Does Aristotle demonstrate it, or does he merely say it because it suited a certain design of his? If contraries are, as he himself declares, things that destroy one another, I fail to see how two moving bodies that collide on a circular line should do each other any less harm than two that collide on a straight one.
Sagredo: Hold on a moment, please. Tell me, Simplicio: when two knights run at each other jousting in the open field, or when two whole squadrons, or two fleets at sea, drive into one another and smash and sink each other — would you call encounters like those contrary to one another?
Simplicio: Let's call them contrary.
Sagredo: Then how is it there's no contrariety in circular motions? These encounters, taking place on the surface of the earth or the water — which, as you know, are spherical — turn out to be circular motions. Do you know, Simplicio, which circular motions really aren't contrary to each other? Those of two circles that touch from the outside: turn one of them, and it naturally makes the other move the opposite way. But if one circle is inside the other, it's impossible for their motions, made in different directions, not to fight each other.
Salviati: Contrary or not contrary, these are quarrels over words; and I know that in fact it's a far simpler and more natural thing to be able to save everything with a single motion than to introduce two — and if you don't want to call them contrary, call them opposite. Nor am I putting this forward as something impossible, or claiming to draw a necessary demonstration from it — only a greater probability. And the improbability is compounded a third time by the way this arrangement disrupts, out of all proportion, the order that we see with certainty holding among those celestial bodies whose circling is not in doubt but absolutely settled. The order is this: the bigger the orb, the longer it takes to complete its revolution, and the smaller, the quicker. Thus Saturn, tracing a circle greater than any other planet's, completes it in thirty years; Jupiter goes around its smaller one in twelve years; Mars in two; the Moon runs through its far smaller circle in a single month. And just as plainly we see that of the Medicean Stars — Jupiter's four little moons — the one nearest Jupiter makes its revolution in a very short time, about forty-two hours; the next in three and a half days; the third in seven days; and the most remote in sixteen. And this thoroughly consistent pattern isn't altered in the least so long as the twenty-four-hour motion is assigned to the terrestrial globe turning on itself. But if you insist on keeping the Earth motionless, then after passing from the Moon's very brief period to the successively greater ones — to Mars's two years, from there to the greater sphere of Jupiter with its twelve, and from that to the still greater sphere of Saturn, whose period is thirty years — you must then leap across to another sphere incomparably bigger yet, and make it finish an entire revolution in twenty-four hours. And even that is the least of the disorder you'd be introducing; for if anyone wanted to pass from Saturn's sphere to the starry sphere, and make it as much bigger than Saturn's as its extremely slow motion of many thousands of years would proportionally require, then the leap from that one to a still bigger sphere — while making it swing clear around in twenty-four hours — would be out of proportion by far more.
And there's a fourth difficulty, which you must necessarily accept the moment the starry sphere is made movable: the immense disparity among the motions of the stars themselves. Some of them would be moving at tremendous speed in vast circles, others extremely slowly in the tiniest circles, according as each lies farther from or nearer to the poles. That has its own awkwardness — both because we see all the bodies whose motion is beyond doubt moving in great circles, and because it seems a poorly judged arrangement to station bodies that are meant to move circularly at immense distances from the center, and then have them move in the smallest circles of all.
And not only will the sizes of the circles, and consequently the speeds of motion, of these stars be utterly different from the circles and motions of those others, but — and this will be the fifth inconvenience — the very same stars keep changing their circles and their speeds. For the stars that two thousand years ago sat on the celestial equator, and so traced great circles with their motion, are found in our own day many degrees away from it; so they must have grown slower in motion and been reduced to moving in smaller circles. And it isn't even far from possible that a time will come when one of them — a star that till then had always moved — will reach the pole, join it, and stand still; and then, after resting for some while, will take up its motion again. Whereas the other stars, the ones whose motion is certain, all trace, as I said, the great circle of their orb and keep to it without change.
The improbability grows again — let it be the sixth inconvenience — for anyone who reasons carefully, in that no one can even conceive what the solidity of that vast sphere would have to be, in whose depths so many stars are riveted so firmly that, without shifting position among themselves in the slightest, they are carried around in concert despite so enormous a disparity of motions. Or, if the heavens are fluid — as it's far more reasonable to believe — so that each star goes wandering through them on its own, then what law will govern their motions, and to what end, so that, watched from the Earth, they appear to be moved by one single sphere? To accomplish that, it seems to me as much easier and more convenient to fix them motionless than to send them roaming, as it is easier to keep in their places the many stones set into a piazza's pavement than the swarms of boys who run around on top of them.
And finally, for the seventh objection: if we attribute the daily rotation to the highest heaven, we have to make it of such force and power that it carries along with it the innumerable multitude of the fixed stars — every one of them a vast body, far bigger than the Earth — and all the planetary spheres besides, even though both stars and planets by their own nature move the other way. And beyond that, we're forced to concede that the element of fire and the greater part of the air are swept along too, and that only the little globe of the Earth stands defiant and resistant to so much power. That, to me, seems very hard to swallow; nor could I understand how the Earth — a body hanging suspended and balanced on its center, indifferent to motion and to rest, placed in and surrounded by a fluid medium — should not yield as well and be carried around with everything else. But we meet no such obstacles in making the Earth move — a tiny body, imperceptible in comparison with the universe, and for that very reason incapable of doing it any violence.
Sagredo: I can feel certain notions whirling around in my imagination, stirred up in a jumble by the arguments we've been hearing; and if I'm going to attend properly to what's still to be said, I'd better see whether I can put them in order and draw out whatever substance is in them — if there turns out to be any. Perhaps proceeding by questions will help me explain myself more easily. So I ask Simplicio, first: does he believe that different motions can naturally belong to one and the same simple movable body, or that only one suits it — its own proper and natural motion?
Simplicio: For a simple movable body there can be only one motion that suits it naturally, and no more; all the others belong to it by accident and by participation. Just as, for a man strolling about a ship, his own proper motion is that of his walking, while by participation he has the motion that carries him into port — where he would never have arrived by strolling, if the ship's motion hadn't brought him there.
Sagredo: Tell me, second: that motion which is communicated by participation to some movable body, while the body itself is moving with another motion of its own, different from the participated one — must that motion reside in some subject of its own, or can it exist in nature with no other support?
Simplicio: Aristotle answers all these questions for you. He tells you that just as of one movable body there is one motion, so of one motion there is one movable body; and consequently that without inhering in its subject, no motion can exist or even be imagined.
Sagredo: Third, I'd like you to tell me whether you believe the Moon and the other planets and celestial bodies have motions of their own — and what those motions are.
Simplicio: They have them; and they are the motions by which they run through the zodiac — the Moon in a month, the Sun in a year, Mars in two, the starry sphere in all those thousands of years. These are their own proper and natural motions.
Sagredo: But that motion by which I see the fixed stars, and with them all the planets, travel together from east to west and return to the east in twenty-four hours — in what way does that belong to them?
Simplicio: They have it by participation.
Sagredo: Then it does not reside in them; and since it doesn't reside in them, and cannot exist without some subject in which it does reside, it must be made the proper and natural motion of some other sphere.
Simplicio: On this account the astronomers and philosophers have found another, highest sphere, without any stars, to which the daily rotation naturally belongs; and they have called it the primum mobile — the "first movable" — which then sweeps all the lower spheres along with it, contributing its own motion to them and letting them share in it.
Sagredo: But when — without introducing other unknown and enormous spheres, without other motions or sweepings-along by participation, leaving to every sphere its own single, simple motion, without mixing contrary motions, but having them all run the same way, as they must if they all depend on a single principle — everything proceeds and answers in the most perfect harmony, why refuse that option, and give your assent to such strange and labored conditions?
Simplicio: The whole point lies in finding this way of yours, so simple and so ready.
Sagredo: The way looks to me found already. Make the Earth the primum mobile — that is, make it turn on itself in twenty-four hours, and in the same direction as all the other spheres — and, without this motion being shared with any other planet or star, they will all have their risings, their settings, and in short every other appearance.
Simplicio: The trick is being able to move it without a thousand inconveniences.
Salviati: All the inconveniences will be removed as fast as you propose them. What's been said so far amounts only to the first and most general motives for holding it not altogether improbable that the daily rotation belongs to the Earth rather than to all the rest of the universe. I don't offer them to you as unbreakable laws, but as motives that carry some appearance of reason. And since I understand perfectly well that a single experiment or one conclusive demonstration to the contrary would be enough to knock these and a hundred thousand other probable arguments flat, we mustn't stop here, but press on and hear what Simplicio answers, and what better probabilities or firmer reasons he brings against us.
Simplicio: First I'll say something in general about all these considerations taken together, and then I'll come to some particulars. It seems to me that you build everything on the greater simplicity and ease of producing the same effects: you judge that, as far as causing them goes, moving the Earth alone comes to the same as moving all the rest of the world except the Earth, but that as far as the doing of it goes, you count the first far easier than the second. To that I answer that it seems the same to me too — so long as I measure by my own power, which is not merely finite but utterly feeble. But measured against the power of the Mover, which is infinite, it is no less easy to move the universe than the Earth — or a straw, for that matter. And if the power is infinite, why should not a great part of it be exercised rather than a tiny one? So it seems to me that the argument, in its general form, has no force.
Salviati: If I had ever said that the universe does not move for lack of power in its Mover, I would have been wrong, and your correction would be well aimed; and I grant you that for an infinite power it is as easy to move a hundred thousand bodies as to move one. But what I said had no reference to the Mover — only to the moving bodies, and in them not just to their resistance, which is without doubt smaller in the Earth than in the whole universe, but to the many other particulars we were considering just now. As for the claim that it is better for an infinite power to exercise a great part of itself rather than a tiny one, I answer that no part of the infinite is greater than another, so long as both are finite; nor can one say that a hundred thousand is a greater part of an infinite number than two is, even though a hundred thousand is fifty thousand times bigger than two. And if moving the universe required a finite power — however enormous compared with what would suffice to move the Earth alone — the part of the infinite employed would be no greater for that, nor would what remained idle be any less than infinite. So applying a little more or a little less power to one particular effect matters not at all; besides which, the operation of such a power does not stop and end at the daily rotation alone — there are plenty of other motions in the world that we know of, and there may be many more unknown to us. Looking, then, at the moving bodies; not doubting that it is a shorter and readier operation to move the Earth than the universe; and keeping an eye, moreover, on the many other savings and simplifications that this one choice secures — a very true axiom of Aristotle, which teaches us that frustra fit per plura quod potest fieri per pauciora — it is pointless to do with more what can be done with less — makes it more probable that the daily rotation belongs to the Earth alone than to the whole universe minus the Earth.
Simplicio: In citing the axiom you have left out a clause that is the whole point, especially in the present case. The phrase omitted is æque bene — "equally well." So we must examine whether the two assumptions can satisfy everything equally well.
Salviati: Whether both positions satisfy equally well will emerge from the particular examination of the appearances they have to satisfy; for so far we have argued, and shall go on arguing, ex hypothesi — as a supposition — assuming that as far as satisfying the appearances goes, the two positions are equally serviceable. As for the phrase you say I left out, I rather suspect you have superfluously added it. "Equally well" is a relation, and a relation necessarily requires at least two terms — a thing cannot stand in relation to itself; one doesn't say, for example, that rest is equally as good as rest. And when we say "it is done in vain by more means what can be done by fewer," we understand that the thing to be done must be the same thing, not two different things; and since the same thing cannot be said to be done equally as well as its very self, the addition of the phrase "equally well" is superfluous — a relation with only one term.
Sagredo: If we don't want the same thing to happen to us as yesterday, please, let's get back to the matter at hand; and let Simplicio begin producing the difficulties that seem to him to tell against this new arrangement of the world.
Simplicio: The arrangement is not new — on the contrary, it is very ancient; and the proof is that Aristotle refutes it, and his refutations are these. "First: if the Earth moved — whether in itself, staying at the center, or in a circle, being outside the center — that motion would necessarily be violent, for it is not her natural motion; if it were hers, every one of her particles would share it, but each of them moves in a straight line toward the center. The motion being therefore violent and preternatural, it could not be everlasting; but the order of the world is everlasting; therefore, and so on. Second: all the other bodies that move circularly appear to lag behind and to move with more than one motion — excepting only the primum mobile, the outermost sphere that carries all the rest. On that account the Earth too would have to move with two motions; and if that were so, of necessity changes would have to show up in the fixed stars — which is not seen; rather, without any variation, the same stars always rise from the same places and set in the same. Third: the motion of the parts and of the whole is naturally toward the center of the universe, and for that reason too the whole rests there." He then raises the question whether the motion of the parts is aimed naturally at the center of the universe or at the center of the Earth, and concludes that its own proper instinct is to go toward the center of the universe, and only per accidens toward the center of the Earth — a doubt we discussed at length yesterday. Finally he confirms the same point with a fourth argument, drawn from the experience of heavy bodies: falling from high to low, they come down plumb onto the surface of the Earth; and likewise projectiles thrown plumb upward return plumb down along the same lines, however immense the height to which they were thrown — arguments that conclude of necessity that their motion is toward the center of the Earth, which, without moving at all, waits for them and receives them. Last of all he notes that the astronomers produce further reasons in confirmation of the same conclusions — I mean, that the Earth is at the center of the universe and immobile — and he cites just one of them: that all the appearances seen in the movements of the stars answer to the Earth's position at the center, a correspondence that would fail if she were not there. The other reasons, produced by Ptolemy and by other astronomers, I can bring forward now, if you like, or after you've said whatever occurs to you in reply to these of Aristotle's.
Salviati: The arguments produced in this matter are of two kinds: some have regard to earthly happenings, without any relation to the stars, and others are drawn from the appearances and observations of things celestial. Aristotle's arguments are mostly drawn from the things around us, and he leaves the others to the astronomers; so it will be well, if you agree, to examine the ones taken from the Earth's own experiences, and then come to the other kind. And since Ptolemy, Tycho, and other astronomers and philosophers — besides taking up, confirming, and fortifying Aristotle's arguments — have produced others of their own, we may as well gather them all together, so as not to have to give the same or similar answers twice. So, Simplicio: would you like to recite them, or shall I relieve you of the trouble? I am happy to oblige either way.
Simplicio: Better that you present them: having studied them more, you'll have them readier to hand, and in greater number too.
Salviati: As the strongest reason of all, everyone produces the argument of heavy bodies: falling from high to low, they come down along a straight line perpendicular to the surface of the Earth — an argument held to be irrefutable proof that the Earth stands still. For if she had the daily rotation, then a tower from whose top a stone was dropped would be carried along by the Earth's spin, and in the time the stone consumed in its fall, the tower would race many hundreds of braccia toward the east — and the stone ought to strike the ground that far from the tower's base. They back this effect up with another experiment: dropping a lead ball from the top of the mast of a ship standing still, and marking where it hits — which is near the foot of the mast; but if the same ball is dropped from the same place while the ship is under way, its impact will land as far from the first mark as the ship has run forward during the time of the lead's fall — and this for no other reason than that the natural motion of the ball, once set free, is in a straight line toward the center of the Earth. They fortify the argument with the experience of a projectile launched upward to a very great height — say, a ball fired from a cannon aimed plumb vertical above the horizon. In its climb and return the ball consumes so much time that, at our latitude, the cannon and we along with it would be carried many miles eastward by the Earth, so that the ball, falling, could never come back near the gun, but would land as far to the west as the Earth had run on ahead. They add, further, a third and very effective experience, which is this: if you fire a culverin — a long cannon — at full range toward the east, and then another, with an equal charge and at the same elevation, toward the west, the westward shot would carry vastly farther than the eastward one. For while the ball travels west and the gun, carried by the Earth, travels east, the ball would strike the ground at a distance from the gun equal to the sum of the two journeys — the one made by the ball itself toward the west, the other by the gun, carried by the Earth, toward the east; and conversely, from the journey of the ball fired eastward you would have to subtract the journey the gun made in following it. Suppose, for example, that the ball's own journey is five miles, and that at that latitude the Earth runs three miles during the ball's flight: in the westward shot, the ball would fall to earth eight miles from the gun — its own five to the west plus the gun's three to the east; but the eastward shot would carry no farther than two miles, which is what remains when you subtract the gun's three miles of travel in the same direction from the shot's five. But experience shows the shots to be equal; therefore the gun stands immobile, and consequently so does the Earth. And no less than these, shots toward the south or the north likewise confirm the Earth's stability: you would never hit the mark you had aimed at, for the target, carried by the Earth toward the east while the ball is in the air, would slide away, and the shots would always land slanting off to the west. Nor is it only shots along the meridian lines: even those fired east or west would fail to fly true — the eastward ones would run high and the westward ones low, whenever you fired point-blank, dead level. For since the ball's journey in both shots is made along the tangent — that is, along a line parallel to the horizon — and since, if the daily rotation belongs to the Earth, the horizon keeps dropping away toward the east and rising in the west (which is why the eastern stars appear to us to climb and the western ones to sink), the eastern target would keep dropping below the line of the shot, so the shot would run high; and the rising of the western target would make the westward shot run low. So you could never fire true in any direction; and since experience says the opposite, one is forced to say the Earth stands still.
Simplicio: Oh, now these are real arguments — arguments to which it is impossible to find any answer worth giving.
Salviati: They come to you as new, perhaps?
Simplicio: Truly they do. And now I see with how many beautiful experiments nature has been kind enough to help us come to knowledge of the truth. Oh, how well one truth chimes with another, and how they all conspire together to make themselves unassailable!
Sagredo: What a pity there was no artillery in Aristotle's day! He'd have stormed ignorance with it, and spoken of the things of this world without the slightest hesitation.
Salviati: I'm very glad these arguments have come to you as new — so that you won't remain of the opinion of most of the Peripatetics, who believe that if anyone departs from Aristotle's doctrine, it must be because he never understood or properly penetrated his demonstrations. But you will certainly hear other novelties yet: you'll hear the followers of the new system produce, against their own case, observations, experiments, and arguments of far greater force than those produced by Aristotle and Ptolemy and the other assailants of the same conclusions; and so you'll come to be certain that it was not out of ignorance or inexperience that they were led to follow this opinion.
Sagredo: This is the moment for me to tell you a few things that have happened to me since I first began hearing this opinion talked about. When I was quite a young man, having only just finished my course of philosophy — which I then set aside, having applied myself to other occupations — it happened that a certain northerner from Rostock, whose name I believe was Christian Wursteisen, a follower of Copernicus's opinion, turned up in these parts and gave two or three lectures on the subject at an academy, with a crowd in attendance — drawn, I think, more by the novelty of the subject than by anything else. I didn't go, having formed the fixed impression that this opinion could be nothing but solemn madness. When I later questioned some who had been there, I heard them all making fun of it — except one, who told me the business was not entirely ridiculous. And since I considered him a thoroughly intelligent and very cautious man, I regretted not having gone; and from that time on, whenever I ran into anyone who held the Copernican opinion, I would ask him whether he had always been of that view. Among all the many I've questioned, I have not found a single one who didn't tell me he had long been of the contrary opinion, and had come over to this one moved by the force of the reasons that argue for it. Then, testing them one by one to see how well they had mastered the reasons of the other side, I found every one of them with those reasons at his fingertips — so I truly cannot say they threw themselves into this opinion out of ignorance, or vanity, or to play, as they say, the clever wit. On the other hand, of all the Peripatetics and Ptolemaics I have asked — and out of curiosity I've asked a good many — what study they had made of Copernicus's book, I found very few who had so much as seen it, and of those I believe actually understood it, none. And among the followers of the Peripatetic doctrine, I've likewise tried to learn whether any of them ever held the other opinion — and likewise found none. Whereupon, considering that everyone who follows Copernicus's opinion first held the contrary one and is perfectly well informed of the reasons of Aristotle and Ptolemy, while on the other hand not one follower of Ptolemy and Aristotle ever formerly held Copernicus's opinion and abandoned it to come over to Aristotle's — considering these things, I say, I began to believe that a man who leaves an opinion drunk in with his mother's milk and followed by countless others, to come over to one held by a bare handful, denied by all the schools, and looking, truly, like an enormous paradox, must of necessity have been moved — not to say forced — by more powerful reasons. And so I have become curious in the extreme to get, as they say, to the bottom of this business; and I count it my great good fortune to have met the two of you, from whom, without any labor of my own, I can hear everything that has been said — and perhaps everything that can be said — on this matter, confident that by the power of your reasonings I shall be pulled out of doubt and set in a state of certainty.
Simplicio: Provided the opinion and the hope don't fail you, and you don't find yourself, at the end, more confused than before.
Sagredo: I feel quite sure that cannot happen in any way whatsoever.
Simplicio: And why not? I am a good witness in my own case: the further we go, the more confused I get.
Sagredo: That is a sign that the reasons which until now seemed conclusive to you, and kept you secure in the truth of your opinion, are beginning to change their look in your mind, and to let you slip little by little — if not all the way over to the contrary opinion, at least into leaning toward it. But I, who am and have been until now indifferent, have great confidence that I shall come to rest and to certainty; and you yourself won't deny it, if you'll hear what persuades me to hope so.
Simplicio: I'll hear it gladly — and I'd be no less pleased if it worked the same effect on me.
Sagredo: Then favor me by answering my questions. First, tell me, Simplicio: isn't the conclusion we are trying to settle precisely this — whether we should hold, with Aristotle and Ptolemy, that the Earth alone stands still at the center of the universe while all the celestial bodies move; or whether, the starry sphere standing still with the Sun at its center, the Earth stands outside it, and the motions that appear to belong to the Sun and the fixed stars are really hers?
Simplicio: These are the conclusions in dispute.
Sagredo: And aren't these two conclusions such that, of necessity, one must be true and the other false?
Simplicio: Just so. We stand in a dilemma, one side of which must of necessity be true and the other false; for between motion and rest, which are contradictories, there is no third possibility — no one can say, "The Earth neither moves nor stands still; the Sun and the stars neither move nor stand still."
Sagredo: The Earth, the Sun, and the stars — what are they in nature? Trifling things, or considerable ones?
Simplicio: They are bodies of the very first rank — most noble, integral parts of the universe, vast, and considerable in the highest degree.
Sagredo: And motion and rest — what sort of conditions are they in nature?
Simplicio: So great and so fundamental that nature herself is defined by them.
Sagredo: So that to move eternally, and to be wholly immobile, are two very considerable conditions in nature, pointing to an enormous difference — above all when attributed to the principal bodies of the universe — from which only the most dissimilar consequences can follow.
Simplicio: Certainly so.
Sagredo: Now answer me on another point. Do you believe that in dialectic, in rhetoric, in physics, in metaphysics, in mathematics — in the whole universe of reasoned argument, in short — there are arguments powerful enough to persuade and demonstrate false conclusions no less than true ones?
Simplicio: No, sir. On the contrary, I hold it firm and certain that for the proof of a true and necessary conclusion there exist in nature not one but many most powerful demonstrations; that one can argue around it and turn it over with thousands upon thousands of cross-checks without ever running into any inconsistency; and that the more some sophist tried to muddy it, the clearer its certainty would always become. And that, on the opposite side, to make a false proposition look true and to persuade people of it, nothing can be produced but fallacies, sophisms, paralogisms, equivocations, and arguments that are empty, incoherent, and riddled with inconsistencies and contradictions.
Sagredo: Now then: if eternal motion and eternal rest are such fundamental conditions in nature, and so different that only the most different consequences can depend on them — above all when applied to the Sun and the Earth, bodies so vast and so eminent in the universe; and if, moreover, it is impossible that one of two contradictory propositions should fail to be true and the other false; and if for proofs of the false one nothing can be produced but fallacies, while the true one can be argued by every kind of conclusive and demonstrative reason — then how can you suppose that whichever of you takes up the defense of the true proposition will fail to persuade me? I would have to be dull of wit, warped in judgment, thick of mind and intellect, and blind in reasoning, not to tell light from darkness, gems from coals, the true from the false.
Simplicio: I tell you, as I have told you before: the greatest master for teaching us to recognize sophisms, paralogisms, and every other fallacy was Aristotle, who in this department can never be deceived.
Sagredo: There you go again with Aristotle, who cannot speak; and I tell you that if Aristotle were here, he would either be persuaded by us, or he would untie our arguments and persuade us with better ones. But come — when you heard the artillery experiments recited, didn't you yourself recognize them, admire them, and confess them more conclusive than Aristotle's? And yet I don't hear Salviati, who produced them and who has surely examined them and sounded them to the bottom with the utmost care, confessing himself persuaded by them — nor even by others of still greater force that he hints he is going to let us hear. And I don't know on what grounds you would scold nature, as though she had grown senile with age and forgotten how to produce speculative minds, and could turn out none anymore except the sort who make themselves Aristotle's slaves, thinking with his brain and sensing with his senses. But let us hear the rest of the arguments favorable to his opinion, so that we can then bring them to the test — refining them in the crucible and weighing them on the assayer's balance.
Salviati: Before we go any further, I have to tell Sagredo that in these discussions of ours I'm playing the Copernican — wearing him, almost, as an actor wears a mask. But as for what these arguments I seem to produce in his favor have actually worked in me, inwardly, I don't want you to judge that from my talk while we're in the heat of performing the play, but after I've taken off the costume — for you may find me a different man from the one you see on stage. Now let's move ahead. Ptolemy and his followers produce another experience, similar to the one about projectiles, drawn from the things that hang in the air a long while, detached from the Earth — the clouds, and birds on the wing. Since one can't say the clouds are carried along by the Earth, not being attached to her, it doesn't seem possible that they could keep up with her speed; rather, it ought to look to us as if they were all racing westward at tremendous velocity. And if we, carried by the Earth, run through our whole parallel in twenty-four hours — and that's at least sixteen thousand miles — how could the birds keep pace with such a course? Whereas in fact we see them fly east just as readily as west, or in any direction whatever, without the least perceptible difference. Besides that: if, when we're galloping on horseback, we feel the air strike our faces pretty briskly, what a wind we ought to feel blowing perpetually out of the east, carried as we'd be on so rapid a course against the air! And yet nothing of the kind is felt at all. Then there's another very ingenious argument, taken from a certain experience, and it goes like this. Circular motion has the power to extrude — to fling off, scatter, and drive away from its center the parts of the moving body, whenever the motion is not quite slow or the parts are not fastened together very solidly. So if, for example, we set one of those great wheels spinning at top speed — the kind inside which one or two men walk in order to move enormous weights, like the massive stones of a mangle-press, or loaded boats that get dragged overland from one waterway to another — then unless the parts of that rapidly whirling wheel were bound together more than solidly, they would all fly apart; and however tenaciously stones or other heavy stuff might be fastened to its outer surface, they couldn't withstand the impetus, which would hurl them with great violence in every direction, far from the wheel and, in consequence, from its center. If the Earth, then, were spinning with so much greater a speed — so very much greater — what weight, what tenacity of mortar or cement, would hold the rocks, the buildings, whole cities, and keep so headlong a whirl from launching them into the sky? And men and beasts, who aren't attached to the Earth at all — how would they resist so great an impetus? Whereas, on the contrary, we see them, and far feebler resistances too — little stones, sand, leaves — resting on the Earth in perfect quiet, and settling back down onto her when they fall, even with the slowest of motions. There, Simplicio, are the most powerful arguments taken, so to speak, from terrestrial things. There remain those of the other kind — the ones that concern celestial appearances — arguments which really aim more at proving that the Earth is at the center of the universe, and hence at stripping her of the annual motion around it that Copernicus assigns her. Being of somewhat different material, they can be brought out after we've weighed the strength of the ones proposed so far.
Sagredo: What do you say, Simplicio? Does it seem to you that Salviati possesses the Ptolemaic and Aristotelian arguments, and knows how to lay them out? Do you think any Peripatetic is as much a master of the Copernican demonstrations?
Simplicio: If it weren't for the high opinion I've formed, from our conversations so far, of Salviati's solid learning and Sagredo's sharpness of wit, I would — with their kind leave — take myself off without hearing another word, since it seems impossible to me that such palpable experiences can be contradicted; and I'd want to rest in my old opinion without listening further, because it seems to me that even if that opinion were false, being propped on such plausible reasons would make it excusable. And if these are fallacies, what true demonstrations were ever so beautiful?
Sagredo: All the more reason, then, that we should hear Salviati's replies. If they are true, they must be more beautiful still — infinitely more beautiful — and those arguments must be ugly, ugly in the extreme, if that metaphysical proposition holds which says the true and the beautiful are one and the same thing, as are the false and the ugly. So, Salviati, let's lose no more time.
Salviati: The first argument Simplicio produced, if I remember rightly, was this: the Earth cannot move in a circle, because such motion would be violent for her, and therefore not perpetual; and the reason it would be violent was that if it were natural, her parts would also move naturally in a circle — which is impossible, because the natural motion of the parts is straight downward. To this I answer that I'd have been glad if Aristotle had made himself a little clearer when he said "the parts would also move circularly," because this moving-in-a-circle can be understood in two ways. One is that every particle separated from its whole would move circularly around its own center, tracing out its own little circlets; the other is that as the whole globe turns around its center in twenty-four hours, the parts also circle that same center in twenty-four hours. The first would be an absurdity no smaller than saying that every part of a circle's circumference must itself be a circle, or that because the Earth is spherical, every piece of earth must be a ball — because that's what the axiom eadem est ratio totius et partium — whole and parts follow the same rule — supposedly demands. But if he meant it the other way — that the parts, imitating the whole, would naturally move around the center of the whole globe in twenty-four hours — then I say that is exactly what they do; and it will fall to you, standing in for Aristotle, to prove that they don't.
Simplicio: Aristotle proves it in that same passage, when he says that the natural motion of the parts is the straight motion toward the center of the universe, so that circular motion cannot naturally belong to them.
Salviati: But don't you see that those very words contain the refutation of this answer too?
Simplicio: How? And where?
Salviati: Doesn't he say that circular motion would be violent for the Earth, and therefore not eternal? And that this is absurd, because the order of the world is eternal?
Simplicio: He says so.
Salviati: But if what is violent cannot be eternal, then, turning it around, what cannot be eternal cannot be natural. Now the Earth's downward motion cannot possibly be eternal; therefore still less can it be natural — nor can any motion be natural to her that isn't also eternal. But if we make the Earth mobile with circular motion, that motion can be eternal for her and for her parts, and therefore natural.
Simplicio: Straight motion is supremely natural to the parts of the Earth, and it is eternal; it will never happen that they fail to move with straight motion — always understanding, of course, that impediments are removed.
Salviati: You're equivocating, Simplicio, and I want to see if I can free you from the equivocation. So tell me: do you believe that a ship sailing from the Strait of Gibraltar toward Palestine could sail toward that shore eternally, moving always at the same steady pace?
Simplicio: Certainly not.
Salviati: And why not?
Simplicio: Because that voyage is confined and bounded between the Pillars of Hercules and the coast of Palestine; and the distance being bounded, it's crossed in a finite time — unless someone chose to turn back with a contrary motion and then repeat the same trip over again; but that would be an interrupted motion, not a continuous one.
Salviati: A perfectly true answer. But the voyage from the Strait of Magellan across the Pacific, through the Moluccas, around the Cape of Good Hope, and from there through the same strait again and across the Pacific once more, and so on — do you believe that voyage could be kept up forever?
Simplicio: It could; for this being a circuit that returns into itself, by repeating it infinitely many times it could be perpetuated without any interruption.
Salviati: So on this route a ship could keep on sailing eternally.
Simplicio: It could, provided the ship were incorruptible; but with the ship falling apart, the voyage would of necessity come to an end.
Salviati: But in the Mediterranean, even if the ship were incorruptible, it still couldn't move perpetually toward Palestine, since that voyage is bounded. So two things are required for a moving body to move eternally without pause: one, that the motion be, by its own nature, unbounded and infinite; the other, that the moving body be likewise incorruptible and eternal.
Simplicio: All of that is necessary.
Salviati: Then you've already confessed, out of your own mouth, that it's impossible for any moving body to move eternally in a straight line — since straight motion, whether you take it upward or downward, is by your own account bounded by the circumference and by the center. So even if the moving body — the Earth — is eternal, still, since straight motion is not by its nature eternal but bounded through and through, it cannot naturally belong to the Earth. Indeed, as was said just yesterday, Aristotle himself is forced to make the terrestrial globe eternally stationary. And when you say that the Earth's parts will always move downward, impediments being removed, you equivocate mightily; because, on the contrary, they have to be impeded, opposed, and forced if you want them to move at all. Once they've fallen, they must be violently thrown back up in order to fall a second time. And as for impediments, these only prevent their reaching the center; for if there were a well passing clear beyond the center, even then no clod of earth would move past that point — except insofar as, carried by its impetus, it overshot it, only to come back and finally settle there. So as for maintaining that motion along a straight line belongs, or can belong, naturally either to the Earth or to any other moving body while the universe keeps its perfect order — give that up entirely, and (unless you're willing to grant her circular motion) put all your strength into maintaining and defending her immobility.
Simplicio: As for the immobility, it seems to me that Aristotle's arguments, and even more the others you've produced, establish it necessarily so far; and it will take great things, in my judgment, to refute them.
Salviati: Then let's come to the second argument, which was this: those bodies of which we're certain that they move circularly all have more than one motion — except the primum mobile, the first and outermost sphere. So if the Earth moved circularly, she would have to move with two motions, from which changes in the risings and settings of the fixed stars would have to follow; but no such thing is seen to follow; therefore, and so on. The simplest and most fitting answer to this objection lies in the argument itself; Aristotle himself puts it into our mouths — and it cannot be, Simplicio, that you haven't seen it.
Simplicio: I haven't seen it, and I still don't.
Salviati: That can't be, because it's too plainly there.
Simplicio: With your permission, I'd like to take a look at the text.
Sagredo: We'll have the text brought in this instant.
Simplicio: I always carry it in my pocket. Here it is — and I know the exact place: the second book of On the Heavens, chapter 14. Here we are, text 97: Praeterea, omnia quae feruntur latione circulari, subdeficere videntur — "Moreover, all bodies carried with circular motion are seen to lag behind, and to move with more than one motion, except the first sphere; hence the Earth too, whether she moves around the center or is placed at the center, must move with two motions. But if that happened, there would necessarily be shifts and turnings among the fixed stars — which is not seen to happen; rather, they always rise and set at the same places." Now here I see no fallacy whatever, and the argument strikes me as absolutely conclusive.
Salviati: And to me this fresh reading has confirmed the fallacy in the reasoning — and uncovered another falsehood besides. So pay attention. There are two positions, or let's say two conclusions, that Aristotle wants to attack. One belongs to those who, placing the Earth at the center, make her turn upon herself, around her own center; the other to those who, setting her far from the center, make her travel with circular motion around that center. And he attacks both of these positions jointly, with the same argument. Now I say he errs in each attack: his error against the first position is an equivocation, a paralogism, and against the second it's a false consequence. Let's come to the first position — the one that puts the Earth at the center and makes her turn upon herself around her own center — and confront it with Aristotle's objection, which runs: all movable bodies that move circularly seem to lag behind, and move with more than one motion, except the first sphere (that is, the primum mobile); therefore the Earth, moving around her own center while placed at the center, must move with two motions and must lag behind; but if that were so, the risings and settings of the fixed stars would have to vary, which is not seen to happen; therefore the Earth does not move, and so on. Here is the paralogism; and to expose it, I argue with Aristotle like this. You say, Aristotle, that the Earth placed at the center cannot move upon herself, because one would then have to assign her two motions. So if it were not necessary to assign her more than a single motion, you would not hold it impossible for her to move with that single one — since it would have been beside the point to locate the impossibility in the plurality of motions if she couldn't move even with one alone. Now of all the moving bodies in the world, you make exactly one move with a single motion, and all the rest with more than one; and you declare that this body is the first sphere — the one by which all the stars, fixed and wandering alike, appear to us to move in concert from east to west. Then if the Earth could be that first sphere, moving with a single motion that made the stars appear to move from east to west, you wouldn't deny it to her. But whoever says that the Earth, placed at the center, turns upon herself assigns her no motion other than the very one by which all the stars appear to move from east to west; and so she turns out to be that very first sphere which you yourself concede moves with a single motion. So, Aristotle, if you want to conclude anything, you must demonstrate that the Earth placed at the center cannot move even with a single motion — or else that not even the first sphere can have a single movement. Otherwise you commit the fallacy inside your own syllogism and put it on open display, denying and granting the same thing at once. I come now to the second position, that of those who, placing the Earth far from the center, make her mobile around it — who make her, that is, a planet, a wandering star. Against this position the argument does have force, and as to its form it is conclusive; but it fails in its matter. For grant that the Earth does move in that fashion, and moves with two motions: it still does not follow of necessity that changes must then occur in the risings and settings of the fixed stars, as I'll explain in its proper place. And here I'm quite willing to excuse Aristotle's error — indeed, I want to praise him for having brought forward the subtlest argument against Copernicus's position that can be brought. And if the objection is acute and, in appearance, utterly conclusive, you'll find the solution that much more subtle and ingenious — one that could not have been found by a mind less acute than Copernicus's; and from the difficulty of understanding it you may gauge the far greater difficulty of finding it in the first place. For now let's leave the answer hanging; you'll hear it at its proper place and time, after we've restated this same objection of Aristotle's and, what's more, fortified it considerably in his favor. Now let's pass to the third argument, also Aristotle's, about which there's no need to say anything further, since it was answered well enough between yesterday and today: he repeats that the motion of heavy bodies is naturally along a straight line toward the center, then inquires whether toward the center of the Earth or the center of the universe, and concludes that it is naturally toward the center of the universe, and per accidens toward that of the Earth. So we can pass to the fourth, on which we'll need to dwell a good while, because it's founded on the very experience from which most of the remaining arguments then draw their force. Aristotle says, then, that a most certain proof of the Earth's immobility is that we see projectiles shot straight up return along the same line to the same place they were fired from — and this even when the motion reaches a very great height. This could not happen if the Earth moved: for during the time the projectile is moving up and down, separated from the Earth, the place where its motion began would slide a long stretch eastward, thanks to the Earth's turning, and in falling the projectile would strike the ground that far away from the said place. Here, then, we can fit in the argument of the ball fired straight up from a cannon, and likewise the other one, used by Aristotle and by Ptolemy, of seeing heavy bodies fall from great heights along a straight line, perpendicular to the Earth's surface. Now, to begin untying these knots, I ask Simplicio: if someone denied to Ptolemy and Aristotle that heavy bodies, falling freely from a height, come down by a straight and perpendicular line — that is, one aimed at the center — by what means would they prove it?
Simplicio: By means of the senses: which assure us that that tower is straight and plumb, and show us the stone, as it falls, grazing along it without leaning a hair's breadth to one side or the other, and striking at the tower's foot exactly below the spot it was dropped from.
Salviati: But if it happened that the terrestrial globe were turning — and consequently carrying the tower along with it — and the stone in falling were still seen to graze the tower's edge, what would its motion then have to be?
Simplicio: In that case one would rather have to say "its motions": for there would be one by which it came down from top to bottom, and it would need another in order to follow the tower's course.
Salviati: Its motion, then, would be a compound of two: the one by which it measures the tower, and the other by which it follows it. And from this compound it would result that the stone no longer traces that simple straight and perpendicular line, but a slanting one — and perhaps not straight at all.
Simplicio: Whether it wouldn't be straight, I can't say; but I understand well that of necessity it would be slanting, and different from the other, straight perpendicular line it traced when the Earth stood still.
Salviati: Therefore, from merely seeing the falling stone graze the tower, you cannot affirm with certainty that it traces a straight and perpendicular line — unless you first suppose that the Earth stands still.
Simplicio: Just so; because if the Earth were moving, the stone's motion would be slanting, not perpendicular.
Salviati: There, then, is the paralogism of Aristotle and Ptolemy, plain and evident — and uncovered by you yourself: the very thing to be demonstrated is assumed as already known.
Simplicio: How so? To me it looks like a syllogism in proper form, not a begging of the question.
Salviati: Here's how. Tell me: in a demonstration, isn't the conclusion set down as unknown?
Simplicio: Unknown — otherwise demonstrating it would be superfluous.
Salviati: But the middle term — mustn't that be known?
Simplicio: Necessarily; otherwise it would be an attempt to prove ignotum per aeque ignotum — the unknown by the equally unknown.
Salviati: Our conclusion to be proved, the unknown one — isn't that the stability of the Earth?
Simplicio: It is.
Salviati: And the middle term, which has to be known — isn't that the straight and perpendicular fall of the stone?
Simplicio: That is the middle term.
Salviati: But wasn't it concluded only a moment ago that we can have no knowledge that the fall is straight and perpendicular unless we first know that the Earth stands still? So in your syllogism the certainty of the middle term is drawn from the uncertainty of the conclusion. You see, then, what the paralogism is — and how big.
Sagredo: For Simplicio's sake I'd like to defend Aristotle, if it can be done — or at least come away with a better grasp of the force of your inference. You say: seeing the stone graze the tower isn't enough to assure us that its motion is vertical — which is the middle term of the syllogism — unless one assumes the Earth stands still, which is the very conclusion to be proved; because if the tower were moving along with the Earth while the stone grazed it, the stone's motion would be slanting, not vertical. But I'll answer this way: if the tower were moving, it would be impossible for the stone to fall grazing it; and therefore from its falling along the tower one infers the stability of the Earth.
Simplicio: Just so. For the stone to come down grazing the tower while the tower was being carried along by the Earth, the stone would have to have two natural motions — the straight one toward the center and the circular one around the center — and that is impossible.
Salviati: So Aristotle's defense comes down to this: that it is impossible — or at least that he judged it impossible — for the stone to move with a motion mixed of straight and circular. For if he had not held it impossible for the stone to move toward the center and around the center at the same time, he would have understood that the falling stone could come down grazing the tower whether the tower was moving or standing still, and consequently he would have realized that from this grazing nothing whatever can be inferred about the motion or rest of the Earth. But that in no way excuses Aristotle — not only because, if he had had such a notion, he ought to have said so, it being so central a point in his argument, but even more because it cannot be said either that the effect is impossible or that Aristotle judged it impossible. The first cannot be said, because in a moment I'll show that it is not merely possible but necessary; nor can the second, because Aristotle himself grants that fire goes upward naturally in a straight line, and also moves in a circle with the daily rotation, which the heavens share with the whole element of fire and with the greater part of the air. If, then, he doesn't hold it impossible to mix the straight-upward motion with the circular one communicated to fire and air by the hollow underside of the Moon's sphere, much less should he count it impossible to mix the stone's straight-downward motion with a circular motion that was natural to the whole terrestrial globe, of which the stone is a part.
Simplicio: That doesn't look right to me. If the element of fire goes around together with the air, it is a very easy — indeed a necessary — thing that a little particle of fire, climbing up from the Earth, should receive that same movement as it passes through the moving air, being a body so thin and light and so very easily moved. But that a very heavy stone, or a cannonball dropping down from on high and already left to its own devices, should let itself be carried along by air or anything else — that is utterly unthinkable. Besides, there is that experiment so exactly to the point: the stone dropped from the top of a ship's mast, which falls at the foot of the mast while the ship stands still, but when the ship is under way falls as far from that same spot as the ship has run ahead during the time of the stone's fall — and that is no few braccia, when the ship's course is swift.
Salviati: There's a great disparity between the case of the ship and that of the Earth, if the terrestrial globe has the daily rotation. For it's perfectly obvious that the ship's motion, just as it is not natural to her, is likewise incidental to everything aboard her; so it's no wonder that the stone which was held at the masthead, once set free, comes down without any obligation to follow the ship's motion. But the daily rotation is attributed to the terrestrial globe as its own natural motion, and consequently to all its parts; and being stamped in them by nature, it is indelible in them. So the stone at the top of the tower has, as its primary instinct, the going around the center of its whole once in twenty-four hours, and this natural tendency it exercises eternally, whatever state you put it in. To be persuaded of this you need only revise one old impression stamped on your mind, and say: "Just as until now — having held it a property of the terrestrial globe to stand motionless about its center — I have never had the least difficulty or reluctance in grasping that each of its particles likewise remains naturally in that same rest, so it stands to reason that if it were the natural instinct of the terrestrial globe to go around in twenty-four hours, then every one of its parts would also have an intrinsic and natural inclination not to stand still, but to follow that same course." And so, without running into any awkwardness at all, one may conclude that since the motion conferred on the ship by the force of the oars — and through her on everything in her — is not natural but foreign, it's only right that the stone, once separated from the ship, should return to its natural state and go back to exercising its pure and simple natural tendency. Add to this that at least the part of the air that lies below the highest mountaintops must be seized and carried around by the roughness of the Earth's surface — or else, mixed as it is with so many earthly vapors and exhalations, must naturally follow the daily rotation; and none of that is true of the air around the ship driven by the oars. So arguing from the ship to the tower carries no inferential force: the stone that falls from the masthead enters a medium that does not share the ship's motion, but the one that leaves the top of the tower finds itself in a medium that has the same motion as the whole terrestrial globe — so that, far from being hindered by the air, it is rather helped by the air's motion, and can follow the universal course of the Earth.
Simplicio: I still can't see how the air could impress upon an enormous stone, or a great ball of iron or lead weighing, say, two hundred pounds, the motion with which it moves itself — a motion it may well communicate to feathers, snow, and other featherweight things. In fact I observe that a weight of that sort, exposed to the most furious wind you please, isn't shifted from its place by so much as a finger's breadth. Now imagine whether the air will carry it along.
Salviati: There's a great disparity between your experience and our case. You have the wind come upon a stone at rest; we are placing into air that is already moving a stone that is moving too, and at the same speed — so the air doesn't have to confer any new motion on it, but only maintain, or rather not impede, the motion it has already received. You want to drive the stone with a motion foreign to it and outside its nature; we want to conserve it in its natural one. If you wanted to produce a better-fitted experiment, you should have said: let someone observe, if not with the eye in his forehead then at least with the mind's eye, what would happen if an eagle, carried on the rush of the wind, let a stone drop from its talons. Since that stone was already flying with the wind when it left the claws, and after leaving them enters a medium moving at the same speed, I strongly suspect it would not be seen to drop straight down, but rather, following the wind's course and adding to it the pull of its own weight, would move on a slant.
Simplicio: One would have to be able actually to perform such an experiment, and then judge by the outcome. Meanwhile the result on the ship has, so far, come out applauding our opinion.
Salviati: "So far" — well said; for perhaps in a moment things will change their look. And so as not to keep you dangling any longer, as they say, tell me, Simplicio: do you honestly feel that the ship experiment fits our purpose so well that we may reasonably believe that whatever is seen to happen on the ship must also happen on the terrestrial globe?
Simplicio: So far, yes; and though you've brought up a few small discrepancies, they don't seem to me weighty enough to shake my opinion.
Salviati: On the contrary, I want you to keep holding it — to hold firm that the effect on the Earth must answer to the one on the ship — provided that, when that turns out to damage your case, you don't take a fancy to change your mind. You say: "Since, when the ship stands still, the stone falls at the foot of the mast, and when she is under way it falls far from the foot, then conversely, from the stone's falling at the foot one infers that the ship stands still, and from its falling far away one argues that the ship is moving; and since what holds for the ship must equally hold for the Earth, from the stone's falling at the foot of the tower one infers of necessity the immobility of the terrestrial globe." Isn't that your argument?
Simplicio: That's it exactly, boiled down to a brevity that makes it very easy to grasp.
Salviati: Now tell me: if the stone dropped from the masthead while the ship was running at great speed were to fall in precisely the same spot on the ship where it falls when she stands still, what service would those falls render you toward determining whether the vessel is standing still or under way?
Simplicio: Absolutely none — just as from the beating of the pulse, for instance, you can't tell whether someone is asleep or awake, since the pulse beats the same way in sleepers as in the waking.
Salviati: Very good. Now, have you ever performed the ship experiment?
Simplicio: I haven't; but I well believe that the authors who cite it have observed it carefully. Besides, the cause of the disparity is so plainly understood that it leaves no room for doubt.
Salviati: That those authors may cite it without ever having performed it, you yourself are a fine witness: without having performed it, you offer it as certain and take it on good faith at their word — just as it is not only possible but necessary that they did the same, I mean relied on their own predecessors, without anyone ever reaching back to someone who had actually done it. For whoever does perform it will find that the experiment shows the exact opposite of what is written: it will show that the stone always falls in the same place on the ship, whether she stands still or moves at any speed you please. And since the same reasoning holds for the Earth as for the ship, from the stone's falling always plumb at the foot of the tower nothing can be inferred about the motion or rest of the Earth.
Simplicio: If you refer me to any means other than experience, I truly believe our disputes won't be finished in a hurry; for this strikes me as a thing so remote from all human reasoning that it leaves not the smallest room for belief or even probability.
Salviati: And yet it has found room in me.
Simplicio: So you haven't made a hundred trials of it — no, not even one — and yet you assert it so freely as certain? I go straight back to my incredulity, and to my conviction that the experiment was performed by the principal authors who make use of it, and that it shows what they affirm.
Salviati: Even without the experiment I am certain the effect will follow as I tell you, because it must follow; and I'll add further that you yourself already know it cannot follow otherwise — however much you feign, or pretend to feign, not to know it. But I'm a good enough breaker-in of minds that I'll wring the confession out of you by sheer force. — But Sagredo sits there very quiet; I thought I saw you stir just now, as if to say something.
Sagredo: I did in fact mean to say something or other; but the curiosity stirred in me by hearing you threaten such violence against Simplicio — forcing him to disclose the knowledge he wants to keep hidden from us — has driven out every other wish. So I beg you to make good the boast.
Salviati: Provided Simplicio is willing to answer my questions, I won't fail to.
Simplicio: I'll answer what I know, confident it will give me little trouble; for about the things I hold to be false, I don't believe I can know anything at all — since knowledge is of truths, not of falsehoods.
Salviati: I don't want you to say or answer anything except what you know for certain. So tell me: suppose you had a flat surface, polished like a mirror and made of a material hard as steel, and not parallel to the horizon but somewhat tilted; and suppose that on it you set a perfectly spherical ball of some heavy, very hard material — bronze, say. Left to itself, what do you think it would do? Don't you believe — as I do — that it would stay still?
Simplicio: If that surface were tilted?
Salviati: Yes — that's what I supposed.
Simplicio: I don't believe it would stay put at all; on the contrary, I'm certain it would move down the slope of its own accord.
Salviati: Careful what you say, Simplicio, because I'm certain it would stay still wherever you set it down.
Simplicio: As long as you help yourself to suppositions of that sort, Salviati, I'll stop being surprised that you arrive at utterly false conclusions.
Salviati: So you're absolutely sure it would move down the slope of its own accord?
Simplicio: What doubt is there?
Salviati: And you hold this firmly not because I taught it to you — I was trying to persuade you of the opposite — but by yourself, by your own natural judgment.
Simplicio: Now I see your game: you said that to test me — to trip me up, as the common phrase has it — not because you really believed it.
Salviati: Just so. And how long would that ball keep moving, and how fast? Bear in mind that I specified a perfectly round ball and an exquisitely polished plane, precisely to remove all external and accidental impediments. In the same way, I want you to set aside the impediment of the air — its resistance to being parted — and any other incidental obstacles there might be.
Simplicio: I've understood the whole thing perfectly well. To your question I answer that it would continue moving indefinitely, as long as the slope of the plane lasted, and with a continually accelerating motion — for such is the nature of heavy moving bodies, that vires acquirant eundo, they gather strength as they go. And the steeper the slope, the greater the speed.
Salviati: But if someone wanted the ball to move upward along that same surface, do you think it would go?
Simplicio: Of its own accord, no; but dragged up, or hurled up by force, yes.
Salviati: And if it were driven by some impetus violently impressed on it, what sort of motion would it have, and how great?
Simplicio: The motion would keep languishing and slowing, being against nature, and it would last a longer or shorter time according to the greater or lesser impulse and the greater or lesser steepness of the climb.
Salviati: So far, then, you've explained to me how a moving body behaves on two different planes: on the downward slope the heavy body descends of its own accord, continually gaining speed, and force is needed to hold it at rest; on the upward slope force is needed to push it, and even to stop it, and the motion impressed on it keeps dwindling until at last it dies away entirely. You say further that in both cases a difference arises from the slope being steeper or gentler, so that a steeper descent brings greater speed, while conversely, on a rising plane, the same body driven by the same force travels a greater distance the smaller the elevation. Now tell me: what would happen to that same body on a surface that sloped neither up nor down?
Simplicio: Here I need to think a moment about my answer. With no downward slope there can be no natural inclination to motion, and with no upward slope there can be no resistance to being moved; so the body would stand indifferent between propensity and resistance to motion. It seems to me, then, that it ought naturally to stay put. But I'm being forgetful — it wasn't long ago that Sagredo gave me to understand that this is what would happen.
Salviati: So I believe, provided someone set it down at rest. But if it were given an impetus toward some direction, what would follow?
Simplicio: It would follow that it moves in that direction.
Salviati: But with what sort of motion? Continually accelerated, as on the downward slope, or progressively retarded, as on the upward one?
Simplicio: I can see no cause for acceleration or for retardation, there being neither descent nor climb.
Salviati: Right. But if there is no cause for retardation, still less should there be any for coming to rest. How long, then, would you have the body keep moving?
Simplicio: As long as the length of that surface — neither rising nor falling — lasted.
Salviati: Then if such a space were unbounded, the motion in it would likewise be without bound — that is, perpetual?
Simplicio: It seems so to me, provided the body were of material durable enough to last.
Salviati: That has already been assumed, since we said that all accidental and external impediments were to be removed — and the brittleness of the moving body is, in this business, one of the accidental impediments. Now tell me: what do you take to be the cause of that ball's moving of its own accord on the downward slope, and only under violence on the rising one?
Simplicio: Because the inclination of heavy bodies is to move toward the center of the Earth, and only by violence upward toward the circumference; and the sloping surface is the one that gains nearness to the center, while the rising one leads away from it.
Salviati: Then a surface that was to be neither downhill nor uphill would have to be, in all its parts, equally distant from the center. Is there any such surface anywhere in the world?
Simplicio: There's no lack of them: there is the surface of our terrestrial globe, if only it were quite smooth, and not, as it actually is, rough and mountainous; and there is the surface of the water, when it lies placid and tranquil.
Salviati: Then a ship moving across a calm sea is one of those bodies running along a surface that is neither downhill nor uphill, and is therefore disposed — if every accidental and external obstacle were removed — to move, with the impulse once received, incessantly and uniformly.
Simplicio: It seems it must be so.
Salviati: And the stone at the top of the mast — doesn't it too move, carried by the ship, along the circumference of a circle about the center, and consequently with a motion that is indelible in it, once the external impediments are removed? And isn't this motion as fast as the ship's?
Simplicio: So far everything runs smoothly. But the rest?
Salviati: Then draw the final consequence yourself, and welcome — if by yourself you've known all the premises.
Simplicio: You mean, as the final conclusion, that the stone, moving with a motion indelibly impressed on it, is not about to abandon the ship but to follow her, and in the end to fall in the very same place where it falls when the ship stands still. And I too say this would follow, if there were no external impediments to disturb the stone's motion once it is set free. But there are two such impediments: one is that the moving body is powerless to cleave the air by its own impetus alone, once it has lost the impetus of the oars' force, which it shared in, as a part of the ship, while it was up on the mast; the other is the new motion of falling downward, which must surely be an impediment to the forward one.
Salviati: As for the impediment of the air, I don't deny it to you; and if the falling body were of light material — a feather, or a tuft of wool — the retardation would be very great; but in a heavy stone it is very small indeed. You yourself said a moment ago that the force of the most furious wind doesn't suffice to budge a big stone from its place; now imagine what the still air will do when met by a stone moving no faster than the whole ship. Nevertheless, as I said, I concede you this small effect that may depend on such an impediment — just as I know you will concede to me that if the air were moving at the same speed as the ship and the stone, the impediment would be absolutely nil. As for the other point, the supervening downward motion: first of all, it is obvious that these two motions — the circular around the center and the straight toward the center — are not contraries, are not destructive of one another, are not incompatible; for on the side of the moving body there is no repugnance at all to such motion. You yourself have already granted that its repugnance is against the motion that carries it away from the center, and its inclination is toward the motion that brings it nearer the center; from which it follows necessarily that toward a motion which neither approaches nor recedes from the center, the body has neither repugnance nor propensity — nor, in consequence, any cause for the faculty impressed on it to be diminished. And since the moving cause is not a single one, which might be weakened by the new operation, but two distinct ones — of which gravity attends solely to drawing the body toward the center, while the impressed force attends to carrying it around the center — there remains no occasion whatever for impediment.
Simplicio: The argument really is quite plausible on the surface, but at its core it's troubled by a snag that's not so easy to get past. Through the whole course of it you've made an assumption that the Peripatetic school will not grant you lightly, since it flatly contradicts Aristotle: namely, taking it as obvious and well established that the projectile, once separated from the thrower, continues its motion by a force impressed on it by that same thrower. Now this impressed force is as odious to Peripatetic philosophy as the passage of any accident from one subject into another; in that philosophy the position is — as I believe you know — that the projectile is carried by the medium, which in our case is the air. So if that stone released from the top of the mast were to follow the ship's motion, the effect would have to be attributed to the air, not to any force impressed on it; but you assume the air does not follow the ship's motion, and is calm. What's more, the man who lets it fall is not supposed to hurl it or give it impetus with his arm — he simply opens his hand and releases it. And so the stone can follow the ship's motion neither by a force impressed on it by the thrower nor by any courtesy of the air; and therefore it will be left behind.
Salviati: What I seem to gather from your speech, then, is that since the stone isn't driven out by the man's arm, it doesn't count as a projection at all.
Simplicio: Properly speaking, it cannot be called projectile motion.
Salviati: Then what Aristotle says about the motion, the moving body, and the mover of projectiles has nothing to do with our question; and if it has nothing to do with it, why do you bring it up?
Simplicio: I bring it up for the sake of that impressed force you named and introduced — which, since it doesn't exist in the world, can accomplish nothing, for non entium nullae sunt operationes — what doesn't exist can't act. And therefore the moving cause not only of projectile motion, but of every other motion that isn't natural, must be attributed to the medium, which hasn't been given its due consideration; and so everything said up to now stands ineffective.
Salviati: Fine — all in good time. But tell me: since your objection rests entirely on the nonexistence of the impressed force, if I demonstrate to you that the medium has nothing to do with continuing the motion of projectiles once they've separated from the thrower, will you let the impressed force stand — or will you mount some fresh assault to destroy it?
Simplicio: Once the action of the medium is removed, I don't see what one could fall back on other than the faculty impressed by the mover.
Salviati: Then it will be well, to cut off as far as possible any endless back-and-forth of objections, for you to explain as distinctly as you can just what the medium's operation is in keeping the projectile in motion.
Simplicio: The thrower has the stone in his hand; he moves his arm with speed and force, and with that motion he moves not just the stone but the surrounding air as well; so the stone, at the moment the hand abandons it, finds itself in air that is already moving with impetus, and it is carried along by that air. If the air weren't doing the work, the stone would drop from the hand to the thrower's feet.
Salviati: And you've been so credulous as to let yourself be talked into these absurdities, when you had your own senses right there to refute them and to learn the truth? Tell me, then: that great stone, and that artillery ball, which merely resting on a table stayed immovable against any wind however fierce, as you affirmed a little while ago — if it had been a ball of cork, or the same bulk of cotton wool, do you think the wind would have shifted it?
Simplicio: On the contrary, I know for certain the wind would have carried it clean away — and the faster, the lighter the material. That's exactly why we see the clouds borne along at a speed equal to that of the very wind that drives them.
Salviati: And what is wind?
Simplicio: Wind is defined as nothing other than moving air.
Salviati: So moving air carries the lightest materials much faster and much farther than the heaviest ones?
Simplicio: Certainly.
Salviati: But if you had to throw with your arm first a stone and then a wisp of cotton, which would move faster and farther?
Simplicio: The stone, by a wide margin — the cotton would just drop at my feet.
Salviati: Well then: if what moves the projectile, after the hand releases it, is nothing but the air set moving by the arm, and moving air pushes light materials more easily than heavy ones, how is it that the cotton projectile doesn't fly farther and faster than the stone one? Something must remain in the stone besides the motion of the air. And furthermore: suppose two strings of equal length hung from that beam, with a lead ball tied to the end of one and a cotton ball to the end of the other; draw both aside equally far from the vertical, and then set them free. No doubt both will swing toward the vertical and, driven by their own impetus, will pass beyond it a certain distance and then return. But which of these two pendulums do you think will keep moving longer before it comes to rest hanging plumb?
Simplicio: The lead ball will swing back and forth a thousand times; the cotton one, two or three at most.
Salviati: So that impetus and that mobility, whatever their cause may be, are conserved longer in heavy materials than in light ones. Now I come to another point, and I ask you: why doesn't the air carry off that citron sitting on the table right now?
Simplicio: Because the air itself isn't moving.
Salviati: Then the thrower must confer the motion on the air, and the air must then use it to move the projectile. But if such a force cannot be impressed — since an accident cannot be made to pass from one subject into another — how does it pass from the arm into the air? Isn't the air a subject distinct from the arm?
Simplicio: The answer given is that the air, being neither heavy nor light in its own region, is disposed to receive every impulse with the greatest ease, and to conserve it as well.
Salviati: But the pendulums have just now shown us that the less heaviness a moving body partakes of, the less fit it is to conserve motion. How then can it be that the air, which in air has no heaviness at all, is the one thing that conserves the motion it has received? I believe — and I know that by now you believe it too — that the arm is no sooner stopped than the air around it stops as well. Let's go into a room and stir the air as hard as we can with a towel; then, the cloth held still, let a small lighted candle be brought into the room, or let a leaf of gold foil be set drifting loose in it: from the quiet wandering of either one you'll see that the air has been brought back to calm immediately. I could bring you a thousand experiments, but if one of these weren't enough, the case had better be given up as altogether hopeless.
Sagredo: When an arrow is shot against the wind, what an incredible thing it is that the little thread of air pushed by the bowstring should travel along with the arrow in defiance of the gale! But there's another particular point I'd like to learn from Aristotle, and I beg Simplicio to favor me with an answer. Suppose two arrows were shot from the same bow, one point-first in the usual way and the other sideways — that is, laid lengthwise along the string and shot in that flat position: I'd like to know which of them would go farther. Do me the kindness of an answer, even though the question may strike you as more ridiculous than not; and forgive me, because I — being, as you can see, rather on the thick side — can't reach any higher with my speculating.
Simplicio: I've never seen arrows shot sideways; still, I believe that shot crosswise one wouldn't go even a twentieth of the distance it goes point-first.
Sagredo: And since I've believed the very same thing, that's what gave me occasion to raise a doubt between Aristotle's pronouncement and experience. Because as far as experience goes, if I set two arrows on that table when a strong wind is blowing — one laid along the line of the wind, the other crosswise to it — the wind will quickly carry off the crosswise one and leave the other lying there. And the same thing, it seems, ought to happen with the two shot from the bow, if Aristotle's doctrine were true: for the crosswise arrow would be driven by a great quantity of air set moving by the string — as much air, that is, as the arrow's whole length — whereas the other arrow receives its push from no more air than the tiny little circle of its thickness. And I can't imagine the cause of such a difference, and I'd dearly like to know it.
Simplicio: The cause seems obvious enough to me: it's because the arrow shot point-first has only a small quantity of air to penetrate, while the other has to cleave as much air as its whole length.
Sagredo: So arrows, when shot, have to penetrate the air? But if the air goes along with them — indeed, if the air is what carries them — what penetration can there be? Don't you see that on this account the arrow would have to be moving faster than the air? And who confers this greater speed on the arrow? Will you say the air gives it a speed greater than its own? Understand, then, Simplicio, that the business works exactly backwards from what Aristotle says: it is as false that the medium confers motion on the projectile as it is true that the medium is the one thing that hinders it. And once you've grasped that, you'll understand without any difficulty that when the air really is moving, it carries the arrow along much better crosswise than straight on, because there's a great deal of air pushing it in that posture and very little in the other; but when the shots come from the bow, since the air is standing still, the crosswise arrow, striking against a great deal of air, is greatly impeded, while the point-first one overcomes with the greatest ease the obstacle of the tiny quantity of air that opposes it.
Salviati: How many propositions I've noted in Aristotle — I mean always in natural philosophy — that are not merely false, but false in such a way that their diametrical opposite is true, as happens with this one! But to keep to our purpose: I believe Simplicio is now persuaded that from seeing the stone always fall in the same place, nothing can be inferred about the ship's motion or its stillness. And if everything said so far weren't enough for him, there is the experiment ready at hand, which can settle the matter for him completely: in that experiment, the most he could ever see would be the falling body left behind if it were made of very light material and the air did not follow the ship's motion; but where the air moves with equal speed, no imaginable difference would be found in this or in any other experiment whatsoever, as I'm shortly going to tell you. Now if, in this case, no difference at all shows itself, what could anyone claim to see in the stone falling from the top of the tower — where the circular motion is not adventitious and accidental to the stone but natural and eternal, and where the air follows the tower's motion exactly, and the tower follows that of the terrestrial globe? Have you anything further to say, Simplicio, on this particular point?
Simplicio: Nothing further — except that so far I don't see the Earth's mobility proved.
Salviati: Nor have I claimed to prove it. My only claim was to show that nothing can be extracted from the experiment our adversaries put forward as an argument for the Earth's being fixed — just as I believe I'll show of the other arguments.
Sagredo: Please, Salviati, before you pass on to anything else, allow me to bring up a certain difficulty that's been turning round in my imagination while you were so patiently grinding this ship experiment down fine for Simplicio.
Salviati: We're here to discuss, and it's good for each of us to raise the difficulties that occur to him — that's the road to knowledge of the truth. So speak.
Sagredo: If it's true that the impetus with which the ship moves remains indelibly impressed in the stone after it has separated from the mast, and if it's furthermore true that this motion brings no hindrance or slowing to the straight downward motion natural to the stone, then a marvelous effect must follow in nature. Let the ship stand still, and let the fall of a stone from the top of the mast take two beats of the pulse. Then let the ship be under way, and let the same stone be dropped from the same place: by what we've said, it will still take the time of two pulse-beats to arrive at the bottom, and in that time the ship will have run, say, twenty braccia — so that the stone's true motion will have been a slanting line, considerably longer than the first straight and vertical one, which is simply the length of the mast; and yet the ball will have traversed it in the same time. Suppose next that the ship's motion is speeded up considerably more, so that the falling stone must pass along a slanting line even longer than the last; and in short, however much you increase the ship's speed, the falling stone will trace out slanting paths longer and longer still, and yet will traverse every one of them in those same two pulse-beats. On the same pattern: if a culverin — a long cannon — were mounted level at the top of a tower and fired point-blank, that is, parallel to the horizon, then whatever charge, small or large, were given the piece, so that the ball fell to earth now a thousand braccia away, now four thousand, now six thousand, now ten thousand, and so on, all these shots would be completed in times equal to one another, and each equal to the time the ball would take to go from the muzzle of the piece to the ground if it were simply allowed to fall straight down, with no other impulse. Now it seems a marvelous thing that in the same short time of a plumb fall to the ground from a height of, say, a hundred braccia, the same ball, driven out by the powder, can pass through now four hundred, now a thousand, now four thousand, now ten thousand braccia — so that in all point-blank shots the ball stays in the air for equal times.
Salviati: The observation is beautiful for its novelty, and if the effect is real, it is marvelous — and of its truth I have no doubt. Setting aside the accidental impediment of the air, I hold it for certain that if, at the instant the ball left the gun, another ball were let fall straight down from the same height, both would reach the ground at the same instant, even though one had traveled ten thousand braccia of distance and the other only a hundred — assuming, that is, that the surface of the Earth were level; and to be safe, the shot could be fired over some lake. The impediment that might come from the air would consist in slowing down the extremely rapid motion of the shot. Now, if you please, let's come to the solutions of the other arguments, since Simplicio is — as far as I can judge — well satisfied of the nullity of this first one, drawn from bodies falling from high to low.
Simplicio: I don't feel all my scruples removed; but perhaps the fault is mine, for not being as quick and nimble of understanding as Sagredo. And it seems to me that if this motion the stone shared in while it was on the ship's mast were, as you say, conserved in it indelibly even after it has separated from the ship, then it should likewise follow that when someone riding a galloping horse lets a ball drop from his hand, that ball, having landed, would continue its motion and follow the horse's course without falling behind. And I don't believe that effect is ever seen — except when the rider throws the ball forcefully in the direction of his run; short of that, I believe it will stay on the ground right where it strikes.
Salviati: I believe you're very much mistaken, and I'm sure experience will show you the contrary: the ball, once it has reached the ground, will run along with the horse, and won't fall behind it except insofar as the roughness and unevenness of the road hinders it. And the reason seems clear enough to me. For if you, standing still, threw that same ball along the ground, wouldn't it continue its motion even after leaving your hand — and for a longer stretch, the smoother the surface, so that on ice, for instance, it would travel a very long way?
Simplicio: No doubt of that, so long as I give it impetus with my arm; but in the other case, we're assuming the man on the horse merely lets it drop.
Salviati: That's exactly what I want to happen. When you throw it with your arm, what remains with the ball, once it has left your hand, except the motion received from your arm — which, conserved in it, keeps carrying it forward? And what does it matter whether that impetus is conferred on the ball by your arm or by the horse? While you're on horseback, doesn't your hand — and consequently the ball — travel as fast as the horse itself? Certainly it does. So at the mere opening of your hand, the ball departs with the motion it has already received — not from your arm by any private motion of your own, but from the motion that depends on the horse itself, which is communicated to you, to your arm, to your hand, and finally to the ball. And I'll tell you more: if the rider, at a run, throws the ball with his arm in the direction opposite to his course, then once it reaches the ground it will sometimes follow the horse's course all the same, despite having been hurled the other way; and sometimes it will lie still on the ground; and it will move against the direction of the run only when the motion received from the arm exceeds the speed of the gallop. And it's nonsense, what some people say — that a horseman can launch a javelin through the air in the direction of his run, then follow it with the horse, catch up to it, and finally take hold of it again. Nonsense, I say, because to have the projectile come back into your hand you must throw it straight up, exactly as if you were standing still; for however fast the run may be, provided it's uniform and the projectile isn't something extremely light, it will always fall back into the thrower's hand, no matter how high it's thrown.
Sagredo: From this doctrine I come to see some quite curious problems in the matter of these projectiles — the first of which is bound to strike Simplicio as very strange. The problem is this: I say it's possible that a ball simply dropped by someone running fast, in whatever manner, once it has reached the ground, will not only follow his course but get well out ahead of him. And that problem is connected to this one: that a body launched by a thrower over the horizontal plane can acquire new speed, considerably greater than what the thrower gave it. I've often watched this effect with astonishment while standing to see people playing at ruzzole — hurling those wooden discs. Once out of the hand, you see the discs going through the air at a certain speed, which then increases considerably when they reach the ground; and if in rolling they strike some obstacle that bounces them up into the air, you see them move through the air quite slowly, and on falling back to earth they move again with greater speed. But what's stranger still, I've also observed not only that they always go faster along the ground than through the air, but that of two stretches both covered along the ground, the motion in the second stretch is sometimes faster than in the first. Now what would Simplicio say to that?
Simplicio: I'd say, first of all, that I've never made any such observation; second, I'd say I don't believe it; and then I'd say, in the third place, that if you convinced me of it and taught it to me demonstratively, you'd be a great demon.
Sagredo: One of Socrates' demons, though — not one of Hell's. But there you go again with this "teaching." I tell you that when a man doesn't know a truth on his own, it's impossible for anyone else to make him know it. I can certainly teach you things that are neither true nor false; but the true ones — that is, the necessary ones, the ones that cannot possibly be otherwise — every mind of ordinary discourse either knows on its own, or can never know at all. And I know Salviati believes the same. And so I tell you that the reasons behind these present problems are known to you — you just may not have noticed them.
Simplicio: Let's set this dispute aside for now, and just let me admit that I don't understand, and don't know, these matters you're discussing — so please, see if you can make me grasp the problems.
Sagredo: This first problem depends on another — namely, why it is that when you throw the ruzzola with a string, it goes much farther, and so with greater force, than when you throw it with your bare hand.
Simplicio: Aristotle too raises some problems or other about these projectiles.
Salviati: Yes, and very ingenious ones — in particular the problem of why round ruzzole travel better than square ones.
Sagredo: And this one, Simplicio — don't you feel up to working out the reason on your own, without anyone teaching you?
Simplicio: All right, all right — but enough of the teasing.
Sagredo: Then you already know the reason for this other one too. So tell me: you know that a thing in motion, when it's obstructed, stops?
Simplicio: I know it — provided the obstruction is enough to do it.
Sagredo: And you know that a moving body meets greater obstruction having to move along the ground than through the air, the ground being rough and hard, the air soft and yielding?
Simplicio: And because I know this, I know the ruzzola will go faster through the air than along the ground — so what I know is the exact opposite of what you were expecting.
Sagredo: Not so fast, Simplicio. Do you know that in the parts of a body spinning about its center, you find motions in every direction — so that some rise, some fall, some go forward, some backward?
Simplicio: I know it — Aristotle taught me that.
Sagredo: And by what demonstration? Do tell me, please.
Simplicio: By the one from the senses.
Sagredo: So Aristotle made you see what you wouldn't have seen without him? Did he ever lend you his eyes? You meant to say Aristotle had told you, pointed it out, reminded you — not taught you. So then: when a ruzzola, without changing place, spins on itself — not lying flat, but standing upright to the horizon — some of its parts rise and the opposite parts fall; the upper parts go one way, the lower the contrary way. Now picture a ruzzola that, without changing place, spins fast on itself while hanging suspended in the air; and while spinning that way, it's let drop straight down to the ground. Do you think that, once it reaches the ground, it will go on spinning in place, as before?
Simplicio: No, it won't.
Sagredo: But what will it do?
Simplicio: It'll run fast along the ground.
Sagredo: And in which direction?
Simplicio: Toward wherever its spin carries it.
Sagredo: But in its spin there are parts — the upper ones — that move contrary to the lower ones; so you have to say which it will obey. As for the rising and falling parts, neither will yield to the other, and the whole won't go down — the ground blocks it — nor up, since it's heavy.
Simplicio: The ruzzola will go rolling along the ground toward wherever its upper parts are heading.
Sagredo: And why not toward where the contrary parts head — the ones touching the ground?
Simplicio: Because the parts at the ground are held back by the roughness of the contact — by the very unevenness of the ground; but the upper parts, in the thin, yielding air, are held back very little or not at all, so the ruzzola will go their way.
Sagredo: So that gripping, so to speak, of the lower parts against the ground keeps them back, and only the upper parts drive forward.
Salviati: And so, if the ruzzola fell on ice or some other very smooth surface, it wouldn't slide forward so well, but might perhaps go on spinning in place without gaining any forward motion.
Sagredo: That could easily happen; at least it wouldn't go rolling along so briskly as when it falls on a somewhat rough surface. But tell me, Simplicio: when the ruzzola, spinning fast on itself, is let fall, why doesn't it move forward through the air too, the way it does once it's on the ground?
Simplicio: Because, with air above and below, neither those parts nor these have anything to grip; and having no reason to go forward rather than back, it falls straight down.
Sagredo: So the spin by itself, without any other impetus, can drive the ruzzola quite fast once it reaches the ground. Now let's get to the rest. That string the thrower ties to his arm, and with which — wound around the ruzzola — he throws it: what effect does it have on it?
Simplicio: It forces it to spin on itself, as it unwinds from the cord.
Sagredo: So when the ruzzola reaches the ground, it arrives already spinning on itself, thanks to the string. Doesn't it then have within itself a cause to move faster along the ground than it did while in the air?
Simplicio: Certainly yes: because in the air it had no impulse but that of the thrower's arm, and though it also had the spin, that — as we said — drives nothing in the air; but on reaching the ground, to the arm's motion is added the forward push of the spin, so the speed doubles. And now I understand perfectly that when the ruzzola bounces up, its speed will drop, because it loses the help of the spinning; and on falling back to the ground it recovers that help, and so goes back to moving faster than in the air. The only thing left for me to grasp is that in this second stretch along the ground it moves faster than in the first — because at that rate it would move forever, always speeding up.
Sagredo: I didn't say flatly that this second stretch is faster than the first, only that it can sometimes happen to be faster.
Simplicio: That's the very thing I don't understand and would like to.
Sagredo: This too you know for yourself. So tell me: if you let the ruzzola drop from your hand without its spinning at all, what would it do on striking the ground?
Simplicio: Nothing — it would just stay put there.
Sagredo: Couldn't it happen that, in striking the ground, it gained some motion? Think it over more carefully.
Simplicio: Unless we let it fall on some stone that had a slope — the way children do in their games — and by striking slantwise on the sloping stone it gained a spinning motion of its own, with which it then kept moving forward along the ground, I wouldn't know any other way it could do anything but stop where it struck.
Sagredo: There — so in some fashion it can gain fresh spin. So when the ruzzola, having bounced up, falls back down, why couldn't it happen to strike the slant of some stone set in the ground and sloped toward the direction of the motion, and — gaining fresh spin from that blow, on top of the first spin from the string — double its motion and make it faster than it was on its first strike against the ground?
Simplicio: Now I see that this could easily happen. And I'm realizing that if the ruzzola were made to spin the opposite way, then on reaching the ground it would produce the opposite effect — that is, the motion of the spin would slow the thrower's.
Sagredo: And it would slow it, and sometimes stop it entirely, when the spin was fast enough. And this is the source of the trick the more expert tennis players use to their advantage — deceiving their opponent by slicing the ball (that's their word for it), that is, returning it with the racquet held at a slant, so that the ball takes on a spin contrary to its projected motion. From which it follows that, on reaching the ground, the bounce — which, if the ball weren't spinning, would carry toward the opponent and give him his usual time to return it — is left as if dead: the ball squashes against the ground, or bounces far less than usual, and breaks the timing of the return. For the same reason you'll see players of wooden bowls, competing to land closest to a set mark, do this: when they play on a stony road full of bumps that would knock the ball off course a thousand ways and keep it from the mark, then, to dodge all those obstacles, they toss the ball not rolling along the ground but straight through the air, as if throwing a flat quoit. But since, in throwing, the ball leaves the hand with some spin imparted by the fingers — whenever the hand is held under the ball, as it usually is — the ball, on striking the ground near the mark, would run far off, carried by the thrower's motion and the spin together. So to make it stop, they cunningly grip the ball with the hand above and the ball below, so that as it escapes, the fingers give it the opposite spin, by which, on striking the ground near the mark, it stops there or runs only a little farther. But to return to the main problem, which was the cause of raising all these others: I say it's possible for someone moving very fast to let a ball leave his hand which, once on the ground, not only keeps up with his motion but even outruns it, moving faster than he does. And to see such an effect, let the moving thing be a cart, to whose outer side is fixed a sloping board, so that its lower end faces the horses and its upper end the rear wheels. Now, at the cart's fastest, if someone inside lets a ball drop down the slope of that board, in coming down it will roll and gain a spin of its own, which — added to the motion impressed by the cart — will carry the ball along the ground much faster than the cart. And if you fitted another sloping board the opposite way, you could tune the cart's motion so that the ball, after running down the board, on reaching the ground would stay still, or even sometimes run backward, against the cart. But we've strayed too long from our subject; and if Simplicio is satisfied with the solution of the first argument against the Earth's mobility — the one drawn from bodies falling straight down — we can move on to the others.
Salviati: The digressions we've made so far aren't so foreign to the subject we're treating that they can be called wholly separate from it. Besides, our reasonings depend on whatever things get stirred up in the imagination — and not one imagination, but three; and, on top of that, we're talking for our own pleasure, and aren't bound by the strictness of someone who ex professo — as a formal undertaking — sets out to treat a subject methodically, meaning also to publish it. I don't want our poem so tied to that unity that it leaves us no open field for episodes; to bring one in, the slightest connection should be enough — as if we'd gathered to swap tales, where I'm free to tell whatever story hearing yours happens to call to mind.
Sagredo: This pleases me greatly; and since we're allowing ourselves this latitude, let me — before we go any further — ask you, Salviati, whether it's ever crossed your mind what one might take to be the line traced by a heavy body falling naturally from the top of a tower to the bottom. If you've reflected on it, do tell me your thought.
Salviati: I've thought about it now and then; and I've no doubt that if one were sure of the nature of the motion by which a heavy body descends to reach the center of the terrestrial globe, and then combined it with the common circular motion of the daily rotation, one would find exactly what sort of line is traced by the body's center of gravity out of the composition of those two motions.
Sagredo: As for the simple motion toward the center, due to gravity, I think one may believe, quite without error, that it's along a straight line — exactly as it would be if the Earth were motionless.
Salviati: On that point we not only may believe it — experience makes us certain of it.
Sagredo: But how does experience assure us of it, if we never see any motion but the compound of the two, circular and downward?
Salviati: On the contrary, Sagredo — we see nothing but the simple downward motion, since the other, the circular one shared by the Earth, the tower, and us, stays imperceptible and as if it didn't exist; the only motion left noticeable to us is the stone's, which we don't share. And of that one, the senses show it to be along a straight line, since it comes down always parallel to the tower itself, which stands built straight up and perpendicular on the Earth's surface.
Sagredo: You're right — and I've shown myself far too dull, not to have hit on something so easy. But since this is perfectly well known, what else do you say we need in order to understand the nature of this downward motion?
Salviati: It's not enough to know that it's straight; we need to know whether it's uniform or non-uniform — that is, whether it keeps always the same speed, or goes on slowing down or speeding up.
Sagredo: It's already clear that it keeps continually speeding up.
Salviati: Nor is that enough; we'd need to know by what proportion this acceleration takes place — a problem that so far, I don't think, has been solved by any philosopher or mathematician, even though whole and enormous volumes have been written on motion by philosophers, and by the Peripatetics in particular.
Simplicio: Philosophers concern themselves chiefly with universals; they find the definitions and the most common properties, then leave certain subtleties and trifling details — which are really more curiosities — to the mathematicians. Aristotle was content to define excellently what motion is in general, and, for local motion, to show its principal attributes: that one kind is natural, another violent; one simple, another compound; one uniform, another accelerated. And for accelerated motion he was content to give the cause of the acceleration, leaving the investigation of the proportion of that acceleration, and of other more particular details, to the mechanic or some lower craftsman.
Sagredo: All very well, my dear Simplicio. But you, Salviati — stepping down now and then from the throne of Peripatetic majesty — have you ever toyed with the investigation of this proportion of the acceleration of falling heavy bodies?
Salviati: I've had no need to think about it, since the Academician, our mutual friend, once showed me a treatise of his on motion, where this was demonstrated, along with many other details. But it would be too great a digression if, for this, we wanted to interrupt the present discussion — which is itself already a digression — and make, as they say, a play within a play.
Sagredo: I'm content to let you off that account for now — on condition, though, that this be one of the propositions set aside to be examined, among the others, in another special session, since that knowledge is something I most keenly want. And meanwhile, let's return to the line traced by the heavy body falling from the top of the tower down to its base.
Salviati: If the straight motion toward the center of the Earth were uniform — the circular motion toward the east being uniform as well — the two together would compose a motion along a spiral line, of the kind Archimedes defined in his book on spirals: those you get when a point moves uniformly along a straight line while that line, also uniformly, turns about one of its endpoints, fixed as the center of its rotation. But because the straight motion of the falling body is continually accelerated, the line composed of the two motions must keep drawing away, in ever greater proportion, from the circumference of the circle that the stone's center of gravity would have traced had it stayed always atop the tower. And this drawing-away must, at the start, be small — indeed tiny, indeed the tiniest of all — since the falling body, setting out from rest (that is, from the absence of downward motion) and entering into the straight downward motion, must pass through all the degrees of slowness between rest and any given speed; and those degrees are infinite, as we discussed and concluded at length earlier.
Granting, then, that such is the course of the acceleration, and given too that the falling body is bound to end at the center of the Earth, the line of its compound motion must be such that it keeps drawing away in ever greater proportion from the top of the tower — or, better put, from the circumference of the circle traced by the top of the tower through the Earth's rotation — yet with those departures growing smaller and smaller without limit, the less and less the body has moved away from the first terminus where it rested. On top of this, this line of the compound motion must necessarily end at the center of the Earth. Now, having made these two assumptions, I went ahead and drew, about the center A with the radius AB, the circle BI, which represents the terrestrial globe to me. Extending the radius AB out to C, I laid off the height of the tower BC, which, carried by the Earth over the circumference BI, traces with its top the arc CD. Then, dividing the line CA in half at E, with center E and radius EC I draw the semicircle CIA — along which I now say that one may quite probably believe a stone, falling from the top of the tower at C, comes to move with the compound motion of the common circular motion and its own straight one. For if I mark on the circumference CD some equal parts CF, FG, GH, HL, and from the points F, G, H, L draw straight lines toward the center A, the segments of those lines caught between the two circumferences CD and BI will always represent that same tower CB, carried by the terrestrial globe toward DI. And on those lines, the points where they're cut by the arc of the semicircle CI are the places where, from moment to moment, the falling stone is found; and those points keep drawing away in ever greater proportion from the top of the tower — which is what makes the straight motion along the tower show itself more and more accelerated. One sees, too, how — thanks to the infinite sharpness of the angle of contact between the two circles DC and CI — the falling body's departure from the circumference CFD, that is from the top of the tower, is at the start the very smallest, which is as much as to say that the downward motion is the very slowest, and slower and slower without limit the nearer it is to the terminus C, that is to the state of rest. And finally one understands how, at the last, such motion would end at the center of the Earth, A.
Sagredo: I understand the whole thing perfectly, and I can't believe the falling body traces, with its center of gravity, any line but one like this.
Salviati: But gently, Sagredo — I still have three little musings to bring you, which perhaps won't displease you. The first is that, if we consider it rightly, the body really moves with nothing but a simple circular motion, just as, when it rested on the tower, it likewise moved with a simple circular motion. The second is even prettier: for it moves not a whit more or less than if it had stayed continuously on the tower, since the arcs CF, FG, GH, and so on, that it would have passed through by staying always on the tower are precisely equal to the arcs of the circumference CI that answer to them beneath those same CF, FG, GH, and so on. From which follows the third marvel: that the true and real motion of the stone is not accelerated at all, but is always steady and uniform, since all the equal arcs marked on the circumference CD, and their counterparts marked on the circumference CI, are passed through in equal times. So we're freed from hunting for new causes of acceleration, or of any other motions, since the body — both while resting on the tower and while descending from it — always moves in the same way, that is, circularly, with the same speed and the same uniformity. Now tell me what you make of this odd fancy of mine.
Sagredo: I tell you, I couldn't put into words how marvelous it seems to me; and as far as it now presents itself to my mind, I don't believe the business goes any other way. Would to God all the demonstrations of the philosophers had half the plausibility of this one. I'd very much like, for my complete satisfaction, to hear the proof that those arcs are equal.
Salviati: The demonstration is very easy. Imagine the line I E is drawn. Since the radius of the circle C D — that is, the line C A — is double the radius C E of the circle C I, the larger circumference will be double the smaller, and every arc of the larger circle will be double the corresponding arc of the smaller, so that half of any arc of the larger circle equals the matching arc of the smaller. Now the angle C E I, formed at the center E of the smaller circle and standing on the arc C I, is double the angle C A D, formed at the center A of the larger circle and subtended by the arc C D. Therefore the arc C D is half of the arc of the larger circle that corresponds to the arc C I, and so the two arcs C D and C I are equal. The same can be shown for all the parts. But that the business proceeds exactly this way as far as the fall of heavy bodies goes, I won't insist on for now. What I will say is that, if the line traced by a falling body isn't precisely this one, it comes very close to it.
Sagredo: But now, Salviati, I find myself dwelling on another marvelous thing — namely, that given these considerations, straight-line motion goes entirely out the window, and nature never makes use of it at all. Even the one job that was granted to it at the outset — to carry the parts of whole bodies back to their proper place when they'd been separated from the whole and were therefore in a bad arrangement — even that is now taken away from it and assigned instead to circular motion.
Salviati: This would follow necessarily if it had been established that the terrestrial globe moves in a circle — something I don't claim we've done. All we've done so far, and all we'll go on doing, is to weigh the force of the reasons the philosophers offer as proof of the Earth's immobility. Of these, the first, drawn from bodies falling straight down, runs into the difficulties you've heard. How much weight those difficulties carry in Simplicio's eyes I don't know, so before we move on to test the other arguments, it would be good if he brought out anything he has to say in reply.
Simplicio: As for this first argument, I confess I've heard several subtleties I hadn't thought of, and since they're new to me, I don't have my answers ready. But this argument from bodies falling straight down I don't count among the strongest proofs of the Earth's immobility, and I don't know how things will turn out with the artillery shots — especially those fired against the daily rotation.
Sagredo: I only wish the flight of birds troubled me as little as the artillery and all the other experiences brought up so far! But these birds, which fly back and forth at their pleasure and wheel about in a thousand ways, and — what matters more — hang suspended in the air for hours on end: these, I say, throw my imagination into confusion. I can't understand how, amid so many spinning turns, they don't lose track of the Earth's motion, or how they can keep pace with a speed that in the end outstrips their own flight many, many times over.
Salviati: Your doubt really isn't without reason, and perhaps Copernicus himself never found a solution to his full satisfaction — which may be why he passed over it in silence. Even in examining the other arguments against him he was quite terse, I think out of loftiness of mind, being grounded on greater and higher contemplations, the way lions stir little at the yapping of small dogs. So we'll save the objection about the birds for last, and meanwhile try to satisfy Simplicio on the others, showing him in the usual way that he himself holds the solutions in hand, though he doesn't realize it. Let's start with the point-blank shots, fired with the same piece, the same powder and ball, one toward the east and the other toward the west. Tell me: what makes you believe that the westward shot (supposing the daily rotation belonged to the terrestrial globe) ought to come out much longer than the eastward one?
Simplicio: I'm moved to believe it because, in the eastward shot, while the ball is outside the cannon it's followed by the cannon itself, which — carried by the Earth — is also racing swiftly in the same direction, so that the ball falls to earth not far from the piece. In the westward shot, on the contrary, before the ball strikes the ground the piece has drawn back a good way toward the east, so that the space between the ball and the piece — that is, the range of the shot — will look longer than the other by as much ground as the artillery, and hence the Earth, has covered during the time both balls were in the air.
Salviati: I wish we could find some way to make an experiment matching the motion of these projectiles, the way the shipboard experiment matched the motion of bodies falling from a height. I'm thinking about how.
Sagredo: I think a very suitable test would be to take an open carriage and fit it with a heavy crossbow for bolts, set at half elevation so the shot comes out the longest possible; then, while the horses are running, fire once toward the direction of travel and once toward the opposite direction, marking very carefully where the carriage is at the exact moment the bolt sticks in the ground, in each shot. That way you could see exactly how much longer one comes out than the other.
Simplicio: It seems to me a very suitable experiment, and I've no doubt the shot — that is, the space between the arrow and where the carriage is at the moment the arrow sticks in the ground — will be much smaller when you fire toward the carriage's motion than when you fire the opposite way. Say, for example, the shot in itself is three hundred arm-lengths, and the carriage's travel while the bolt is in the air is a hundred. Then, firing toward the direction of travel, out of the three hundred arm-lengths of the shot the carriage covers a hundred, so that when the bolt strikes the ground the space between it and the carriage will be only two hundred arm-lengths. But in the other shot, on the contrary, the carriage running opposite to the bolt, when the bolt has covered its three hundred arm-lengths and the carriage its hundred in the opposite direction, the distance between them will turn out to be four hundred arm-lengths.
Salviati: Would there be any way to make these two shots come out equal?
Simplicio: I know of no way except to hold the carriage still.
Salviati: That's obvious. But I'm asking with the carriage running at full speed.
Simplicio: You'd have to strengthen the bow when firing with the direction of travel, and then weaken it for firing against it.
Salviati: So there's yet another remedy after all. But by how much would you need to strengthen it, and by how much then weaken it?
Simplicio: In our example, where we supposed the bow shot three hundred arm-lengths, you'd need — for the shot with the direction of travel — to strengthen it so it shot four hundred, and for the other to weaken it so it shot no more than two hundred. That way each shot would come out at three hundred arm-lengths relative to the carriage, which with its own travel of a hundred arm-lengths — subtracting them from the four-hundred shot and adding them to the two-hundred — would bring both back to three hundred.
Salviati: But what effect does the greater or lesser strength of the bow have on the arrow?
Simplicio: A strong bow drives it with greater speed, a weaker one with less; and the same arrow flies farther one time than another in proportion to how much greater the speed with which it leaves the nock one time than the other.
Salviati: So, to make the arrow — fired equally one way and the other — move away from the running carriage by the same amount, if in the first shot of the proposed example it leaves with, say, four degrees of speed, in the other shot it must leave with only two. But if you use the same bow, it always gets three degrees from it.
Simplicio: Just so; and that's why, firing with the same bow while the carriage is running, the shots can't come out equal.
Salviati: I forgot to ask with what speed we're supposing, in this particular experiment, that the carriage runs.
Simplicio: We have to suppose the carriage's speed at one degree, compared with the bow's, which is three.
Salviati: Yes, yes, that makes the reckoning come out right. But tell me: when the carriage runs, don't all the things in the carriage move with the same speed too?
Simplicio: Without a doubt.
Salviati: So the bolt too, and the bow, and the string it's drawn on.
Simplicio: Just so.
Salviati: So, in discharging the bolt toward the carriage's direction of travel, the bow impresses its three degrees of speed on a bolt that already has one degree — thanks to the carriage, which carries it that way with just that speed — so that as it leaves the nock it finds itself with four degrees of speed. On the contrary, firing the other way, the same bow confers its same three degrees on a bolt that's moving the opposite way with one degree, so that as it parts from the string it's left with only two degrees of speed. But you yourself have already granted that to make the shots equal the bolt must leave one time with four degrees and the other with two. So, without changing the bow, it's the carriage's own motion that squares the accounts, and experience then seals the matter for those who wouldn't or couldn't grasp the reasoning. Now apply this discussion to the artillery, and you'll find that whether the Earth moves or stands still, shots fired with the same force must always come out equal, aimed in whatever direction you please. The error of Aristotle, of Ptolemy, of Tycho, of yourself, and of everyone else, is rooted in that fixed and inveterate impression that the Earth stands still — an impression you can't or don't know how to strip off, not even when you want to philosophize about what would happen supposing the Earth did move. It's the same in the other argument: not considering that while the stone is on the tower it does, as regards moving or not moving, exactly what the terrestrial globe does — because you have it fixed in your mind that the Earth stands still — you reason about the stone's fall always as though it set off from rest. Whereas you ought to say: if the Earth stands still, the stone sets off from rest and descends straight down; but if the Earth moves, the stone likewise moves with equal speed, and doesn't set off from rest, but from a motion equal to the Earth's, with which it blends the added downward motion and composes a slanting one.
Simplicio: But, good God, if it moves on a slant, how is it I see it move straight down and perpendicular? This is simply to deny plain sense; and if we're not to trust the senses, by what other door are we to enter into philosophizing?
Salviati: With respect to the Earth, the tower, and ourselves — all of which move together, with the daily rotation, along with the stone — the daily rotation is as if it weren't there: it stays imperceptible, undetectable, without any effect at all, and the only motion left observable to us is the one we don't share, which is the stone's coming down grazing the tower. You're not the first to feel great reluctance in grasping this — that motion has no effect among the things that share in it.
Sagredo: Now I recall a certain fancy of mine that passed through my imagination one day while I was sailing on the voyage to Aleppo, where I was going as consul of our nation. It might perhaps be of some help in explaining how motion shared in common has no effect and is as if it weren't there for all who share in it. And if it please Simplicio, I'd like to discuss with him what I was daydreaming then, all by myself.
Simplicio: The novelty of the things I'm hearing makes me not just tolerant but curious to listen. So do go on.
Sagredo: If the point of a writing pen that had been aboard ship throughout my whole voyage from Venice to Alexandretta had had the power to leave a visible trace of its entire journey, what mark, what track, what line would it have left?
Simplicio: It would have left a line stretched from Venice all the way there — not perfectly straight, or rather, not stretched in a perfect arc of a circle, but here more and there less wavering, according as the vessel had pitched now more, now less. But this bending, in some places by an arm-length or two, right or left, up or down, over a length of many hundreds of miles, would have made only a small alteration in the whole stretch of the line — so slight it would scarcely have been noticeable, and without any error worth mentioning you could have called it a part of a perfect arc.
Sagredo: So the true, true, very truest motion of that pen-point would also have been a perfect arc of a circle, provided the vessel's motion, setting aside the tossing of the waves, had been calm and smooth. And if I had held that same pen continually in my hand, and only now and then moved it a finger's-width or two this way or that, what alteration would I have made to that main and very long stretch?
Simplicio: Less than the deviation, here and there, from absolute straightness by the breadth of a flea's eye would make to a straight line a thousand arm-lengths long.
Sagredo: So if a painter, on setting out from port, had begun to draw on a sheet of paper with that pen, and continued the drawing all the way to Alexandretta, he could have derived from the pen's motion a whole story of many figures perfectly outlined and cross-hatched in a thousand thousand directions, with landscapes, buildings, animals, and other things — even though the whole true, real, and essential movement traced by the point of that pen would have been nothing but one very long but utterly simple line. And as for the painter's own proper work, he would have drawn exactly the same thing, to a hair, had the ship stood still. That no trace of the pen's very long motion remains except those strokes marked on the paper — the reason is that the great motion from Venice to Alexandretta was shared in common by the paper, the pen, and everything else aboard the ship. But the little motions back and forth, right and left, imparted by the painter's fingers to the pen and not to the sheet, being proper to the pen alone, could leave a trace of themselves on the paper, which stayed motionless with respect to those movements. In the same way it's true that, the Earth moving, the stone's motion in coming down was really a long stretch of many hundreds and even many thousands of arm-lengths; and if it could have marked in still air, or on some other surface, the track of its course, it would have left a very long slanting line. But that part of this whole motion which is shared by the stone, the tower, and ourselves stays imperceptible to us, as if it weren't there, and the only part that stays observable is the one neither the tower nor we share — which in the end is what the stone, in falling, measures the tower by.
Salviati: A very subtle thought for explaining this point, which many find quite hard to grasp. Now, if Simplicio has nothing further to reply, we can move on to the other experiences, whose solution will draw no small ease from what's been laid out so far.
Simplicio: I have nothing more to say, and I was half lost in that image, and in thinking how those strokes drawn in so many directions — here, there, up, down, back and forth, and interwoven with a hundred thousand curlicues — are, in essence and in strictest reality, nothing but little pieces of a single line drawn all in one same direction, with no other alteration than a slight leaning, now and then, a little to right and left from the perfectly straight track, and the pen-point moving now faster, now slower, but with the least inequality. And I consider that a letter would be written the same way; and that those more elegant penmen who, to show off the freedom of their hand, without lifting the pen from the paper trace in a single stroke, with a thousand thousand windings, a lovely interlacing — if they were in a boat running swiftly, they would convert the whole motion of the pen (which in essence is a single line drawn all toward the same side, and very little bent or leaning from perfect straightness) into a mere flourish. And I'm delighted that Sagredo has awakened this thought in me. So let's press on, for the hope of hearing more of the same will keep me more attentive.
Sagredo: If you're curious to hear subtleties of this kind, which don't occur to just anyone, we've no shortage of them — especially in this matter of navigation. Won't you find it a fine thought, this one that occurred to me on that same voyage, when I noticed that the ship's mast, without breaking or bending, had made a longer journey with its top — that is, with the crow's-nest — than with its foot? Because the top, being farther from the center of the Earth than the foot is, came to describe the arc of a larger circle than the circle the foot passed through.
Simplicio: And so, when a man walks, he makes a longer journey with his head than with his feet?
Sagredo: You've penetrated it beautifully, by yourself and by your own wit. But let's not interrupt Salviati.
Salviati: I'm glad to see Simplicio getting some training — provided, that is, the thought is his own, and he didn't learn it from a certain little book of conclusions, where there are several others no less pretty and clever. Let's go on to speak of the artillery aimed straight up, perpendicular to the horizon — that is, of the shot toward our zenith — and finally of the ball's return down the same line onto the same piece, even though during the long while it stays separated from the piece the Earth has carried it many miles toward the east; so it would seem that over so much ground the ball ought to fall far from the piece, toward the west. This doesn't happen; therefore the artillery, without having moved, has waited for it. The solution is the same as that of the stone falling from the tower, and the whole fallacy and equivocation consists in always supposing as true the very thing in question — because our opponent has it firmly in his head that the ball sets off from rest when it's driven out of the piece by the fire, and to set off from a state of rest can only be assumed on the supposition that the terrestrial globe is at rest, which is then the very conclusion under dispute. So I reply once more that those who make the Earth mobile answer that the artillery and the ball inside it share the same motion the Earth has — indeed, that they have this motion, along with her, by nature — and that the ball therefore doesn't set off from rest at all, but joined to its motion around the center, which the upward projection neither takes away nor hinders. In this way, following the universal motion of the Earth toward the east, it stays continually over the same piece, both in rising and in returning. And you'll see the same thing happen by making the experiment aboard ship with a ball shot straight up with a crossbow, which returns to the same place whether the ship moves or stands still.
Sagredo: This satisfies everything perfectly. But since I've seen that Simplicio takes pleasure in certain clever tricks for catching (as they say) his companion, I want to ask him whether — supposing for now that the Earth stands still, and on it the artillery raised perpendicularly and aimed at our zenith — he has any difficulty in understanding that this is the true perpendicular shot, and that the ball, in setting off and in returning, will travel along the same straight line, always understanding all external and accidental impediments removed.
Simplicio: I follow you — that's exactly how the thing must turn out.
Sagredo: But suppose the cannon were set up not straight up, but tilted off to one side — what would the ball's motion be then? Would it perhaps travel, as in the other shot, along the vertical line, and then come back down along that same line?
Simplicio: No, it wouldn't do that. Once it left the gun it would keep moving along the straight line that continues the line of the barrel — except insofar as its own weight would pull it down, away from that line, toward the ground.
Sagredo: So the line of the barrel is what governs the ball's motion; the ball doesn't move — and wouldn't move — outside that line, unless its own weight pulled it downward. And that's why, when the barrel is set straight up and the ball is driven upward, it comes back down along that same straight line: because the motion the ball gets from its heaviness is downward along that very vertical. So the ball's journey outside the gun continues the line of that little stretch of journey it made inside the gun — isn't that so?
Simplicio: So it seems to me.
Sagredo: Now picture the barrel standing straight up, and the Earth turning on itself with the daily rotation, carrying the cannon along with it. Tell me: once the powder is fired, what will the ball's motion be inside the barrel?
Simplicio: It will be a straight, vertical motion, since the barrel is aimed straight up.
Sagredo: Look carefully, because I don't think it will be vertical at all. It would indeed be vertical if the Earth stood still, because then the ball would have no motion except what the firing gives it. But if the Earth turns, the ball inside the gun already shares the daily rotation too; so when the push of the powder comes on top of that, it travels from the breech of the gun to the muzzle with two motions, and out of the compound of the two it turns out that the path traced by the ball's center of gravity is a slanted line. To make it clearer: let the cannon AC stand upright, with the ball B inside it. Plainly, if the gun stays still and is fired, the ball will come out at the muzzle A, and its center, traveling up the barrel, will have traced the vertical line BA, and it will go on following that same line outside the gun, moving up toward the point overhead. But if the Earth were turning, and so carried the cannon along with it, then during the time the ball driven by the powder moves up the barrel, the cannon carried by the Earth would pass to the position DE, and the ball B, as it emerged, would be at the mouth D; and the motion of the ball's center would have followed the line BD — no longer vertical, but slanted toward the east. And since (as we've already concluded) the ball must go on moving through the air along the direction of the motion it made inside the gun, its flight will follow the slant of the line BD: and so it won't be vertical after all, but tilted toward the east — toward where the gun itself is also traveling — so that the ball can keep up with the motion of the Earth and of the gun. And there, Simplicio, I've shown you how the shot that seemed bound to go straight up doesn't, after all.
Simplicio: I'm not quite satisfied about this business. What about you, Salviati?
Salviati: I'm partly satisfied; but I have some scruple or other — God grant I can put it into words. It seems to me that, by what's just been said, when the gun points straight up and the Earth moves, the ball ought not only to fail to fall back far from the gun toward the west, as Aristotle and Tycho want, but not even back onto the gun, as you'd have it — rather, quite far off toward the east. Because, on your explanation, it would have two motions, both driving it in that direction together: the shared motion of the Earth, which carries the cannon and the ball from CA toward ED, and the firing, which drives it along the slanted line BD — both motions eastward, and so greater than the Earth's motion alone.
Sagredo: No, sir. The motion that carries the ball eastward comes entirely from the Earth; the firing has no part in it. And the motion that drives the ball upward comes entirely from the firing, with which the Earth has nothing to do. To see that this is true: don't fire, and the ball will never leave the gun, nor rise so much as a hair; and likewise, stop the Earth and fire — the ball, without leaning aside at all, will go straight up the vertical. So the ball has two motions, one upward and one circular, which together make up the slanting line BD: the upward push is all from the firing, the circular is all from the Earth and equal to the Earth's; and because it's equal, the ball stays always straight above the mouth of the gun, and in the end falls back into it. And since it stays always over the line of the barrel, it also keeps appearing continuously over the head of anyone standing near the gun — and so it looks to us as if it rises exactly straight up toward the point overhead.
Simplicio: I have another difficulty left. Since the ball's motion inside the gun is extremely fast, it doesn't seem possible that in that instant of time the shift of the cannon from CA to ED could give the slanting line CD enough tilt for the ball to be able, afterward, through the air, to keep pace with the Earth's course.
Sagredo: You're mistaken on several counts. First, the tilt of the diagonal CD is, I believe, much greater than you imagine, because I hold it beyond doubt that the speed of the Earth's motion — not only at the equator, but even at our own latitude — is greater than that of the ball while it moves inside the gun; so that the interval CE would be absolutely greater than the whole length of the gun, and the tilt of the diagonal, consequently, greater than half a right angle. But whether the Earth's speed is small or large compared with the firing's, that doesn't matter in the least: for if the Earth's speed is small, and so the tilt of the diagonal is small, then only a small tilt is needed to make the ball keep to its flight over the gun. In short, if you consider it attentively, you'll see that the motion of the Earth, by carrying the gun along with it from CA to ED, gives the diagonal CD exactly as much tilt — less or more — as is required to adjust the shot to its need. But you're mistaken in a second way, when you'd credit the ball's ability to keep up with the Earth's motion to the impetus of the firing; there you fall back into the very error Salviati seemed to slip into a moment ago. For keeping up with the Earth is that most ancient and perpetual motion, shared indelibly and inseparably by the ball itself, as by a thing that is earthly and by its own nature possesses that motion and always will.
Salviati: Let's set our minds at rest, Simplicio, because the business really does work just like this. And now, from this discussion, I've come to understand the reason behind a hunting puzzle of those fowlers who bring down birds on the wing with the harquebus — a shoulder gun. I'd imagined that to bag the bird they aimed the sight some distance ahead of it, leading it by a certain interval — more or less according to the speed of the flight and the bird's distance — so that, firing and sending the ball straight along the line of sight, the ball with its motion and the bird with its flight would arrive at the same point at the same moment, and so meet. But when I asked one of them whether that was their practice, he told me no: the trick was far easier and surer, and they do exactly the same thing as when they shoot at a bird sitting still — that is, they fix the sight on the flying bird and follow it by swinging the gun, keeping the sight always on it until they fire, and so they hit the flying birds just like the still ones. So that motion, slow though it is, which the gun makes as it turns to follow the bird's flight with the sight, must be communicated to the ball as well, and must join in the ball with the other motion from the firing — so that the ball gets from the firing its straight motion upward, and from the barrel its leaning to follow the bird's flight, just as was said just now about the artillery shot; where the ball gets from the firing its going up toward the point overhead, and from the Earth's motion its bending toward the east, and out of both makes a compound that follows the Earth's course and that, to anyone watching, seems only to go straight up, coming back down afterward along the same line. So keeping the sight steadily fixed on the target is what makes the shot strike true; and to keep the sight on the mark: if the target stands still, the barrel must be held still too; and if the target moves, the barrel is kept on the mark by moving with it. And on this depends the proper answer to that other argument about firing artillery at a target set toward the south or toward the north — where they urged that if the Earth moved, the shots would all veer off toward the west, because in the time the ball, once out of the gun, travels through the air to the mark, the mark, carried eastward, leaves the ball behind to the west. So I answer by asking: once the cannon has been adjusted to the mark and left just so, does it go on aiming always at the same mark, whether the Earth moves or stands still? The answer must be that the aim doesn't change at all: for if the mark stands still, the cannon likewise stands still, and if the mark, carried by the Earth, moves, the cannon moves right along with it in the same measure; and since the aim is kept, the shot always comes out true, as is clear from what's been said above.
Sagredo: Hold on a moment, please, Salviati, while I put forward a thought that's stirred in me about these shooters of birds on the wing. The way they work is, I believe, just as you say, and I believe the result — hitting the bird — follows just as you describe; but it doesn't seem to me that this operation is entirely of a piece with that of the artillery shots, which must strike both when the gun and the target are in motion and when both are at common rest. And the differences seem to me these. In the artillery shot, the gun and the target move with equal speed, both being carried by the motion of the terrestrial globe; and even if sometimes the gun's being planted more toward the pole than the target — and so its motion somewhat slower, as made in a smaller circle — such a difference is imperceptible, given how little distance there is from gun to mark. But in the fowler's shot, the motion of the gun, with which he follows the bird, is extremely slow compared with the bird's flight; from which it seems to me to follow that the small motion the turning of the barrel gives to the ball inside it cannot, once the ball is out, multiply itself through the air up to the speed of the bird's flight, so that the ball would stay always aimed at it — rather, it seems the ball must fall behind and be left at the bird's tail. Add to this that in this case the air through which the ball has to pass isn't supposed to share the bird's motion; whereas in the artillery's case the gun and the target and the air between them all share equally in the universal daily motion. So for the fowler's hitting, I'd believe the causes were — besides following the flight with the motion of the barrel — leading it somewhat, by keeping the sight ahead; and besides that, firing (as I believe) not with a single ball but with a good number of little pellets, which, spreading through the air, take up a very large space; and besides this, the extreme speed with which, coming out of the barrel, they're carried to the bird.
Salviati: And there's how far the flight of Sagredo's wit outruns and forestalls the slowness of mine — which would perhaps have noticed these disparities, but not without a long application of thought. Now, coming back to our subject, we still have to consider the point-blank shots toward the east and toward the west. The first of these, if the Earth moved, ought always to come out high above the target, and the second low; seeing that, by the daily rotation, the eastern parts of the Earth are continually sinking below the tangent line parallel to the horizon — which is why the eastern stars appear to us to rise — while, on the contrary, the western parts are rising, so that the western stars appear to sink. And so the shots aimed along that tangent at an eastern target, which sinks while the ball travels along the tangent, ought to come out high; and the western ones low, because the target rises while the ball runs along the tangent. The answer is like the others: just as the eastern target, by the Earth's motion, keeps sinking below a tangent that stayed fixed, so likewise the gun, for the same reason, keeps tilting and goes on aiming always at the same target, so that the shots come out true. But here it seems a fitting occasion to point out a certain generosity — shown, perhaps, with too much liberality — by the followers of Copernicus toward the opposing side: I mean, granting them as sure and certain some experiments the opponents have in truth never made — such as, for example, that of the bodies dropping from the mast of the ship while it's in motion, and many others; among which I hold it for certain that one is this — testing whether the eastern artillery shots come out high and the western low. And because I believe they've never made it, I'd like them to tell me what difference they think ought to be seen between these same shots, whether the Earth is set at rest or set in motion; and let Simplicio answer for them now.
Simplicio: I won't presume to answer as soundly as someone more knowledgeable than me perhaps could, but I'll say what I think, off the top of my head, they would answer — which is, in effect, what's already been brought up: namely, that if the Earth moved, the eastern shots would always come out high, and so on, since the ball, as seems likely, must move along the tangent.
Salviati: But if I said that this is in fact what happens, how would you go about refuting what I said?
Simplicio: One would have to come to experiment to clear it up.
Salviati: But do you believe you'd find a gunner so skilled that he'd undertake to hit the target with every single shot at a distance of, say, five hundred braccia?
Simplicio: No, sir; and I don't think there'd be anyone, however expert, who'd promise not to miss, on average, by more than a braccio.
Salviati: How, then, could we settle what we're in doubt about with shots as unreliable as that?
Simplicio: We could settle it in two ways: one, by firing many shots; the other, because, given the great speed of the Earth's motion, the deviation from the target would, in my opinion, be enormous.
Salviati: Enormous — that is, much more than a braccio; seeing that a variation of that much, and even more, is admitted to happen ordinarily even when the terrestrial globe is at rest.
Simplicio: I firmly believe the variation would be much greater.
Salviati: Now, for our own satisfaction, let's do a bit of rough calculation, if you like — one that will also serve us (if the reckoning comes out as I hope) as a warning not to let ourselves be so easily carried away, as the saying goes, by the shouting, giving our assent to everything that first presents itself to our fancy. And, to give every advantage to the Peripatetics and the Tychonians, let's imagine ourselves at the equator, firing point-blank westward with a culverin at a target five hundred braccia away. First let's find, roughly (as I said), how much time the ball takes, once out of the gun, to reach the mark — which we know to be very brief, and certainly no more than the time in which a man on foot takes two steps; and this is still less than one second of an hour. For, granting the walker goes three miles an hour, which is nine thousand braccia, and since an hour holds three thousand six hundred seconds, that comes to two and a half steps in a second: so a second is more than the time of the ball's motion. And since the daily revolution is twenty-four hours, the western horizon rises fifteen degrees an hour — that is, fifteen first minutes of a degree for one first minute of an hour, that is, fifteen seconds of a degree for one second of an hour; and since one second is the time of the shot, in this time the western horizon rises fifteen seconds of a degree, and so does the target: fifteen seconds, that is, of that circle whose radius is five hundred braccia (for that's what we set the target's distance from the culverin to be). Now let's look in the table of arcs and chords — and here's Copernicus's book, right at hand — for what part the chord of fifteen seconds is of a radius of five hundred braccia. Here we see that the chord of one first minute is less than thirty of the parts of which the radius holds a hundred thousand; so, of those same parts, the chord of one second minute will be less than half — that is, less than one of the parts of which the radius is two hundred thousand — and therefore the chord of fifteen seconds will be less than fifteen of those same two-hundred-thousandth parts. Now fifteen of those two-hundred-thousandth parts, taken of a radius of five hundred braccia, come to less than four hundredths of a braccio; and so the rise of the target during the ball's flight is less than four hundredths — that is, a twenty-fifth — of a braccio, and thus about a finger's width. And a single finger's width, consequently, will be the deviation of each westward shot, if the daily rotation belonged to the Earth. Now, if I tell you that this deviation actually happens in every shot — I mean that the shots strike a finger's width lower than they would if the Earth didn't move — how, Simplicio, would you go about convincing me, showing me by experiment that it doesn't happen? Don't you see it's impossible to shake me off, unless you first find a way of aiming so exact that you never miss by a hair? Because, so long as the shots come out varying by whole braccia, as they in fact do, I'll always say that contained in each of those variations is that one finger's width, caused by the motion of the Earth.
Sagredo: Forgive me, Salviati, you're too generous; for I'd say to the Peripatetics that even if every shot struck the very center of the target, that wouldn't contradict the motion of the Earth in the least: because the gunners have always trained themselves to fit the aim to the target, and have made a practice of setting the gun on the mark in such a way that they hit it, given the motion of the Earth; and I say that if the Earth stopped, the shots would not come out true, but the western ones would come out high and the eastern low. Now let Simplicio convince me.
Salviati: A subtlety worthy of Sagredo. But whether this variation is to be seen in the Earth's motion or in its rest — since it can only be extremely tiny — it can only stay submerged among the very large ones that continually happen through many accidents. And let all this be said and granted, in full measure, to Simplicio, and only as a warning of how cautious one must be in granting as true so many experiments to people who have never made them, but boldly put them forward just as they'd need them to be, to serve their cause. I say this is thrown in as a bonus to Simplicio, because the plain truth is that, as regards the effects of these shots, exactly the same thing must happen whether the terrestrial globe is in motion or at rest — just as it will with all the other experiments brought forward, and that can be brought forward, which have at first sight some semblance of truth only insofar as the old, ingrained notion of the Earth's immobility keeps us among the ambiguities.
Sagredo: For my part, I'm fully satisfied up to this point. I understand perfectly well that anyone who fixes in his imagination this general sharing of the daily rotation among all earthly things — a rotation that naturally belongs to them all, in just the way the old conception supposed that rest around the center belonged to them — will have no trouble at all making out the fallacy and the equivocation that made the arguments brought against us seem conclusive. There's only one scruple I have left, the one I hinted at earlier, about the flight of birds. Birds are living creatures, so they can move themselves at will through a hundred thousand different motions, and can keep themselves aloft, cut off from the Earth, hanging in the air for a long time, and go wandering about with the most disorderly twists and turns. So I don't quite grasp how, in such a great jumble of motions, they don't get confused and lose that first shared motion — and how, once they've been stripped of it, they can make it up and match it again by flying, and keep pace with the towers and the trees that go rushing eastward at such a headlong speed. And I mean truly headlong: on the greatest circle of the globe it comes to a little under a thousand miles an hour, of which I don't believe a swallow's flight makes even fifty.
Salviati: If the birds had to keep pace with the racing trees by the help of their wings, they'd be in a sorry state; and if they were stripped of the universal rotation, they'd be left so far behind, and their course toward the west would look so furious — to anyone who could see them — that it would far outstrip an arrow's. But I don't think we could make them out at all, any more than we can see cannonballs while they streak through the air, driven by the fury of the gunpowder. The truth is that the birds' own motion — I mean their flying — has nothing to do with the universal motion, to which it neither adds help nor gives hindrance. What keeps that motion unaltered in the birds is the very air they go wandering through, which, following the Earth's spin naturally, carries the clouds along with it and likewise carries the birds and everything else hanging in it. So as for keeping up with the Earth, the birds needn't give it a thought — for that service, they could sleep forever.
Sagredo: That the air can carry the clouds along with it — those being materials very easily moved because of their lightness, and stripped of any contrary inclination, or rather materials that themselves share in the conditions and properties of the Earth — that I grasp without any difficulty. But that the birds, which, being living creatures, can move even with a motion contrary to the daily one, should have it restored to them by the air once they've broken it off — that seems to me a bit hard to swallow. Especially since they're solid, heavy bodies; and we, as was said above, see that stones and other heavy bodies stay stubborn against the push of the air, and even when they do let themselves be overcome, they never pick up as much speed as the wind that carries them.
Salviati: Let's not credit moving air with so little force, Sagredo. When it moves quickly it's powerful enough to shift and drive fully loaded ships, to uproot forests and topple towers — and yet in these very violent operations you can't say its motion is anywhere near as fast as that of the daily revolution.
Simplicio: So there it is — moving air can indeed keep up the motion of projectiles, in line with Aristotle's doctrine. And I did think it strange that he should have gone wrong on this particular point.
Salviati: It could, no doubt, if it were able to keep the motion up in itself. But just as, once the wind dies, the ships stop traveling and the trees stop being uprooted, so, since the motion isn't kept up in the air after the stone has left the hand and the arm has stopped, it follows that something other than the air is what makes the projectile move.
Simplicio: And how is it that when the wind stops, the ship's motion stops? On the contrary, you can see that even when the wind has died and the sails have been furled, the vessel keeps running on for whole miles.
Salviati: But that's against you, Simplicio, since once the air is stilled — the air that, striking the sails, was driving the ship — the vessel nevertheless keeps up its course without the help of the medium.
Simplicio: One might say the water was the medium that carried the ship along and kept up its motion.
Salviati: One might indeed say so — to say the exact opposite of the truth. The truth is that the water, with its great resistance to being parted by the body of the vessel, fights it with a great roar, and won't let it take on anything like the speed the wind would give it if the water's obstacle weren't there. You, Simplicio, can never have paid attention to the fury with which the water goes scraping around the boat while it's driven swiftly along by oars or by wind, running through still water. If you'd noticed such an effect, it wouldn't now occur to you to come out with such nonsense. And I'm beginning to suspect that up to now you've been one of the flock of those who, to learn how such matters proceed and to acquire knowledge of nature's effects, don't go out on boats or around crossbows and cannon, but shut themselves up in the study to leaf through the indexes and reference-lists, hunting to see whether Aristotle has said anything about it — and once they've made sure of the true sense of the text, they desire nothing further and reckon there's nothing else worth knowing.
Sagredo: A great happiness, and much to be envied. For if knowledge is naturally desired by all, and if to be is as good as to fancy oneself to be, then they enjoy an enormous good: they can persuade themselves that they understand and know all things — snapping their fingers at those who, knowing that they don't know what they don't know, and consequently seeing that they don't know even the tiniest little particle of what can be known, wear themselves out with late nights and contemplations, and grind themselves down over experiments and observations. But please, let's get back to our birds. On their account you'd said that air moving with tremendous speed could restore to them that part of the daily motion which, amid the play of their flights, they might have lost. To which I object that moving air doesn't seem able to give a solid, heavy body as much speed as it has itself; and since the air's speed is only equal to the Earth's, it didn't seem that the air would be enough to make good the loss in the birds' flight.
Salviati: Your argument has a good deal of the plausible about it in appearance, and to raise a doubt at just the right point is no mark of an ordinary mind. All the same, once you strip away the appearance, I think that in reality it hasn't a hair more force than the others already considered and dissolved.
Sagredo: There's no doubt whatever that when an argument isn't necessarily conclusive, its force can only be absolutely nothing; because when the conclusion holds necessarily in one way only, no reasoning of any weight can be produced for the other side.
Salviati: Your finding more difficulty in this case than in the others seems to me to hinge on the birds' being living creatures, and therefore able to use force at their own pleasure against the primary motion inborn in earthly things — in just the way we see, while they're alive, that they can fly upward too, a motion impossible for them as heavy bodies, whereas when dead they can only fall. And so you reckon that the reasons which hold for all the sorts of projectiles mentioned above can't hold for the birds. That's perfectly true; and because it's true, you don't see those projectiles doing what the birds do, Sagredo. For if from the top of the tower you let a dead bird and a live one drop, the dead one will do just what a stone does — it will first follow the general daily motion, and then the downward motion, as a heavy body. But if the bird let go is alive, what's to stop it — the daily motion always remaining in it — from throwing itself, by beating its wings, toward whatever quarter of the horizon it pleases? And this new motion, being its own particular one and not shared by us, must become perceptible to us. And once it has moved by its flight toward the west, what's to stop it from returning to the tower with an equal beating of feathers? For, in the end, setting off in flight toward the west was nothing but subtracting one single degree from the daily motion, which has, say, ten degrees of speed, leaving it nine while it was flying; and once it settled on the ground, the ten shared degrees came back to it, to which, by flying eastward, it could add one, and with the eleven return to the top of the tower. In sum, if we consider carefully and contemplate more intimately the effects of the birds' flying, they differ in nothing from projectiles moving toward every part of the world, except that these are moved by an external thrower and those by an internal principle.
And here, as a final seal on the nullity of all the experiences brought forward, I think it's the time and place to show the way to test them all with the greatest ease. Shut yourself up with a friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying creatures. Have a big bowl of water with some fish in it; hang up a little bucket that drips water, drop by drop, into another vessel with a narrow neck placed underneath. Then, with the ship standing still, watch carefully how those little flying creatures go with equal speed toward every part of the cabin; the fish will be seen swimming indifferently in all directions; the falling drops will all go into the vessel placed below; and if you throw something to your friend, you won't need to throw it any harder toward one side than the other, when the distances are equal; and if you jump, as they say, with both feet together, you'll cover equal spaces in every direction. Once you've carefully observed all these things — though there's no doubt they must happen this way while the ship stands still — have the ship move with as much speed as you please. So long as the motion is uniform and not rocking this way and that, you won't recognize the slightest change in any of the effects just named, nor from any of them will you be able to tell whether the ship is moving or standing still. In jumping, you'll cover the same distances on the deck as before, and you won't make bigger jumps toward the stern than toward the bow just because the ship is moving very fast — even though, during the time you're in the air, the deck beneath you runs the opposite way to your jump. If you throw something to your companion, you won't need any more force to reach him whether he's toward the bow and you toward the stern or the other way around. The drops will fall as before into the lower vessel, without a single one falling toward the stern, even though, while the drop is in the air, the ship runs on many handbreadths. The fish in their water will swim toward the front of the bowl with no more effort than toward the back, and will come with equal ease to food set on any spot along the bowl's rim. And finally the butterflies and the flies will go on with their flights indifferently toward every part, and it will never happen that they gather toward the wall facing the stern, as though tired out from keeping up with the ship's swift course — from which they've been separated a long while by staying up in the air. And if you burn a little grain of incense so that a bit of smoke rises, you'll see it climb upward and, like a little cloud, hang there, moving no more toward one side than the other. The cause of all this correspondence of effects is that the ship's motion is shared by everything contained in it, and by the air too — which is why I said you should be below decks. If you were up above, in the open air that doesn't follow the ship's course, you'd see more or less noticeable differences in some of the effects named: there's no doubt the smoke would be left behind, along with the air itself; the flies too and the butterflies, hindered by the air, wouldn't be able to follow the ship's motion once they'd separated from it by any considerable distance. But keeping close by, they'd follow the ship without any hindrance or effort, because the ship — being of a rambling, hollowed-out shape — carries along with it part of the air nearest to it; and for a like reason we sometimes see, in riding post, the pestering flies and horseflies following the horses, flying now to this part of their body and now to that. But with the falling drops the difference would be very slight, and in the jumps and in the heavy projectiles altogether imperceptible.
Sagredo: Even though it never occurred to me, while sailing, to make these observations on purpose, still I'm more than sure they'd turn out in the way you've described. In confirmation of which, I remember that a hundred times, being in my cabin, I've wondered whether the ship was moving or standing still; and sometimes, lost in a daydream, I've believed it was going one way when the motion was the opposite. So up to this point I'm satisfied, and entirely convinced of the nullity of all the experiences brought forward to prove the negative rather than the affirmative side of the Earth's rotation. There now remains the objection founded on seeing by experience how a swift whirling has the power to extrude and scatter the materials clinging to the machine that goes spinning around. Because of this it seemed to many — and to Ptolemy too — that if the Earth turned upon itself with such speed, the stones and the animals would have to be flung off toward the stars, and that the buildings couldn't be fastened to their foundations with mortar tough enough to keep them from suffering the same ruin.
Salviati: Before coming to the solution of this objection, I can't keep silent about something I've noticed a thousand times, not without a laugh, coming into the minds of almost all men at the first word they hear of this moving of the Earth. They've believed it so utterly fixed and motionless that not only have they never doubted that rest, but they've firmly believed that all other men, along with themselves, have reckoned it was created immovable and has stayed that way through all the centuries gone by. Settled in this notion, they're then astonished to hear that someone grants it motion — as if, after he had held it motionless, he foolishly supposed that only then, and not before, did it set itself in motion, at the moment when Pythagoras (or whoever it was) first said it moved. Now, that such a foolish thought — I mean the belief that those who admit the Earth's motion first held it fixed from its creation down to Pythagoras's time, and only made it mobile afterward, once Pythagoras reckoned it so — should find a place in the minds of common men of light judgment, doesn't surprise me. But that the Aristotles and the Ptolemies should have fallen into this childishness too seems to me a much stranger and more inexcusable simplicity.
Sagredo: So then, Salviati, you believe that Ptolemy thought he had to maintain, in his disputation, the stability of the Earth against men who, granting that it had been motionless down to Pythagoras's time, only then asserted that it had become mobile, when Pythagoras attributed motion to it?
Salviati: One can't believe otherwise, if we consider carefully the manner he uses in refuting their claim. His refutation consists in the demolition of buildings and the flinging of stones, of animals, and of men themselves toward the sky. And since such a ruin and hurling-off can't be done to buildings and animals that aren't first on the Earth, and men can't be set on the Earth nor buildings raised except while it stands still, it's clear from this that Ptolemy is proceeding against those who, having for some time granted rest to the Earth — that is, while the animals, the stones, and the builders could dwell on it and raise the palaces and the cities — then suddenly make it mobile, to the ruin and destruction of the buildings and the animals, and so on. For if he had undertaken to dispute against someone who attributed such a whirling to the Earth from its first creation, he'd have refuted him by saying that if the Earth had always moved, there could never have been established on it either beasts or men or stones, much less buildings raised or cities founded, and so on.
Simplicio: I don't quite grasp this Aristotelian and Ptolemaic inconsistency.
Salviati: Ptolemy either argues against those who have reckoned the Earth always mobile, or against those who have reckoned that it stood still for some time and then set itself in motion. If against the first, he ought to have said: "The Earth hasn't always moved, because there would never have been men or animals or buildings on the Earth, the terrestrial whirling not allowing them to dwell there." But since, in arguing, he says instead: "The Earth doesn't move, because the beasts, the men, and the buildings already set on the Earth would fall headlong" — he's supposing that the Earth was once found in such a state that it allowed the beasts and the men to dwell there and to build; which carries as a consequence that it was for some time at rest, that is, fit for the dwelling of animals and the raising of buildings. Are you now clear on what I've been trying to say?
Simplicio: I am and I'm not. But this matters little to the merit of the case, nor can a little slip of Ptolemy's, committed through inadvertence, be enough to move the Earth when it's motionless. But leaving the jokes aside, let's come at last to the nerve of the argument, which seems to me insoluble.
Salviati: And I, Simplicio, want to knot it up and tighten it still further, by showing even more palpably how it's true that heavy bodies, whirled with speed around a stable center, acquire an impetus to move away from that center, even when they have a natural propensity to go toward it. Tie a little bucket to the end of a cord, with water in it, and holding the other end firmly in your hand, making the cord and your arm the radius and the joint of your shoulder the center, swing the vessel quickly around so that it describes the circumference of a circle. Whether that circle is parallel to the horizon, or upright to it, or inclined in any way you please, in every case it will follow that the water doesn't spill out of the vessel; in fact, the one swinging it will always feel the cord pull and strain to get farther from the shoulder. And if you make a hole in the bottom of the bucket, you'll see the water spurt out no less toward the sky than sideways and toward the ground. And if instead of water you put in little pebbles, swinging them the same way, you'll feel them make the same force against the cord. And finally, we see children throw stones to a great distance by swinging around a piece of cane with the stone lodged in its tip — all arguments for the truth of the conclusion, namely that whirling confers on the moving body an impetus toward the circumference when the motion is fast; and therefore, if the Earth turned upon itself, the motion of its surface — especially toward the greatest circle, being incomparably faster than the ones just named — would have to extrude everything toward the sky.
Simplicio: The objection seems to me very well set up and tightly knotted, and it'll take something considerable, I believe, to shift it and untie it.
Salviati: Untying it depends on certain facts that you know and believe no less than I do; but because they don't come to mind, you don't see the solution. So without my teaching them to you — since you already know them — simply by reminding you of them I'll get you to resolve the objection yourself.
Simplicio: I've paid attention more than once to your way of reasoning, and it's stirred up a thought in me — that you lean toward that opinion of Plato's, that nostrum scire sit quoddam reminisci — that our knowing is a kind of recollection. So please, clear up this doubt for me by telling me what you really think.
Salviati: What I think of Plato's opinion I can convey to you both in words and in deeds. More than once already, in the discussions we've had so far, I've shown my hand by deed; I'll keep to the same style in the particular case we have in hand, which can then serve you as an example for grasping more easily my notion about how knowledge is acquired — that is, if we have time left over on another day, and if it won't bore Sagredo to have us make this digression.
Sagredo: On the contrary, it'll be most welcome, because I remember that when I studied logic I could never get my head around that so-vaunted demonstratio potissima — the "most powerful proof" — of Aristotle's.
Salviati: Let's go on, then. Simplicio, tell me: what is the motion of that little stone gripped in the notch of the staff while the boy swings it to throw it far?
Simplicio: The stone's motion, as long as it's in the notch, is circular — that is, it travels along an arc of a circle, whose fixed center is the joint of the shoulder, and whose radius is the staff together with the arm.
Salviati: And when the stone escapes from the staff, what is its motion? Does it go on continuing its earlier circular motion, or does it travel along some other line?
Simplicio: It doesn't go on moving in a circle any longer, because if it did it wouldn't get away from the thrower's shoulder — whereas we see it fly off very far indeed.
Salviati: By what motion, then, does it move?
Simplicio: Let me think about it a little, because I've never turned my mind to it before.
Salviati: Sagredo, a word in your ear: there's the quoddam reminisci out in the open field, plain as day. — You're thinking hard, Simplicio!
Simplicio: As I see it, the motion taken on as the stone leaves the notch can only be along a straight line — indeed it must necessarily be along a straight line, if we mean the pure acquired impetus alone. It bothered me a bit to see it trace an arc; but since that arc always bends downward, and not to any other side, I realize that the bending comes from the stone's own weight, which naturally pulls it down. The impressed impetus, I say without hesitation, is along a straight line.
Salviati: But along which straight line? For infinitely many, running off in every direction, can be drawn from the notch of the staff and from the point where the stone separates from it.
Simplicio: It moves along the one that lies in line with the motion the stone made together with the staff.
Salviati: The stone's motion, while it was in the notch, you've already said was circular; now, "circular" and "in a straight line" are at odds, since there's no straight part anywhere in a circular line.
Simplicio: I don't mean the projected motion is in line with the whole of the circular motion, but with that last point where the circular motion ended. I understand it inside myself, but I can't quite put it into words.
Salviati: And I too can see that you understand the thing, but you don't have the proper terms to express it. Well, those I can certainly teach you — teach you the words, that is, not the truths, which are things. And to let you feel it with your own hands, that you know the thing and only lack the terms to express it, tell me: when you fire a ball from a harquebus, in what direction does it acquire its impetus to travel?
Simplicio: It acquires the impetus to travel along that straight line which follows the line of the barrel — that is, one that veers neither right nor left, neither up nor down.
Salviati: Which in short amounts to saying that it makes no angle at all with the line of the straight motion made along the barrel.
Simplicio: That's what I meant to say.
Salviati: If, then, the line of the projectile's motion is to continue without making an angle upon the circular line it described while it was with the thrower, and if it must pass from this circular motion to straight motion, what will this straight line have to be?
Simplicio: It can only be the one that touches the circle at the point of separation, because all the others, it seems to me, would — if extended — cut the circumference, and so would contain some angle with it.
Salviati: You've reasoned very well, and shown yourself half a geometer. Keep it in memory, then, that your real idea is spelled out in these words: the projectile acquires the impetus to move along the tangent to the arc described by the thrower's motion, at the point where the projectile separates from the thrower.
Simplicio: I understand perfectly, and that's just what I wanted to say.
Salviati: Of a straight line that touches a circle, which of its points is the closest of all to the center of that circle?
Simplicio: The point of contact, without a doubt; because that one is on the circle's circumference, and the others outside it, and the points of the circumference are all equally distant from the center.
Salviati: Therefore a moving body, setting out from the point of contact and moving along the straight tangent, goes continually farther from the point of contact, and also from the center of the circle.
Simplicio: That's certainly so.
Salviati: Now, if you've kept in mind the propositions you've told me, put them back together and tell me what follows from them.
Simplicio: I don't think I'm so forgetful that I can't recall it. From what's been said it follows that the projectile, swung rapidly around by the thrower, on separating from it keeps the impetus to continue its motion along the straight line that touches the circle described by the thrower's motion, at the point of separation; and by this motion the projectile goes ever farther from the center of the circle described by the thrower's motion.
Salviati: So by now you know the reason why heavy bodies clinging to the surface of a rapidly turning wheel are extruded — flung off, I mean, beyond the circumference, ever farther from the center.
Simplicio: Of this I feel I've got a pretty good grasp; but this new understanding rather increases than lessens my disbelief that the Earth could turn with such speed without flinging stones, animals, and the rest up toward the sky.
Salviati: In the same way you've known things up to now, you'll know — indeed you already know — the rest too; and by thinking it over you'd recall it on your own again. But to save time, I'll help you remember it. So far you've known by yourself that the thrower's circular motion impresses on the projectile the impetus to move (whenever they happen to separate) along the straight tangent to the circle of the motion, at the point of separation, and that, continuing its motion along that tangent, it goes ever farther from the thrower. And you've said that the projectile would keep moving along that straight line if its own weight didn't add to it a downward inclination, from which comes the curving of the line of motion. It also seems to me you've known by yourself that this bending always tends toward the center of the Earth, because that's where all heavy bodies tend. Now I go a little further, and ask you whether the moving body, after separation, in continuing its straight motion, goes ever equally farther from the center — or, if you like, from the circumference — of that circle of which the earlier motion was a part; which is the same as asking whether a moving body that sets out from the point of the tangent, and moves along that tangent, gets equally farther from the point of contact and from the circumference of the circle.
Simplicio: No, sir; because near the point of contact the tangent departs very little from the circumference, with which it contains a very tight angle, but as it goes farther and farther, the separation always grows in greater proportion. So that in a circle with, say, a diameter of ten braccia, a point on the tangent two palms away from the contact would be found three or four times farther from the circumference than a point one palm away from the touch; and the point half a palm away, likewise, I believe, would barely be a quarter as far as the second; so that within a finger or two of the contact, one can hardly make out that the tangent is separated from the circumference at all.
Salviati: So that the projectile's departure from the circumference of the earlier circular motion is, at the very start, extremely small?
Simplicio: Almost imperceptible.
Salviati: Now tell me: the projectile that from the thrower's motion receives the impetus to move along the straight tangent — and would still go on along it if its own weight didn't pull it down — how long does it take, after separation, to begin to bend downward?
Simplicio: I believe it begins at once, because having nothing to hold it up, it can't be that its own weight doesn't act.
Salviati: So that if that stone flung from that wheel turning at great speed had a natural tendency to move toward the center of that same wheel, just as it has one to move toward the center of the Earth, it would be an easy thing for it to return to the wheel — or rather, for it never to leave it; because, at the start of separation, the departure being so very minimal, thanks to the infinite sharpness of the angle of contact, every least bit of inclination drawing it back toward the wheel's center would be enough to keep it on the circumference.
Simplicio: I have no doubt at all that, granting what is not and cannot be — namely, that the inclination of those heavy bodies were to go to the center of that wheel — they wouldn't be extruded or flung off.
Salviati: Nor do I suppose, or need to suppose, what is not, because I don't want to deny that stones do get flung off; I'm just saying it by way of supposition, so that you'll tell me the rest. Now picture the Earth as the great wheel that, turning with such speed, is to fling off the stones. You've already been able to tell me very well that the projected motion will have to be along that straight line which touches the Earth at the point of separation. And how far, notably, does this tangent get from the surface of the terrestrial globe?
Simplicio: I believe that in a thousand braccia it doesn't get a finger's width away.
Salviati: And don't you say that the projectile, pulled by its own weight, bends away from the tangent toward the center of the Earth?
Simplicio: I've said it — and I'll say the rest too, and I understand perfectly that the stone won't separate from the Earth, since its departure at the start would be so very minimal that the stone's inclination to move toward the center of the Earth is fully a thousand times greater; and in this case that center is also the center of the wheel. And really one is forced to grant that stones, animals, and other heavy bodies can't be extruded. But now the very light things give me a new difficulty — the ones that have a very feeble inclination to sink toward the center; so that, since they lack the power to draw themselves back to the surface, I don't see why they wouldn't be flung off. And you know that ad destruendum sufficit unum — one instance is enough to destroy the claim.
Salviati: We'll satisfy this point too. But first tell me what you mean by "light things" — whether you mean stuff so truly light that it goes upward, or not absolutely light, but so slightly heavy that it does come down, only slowly; because if you mean the absolutely light ones, I'll let them be flung off even more than you'd like.
Simplicio: I mean the second kind — things like feathers, wool, cotton wadding, and the like, which the least force is enough to lift; yet we see them resting quite peacefully on the ground.
Salviati: As long as this feather has some natural tendency to descend toward the surface of the Earth, however slight it may be, I tell you it's enough to keep it from being lifted; and this isn't unknown to you either. So tell me: if the feather were flung off by the Earth's whirling, along what line would it move?
Simplicio: Along the tangent at the point of separation.
Salviati: And if it had to come back and rejoin, along what line would it move?
Simplicio: Along the one that goes from it to the center of the Earth.
Salviati: So that here two motions come into consideration: one of projection, which begins at the point of contact and follows along the tangent; and the other of the downward inclination, which begins at the projectile and goes along the secant toward the center. And for the projection to take place, the impetus along the tangent must prevail over the inclination along the secant — isn't that so?
Simplicio: So it seems to me.
Salviati: But what do you think must be present in the projecting motion, so that it prevails over that of the inclination, and from that follows the feather's detachment and departure from the Earth?
Simplicio: I don't know.
Salviati: How do you not know? Here the moving body is the same — the same feather; now how can one and the same moving body outdo itself in motion and prevail over itself?
Simplicio: I don't see how it could prevail over or yield to itself in motion, except by moving now faster and now slower.
Salviati: There, you see, you did know it after all. So then, if the feather's projection is to take place, and its motion along the tangent is to prevail over the motion along the secant, what must their speeds be?
Simplicio: The motion along the tangent must be greater than the other along the secant. Oh, poor me! But isn't it even a hundred thousand times greater — and not only than the downward motion of the feather, but even than that of the stone? And I, like a real simpleton, had let myself be persuaded that stones couldn't be flung off by the Earth's whirling! So I take it all back, and say that if the Earth moved, the stones, the elephants, the towers, and the cities would necessarily fly up toward the sky; and since that doesn't happen, I say the Earth does not move.
Salviati: Oh, Simplicio, you fly up so quickly that I'll start fearing more for you than for the feather. Calm down a little, and listen. If, to keep the stone or the feather attached to the surface of the Earth, it were necessary that its descent downward be more than — or as much as — the motion made along the tangent, you'd be right to say it would have to move as fast or faster along the secant downward as along the tangent toward the east. But didn't you tell me just now that a thousand braccia of distance along the tangent from the contact scarcely move it a finger's width from the circumference? It's not enough, then, for the motion along the tangent — which is the motion of the daily whirl — simply to be faster than the motion along the secant, which is the feather's downward motion; it has to be so much faster that the time enough to carry the feather, say, a thousand braccia along the tangent is too little for it to move a single finger's width downward along the secant. And this, I tell you, will never be — make that motion as fast, and this one as slow, as you please.
Simplicio: And why couldn't the one along the tangent be so fast that it gave the feather no time to reach the surface of the Earth?
Salviati: Try putting the case in definite terms, and I'll answer you. So tell me how much faster you think that motion would have to be than this one.
Simplicio: I'll say, for example, that if that one were a million times faster than this one, the feather — and the stone too — would be flung off.
Salviati: You say so, and you say what's false, only for a lack — not of logic, or of physics, or of metaphysics, but of geometry. Because if you understood only the first elements, you'd know that from the center of the circle one can draw a straight line out to the tangent that cuts it in such a way that the part of the tangent between the contact and the secant is one, two, three million times greater than that part of the secant left between the tangent and the circumference; and as the secant comes closer and closer to the contact, this ratio grows greater without limit. So there's no fear that, however fast the whirl and slow the downward motion, the feather — or anything else lighter — could begin to rise; because the downward inclination always overcomes the speed of the projection.
Sagredo: I'm not entirely satisfied about this business.
Salviati: I'll give you a thoroughly universal demonstration of it, and quite an easy one too. Let the given ratio be that of BA to C, and let BA be greater than C by as much as you like; and let there be the circle whose center is D, from which we must draw a secant such that the tangent bears to that secant the ratio of BA to C. Take AI, the third proportional of the two lines BA and C; and as BI is to IA, so make the diameter FE to EG; and from the point G draw the tangent GH. I say that what was required has been done, and that as BA is to C, so HG is to GE. For, since as BI is to IA so FE is to EG, then — componendo, combining the terms — as BA is to AI so FG is to GE; and because C is the mean proportional between BA and AI, and GH is the mean between FG and GE, therefore as BA is to C, so will FG be to GH, that is, HG to GE — which is what needed to be done.
Sagredo: I follow this demonstration; yet it doesn't entirely take away every scruple — rather, I feel a certain confusion turning about in my mind which, like a thick, dark fog, doesn't let me make out, with the clarity that's usually proper to mathematical reasoning, the plainness and necessity of the conclusion. And what confuses me is this. It's true that the spaces between the tangent and the circumference go on diminishing without limit toward the contact; but it's also true, on the other hand, that the moving body's tendency to descend keeps growing ever smaller in it the closer it finds itself to the first terminus of its descent — that is, to the state of rest — as is clear from what you declared to us, showing that a descending heavy body, setting out from rest, must pass through all the intermediate degrees of slowness between that rest and any given degree of speed, degrees that are smaller and smaller without limit. Add to this that this speed and tendency to motion goes on diminishing, for another reason, likewise without limit, and this comes about because the heaviness of the moving body itself can be diminished without limit. So that the causes that diminish the tendency to descend — and consequently favor the projection — are two, namely the lightness of the moving body and its nearness to the terminus of rest, both of them increasable without limit; and against them, on the other hand, stands the opposition of a single cause producing the projection, which, though it too is increasable without limit, I can't grasp how, all by itself, it wouldn't end up overcome by the union and coupling of the other two, likewise increasable without limit.
Salviati: A doubt worthy of Sagredo; and to clear it up, so that we may grasp it more distinctly — since you say yourself that you hold it only confusedly — let us sort it out by reducing it to a figure, which may perhaps also make it easier to resolve. So let us draw a line perpendicular toward the center, and let this be AC, and at right angles to it the horizontal AB, along which the motion of the projection would take place, and along which the projectile would keep traveling with uniform motion, if gravity did not draw it downward. Now imagine a straight line drawn from the point A, making any angle you please with AB, and let this be AE; and let us mark off on AB some equal spaces AF, FH, HK, and from them draw the perpendiculars FG, HI, KL up to AE. And because, as we've said before, a heavy body falling from rest keeps acquiring an ever greater degree of speed from one moment to the next, as the time itself increases, we can picture the spaces AF, FH, HK as representing equal times, and the perpendiculars FG, HI, KL as the degrees of speed acquired in those times — so that the degree of speed acquired in the whole time AK is as the line KL, compared with the degree HI acquired in the time AH, and the degree FG in the time AF; and these degrees KL, HI, FG have (as is plain) the same proportion as the times KA, HA, FA. And if other perpendiculars are drawn from points marked at will on the line FA, we shall always find smaller and smaller degrees, on to infinity, as we proceed toward the point A, which represents the first instant of time and the first state of rest. And this drawing-back toward A represents to us the first propensity toward downward motion, diminished to infinity by the body's approach to that first state of rest — an approach that can itself be increased to infinity.
Now let us find the other diminution of speed, which can likewise be carried on to infinity through the diminution of the body's heaviness; and this will be represented by drawing other lines from the point A, making angles smaller than the angle BAE — as this line AD would be, which, cutting the parallels KL, HI, FG at the points M, N, O, pictures for us the degrees FO, HN, KM acquired in the times AF, AH, AK, smaller than the other degrees FG, HI, KL acquired in the same times — but these last as if by a heavier body, and those first by a lighter one. And it's plain that by drawing the line EA toward AB, narrowing the angle EAB (which can be done to infinity, just as heaviness can be diminished to infinity), the speed of the falling body is likewise diminished to infinity, and with it the cause that hindered the projection. And so it seems that, from the union of these two grounds against the projection — both diminished to infinity — the projection cannot possibly be hindered.
And reducing the whole argument to a few words, we'll say: by narrowing the angle EAB the degrees of speed LK, IH, GF are diminished; and moreover, by drawing the parallels KL, HI, FG back toward the angle A, the same degrees are likewise diminished; and each of the two diminutions extends to infinity. Therefore the speed of the downward motion can be diminished so far and so far (being diminishable doubly to infinity) that it will not suffice to restore the body onto the circumference of the wheel, and consequently to make the projection be hindered and eliminated. On the other hand, to keep the projection from happening, the spaces through which the projectile must descend to rejoin the wheel would have to be made so short and narrow that, however slow — indeed, however infinitely diminished — the body's descent may be, it still suffices to carry it back; and so there would have to be found a diminution of those spaces made not only to infinity, but of such an infinity as would exceed the double infinity produced in the diminution of the falling body's speed. But how shall one magnitude be diminished more than another that is being diminished doubly to infinity? Now let Simplicio note how well one may philosophize about nature without geometry! The degrees of speed, diminished to infinity — both by the diminution of the body's heaviness and by the approach to the first terminus of motion, that is, to the state of rest — are always determinate, and correspond proportionally to the parallels contained between two straight lines meeting at an angle, whether the angle BAE or BAD, or another infinitely more acute, but always rectilinear. But the diminution of the spaces through which the body has to be carried back onto the circumference of the wheel is proportional to another sort of diminution altogether — one contained within lines that make an angle infinitely narrower and more acute than any acute rectilinear angle whatsoever. And here it is. Take any point C on the perpendicular AC, and making it the center, describe with the radius CA an arc AMP, which will cut the parallels that determine the degrees of speed, however small they may be and however contained within a most narrow rectilinear angle. Of these parallels, the parts that remain between the arc and the tangent AB are the amounts of the spaces and of the returns onto the wheel — always smaller, and smaller in ever greater proportion the closer they come to the point of contact; smaller, I say, than those parallels of which they are parts.
The parallels contained between the straight lines, as they draw back toward the angle, always diminish in the same proportion: as, for example, AH being divided in half at the point F, the parallel HI will be double FG, and subdividing FA in half, the parallel produced from the point of division will be half of FG, and continuing the subdivision to infinity, the successive parallels will always be half of the ones just before. But it does not go this way with the lines intercepted between the tangent and the circumference of the circle; for, making the same subdivision on FA and supposing, say, that the parallel coming from the point H were double the one coming from F, this one will then be more than double the following one; and continually, as we come toward the point of contact A, we shall find the preceding lines containing the next following ones three, four, ten, a hundred, a thousand, a hundred thousand, a hundred million times over, and more, to infinity. The shortness, then, of such lines is reduced to such a degree that it far exceeds what is needed to make the projectile — however light it may be — return, indeed even keep itself, upon the circumference.
Sagredo: I follow the whole argument perfectly well, and the force with which it presses home; still, it seems to me that anyone who wanted to give it more trouble could raise a difficulty for us, by saying that of the two causes which make the body's descent slower and slower to infinity, it's plain that the one depending on nearness to the first terminus of the descent always grows in the same proportion — just as the parallels always keep the same proportion among themselves, and so on. But that the diminution of that same speed depending on the diminution of the body's heaviness (which was the second cause) is also made in the same proportion — that doesn't seem so plain. And who assures us that it isn't made according to the proportion of the lines intercepted between the tangent and the circumference, or even in a greater proportion still?
Salviati: I had taken it as true that the speeds of naturally descending bodies follow the proportion of their heavinesses — as a favor to Simplicio and to Aristotle, who in several places asserts it as an obvious proposition. You, as a favor to our adversary, put this in doubt, and assert that the speed may increase in a greater proportion — even infinitely greater — than that of the heaviness, so that the whole preceding argument falls to the ground. It remains for me, in order to uphold it, to say that the proportion of the speeds is much smaller than that of the heavinesses, and thus not only to sustain but to fortify what has been said. And as proof of this I bring in experience, which will show us that a body even thirty or forty times heavier than another — as, for example, a ball of lead and one of cork — will not move even by a long way twice as fast. Now, if the projection would not occur even when the falling body's speed were diminished according to the proportion of the heaviness, much less will it occur whenever the speed is lessened only a little, however much weight is taken away. But even granting that the speed were diminished in a proportion far greater than that by which the heaviness is lessened — even if it were the very proportion by which those parallels between the tangent and the circumference diminish — I still perceive no necessity whatsoever that would persuade me the projection must occur with materials however light you please; indeed, I affirm that it will not occur — understanding, however, materials that are not properly weightless, that is, devoid of all heaviness and by their nature rising upward, but materials that descend most slowly and have the very least heaviness. And what moves me to believe so is this: the diminution of heaviness, made according to the proportion of the parallels between the tangent and the circumference, has for its last and utmost terminus the nullity of weight, just as those parallels have for the last terminus of their diminution the contact itself, which is an indivisible point. Now heaviness is never diminished all the way to that last terminus, for then the body would not be heavy at all; but the space of the projectile's return to the circumference is indeed reduced to the utmost smallness — which is when the body rests upon the circumference at the very point of contact, so that to return there it needs no space at all. And therefore, however slight the propensity toward downward motion may be, it is always more than enough to bring the body back onto the circumference, from which it is distant by the smallest space — that is, by nothing.
Sagredo: Truly the argument is very subtle, but just as conclusive; and one is forced to confess that to try to treat questions of nature without geometry is to attempt what is impossible to be done.
Salviati: But Simplicio won't say so — though I don't believe he's one of those Peripatetics who dissuade their disciples from the study of mathematics, on the grounds that it corrupts the reasoning and makes it less fit for contemplation.
Simplicio: I wouldn't do Plato that wrong; but I would say, with Aristotle, that he immersed himself too deeply and grew too enamored of that geometry of his. For in the end these mathematical subtleties, Salviati, are true in the abstract, but applied to sensible, physical matter they don't answer. The mathematicians will prove very well, with their principles, that (for example) sphaera tangit planum in puncto — a sphere touches a plane at a point — a proposition much like the present one; but when it comes to matter, things go another way. And I'd say the same of these angles of contact and these proportions: they all come to nothing when one comes to material, sensible things.
Salviati: So you don't believe, then, that the tangent touches the surface of the terrestrial globe at a point?
Simplicio: Not at a single point; I believe that a straight line goes on touching the surface even of water — let alone of the Earth — for many, many dozens, and perhaps hundreds, of braccia before it separates from it.
Salviati: But if I grant you this, don't you see that it's so much the worse for your case? For if, even granting that the tangent were separated from the Earth's surface everywhere but a single point, it has nonetheless been demonstrated that, because of the great narrowness of the angle of contact (if it should even be called an angle), the projectile would not separate — how much less cause will it have to separate if that angle is closed up altogether, and the surface and the tangent proceed together as one? Don't you see that in this way the projection would take place upon the Earth's very surface, which is as much as to say that it wouldn't take place at all? You see, then, the force of truth: while you try to knock it down, your own assaults raise it up and strengthen it. But now that I've drawn you out of this error, I wouldn't want to leave you in this other one — your supposing that a material sphere does not touch a plane at a single point. I'd wish, rather, that this conversation, of just a few hours though it be, held with people who have some knowledge of geometry, might make you appear a little more intelligent among those who know nothing of it. Now, to show you how great is the error of those who say that a sphere — say, of bronze — does not touch a plane — say, of steel — at a point, tell me: what would you make of someone who said, and constantly maintained, that the sphere were not truly a sphere?
Simplicio: I'd judge him utterly devoid of reason.
Salviati: In just this state is the man who says that a material sphere doesn't touch a plane — a material one too — at a point; for to say this is the same as saying that the sphere is not a sphere. And to prove that this is so, tell me: in what do you place the essence of the sphere? That is, what is it that makes the sphere differ from all other solid bodies?
Simplicio: I believe that being a sphere consists in having all the straight lines drawn from its center to the circumference equal.
Salviati: So that when such lines were not equal, that solid would no longer be a sphere.
Simplicio: No, sir.
Salviati: Tell me next whether you believe that, of the many lines that can be drawn between two points, there can be more than a single straight one.
Simplicio: No, sir.
Salviati: But you understand, too, that this single straight line will then of necessity be the shortest of all the others.
Simplicio: I do, and I even have a clear demonstration of it, brought forward by a great Peripatetic philosopher; and it seems to me, if I remember rightly, that he offers it while reproving Archimedes, who assumes it as known when it could be demonstrated.
Salviati: This must have been a great mathematician, to have been able to demonstrate what Archimedes neither knew how nor was able to demonstrate; and if the demonstration comes back to you, I'd gladly hear it, for I remember perfectly well that Archimedes, in his books On the Sphere and the Cylinder, puts this proposition among the postulates, and I hold it for certain that he took it to be indemonstrable.
Simplicio: I think it will come back to me, for it's quite easy and short.
Salviati: So much the greater, then, will be Archimedes' shame, and the glory of this philosopher.
Simplicio: I'll draw his figure. Between the points A and B draw the straight line AB and the curve ACB, of which he wants to prove the straight one to be the shorter; and the proof runs like this. On the curve take a point, which would be C, and draw two other straight lines AC, CB, which two are longer than AB alone — as Euclid demonstrates. But the curve ACB is greater than the two straight lines AC, CB; therefore, a fortiori — all the more so — the curve ACB will be much greater than the straight line AB, which is what was to be demonstrated.
Salviati: I don't believe that if you searched out all the paralogisms in the world you could find one more fitting than this to give an example of the most solemn fallacy among all fallacies — namely, the one that proves ignotum per ignotius, the unknown by the more unknown.
Simplicio: How so?
Salviati: How so? The unknown conclusion you want to prove — isn't it that the curve ACB is longer than the straight line AB? And the middle term, taken as known — isn't it that the curve ACB is greater than the two lines AC, CB, which are known to be greater than AB? And if it's unknown to you that the curve is greater than the straight line AB alone, how will it not be much more unknown that it's greater than the two lines AC, CB, which are known to be greater than AB alone? And yet you take that as known?
Simplicio: I still don't quite understand where the fallacy lies.
Salviati: Since the two straight lines are greater than AB (as is known from Euclid), then whenever the curve is greater than the two lines AC, CB, will it not be much greater than the straight line AB alone?
Simplicio: Yes, sir.
Salviati: That the curve ACB is greater than the straight line AB is the conclusion — better known than the middle term, which is that the same curve is greater than the two lines AC, CB. Now, when the middle is less known than the conclusion, that's called proving ignotum per ignotius. Now let's get back to our subject: it's enough that you grant the straight line to be the shortest of all the lines that can be drawn between two points. And as for the main conclusion — you say the material sphere doesn't touch the plane at a single point: what, then, is its contact?
Simplicio: It will be a part of its surface.
Salviati: And the contact, likewise, of another sphere equal to the first — will that too be a similar little piece of its surface?
Simplicio: There's no reason it shouldn't be so.
Salviati: Then the two spheres too, in touching, will touch with those same two little pieces of surface; because, since each of them fits the same plane, they must necessarily fit each other as well. Now imagine the two spheres, whose centers are A and B, touching, and let their centers be joined by the straight line AB, which will pass through the point of contact. Let it pass through the point C, and taking another point D in the contact, let the two lines AD, BD be joined, so that the triangle ADB is formed, of which the two sides AD, DB will be equal to the single other line ACB — since both those and this contain two radii, which by the definition of the sphere are all equal. And thus the straight line AB, drawn between the two centers A and B, will not be the shortest of all, there being the two AD, DB equal to it — which, by your own concessions, is absurd.
Simplicio: This demonstration holds for spheres in the abstract, not for material ones.
Salviati: Then point out to me where the fallacy of my argument lies, since it doesn't hold for material spheres but does hold for immaterial, abstract ones.
Simplicio: Material spheres are subject to many accidents that immaterial ones aren't. And why couldn't it be that, when a metal sphere rests on a plane, its own weight presses in such a way that the plane gives a little, or else that the sphere itself gets dented at the contact? Besides, that plane can hardly be perfect — if for no other reason, at least because matter is porous; and perhaps it will be no less hard to find a sphere so perfect that it has all the lines from center to surface exactly and precisely equal.
Salviati: Oh, all these things I readily grant you, but they're quite beside the point; for while you want to show me that a material sphere doesn't touch a material plane at a point, you make use of a sphere that isn't a sphere and a plane that isn't a plane — since, by your own account, either these things aren't to be found in the world, or, if they are found, they get spoiled in being applied to produce the effect. It would have been less bad, then, for you to grant the conclusion, but conditionally — that is, that if there were given in matter a sphere and a plane that were, and stayed, perfect, they would touch at a single point — and then to deny that this can ever be had.
Simplicio: I believe the philosophers' proposition should be understood in that sense; for there's no doubt that the imperfection of matter makes it so that things taken in the concrete don't answer to those considered in the abstract.
Salviati: Don't answer? On the contrary — what you yourself have just said proves that they answer exactly.
Simplicio: How so?
Salviati: Don't you say that, because of the imperfection of matter, that body which ought to be a perfect sphere, and that plane which ought to be a perfect plane, don't turn out in the concrete to be such as one pictures them in the abstract?
Simplicio: Just so.
Salviati: So then, whenever you actually bring a material sphere up against a material plane, you're bringing an imperfect sphere against an imperfect plane; and these, you say, don't touch at a point. But I tell you that in the abstract too, an immaterial sphere that isn't a perfect sphere can touch an immaterial plane that isn't a perfect plane — not at a point, but along part of its surface. So that so far, what happens in the concrete happens in exactly the same way in the abstract. And it would be a strange new thing indeed if the sums and reckonings done in abstract numbers didn't then match up with the gold and silver coins and the goods in the concrete world. But do you know what really happens, Simplicio? Just as, to make the accounts come out right on sugar, silk, and wool, the accountant has to make his deductions for the weight of crates, wrappings, and other packaging, so too, when the geometer-philosopher wants to recognize in the concrete the effects he's proved in the abstract, he has to subtract the hindrances of matter. And if he knows how to do that, I assure you the results will tally every bit as exactly as arithmetical calculations. So the errors lie neither in the abstract nor in the concrete, neither in geometry nor in physics, but in the reckoner who doesn't know how to do his sums correctly. So if you had a perfect sphere and a perfect plane, material though they were, have no doubt they would touch at a point; and if that was and is impossible to obtain, then it was quite beside the point to say that sphaera aenea non tangit in puncto — a bronze sphere does not touch at a point. But let me add one thing more, Simplicio: granting you that no perfect spherical shape and no perfect plane can be had in matter, do you believe two material bodies can be had whose surfaces are curved in some part and in some way — even as irregularly as you please?
Simplicio: Of those, I don't think we're short.
Salviati: Well, if there are such, these too will touch at a point — for touching at a single point is by no means the special privilege of the perfect sphere and the perfect plane. In fact, anyone who looked into this matter more closely would find it far harder to find two bodies that touch along part of their surfaces than at a single point. Because for two surfaces to fit snugly together, either both must be exactly flat, or, if one bulges out, the other must be hollowed — and hollowed with a curve that answers exactly to the bulge of the other; and these conditions, by their too narrow specification, are far harder to meet than the others, which in their loose randomness are infinite in number.
Simplicio: So you believe that two stones, or two pieces of iron, taken at random and set together, most of the time touch at a single point?
Salviati: In random encounters, I think not — partly because there'll usually be a bit of yielding grime on them, partly because no care is taken to bring them together without some knock, and the slightest one is enough to make one surface give a little to the other, so that they mutually shape themselves, at least in some tiny patch, each to the imprint of the other. But if their surfaces were well polished, and both were laid on a table — so that neither pressed down on the other — and pushed gently toward each other, I have no doubt they could be brought to simple contact at a single point.
Sagredo: With your leave, I really must raise a certain difficulty of mine, which came to me on hearing Simplicio put forward the impossibility of finding a solid material body with a perfectly spherical shape, and on seeing Salviati in a way grant him his assent by not contradicting him. So I'd like to know whether the same difficulty arises in shaping a solid into some other figure — that is, to put it more clearly, whether there's any greater difficulty in reducing a block of marble to the shape of a perfect sphere than to that of a perfect pyramid, or a perfect horse, or a perfect locust.
Salviati: I'll take this first answer myself. And first let me excuse the assent you think I gave Simplicio — it was only for the moment, because I too had it in mind, before moving on to another subject, to say something that may well be the same as your thought, or very close to it. And in answer to your first question, I say that if any shape can be given to a solid, the spherical is the easiest of them all — as it's also the simplest, and holds among solid figures the place the circle holds among plane ones. The drawing of that circle, being easier than any other, has alone been judged by mathematicians worthy of a place among the postulates governing the drawing of every other figure. And forming a sphere is so easy that if you cut a circular hollow in a flat plate of hard metal, and inside it you roll about at random any solid roughly rounded off, it will by itself, with no further contrivance, be reduced to a spherical shape as perfect as can be — provided that solid isn't smaller than the sphere that would pass through that circle. And what's still more worth noting is that within that same hollow, spheres of different sizes will be formed. As for what it takes to form a horse — or, as you say, a locust — I leave that for you to judge, knowing as you do that very few sculptors in the world are up to it. And I believe Simplicio won't disagree with me on this particular point.
Simplicio: I don't know that I disagree with you in the least. My opinion is that none of the shapes named can be perfectly obtained; but as for coming as close as possible to the most perfect degree, I think it's incomparably easier to reduce the solid to a spherical shape than to the form of a horse or a locust.
Sagredo: And this greater difficulty — what do you think it depends on?
Simplicio: Just as the great ease in forming the sphere derives from its absolute simplicity and uniformity, so the utmost irregularity makes it extremely difficult to introduce the other figures.
Sagredo: So then, since irregularity is the cause of difficulty, the shape of a stone broken at random with a hammer will also be among the hard ones to bring about — being itself irregular, perhaps more so than the horse's?
Simplicio: So it must be.
Sagredo: But tell me: that shape, whatever it may be, that the stone has — does it have it most perfectly, or not?
Simplicio: The one it has, it has so perfectly that no other fits it so exactly.
Sagredo: So then, if among irregular shapes — hard, therefore, to achieve — we nonetheless find infinitely many obtained most perfectly, by what reasoning can it be said that the simplest, and therefore the easiest of all, is impossible to find?
Salviati: Gentlemen, by your leave, it seems to me we've wandered into a dispute not much weightier than the old squabble over goat's wool; and whereas our discussions ought to go on being about serious and weighty matters, we're spending our time in frivolous, trifling wrangles. Let's remember, please, that the search for the constitution of the world is one of the greatest and noblest problems there is in nature — and all the greater for being aimed at the solution of that other one, I mean the cause of the ebb and flow of the sea, sought by every great man there's ever been and perhaps found by none. So, when we've nothing left to bring forward for the complete resolution of the objection drawn from the whirling of the Earth — which was the last one raised as an argument for its immobility about its own center — we can move on to examining the things for and against the annual motion.
Sagredo: I wouldn't have you, Salviati, measure the rest of our minds by the measure of your own. You, always used to busying yourself with the loftiest contemplations, judge as frivolous and low some of the very things that seem to us worthy food for our intellects. So now and then, for our satisfaction, don't scorn to stoop and grant something to our curiosity. As for the resolution of that last objection, drawn from the flinging-off of the daily whirl, far less than what's been offered would have satisfied me. Still, the things that have been said over and above the need struck me as so intriguing that, far from tiring my imagination, they've kept it entertained by their novelty, with a delight I couldn't wish greater. So if you have some further speculation to add, do bring it out — for my part I'll very gladly hear it.
Salviati: In the things I've discovered myself I've always felt the greatest delight; and after that, which is the greatest of all, I take great pleasure in sharing them with some friend who understands them and shows a taste for them. Now, since you're one of these, I'll loosen the rein a little on my ambition — which quietly enjoys itself when I show myself sharper than some other reputed to be keen-sighted — and produce, to cap off and round out our past discussion, another fallacy of the followers of Ptolemy and Aristotle, drawn from the very argument already put forward.
Sagredo: There — I'm eagerly bracing myself to hear it.
Salviati: So far we've passed over and granted Ptolemy, as an undoubted fact, that since the flinging-off of the stone proceeds from the speed of the wheel turned about its center, the cause of that flinging grows exactly as the speed of the whirl increases. From which it was inferred that, since the speed of the Earth's whirl is vastly greater than that of any machine we can artificially set spinning, the extrusion of stones and animals and so on would consequently have to be violent in the extreme. Now I note that in this reasoning there's a very great fallacy, in that we compare the speeds with one another indiscriminately and absolutely. It's true that if I compare the speeds of the same wheel, or of two wheels equal to each other, the one turned faster will fling the stones with greater impetus, and as the speed grows, the cause of the projection grows in the same proportion. But when the speed is made greater not by increasing the speed in the same wheel — which would be by making it turn more times in equal stretches of time — but by increasing the diameter and making the wheel bigger, so that the time of one turn stays the same in the small wheel as in the great one, and only in the great one is the speed greater because its circumference is greater: let no one believe that the cause of the flinging in the great wheel grows according to the proportion of the speed of its circumference to the speed of the circumference of the smaller wheel — for this is utterly false, as a very quick experiment can show us roughly for now. A stone that we could fling with a rod one braccio long, we couldn't fling with one six braccia long — even though the motion of the end of the long rod, that is, of the stone set into it, were twice as fast as the motion of the tip of the shorter rod, which would be the case if the speeds were such that in the time of one full turn of the longer rod, the shorter made three.
Sagredo: What you tell me, Salviati, I already grasp must necessarily come out so; but the reason doesn't readily come to me — why equal speeds shouldn't act equally in extruding projectiles, but the smaller wheel's far more than the larger's. So please explain to me how the matter runs.
Simplicio: You, Sagredo, have this time shown yourself unlike your usual self — you who ordinarily see into everything in a moment, and now you've passed over a fallacy lodged in the experiment of the rods, one that I've managed to see into. And it's the different way of operating when you make the throw now with the short rod, now with the long one. Because to make the stone fly out of the notch, you mustn't keep its motion uniform; rather, at the moment it's fastest, you have to hold back your arm and check the rod's speed, whereupon the stone, already in very swift motion, flies off and moves with impetus. But such a check can't be made with the longer rod, which, by its length and flexibility, doesn't wholly obey the arm's braking; instead, going on to accompany the stone for some distance, by gently reining it in it keeps it attached, and doesn't — as if it had struck a hard obstacle — let it fly free of itself. For if both rods were to strike against a stop that halted them, I believe the stone would fly off equally from the one and the other, even though their motions were equally fast.
Sagredo: With Salviati's leave, I'll make some reply to Simplicio, since he's turned to me. And I say that in his account there's good and bad: good, because nearly all of it is true; bad, because it doesn't quite bear on our point. Very true it is that when the thing carrying the stones at speed strikes an immovable stop, they run on with impetus — the same effect one sees happen all the time in a boat that, running swiftly, runs aground or strikes some obstacle: everyone aboard, caught off guard, suddenly pitches and falls toward the way the vessel was going. And if the terrestrial globe were to meet an obstacle such that it wholly resisted its whirl and stopped it, then indeed I believe that not only the beasts, the buildings, and the cities, but the mountains, the lakes, and the seas would be overturned — and it would be a wonder if the globe itself didn't fall to pieces. But none of this bears on our point, for we're speaking of what might follow from the motion of the Earth turning uniformly and placidly upon itself, even if at great speed. Likewise what you say about the rods is in part true, but Salviati didn't bring it forward as something that fits our subject exactly — only as an example that might roughly rouse our minds to consider more carefully whether, when the speed is increased in whatever way, the cause of the projection increases in the same proportion. So that, for example, if a wheel ten braccia in diameter, moving so that a point on its circumference passed over a hundred braccia in a minute of an hour, thereby had the impetus to fling a stone — whether that impetus grows a hundred thousand times over in a wheel a million braccia in diameter. This Salviati denies, and I'm inclined to believe the same; but not knowing the reason, I've asked him for it, and I'm eagerly awaiting it.
Salviati: Here I am to give you what satisfaction lies within my powers; and though in my first words it may seem I'm going after things foreign to our point, I believe that as the reasoning proceeds we'll find they aren't so after all. So let Sagredo tell me in what things he's observed the resistance of a movable body to being moved to consist.
Sagredo: For now I don't see any internal resistance in the body to being moved except its natural inclination and propensity toward the contrary motion — as in heavy bodies, which have a propensity to motion downward, the resistance is to motion upward. And I said internal resistance because I believe that's the one you mean, not the external ones, which are accidental and many.
Salviati: That's what I meant, and your sharpness has outrun my care in asking. But if I've been sparing in my questioning, I suspect that Sagredo hasn't, with his answer, fully matched the question — and that in the body, besides the natural inclination toward the contrary terminus, there's another quality, likewise intrinsic and natural, that makes it resistant to motion. So tell me again: don't you believe that the inclination, say, of heavy bodies to move downward is equal to their resistance to being pushed upward?
Sagredo: I believe it's exactly so; and that's why I see two equal weights in a balance stay still in equilibrium, the heaviness of the one resisting being lifted against the heaviness with which the other, pressing down, would raise it.
Salviati: Very good; so that to have the one lift the other, you'd have to add weight to the one pressing down, or take some from the other. But if the resistance to upward motion consists in heaviness alone, how does it come about that in a balance with unequal arms — that is, in the steelyard — a weight of a hundred pounds, by its pressing down, sometimes isn't enough to lift one of four pounds that opposes it, while this four-pound one, by lowering, can lift the hundred-pound one? For such is the effect of the sliding weight against the heavy load we want to weigh. If the resistance to being moved resides in heaviness alone, how can the sliding weight, with its mere four pounds, resist the weight of a bale of wool or silk that runs to eight hundred or a thousand — indeed, how can it overcome the bale with its moment and lift it? We really must say, Sagredo, that here we're working with a resistance and a force other than that of simple heaviness.
Sagredo: It must be so; but tell me, what is this second power?
Salviati: It's what wasn't there in the equal-armed balance. Consider what's new in the steelyard — and in that novelty necessarily lies the cause of the new effect.
Sagredo: I think your prompting has jogged something in me. In both instruments we work with weight and with motion: in the balance the motions are equal, and so one weight has to exceed the other in heaviness to move it; in the steelyard the smaller weight won't move the larger unless the larger moves little — hanging at the smaller distance — while the smaller moves much, hanging at the greater distance. So we must say that the smaller weight overcomes the larger's resistance by moving much, while the other moves little.
Salviati: Which is as much as to say that the speed of the less heavy body makes up for the heaviness of the heavier, slower one.
Sagredo: But do you believe that speed makes up for heaviness exactly? That is, that the moment and force of a body of, say, four pounds is as great as that of one of a hundred, whenever the first has a hundred degrees of speed and the second only four?
Salviati: Certainly, as I could show you with many experiments; but for now let the confirmation of this one alone, the steelyard, suffice — where you'll see the light sliding weight able to hold up and balance the very heavy bale just when its distance from the center, on which the steelyard rests and turns, is as much greater than the bale's smaller distance as the bale's absolute weight is greater than the sliding weight's. And that the great bale can't with its weight lift the sliding weight, so much lighter — no cause for this can be seen but the disparity of the motions each would have to make, since the bale, by lowering a single finger's width, would raise the sliding weight a hundred fingers' width (granting that the bale weighed as much as a hundred sliding weights, and that the sliding weight's distance from the steelyard's center was a hundred times the distance between that same center and the point where the bale hangs). And the sliding weight's moving a hundred fingers' width in the time the bale moves a single one is the same as saying the speed of the sliding weight's motion is a hundred times greater than the speed of the bale's. Now fix it firmly in your imagination, as a true and well-known principle, that the resistance coming from the speed of motion makes up for what depends on the heaviness of another body. So that, consequently, a body of one pound moving with a hundred degrees of speed resists being checked exactly as much as another body of a hundred pounds whose speed is a single degree. And two equal bodies will resist being moved equally, if they're to be made to move with equal speed; but if one is to be moved faster than the other, it will offer greater resistance, in proportion to the greater speed you want to give it. These things settled, let's come to the working-out of our problem; and for easier understanding let's draw ourselves a little figure. Let there be two unequal wheels about this center A: let the circumference of the smaller be BG, and of the larger CEH, and let the semidiameter ABC stand upright to the horizon; through the points B and C let's mark the straight tangent lines BF and CD, and on the arcs BG, CE let two equal parts BG, CE be taken. And let it be understood that the two wheels are turned about their centers with equal speeds, so that two bodies — which would be, say, two stones — placed at the points B and C are carried along the circumferences BG, CE with equal speeds, such that in the same time the stone B would run through the arc BG, the stone C would pass through the arc CE. I now say that the whirl of the smaller wheel is far more powerful to make the projection of stone B than the whirl of the larger wheel is for stone C. For since, as already explained, the projection must be made along the tangent, when the stones B, C were to separate from their wheels and begin the motion of projection from the points B, C, they'd be flung along the tangents BF, CD by the impetus conceived from the whirl. Along the tangents BF, CD, then, the two stones have equal impetuses to run, and would run along them if they weren't deflected by some other force. Isn't that so, Sagredo?
Sagredo: That's how the matter seems to stand.
Salviati: But what force do you suppose could be the one that deflects the stones from moving along the tangents, where the impetus of the whirl truly flings them?
Sagredo: It's either their own gravity, or some glue that keeps them settled and stuck onto the wheels.
Salviati: But to deflect a moving body from the path in which it has its impetus, doesn't it take a greater or a smaller force depending on whether the deflection has to be greater or smaller — that is, depending on whether, in the deflection, the body must in the same time cross a greater or a smaller space?
Sagredo: Yes, because we already concluded above that to make a body move, the greater the speed you have to give it, the greater the moving power must be.
Salviati: Now consider this. To deflect the stone on the smaller wheel from the projectile motion it would make along the tangent BF, and to keep it fastened to the wheel, its own gravity has to draw it back by the length of the secant FG — that is, by the perpendicular dropped from point G onto the line BF. On the larger wheel, though, the drawing-back need be no more than the secant DE — the perpendicular dropped from point E onto the tangent DC — which is far shorter than FG, and shorter and shorter still as the wheel is made larger. And since these drawings-back must be accomplished in equal times — that is, in the while that the two equal arcs BG and CE are traversed — the one belonging to stone B, namely the pull-back FG, will have to be faster than the other, DE. So much greater force is needed to keep stone B joined to its little wheel than to keep stone C joined to its big one; which is the same as saying that some trifling thing will block the flinging-off on the big wheel that would not prevent it on the little one. Plainly, then, the larger the wheel grows, the weaker the cause of projection becomes.
Sagredo: From what I now understand, thanks to your patient breaking-down of it, I think I can satisfy my mind with a fairly brief account. Since the equal speed of the two wheels impresses an equal impetus along the tangents into both stones, one sees that the great circumference, parting only slightly from its tangent, goes along humoring the stone, in a way — with a gentle bit softly curbing in it the appetite, so to speak, to leave the circumference — so that any small restraint, whether of the stone's own downward inclination or of some glue, is enough to keep it joined. But that same restraint turns out too weak to do the job on the little wheel, which, humoring the tangent's direction so little, tries with too greedy a hunger to hold the stone to itself; and since the curb and the glue are no stronger than what kept the other stone united with the larger wheel, the halter snaps and off it runs along the tangent. So I not only see that everyone was mistaken who believed the cause of projection grows as the speed of the whirl grows; I go further, and consider that, since the projection diminishes as the wheel grows — provided the same speed is kept in the wheels — it might perhaps be true that, to make the big wheel fling like the little one, you'd have to increase its speed by as much as you increase its diameter. That would be the case when the whole revolutions are completed in equal times; and so one might reckon that the whirl of the Earth is no more able to fling off stones than any other little wheel turning so slowly that in twenty-four hours it makes a single turn.
Salviati: For now I don't want us to press the inquiry that far. It's enough that we've shown — abundantly enough, if I'm not mistaken — the emptiness of an argument that at first glance looked utterly conclusive, and was reckoned so by very great men. And I'll count the time and the words well spent if I've won even a little belief in Simplicio's mind — not, I'll say, in the mobility of the Earth, but at least in this: that the opinion of those who believe it is not so ridiculous and foolish as the ranks of the common philosophers hold it to be.
Simplicio: The solutions offered so far to the objections raised against this daily revolution of the Earth — the ones drawn from heavy bodies falling from the top of a tower, and from projectiles shot straight up, or at any sideways slant, toward east, west, south, or north, and so on — have in some measure lessened the old disbelief I'd conceived against this opinion. But other, larger difficulties are now turning in my imagination, ones I absolutely would not know how to work myself free of — nor perhaps do I think you yourselves could untangle them. It may even be that they haven't reached your ears, since they're quite recent. These are the objections of two authors who write ex professo against Copernicus. The first are read in a little book of natural conclusions; the others are by a great philosopher and mathematician both, set into a treatise he wrote in favor of Aristotle and his opinion about the unalterability of the heavens, where he proves that not only the comets but also the new stars — I mean the one of '72 in Cassiopeia and the one of 1604 in Sagittarius — were not above the spheres of the planets at all, but absolutely below the concave of the Moon, in the elemental sphere. And this he demonstrates against Tycho, Kepler, and many other observing astronomers, beating them with their own weapons, that is, by way of the parallaxes. If it please you, I'll lay out the reasons of the one and the other, for I've read them more than once with attention; and you can weigh their force and give your opinion.
Salviati: Since our chief aim is to bring out and weigh everything that has been urged for and against the two systems, the Ptolemaic and the Copernican, it's not right to pass over anything written on the matter.
Simplicio: Then I'll begin with the objections in the little book of conclusions, and come to the others afterward. First, then, the author very shrewdly goes calculating how many miles per hour a point on the Earth's surface set under the equinoctial line travels, and how many are traveled by other points set on other parallels; and not content to investigate these motions by the hour, he finds them also for a single minute, and not content with the minute, he tracks it down to a single second. And more: he goes on to show, as plainly as could be, how many miles an artillery ball would travel in such spans of time if it were placed in the concave of the lunar sphere — supposing that concave even as large as Copernicus himself imagines it, so as to strip the adversary of every loophole. And having made this most ingenious and exquisite reckoning, he demonstrates that a heavy body falling from up there would take a good deal more than six days to reach the center of the Earth, toward which all heavy things naturally tend. Now, if by God's absolute power, or by some angel, a very large artillery ball were miraculously carried up there and set at the point directly above us, our vertical point, and from there let go free, it is — in his view and mine — a most incredible thing that in coming down it would keep itself always in our vertical line, continuing to turn with the Earth about its center for so many days, tracing under the equinoctial a spiral line in the plane of that greatest circle, and under other parallels spiral lines around cones, and under the poles falling by a simple straight line. He then establishes and confirms this great improbability by putting forward, in the form of questions, many difficulties impossible for the followers of Copernicus to remove; and they are, if I remember rightly —
Salviati: Gently, a moment — please, Simplicio, don't tangle me up with so many novelties at one stroke. I have a poor memory, and so I need to go step by step. And since it comes back to me that I once wanted to calculate how long a similar heavy body, falling from the concave of the Moon, would take to arrive at the center of the Earth — and I seem to recall that the time wouldn't be so long — it'll be well for you to tell us by what rule this author made his computation.
Simplicio: He made it so as to prove his point a fortiori, granting a great advantage to the opposing side: he supposes that the speed of the falling body down the vertical line toward the center of the Earth was equal to the speed of its circular motion made on the greatest circle of the concave of the lunar sphere — at which rate it would come to travel twelve thousand six hundred German miles in an hour, a thing that truly has the impossible about it. Yet, to abound in caution and give every advantage to the other side, he supposes it true, and concludes that the time of the fall must in any case be more than six days.
Salviati: And that's the whole of his procedure? And with this demonstration he proves the time of such a fall must be more than six days?
Sagredo: It seems to me he's conducted himself all too modestly. Since it lay within his own choosing to give the falling body whatever speed he liked — and consequently to make it reach the Earth in six months, or even six years — he contented himself with six days. But please, Salviati, restore my appetite a little by telling me how your own computation went, since you say you once did it. For I'm quite sure that if the problem hadn't called for some clever operation, you'd never have set your mind to it.
Salviati: It isn't enough, Sagredo, that the conclusion be noble and grand; the point is to treat it nobly. Who doesn't know that in cutting up the limbs of an animal one can uncover infinite marvels of provident and most wise nature? Yet for every one that the anatomist cuts, the butcher hacks up a thousand. And I, in trying now to satisfy your request, don't know in which of the two costumes I'm to appear on stage. Still, taking heart from the entrance of Simplicio's author, I won't refuse to recite for you — if it comes back to me — the method I used. But before I set my hand to anything else, I can't help saying that I strongly doubt Simplicio has faithfully reported the way this author of his finds that the artillery ball, in coming from the concave of the Moon to the center of the Earth, would take more than six days. For if he had supposed its speed in descending to be equal to that of the concave — as Simplicio says he supposes — he'd have shown himself utterly stripped even of the first and simplest notions of geometry. Indeed, I marvel that Simplicio himself, in accepting the supposition he describes, doesn't see the immense absurdity it contains.
Simplicio: That I may have blundered in reporting it is possible; but that you should uncover a fallacy inside it — that, surely, is not.
Salviati: Perhaps I haven't rightly grasped what you reported. Don't you say this author makes the speed of the ball's motion in descending equal to the speed it had while going around, standing in the concave of the Moon — and that, dropping with that speed, it would take itself to the center in six days?
Simplicio: So he seems to write.
Salviati: And you don't see so great an absurdity? But surely you're dissembling — for it can't be that you don't know that the semidiameter of a circle is less than a sixth part of the circumference; and that, in consequence, the time in which a moving body will pass over the semidiameter will be less than a sixth part of the time in which, moved with the same speed, it would pass over the circumference; and therefore the ball, descending with the speed at which it was moving in the concave, will arrive at the center in less than four hours — granting that in the concave it completed one revolution in twenty-four hours, as he must suppose in order to keep it always in the same vertical line.
Simplicio: Now I understand the error perfectly; but I wouldn't want to lay it on him undeservedly, and it must be that I erred in reciting his argument. To avoid saddling him with still more, I'd like to have his book; and if there were someone to go and fetch it, I'd be much obliged.
Sagredo: There'll be no shortage of a footman to go flying for it; and it can be done without any loss of time, for meanwhile Salviati will favor us with his computation.
Simplicio: He can go — he'll find it lying open on my desk, together with the other man's, who also argues against Copernicus.
Sagredo: Let's have that one brought as well, for extra safety; and meanwhile Salviati will make his calculation. I've dispatched a servant.
Salviati: Before anything else, we have to consider that the motion of descending heavy bodies is not uniform: starting from rest, they go on continually accelerating — an effect known and observed by everyone except the aforesaid modern author, who, saying nothing of acceleration, makes it steady. But this general knowledge is of no use unless one knows according to what proportion this increase of speed is made — a conclusion that, down to our own times, was unknown to all philosophers, and was first discovered and demonstrated by the Academician, our mutual friend. In certain of his writings, not yet published but shown in confidence to me and to some others of his friends, he demonstrates how the acceleration of the straight-line motion of heavy bodies follows the odd numbers ab unitate — starting from one. That is: mark off however many equal intervals of time you please; if in the first interval the moving body, setting out from rest, has passed over a certain space — say, one canna, a rod's length — then in the second interval it will pass three canne, in the third five, in the fourth seven, and so on in order according to the succeeding odd numbers. Which in sum is the same as saying that the spaces passed by the moving body, starting from rest, stand to one another in the doubled ratio of the times in which those spaces are measured — or, if you like, that the spaces passed are to one another as the squares of the times.
Sagredo: A marvelous thing I'm hearing. And you say there's mathematical demonstration of this?
Salviati: Purest mathematics — and not of this alone, but of many other beautiful properties belonging to natural motions, and to projectiles too, all discovered and demonstrated by our friend. I've seen and studied them all, with the greatest delight and wonder, watching a whole new field of knowledge spring up around a subject on which hundreds of volumes have been written — and not a single one of the infinite admirable conclusions it contains had been observed and understood by anyone before our friend.
Sagredo: You're making me lose my appetite to hear more of the discussions we've begun, and want only to hear some of the demonstrations you're hinting at. So either tell them to me now, or at least give me your firm word to hold a special session on them with me — and with Simplicio present too, if he'd care to hear the properties and incidents of nature's primary effect.
Simplicio: I'll certainly have the will for it, though as far as the natural philosopher is concerned, I don't believe that descending to certain minute particulars is necessary — a general knowledge of the definition of motion, and of the distinction between natural and violent, equable and accelerated, and the like, being enough. For if that had not been enough, I don't believe Aristotle would have failed to teach us all that was lacking.
Salviati: Maybe so. But let's lose no more time on this, for I promise to spend half a day on it separately, for your satisfaction — indeed, it comes back to me now that I once before promised you this very satisfaction. And returning to our begun calculation of the time in which the falling heavy body would come from the concave of the Moon to the center of the Earth: to proceed not arbitrarily and by chance, but by a thoroughly conclusive method, we'll first try to make sure, by experience repeated many times, in how much time a ball — of iron, say — comes to the ground from a height of a hundred braccia.
Sagredo: Taking, though, a ball of some determinate weight — the very one on which we mean to make the computation of the time of the descent from the Moon.
Salviati: That matters not at all, because balls of one, of ten, of a hundred, of a thousand pounds will all measure out the same hundred braccia in the same time.
Simplicio: Oh, that I don't believe — nor does Aristotle believe it, who writes that the speeds of descending heavy bodies stand to one another in the same proportion as their weights.
Salviati: If you, Simplicio, want to admit that as true, then you must also believe that, when two balls of the same material are let fall at the same instant — one of a hundred pounds, the other of one — from a height of a hundred braccia, the big one arrives at the ground before the smaller has descended a single braccio. Now fit your brain, if you can, to imagining that you see the big ball landed on the ground while the little one is still within less than a braccio of the top of the tower.
Sagredo: That this proposition is utterly false, I haven't a doubt in the world; but that yours is entirely true, I'm not quite able to grasp — still, I believe it, since you affirm it so resolutely, which I'm sure you wouldn't do unless you had sure experience or firm demonstration of it.
Salviati: I have both; and when we treat the matter of motions separately, I'll share it with you. Meanwhile, so as not to have occasion to interrupt the thread further, let's set ourselves to make the computation on an iron ball of a hundred pounds, which by repeated experiments descends from a height of a hundred braccia in five seconds. And since, as I told you, the spaces measured by the falling body increase in the doubled proportion — that is, as the squares of the times — then, the time of one minute being twelve times the time of five seconds, if we multiply the hundred braccia by the square of 12, that is, by 144, we'll have 14,400, which will be the number of braccia the same body will pass in one minute. Following the same rule, since an hour is 60 minutes, by multiplying 14,400 — the number of braccia passed in a minute — by the square of 60, that is, by 3,600, we get 51,840,000, the number of braccia to be passed in an hour, which is 17,280 miles. And wanting to know the space that would be passed in 4 hours, we'll multiply 17,280 by 16 (which is the square of 4), and we'll get 276,480 miles — a number far greater than the distance from the concave of the Moon to the center of the Earth, which is 196,000 miles, making the distance of the concave 56 Earth semidiameters, as the modern author does, and the Earth's semidiameter 3,500 miles of 3,000 braccia each, which are our Italian miles. So, Simplicio, that stretch from the concave of the Moon to the center of the Earth, which your reckoner said could not be traversed except in a good deal more than six days — see how, making the computation on experience and not on one's fingers, it would be traversed in a good deal less than 4 hours; and, making the exact computation, it's traversed in 3 hours, 22 minutes, and 4 seconds.
Sagredo: Please, my dear sir, don't cheat me of this exact calculation, for it must be a most beautiful thing.
Salviati: So it truly is. Having, then (as I said), observed by careful experiment how such a body, falling, passes the height of 100 braccia in 5 seconds, we'll say: if 100 braccia are passed in 5 seconds, in how many seconds will 588,000,000 braccia be passed (for that is what 56 semidiameters of the Earth come to)? The rule for this operation is that the third number be multiplied by the square of the second; that gives 14,700,000,000, which is to be divided by the first, that is, by 100; and the square root of the quotient, which is 12,124, is the number sought — that is, 12,124 seconds, which are 3 hours, 22 minutes, and 4 seconds.
Sagredo: I've watched the operation, but I understand nothing of the reason for operating so — nor does it seem the moment now to ask it.
Salviati: On the contrary, I want to tell you, even though you don't ask, because it's quite easy. Let's mark these three numbers with the letters A first, B second, C third: A and C are the numbers of the spaces, B is the number of the time; the fourth number is sought, likewise of the time. And since we know that whatever proportion space A has to space C, the same must the square of time B have to the square of the time sought, therefore, by the golden rule — the rule of three — the number C will be multiplied by the square of the number B, and the product divided by the number A, and the quotient will be the square of the number sought, and its square root will be the very number sought. Now see how easy it is to understand.
Sagredo: All true things are like that, once they've been found — the whole difficulty is in knowing how to find them. I'm entirely satisfied, and I thank you. And if any other curiosity remains for you on this subject, please, tell it — because, if I may speak freely, I'll say, with Simplicio's leave, that from your discourses I always learn some fine new thing, but from those of his philosophers I can't say I've yet learned anything of much weight.
Salviati: There's unfortunately a great deal more we could say about these matters of local motion — motion from place to place — but, as we agreed, we'll save that for a session of its own. For now I'll say something bearing on the author Simplicio has put forward, who thinks he's granted a great advantage to our side in conceding that the cannonball, in falling from the hollow of the Moon's sphere, could arrive with a speed equal to the speed at which it would have moved in its circle had it stayed up there and turned with the daily rotation. Now I tell him that that ball, falling from the hollow all the way to the center, will pick up a degree of speed well more than double the speed of the daily motion of the Moon's hollow; and I'll show this with assumptions that are perfectly true, and not arbitrary.
You must know, then, that a heavy body, as it falls and keeps gaining fresh speed by the proportion already stated, has in itself, at whatever point of its line of motion it happens to be, such a degree of speed that, if it went on moving with that speed uniformly, without increasing it any further, then in a time equal to the time of its descent it would pass twice the space it had passed in the line of its earlier downward motion. So, for example, if that ball, in coming from the hollow of the Moon to its center, has used up 3 hours, 22 minutes, and 4 seconds, I say that on reaching the center it finds itself established in such a degree of speed that, if with that speed — without increasing it any further — it went on moving uniformly, it would pass in another 3 hours, 22 minutes, and 4 seconds twice the space, that is, as much as the whole diameter of the lunar orb. And since from the hollow of the Moon to the center is 196,000 miles, which the ball passes in 3 hours, 22 minutes, and 4 seconds, then (given what has been said) if the ball went on moving with the speed it has on arriving at the center, it would pass, in another 3 hours, 22 minutes, and 4 seconds, twice that space, that is, 392,000 miles: but the same ball, staying in the hollow of the Moon — whose circuit is 1,232,000 miles — and moving with it at the daily motion, would cover in the same time, that is, in 3 hours, 22 minutes, and 4 seconds, 172,880 miles, which is far less than half of the 392,000 miles. There, then, you see how the motion in the hollow is not what the modern author says — of a speed impossible for the falling ball to share, and so on.
Sagredo: The argument would run beautifully and set my mind at rest, if only that one item were settled for me — the moving body's passing twice the space it fell through, in another time equal to the time of its descent, supposing it went on moving uniformly with the greatest degree of speed it had acquired in falling. That's a proposition you've assumed as true once before too, but never proved.
Salviati: That's one of the things our friend has demonstrated, and you'll see it in due time; but meanwhile, with a few conjectures, I want — not to teach you anything new — but to shake you loose from a certain contrary opinion, by showing you that perhaps it can be so. Hang a lead ball by a long, thin thread fastened to the ceiling; if we pull it aside from the vertical and then let it go free, haven't you noticed that as it swings down it passes, of its own accord, beyond the vertical by very nearly as much again?
Sagredo: I've observed it very well, and seen — especially if the ball is quite heavy — that it rises so little short of its drop that I've sometimes believed the upward arc equal to the downward, and so wondered whether its swings might go on forever; and I'd believe they would, if one could remove the hindrance of the air, which, resisting being parted, slows and impedes the pendulum's motion a little. But the hindrance is slight indeed — witness the great number of swings that happen before the moving body comes fully to rest.
Salviati: The motion wouldn't go on forever, Sagredo, even if the air's hindrance were removed entirely, because there's another one, far more hidden.
Sagredo: And what's that? Nothing else comes to my mind.
Salviati: You'll enjoy hearing it, but I'll tell you later; for now let's go on. I put the observation of this pendulum to you so that you'd grasp that the impetus acquired in the downward arc, where the motion is natural, is of itself powerful enough to drive that same ball, by violent motion, through just as much space in the matching upward arc; of itself, I say, once all external hindrances are removed. And I think it's understood without any doubt that, just as in the downward arc the speed keeps growing right down to the lowest point of the vertical, so from that point, up the other arc, it keeps diminishing to the topmost extreme point — diminishing by the very same proportions by which it first went on increasing, so that the degrees of speed at points equally distant from the lowest point are equal to one another. From this it seems to me — reasoning by a certain fittingness — that I may believe that, if the terrestrial globe were bored through the center, a cannonball dropping down such a well would pick up, by the time it reached the center, such an impetus of speed that, having passed the center, it would drive it up on the far side through just as much space as the fall had been, its speed always diminishing beyond the center by decrements matching the increments gained in descending; and the time spent in this second, upward motion would, I think, be equal to the time of the descent.
Now, if the moving body — by successively diminishing, down to total extinction, the highest degree of speed it had at the center — carries itself in a given time through a given space, the same space it had traversed in an equal time while gaining speed from the total lack of it up to that highest degree, then it seems quite reasonable that, if it moved always with the highest degree of speed, it would pass in an equal time both those spaces together. For if we go through in our mind dividing those speeds into growing and shrinking degrees — like, say, these numbers, so that the first up to 10 are the growing ones and the rest down to 1 the shrinking ones, the former belonging to the time of the descent and the latter to the time of the rise — you'll see that, all joined together, they add up to as much as if one of the two parts had been made entirely of the greatest degrees. And therefore the whole space passed with all the degrees of speed, growing and shrinking (which is the whole entire diameter), must equal the space passed by the greatest speeds, which are half as many in number as the aggregate of the growing and the shrinking together. I know I've explained myself rather clumsily, and God grant I make myself understood.
Sagredo: I think I've understood it very well, and can even show in a few words that I've understood. You meant to say that, when the motion begins from rest and the speed goes on growing successively by equal increments — like those of the counting numbers, starting from one, or rather from zero, which represents the state of rest — laying them out like this, and going on for as many as you please, so that the least degree is zero and the greatest is, say, 5: all these degrees of speed, with which the moving body has moved, make the sum of 15. But if the moving body were to move with just as many degrees in number as these, and each of them equal to the greatest, which is 5, the aggregate of all these speeds would be double the others, that is, 30. And so, moving for an equal time, but with a steady speed equal to that of the highest degree, 5, it will have to pass twice the space it passed in the accelerated time, which began from the state of rest.
Salviati: You, true to your very quick and very subtle grasp, have explained the whole thing far more clearly than I did, and have even put me in mind to add something more. For since in accelerated motion the increase is continuous, one cannot parcel out the degrees of speed — which is forever growing — into any fixed number, because, changing from moment to moment, they are always infinite. So we can better illustrate our meaning by picturing a triangle, which would be this one, ABC. Take on the side AC as many equal parts as you like — AD, DE, EF, FG — and through the points D, E, F, G draw straight lines parallel to the base BC. Here I want us to imagine that the parts marked off on the line AC are equal times, and that the parallels drawn through the points D, E, F, G represent for us the degrees of speed, accelerated and increasing equally in equal times; and that the point A is the state of rest, from which the moving body, setting out, has, say, in the time AD acquired the degree of speed DH; in the next stretch of time it has increased the speed above the degree DH up to the degree EI; and so it has made it greater in the times that follow, according to the growth of the lines FK, GL, and so on. But because the acceleration happens continuously, from moment to moment, and not in discrete jumps from one whole chunk of time to another — the terminus A being posited as the least moment of speed, that is, as the state of rest and as the first instant of the ensuing time AD — it's clear that before the degree of speed DH is acquired in the time AD, the body has passed through infinitely many other degrees, smaller and smaller, gained in the infinitely many instants that are in the time DA, corresponding to the infinitely many points in the line DA. So, to represent the infinity of degrees of speed that come before the degree DH, we must imagine infinitely many lines, always smaller and smaller, drawn from the infinitely many points of the line DA, parallel to DH; and this infinity of lines represents for us, in the end, the surface of the triangle AHD. And in this way we'll understand that any space passed by the moving body with a motion that, beginning from rest, goes uniformly accelerating, has used up and made use of infinitely many degrees of growing speed, answering to the infinitely many lines that, beginning from the point A, are imagined drawn parallel to the line HD and to IE, KF, LG, BC, the motion continuing as far as you please. Now let's complete the whole parallelogram AMBC, and prolong up to its side BM not only the parallels marked in the triangle, but the infinity of those imagined produced from all the points of the side AC. And just as BC was the greatest of the triangle's infinite lines, representing for us the greatest degree of speed the moving body acquired in the accelerated motion, and the whole surface of that triangle was the mass and the sum of all the speed with which, in the time AC, it passed such a space, so the parallelogram comes to be a mass and aggregate of just as many degrees of speed, but each one equal to the greatest, BC — and this mass of speed turns out to be double the mass of the growing speeds of the triangle, just as the parallelogram is double the triangle. And therefore, if the moving body that fell made use of the degrees of accelerated speed answering to the triangle ABC, and passed a certain space in a certain time, it's quite reasonable and probable that, making use of the uniform speeds answering to the parallelogram, it will pass, with steady motion in the same time, twice the space passed by the accelerated motion.
Sagredo: I'm entirely satisfied. And if you call this a merely probable argument, what will the necessary demonstrations be like? Would to God that in all of common philosophy even one could be found as conclusive as this!
Simplicio: In natural science one mustn't go looking for exact mathematical proof.
Sagredo: But isn't this matter of motion a natural question? And yet I find that Aristotle doesn't demonstrate for me even the least little property of it. But let's not sidetrack our discussion any further; and you, Salviati, please don't fail to tell me what you hinted was the cause of the pendulum's stopping, over and above the medium's resistance to being parted.
Salviati: Tell me: of two things hanging from unequal lengths, doesn't the one fastened to the longer cord make its swings less frequent?
Sagredo: Yes — provided they moved through equal distances from the vertical.
Salviati: That moving out more or less matters not at all, because the same pendulum always makes its swings in equal times, whether they're very long or very short — that is, whether the pendulum is drawn very far or very little from the vertical; and even if they aren't perfectly equal, they differ imperceptibly, as experience can show you. But even were they very unequal, that wouldn't hurt our case — it would help it. So let's mark the vertical AB, and let a weight C hang from the point A on the cord AC, and another, higher up on the same cord, be E. Draw the cord AC aside from the vertical, and then let it go free: the weights C and E will move through the arcs CBD and EGF. And the weight E, hanging from a shorter distance — and also, by your own account, drawn aside less — wants to come back sooner and make its swings more frequent than the weight C, and so it will keep C from running as far out toward the terminus D as it would if it were free; and thus, bringing it a continual hindrance at every swing, it will finally reduce it to rest. Now the cord itself (take away the weights) is a compound of many heavy pendulums — that is, each of its parts is such a pendulum, attached nearer and nearer to the point A, and so disposed to make its swings ever more and more frequent; and consequently it's able to bring a continual hindrance to the weight C. A sign of this is that, if we observe the cord AC, we'll see it stretched not in a straight line but in an arc; and if, instead of a cord, we take a chain, we'll see this effect far more plainly, especially by drawing the heavy weight C well aside from the vertical AB — for, the chain being composed of many jointed links, each quite heavy, the arcs AEC and AFD will be seen noticeably curved. For this reason, then — that the parts of the chain, the nearer they are to the point A, want to make their swings more frequent — they don't let the lower parts run on as far as they naturally would; and by continually subtracting from the swings of the weight C, they finally stop it, even if the air's hindrance could be taken away.
Sagredo: The books have just arrived, right on time. Take them, Simplicio, and find the passage in question.
Simplicio: Here it is, where he begins to argue against the Earth's daily rotation, having first refuted the annual one: Motus Terrae annuus asserere Copernicanos cogit conversionem eiusdem quotidianam; alias idem Terrae hemispherium continenter ad Solem esset conversum, obumbrato semper averso — and so half the Earth would never see the Sun.
Salviati: It seems to me, from this very first step, that this man hasn't rightly pictured Copernicus's position; for if he'd noticed how Copernicus keeps the axis of the terrestrial globe perpetually parallel to itself, he wouldn't have said that half the Earth would never see the Sun, but that the year would have been a single natural day — that is, that over all parts of the Earth there'd have been six months of day and six months of night, as happens now to those who live under the pole. But let that be forgiven him, and let's come to the rest.
Simplicio: It goes on: Hanc autem gyrationem Terrae impossibilem esse, sic demonstramus — this whirling of the Earth we prove to be impossible, as follows. What comes next is the explanation of the following figure, where you can see drawn a lot of heavy bodies descending, and light ones ascending, and birds that hold themselves up in the air, and so on.
Sagredo: Show me, please. Oh, what lovely pictures — what birds, what balls, and what other pretty things are these?
Simplicio: These are balls coming from the hollow of the Moon.
Sagredo: And this one, what is it?
Simplicio: It's a snail — the kind we call buovoli here in Venice — and it too comes from the hollow of the Moon.
Sagredo: Yes, yes — that's because the Moon has such great power over these shelled creatures, which we call pesci armai.
Simplicio: This next is that calculation I mentioned, of the journey that a point of the Earth placed under the equator — and also on the parallel of 48 degrees — would make in a natural day, in an hour, in a minute, and in a second. And then follows this, where I fear I may have gone wrong in reporting it; so let's read it: His positis, necesse est, Terra circulariter mota, omnia ex aëre eidem etc. Quod si hasce pilas aequales ponemus pondere, magnitudine, gravitate, et in concavo spherae lunaris positas libero descensui permittamus, si motum deorsum aequemus celeritate motui circum (quod tamen secus est, cum pila A etc.), elabentur minimum (ut multum cedamus adversariis) dies sex: quo tempore sexies circa Terram etc.
Salviati: You reported this man's objection all too faithfully. From this you can see, Simplicio, with how much caution people ought to proceed who want to talk others into believing things that perhaps they don't believe themselves: because it seems impossible to me that this author shouldn't have noticed he was imagining a circle whose diameter — which, for mathematicians, is less than a third of the circumference — was more than 12 times greater than the circumference itself; an error that makes something less than one out to be more than 36.
Sagredo: Perhaps these mathematical proportions, which are true in the abstract, don't answer quite so exactly once they're applied concretely to physical, material circles — though it does seem to me that coopers, to find the radius of the head they need to make for a barrel, use the mathematicians' abstract rule, even though such barrel-heads are very material, concrete things. So let Simplicio give this author's excuse, and tell us whether he thinks physics can differ so much from mathematics.
Simplicio: The retreat doesn't seem enough to me, because the discrepancy is too great; and in this case I wouldn't know what else to say, except that quandoque bonus etc. — even the best of them nods now and then. But granting that Salviati's calculation is the sounder one, and that the time of the ball's fall was no more than three hours, it still seems to me that, coming from the hollow of the Moon — so vast an interval away — it would be a marvelous thing for it to have an instinct from nature to keep itself always over the same point of the Earth that it stood above when it set out, rather than falling behind by an enormous interval.
Salviati: The effect may be marvelous, or not marvelous but natural and ordinary, according to what the preceding conditions are. For if the ball (in keeping with the author's own assumptions), while it lingered in the hollow of the Moon, had the circular motion of the twenty-four hours together with the Earth and with the rest of what's contained inside that hollow, then the very same power that made it go around before it descended will go on making it go around during the descent too; and so far is it from failing to follow the Earth's motion — from having to fall behind — that it ought rather to run ahead of it, since, as it draws nearer to the Earth, the circular motion has to be made through continually smaller circles: so that, the ball keeping the same speed it had in the hollow, it ought, as I said, to outrun the Earth's whirl. But if the ball, up in the hollow, had no such circling, then in descending it's under no obligation to keep itself perpendicularly over that point of the Earth which lay beneath it when the fall began; nor will Copernicus, nor any of his followers, say so.
Simplicio: But the author will press the point, as you see, asking from what principle this circular motion of heavy and light bodies derives — that is, whether from an internal principle or an external one.
Salviati: Keeping to the problem we're dealing with, I say that the principle which made the ball go around while it was in the Moon's hollow is the same one that keeps up its circling during the descent too; I'll then leave the author free to make it internal or external as he likes.
Simplicio: The author will prove that it can be neither internal nor external.
Salviati: And I'll answer that the ball up in the concave wasn't moving at all — which frees me from having to explain how, in coming down, it stays forever vertical over the same point, seeing that it won't stay there in the first place.
Simplicio: Fine; but since heavy and light bodies can have no principle, internal or external, for moving in a circle, neither will the terrestrial globe move with circular motion — and so we'll have exactly what we set out to prove.
Salviati: I never said the Earth has no principle of circular motion, internal or external; I said I don't know which of the two it has — and my not knowing has no power to strip it of one. But if this author knows from what principle the other bodies of the world are moved around in their circles — bodies that certainly do move — then I say that whatever makes the Earth move is something like whatever moves Mars and Jupiter, and like whatever he believes moves the starry sphere as well. And if he'll assure me who the mover is of any one of these moving bodies, I bind myself to tell him who makes the Earth move. What's more, I'll do the very same thing if he can teach me who moves the parts of the Earth downward.
Simplicio: The cause of that effect is perfectly well known — everyone knows it's gravity.
Salviati: You're mistaken, Simplicio; you should have said that everyone knows it's called gravity. But I'm not asking its name — I'm asking the essence of the thing; and of that essence you know not one bit more than you know of the essence of whatever moves the stars around. The only difference is the name: to this one we've given a name and made it familiar and homely through the frequent experience of seeing it happen a thousand times a day. But we don't really understand any better what principle or power moves a stone downward than we understand what moves it upward once it's parted from the thrower, or what moves the Moon around — except, as I said, the name: to this one we've assigned the more particular and proper name of gravity, whereas to that one, in a more general term, we assign impressed force; to another we give an intelligence, or an assisting spirit, or an informing one; and to countless other motions we give nature as their cause.
Simplicio: It seems to me this author asks far less than what you're refusing to answer; for he doesn't ask you what, particularly and by name, the principle is that moves heavy and light bodies in a circle — whatever it may be, he only asks whether you judge it intrinsic or extrinsic. So that, for example, even though I don't know what gravity is — the gravity by which the Earth descends — I do know that it's an internal principle, since, unimpeded, it moves spontaneously; and, on the other hand, I know that the principle moving it upward is external, even though I don't know what the force impressed on it by the thrower actually is.
Salviati: Into how many questions we'd have to wander off, if we wanted to settle every difficulty that keeps hooking onto the last one in a chain! You call external — and preternatural and violent too — the principle that moves a heavy projectile upward. But perhaps it's no less internal and natural than the one that moves it down. It might, if you like, be called external and violent while the moving body is still joined to the thrower; but once they're separated, what external thing is left to move the arrow or the ball? So we're forced to admit that the power carrying it upward is no less internal than the one that moves it down; and I hold the upward motion of heavy bodies, from the impetus they've taken on, to be every bit as natural as their downward motion, which depends on gravity.
Simplicio: This I'll never grant; because the one has an internal principle, natural and perpetual, while the other has an external one, violent and finite.
Salviati: If you back away from granting me that the principles of the downward and upward motions of heavy bodies are equally internal and natural, what would you do if I told you they might even be one and the same in number?
Simplicio: I'll leave that for you to judge.
Salviati: No, I want you yourself for judge. So tell me: do you believe that in one and the same natural body there can reside internal principles that are contrary to each other?
Simplicio: Absolutely not, I believe.
Salviati: Of earth, of lead, of gold — in short, of the heaviest kinds of matter — what do you take their natural, intrinsic inclination to be? That is, toward what motion do you believe their internal principle draws them?
Simplicio: Toward motion to the center of heavy things — that is, to the center of the universe and of the Earth, where, unimpeded, they would take themselves.
Salviati: So that if the terrestrial globe were bored through by a well passing through its center, a cannonball dropped down it, moved by a natural and intrinsic principle, would carry itself to the center; and all this motion it would perform spontaneously, by an intrinsic principle — isn't that so?
Simplicio: That I hold for certain.
Salviati: But once it reached the center, do you believe it would pass on beyond, or that right there it would immediately cease from motion?
Simplicio: I believe it would go on moving for a very long stretch.
Salviati: But this motion past the center — wouldn't it be upward, and, by your own account, preternatural and violent? And on what other principle will you make it depend, except that very same one that carried the ball to the center — the one you called intrinsic and natural? Find me an external thrower that comes along again to drive it up. And what we say about the motion through the center can be seen up here among us too: for the internal impetus of a heavy body falling down a sloping surface, if that same surface curves up at the bottom and bends back upward, will carry the body up as well, without interrupting its motion in the least. A lead ball hanging from a string, drawn aside from the vertical, descends spontaneously, pulled by its internal inclination, and — without any pause of rest in between — passes through the lowest point and, with no fresh mover arriving, moves upward. I know you won't deny that the principle moving heavy bodies down is every bit as natural and internal to them as the one moving light bodies up. So I put before you a ball of wood, which, coming down through the air from a great height — and therefore moving by an internal principle — reaches the surface of a deep pool of water and continues its descent, sinking for a long stretch with no other external mover; and yet its downward motion through the water is preternatural to it, and for all that it depends on a principle that is internal, not external, to the ball. There, then, you have it demonstrated: one and the same internal principle can move a moving body in contrary motions.
Simplicio: I believe there are answers to all these objections, though for the moment they don't come to me. But however that may be, the author goes on to ask on what principle this circular motion of heavy and light bodies depends — that is, whether on an internal or an external one — and proceeds to prove that it can be neither, saying: Si ab externo, Deusne illum excitat per continuum miraculum? an vero angelus? an aër? Et hunc quidem multi assignant. Sed contra... — "If from something external, is it God who stirs it up by a continual miracle? Or is it an angel? Or the air? And indeed many assign it to the air. But against this..."
Salviati: Don't wear yourself out reading the objections, because I'm not one of those who attribute such a principle to the surrounding air. As for the miracle or the angel, I'd lean rather that way; for something that begins from a divine miracle or an angelic operation — such as the carrying of a cannonball up to the concave of the Moon — makes it not at all improbable that, by virtue of the same principle, it should do the rest as well. But as for the air, it's enough for me that it doesn't hinder the circular motion of the bodies that are said to move through it; and to do that, it's enough — nothing more is required — that the air move with the same motion and complete its circuits at the same speed as the terrestrial globe.
Simplicio: And he'll rise up against this too, asking who carries the air around — nature, or violence? And he refutes nature, saying that this goes against truth, against experience, against Copernicus himself.
Salviati: Against Copernicus it's nothing of the kind — Copernicus writes no such thing, and this author credits it to him with far too much courtesy. On the contrary, Copernicus says — and to my mind says it well — that the part of the air near the Earth, being rather a terrestrial exhalation, may share the Earth's nature and naturally follow its motion; or else, being right next to it, follow it in the way the Peripatetics say the upper region and the element of fire follow the motion of the Moon's concave. So it's for them to explain whether that motion is natural or violent.
Simplicio: The author will reply that if Copernicus makes only a lower part of the air move, the upper part lacking such motion, he won't be able to account for how that still air could carry the heavy bodies along with it and make them follow the Earth's motion.
Salviati: Copernicus will say that this natural propensity of the elemental bodies to follow the Earth's motion has a limited sphere, beyond which that natural inclination would cease; and besides, as I've said, it isn't the air that carries the moving bodies along — bodies that, once separated from the Earth, still follow its motion. So all the objections this author brings to prove that the air might not cause such effects collapse.
Simplicio: Since, then, that's not how it is, we'll have to say that such effects depend on an internal principle; against which position oboriuntur difficillimae, immo inextricabiles, quaestiones secundae — "there arise most difficult, indeed inextricable, second-order questions" — which are these: Principium illud internum vel est accidens, vel substantia: si primum, quale nam illud? nam qualitas loco motiva circum hactenus nulla videtur esse agnita. — "That internal principle is either an accident or a substance: if the first, what is it, then? For no quality producing motion in a circle has, up to now, been recognized to exist."
Salviati: How is it that none is known? Aren't these here the very ones — the qualities that move all this elemental matter around, together with the Earth? See how this author assumes as true the very thing in question.
Simplicio: He says that this isn't seen, and on this point it seems to me he's right.
Salviati: It isn't seen by us, because we're going around together with them.
Simplicio: Listen to the next objection:
Salviati: Granting for now that water and fire are contraries — and likewise air and earth (though there'd be plenty to say about that) — the most that could follow from it is that motions which are contrary to each other can't be common to them: so that, for example, the upward motion which naturally belongs to fire couldn't belong to water; rather, since water is by nature contrary to fire, the motion that suits it is the one contrary to fire's motion, which will be the motion deorsum — downward. But circular motion, which is contrary neither to sursum nor to deorsum — neither to up nor to down — and can in fact be mixed with both, as Aristotle himself affirms, why shouldn't it belong equally to heavy and to light bodies? Then again, the motions that can't be common to the living and the non-living are those that depend on the soul; but the motions that belong to the body, insofar as it is elemental and consequently shares in the qualities of the elements — why shouldn't those be common to the corpse and to the living thing? And so, if circular motion is proper to the elements, it will have to be common to the compounds as well.
Sagredo: This author must believe that when a dead cat falls from a window, it can't be that a live one could fall too — since it wouldn't be fitting for a corpse to share the qualities that belong to a living thing.
Salviati: So this author's argument doesn't hold against anyone who'd say that the principle of the circular motion of heavy and light bodies is an internal accident. How well he'll manage to prove it can't be a substance, I don't know.
Simplicio: He rises up against this with many objections, the first of which is this: Si secundum (nempe si dicas, tale principium esse substantiam), illud est aut materia, aut forma, aut compositum; sed repugnant iterum tot diversae rerum naturae, quales sunt aves, limaces, saxa, sagittae, nives, fumi, grandines, pisces, etc., quae tamen omnia, specie et genere differentia, moverentur a natura sua circulariter, ipsa naturis diversissima, etc. — "If the second — namely, if you say that such a principle is a substance — then it is either matter, or form, or a composite; but again there stand in the way so many different natures of things, such as birds, snails, stones, arrows, snow, smoke, hail, fish, and so on — all of which, differing in species and in genus, would nonetheless be moved by their own nature in a circle, they themselves being utterly different in nature, and so forth."
Salviati: If these things he lists are of different natures, and things of different natures can't have a common motion, then, if we're to satisfy them all, we'll have to think of something more than just two motions, up and down. And if we must find one motion for arrows, one for snails, another for stones, one for fish, then we'll also have to think about earthworms, and topazes, and agaric — which are no less different in nature from one another than hail and snow.
Simplicio: It seems you're making fun of these arguments.
Salviati: Not at all, Simplicio; but it's already been answered above — namely, that if a downward or an upward motion can belong to the things he lists, a circular one can belong to them no less. And staying within Peripatetic doctrine: wouldn't you put a greater difference between an elemental comet and a celestial star than between a fish and a bird? And yet those two both move in a circle. Now go on to the second argument.
Simplicio: Si Terra staret per voluntatem Dei, rotarentne caetera annon? si hoc, falsum est a natura gyrari; si illud, redeunt priores quaestiones; et sane mirum esset, quod gavia pisciculo, alauda nidulo suo et corvus limaci petraeque, etiam volens, imminere non posset. — "If the Earth stood still by the will of God, would the rest go on turning or not? If yes, then it's false that they spin by nature; if no, the earlier questions come back. And it would surely be a marvel that a gull could not hover — even if it wanted to — over its little fish, nor a lark over its nest, nor a crow over a snail or a stone."
Salviati: For my part, I'd give a general answer: that, granting the Earth were to stop its daily whirl by the will of God, those birds would do whatever that same will of God pleased. But if this author wants a more particular answer, I'd tell him they'd do exactly the opposite of what they would do if, while they were up in the air separated from the Earth, the terrestrial globe were by divine will suddenly thrown into a headlong motion. It's now for this author to assure us what would happen in that case.
Sagredo: Please, Salviati, grant this author my request — that, the Earth having stopped by the will of God, the other things separated from it went on wheeling around in their natural motion — and let's hear what impossibilities or absurdities would follow. For my own part, I can't see any greater disorders than the ones the author himself produces: namely, that the larks, however much they wanted to, couldn't keep themselves over their nests, nor the crows over the snails or the stones; from which it would follow that the crows would have to go without their craving for snails, and the little larks would die of hunger and cold, since they could be neither fed nor brooded by their mothers. That's the whole ruin I can draw out of it, going by what the author says. See for yourself, Simplicio, whether any greater troubles ought to follow.
Simplicio: I can't make out any greater ones myself, but it's quite believable that the author sees, beyond these, other disorders in nature which perhaps, for reasons of his own worthy of respect, he chose not to bring forward. So I'll go on to the third objection: Insuper, quî fit ut istae res tam variae tantum moveantur ab occasu in ortum parallelae ad aequatorem? ut semper moveantur, numquam quiescant? — "Besides, how does it come about that things so various all move only from west to east, parallel to the equator? That they always move and never rest?"
Salviati: They move from west to east, parallel to the equinoctial, without stopping — in exactly the way you believe the fixed stars move from east to west, parallel to the equinoctial, without stopping.
Simplicio: Quare quo sunt altiores celerius, quo humiliores tardius? — "Why do the higher ones move faster, the lower ones slower?"
Salviati: Because in a sphere or a circle turning about its center, the parts farther out trace larger circles, and the nearer ones trace smaller circles in the same time.
Simplicio: Quare quae aequinoctiali propiores in maiori, quae remotiores in minori, circulo feruntur? — "Why are the ones nearer the equinoctial carried in a larger circle, and those farther off in a smaller one?"
Salviati: To imitate the starry sphere, in which the ones nearer the equinoctial move in larger circles than the ones farther away.
Simplicio: Quare pila eadem sub aequinoctiali tota circa centrum Terrae ambitu maximo, celeritate incredibili, sub polo vero circa centrum proprium gyro nullo, tarditate suprema, volveretur? — "Why would one and the same ball, under the equinoctial, revolve wholly around the center of the Earth in the greatest circuit, with incredible speed, but under the pole revolve around its own center with no circuit at all, at the utmost slowness?"
Salviati: To imitate the stars of the firmament, which would do the same if the daily rotation were theirs.
Simplicio: Quare eadem res, pila v. g. plumbea, si semel Terram circuivit descripto circulo maximo, eamdem ubique non circummigret secundum circulum maximum, sed translata extra aequinoctialem in circulis minoribus agetur? — "Why does the same thing — a lead ball, say — if it has once gone around the Earth describing a great circle, not travel everywhere along a great circle, but instead, carried away from the equinoctial, get driven in smaller circles?"
Salviati: Because that's just what they'd do — indeed, on Ptolemy's doctrine, what they have done: certain fixed stars that were once very close to the equinoctial and traced enormous circles, and now, being far from it, trace smaller ones.
Sagredo: Oh, if only I could keep all these fine things in my head, I'd feel I'd made a real fortune! Simplicio, you simply must lend me this little book — there's bound to be a whole sea of rare and exquisite things inside it.
Simplicio: I'll make you a present of it.
Sagredo: Oh no, that I'd never do — I wouldn't deprive you of it for anything. But are the questions finished yet?
Simplicio: No, sir; just listen: Si latio circularis gravibus et levibus est naturalis, qualis est ea quae fit secundum lineam rectam? nam si naturalis, quomodo et is motus qui circum est, naturalis est, cum specie differat a recto? si violentus, quî fit ut missile ignitum, sursum evolans, scintillosum caput sursum a Terra, non autem circum, volvatur, etc.? — "If circular motion is natural to heavy and light bodies, what sort of motion is the one that goes in a straight line? For if it's natural, how is the motion that goes around also natural, since it differs in species from the straight? And if it's violent, how does it come about that a fiery missile, flying upward, turns its sparkling head upward, away from the Earth, and not around it, and so on?"
Salviati: It's been said a thousand times already that circular motion is natural to the whole and to the parts, so long as they're in their best arrangement; the straight is there to bring disordered parts back into order — though it's better to say that they never, whether ordered or disordered, move with straight motion, but with a mixed motion, which might even be pure circular. Only, of this mixed motion just one part stays visible and observable to us, namely the straight part, while the other part, the circular, remains imperceptible to us, because we share in it too. And this answers the case of the rockets, which move upward and around, but we can't make out the circular part, because we're moving along with it. But I don't think this author has ever grasped this mixture, since one can see how flatly he says that rockets go straight up and don't go around at all.
Simplicio: Quare centrum spherae delapsae sub aequatore spiram describit in eius plano, sub aliis parallelis spiram describit in cono? sub polo descendit in axe, lineam gyralem decurrens in superficie cylindrica consignatam? — "Why does the center of a falling sphere, under the equator, describe a spiral in the plane of the equator; under the other parallels, describe a spiral on a cone; while under the pole it descends along the axis, running out a spiral line traced on the surface of a cylinder?"
Salviati: Because of the lines drawn from the center to the circumference of the sphere — the lines along which heavy bodies descend — the one ending at the equinoctial marks out a circle, and those ending at the other parallels trace conical surfaces, while the axis traces nothing at all, but stays as it is. And if I'm to tell you my opinion freely, I'll say that I can't get out of all these questions any conclusion that weighs against the motion of the Earth; because if I asked this author — granting him that the Earth doesn't move — what would happen with all these particulars supposing it did move as Copernicus wants, I'm quite sure he'd say that all these very effects would follow: the ones he now urges as absurdities to rule out the Earth's mobility. So that in this man's mind, necessary consequences are reckoned as absurdities. But please, if there's anything more, let's get ourselves free of this tedious business.
Simplicio: In what comes next, there's an attack on Copernicus and his followers, who hold that the motion of the parts, once separated from their whole, is only for the sake of reuniting with that whole, but that what's absolutely natural is to move in a circle with the daily whirl. Against them he presses, saying that, according to these men's opinion, si tota Terra, una cum aqua, in nihilum redigeretur, nulla grando aut pluvia e nube decideret, sed naturaliter tantum circumferretur; neque ignis ullus aut igneum ascenderet, cum, illorum non improbabili sententia, ignis nullus sit supra. — "if the whole Earth, together with the water, were reduced to nothing, no hail or rain would fall from a cloud, but would only be carried around naturally; nor would any fire or fiery thing rise, since, by their not improbable opinion, there is no fire up above."
Salviati: This philosopher's foresight is marvelous, and worthy of great praise, seeing that he isn't content to think about the things that might happen while nature runs its course, but wants to be provided in advance in case those things should come about that we know absolutely will never come about. So then — just to hear some fine subtlety — I'll grant him that if the Earth and the water went to nothing, neither hail nor rain would fall anymore, nor would fiery matter rise any higher but would keep going around: what then? And what will the philosopher have to raise against me?
Simplicio: The objection is in the words that come right after; here they are: Quibus tamen experientia et ratio adversatur — yet experience and reason stand against these.
Salviati: Now I have to give in, since he has so great an advantage over me — namely experience, which I lack; for up to now I've never once had the luck to see the terrestrial globe, together with the element of water, reduced to nothing, so that I might have observed what the hail and the water got up to in this little end-of-the-world. But does he at least tell us, for our instruction, what they were doing?
Simplicio: He doesn't say.
Salviati: I'd pay anything to be able to have a word with this person, to ask him whether, when this globe vanished, it carried off the common center of gravity as well — as I believe it did; in which case I think the hail and the water would have been left dazed and stupefied up among the clouds, with no idea what to do with themselves. It could also be that, drawn by that great empty space left behind by the departure of the terrestrial globe, all the surroundings would rarefy — the air in particular, being supremely stretchable — and would rush in at top speed to fill it; and perhaps the more solid and material bodies, like the birds, of which by rights there must have been many up in the air, would have drawn in more toward the center of the great empty sphere (it seems quite reasonable that substances which pack a lot of matter into a smaller bulk should be assigned the tighter quarters, leaving the roomier ones to the rarer substances); and there, having finally died of hunger and dissolved into earth, they'd have formed a new little globe, with the bit of water that happened to be among the clouds at the time. It could also be that these same materials, seeing no light, wouldn't have noticed the Earth's departure, and would have gone on falling as usual, blindly, expecting to meet it, and little by little would have made their way to the center — where they'd go even now, if the globe itself weren't in the way. And finally, to give this philosopher a less wishy-washy answer, I tell him that I know as much about what would follow the annihilation of the terrestrial globe as he would have known about what was going to happen to it and around it before it was created; and since I'm sure he'd say that he couldn't even have imagined any of the things that in fact followed — of which experience alone has made him the expert — he'll have to grant me pardon and excuse me if I don't know what he knows about the things that would follow the annihilation of that globe, seeing that I lack this experience of his. Now tell me if there's anything else.
Simplicio: There's this figure, which represents the terrestrial globe with a great cavity around its center, filled with air; and to show that heavy bodies don't move downward to join the terrestrial globe, as Copernicus says, he sets this stone at the center and asks what it would do if set free; and he places another in the hollow of this great cavern and puts the same question, saying, as to the first: Lapis in centro constitutus aut ascendet ad Terram in punctum aliquod, aut non: si secundum, falsum est partes ob solam seiunctionem a toto ad illud moveri; si primum, omnis ratio et experientia renititur, neque gravia in suae gravitatis centro conquiescent. Item, si suspensus lapis liberatus decidat in centrum, separabit se a toto, contra Copernicum; si pendeat, refragatur omnis experientia, cum videamus integros fornices corruere — A stone placed at the center will either rise toward the Earth to some point, or it will not: if it will not, it is false that parts move toward the whole merely because they have been separated from it; if it does rise, all reason and experience fight against it, and heavy bodies will not rest at the center of their own gravity. Likewise, if a suspended stone, once released, drops to the center, it separates itself from the whole, against Copernicus; and if it stays hanging, all experience is contradicted, since we see whole vaults collapse.
Salviati: I'll answer, though at great disadvantage to myself, since I'm up against someone who has seen by experience what these stones do in this great cavern — something I've never seen. And I'll say that I believe the heavy bodies come before the common center of gravity; so that it is not a center — which is nothing but an indivisible point, and therefore of no power — that draws the heavy materials to itself, but rather that these materials, conspiring naturally toward union, form for themselves a common center, the one around which parts of equal moment come to rest. So I reckon that, if the great aggregate of heavy bodies were transported to any place whatever, the particles separated from the whole would follow it, and, unimpeded, would penetrate it until they found parts less heavy than themselves; but once they reached the point where they met heavier matter, they would sink no farther. And so I reckon that in the cavern filled with air, the whole vault would press down, and would hold itself up over that air only by force — that is, only when its hardness could not be overcome and broken by its weight; but detached stones, I believe, would descend to the center and would not float on top of the air. Nor could one say for that reason that they weren't moving toward their whole, since they'd be moving to just the place where all the parts of the whole would move, if they weren't impeded.
Simplicio: What's left is a certain error he points out in a follower of Copernicus who, in making the Earth move with the annual and the daily motion in the way that a cart wheel moves along the ground and on its own axle, ended up making either the terrestrial globe too big or the great orb — the annual orbit — too small; since 365 revolutions of the equinoctial are far less than the circumference of the great orb.
Salviati: Watch out — you're mixing it up, and saying the opposite of what must be written in the pamphlet: for it has to say that this author ended up making the terrestrial globe too small or the great orb too big, not the globe too big and the annual orbit too small.
Simplicio: The mix-up isn't mine at all: here are the pamphlet's own words: Non videt quod vel circulum annuum aequo minorem, vel orbem terreum iusto multo fabricet maiorem — He does not see that he makes either the annual circle too small, or the terrestrial globe much too large.
Salviati: Whether the first author erred, I can't know, since the pamphlet's author doesn't name him; but the pamphlet's own error is plain and inexcusable, whether or not that first follower of Copernicus erred, since the pamphleteer passes right over so gross a mistake without noticing it, and neither flags it nor corrects it. But let that be forgiven him, as an error of carelessness rather than anything else. Besides — were I not by now tired and sick of spending any more time, to very little profit, on these very slight squabbles — I could show how it's not impossible for a circle, no bigger even than a cart wheel, by making not just 365 but even fewer than 20 revolutions, to trace out or measure the circumference not only of the great orb but of one a thousand times bigger. I say this to show that there's no shortage of subtleties far greater than the one this author uses to catch Copernicus in error. But please, let's catch our breath a moment, and then come to this other philosopher, another opponent of the same Copernicus.
Sagredo: I really need it too, even though I've only worn out my ears; and if I thought I wasn't going to hear anything more ingenious from this other author, I don't know but I might just decide to go take the cool air out in a gondola.
Simplicio: I think you'll hear things with more weight to them, because this is a most accomplished philosopher, and a great mathematician besides, and he has refuted Tycho on the matter of the comets and the new stars.
Salviati: Is he perhaps the very author of the Anti-Tycho?
Simplicio: He's the very same one: but the refutation against the new stars isn't in the Anti-Tycho, except insofar as he shows there that they were no threat to the inalterability and ungenerability of the heavens, as I already told you. But after the Anti-Tycho, having found a way — by means of parallax — to demonstrate that they too are elemental things, contained within the sphere of the Moon, he wrote this other book, De tribus novis stellis, and so on, and inserted into it his arguments against Copernicus as well. Last time I brought you what he'd written about these new stars in the Anti-Tycho, where he didn't deny that they were up in the heavens, but showed that their appearance didn't upset the heavens' inalterability — and he did this by pure philosophical reasoning, in the way I described. It slipped my mind to tell you how he later found a way to remove them from the heavens, because, since he proceeds in this refutation by way of calculations and parallaxes — matters I understand little or not at all — I hadn't read it, and had only made a study of these objections against the Earth's motion, which are, after all, matters of natural philosophy.
Salviati: I understand perfectly, and it will be fitting — once we've heard the objections to Copernicus — for us to hear, or at least see, the way in which, by means of parallax, he demonstrates that those new stars were elemental — the very stars that so many astronomers of great renown all placed extremely high up, among the stars of the firmament. And if this author brings so great an enterprise to completion — pulling the new stars down out of the heavens and into the elemental sphere — he'll be well worthy of being exalted on high himself and carried up among the stars, or at least of having his name immortalized in fame among them. But let's dispatch as quickly as we can this part that opposes Copernicus's view, and start bringing forward his objections.
Simplicio: There'll be no need to read these ad verbum — word for word — since they're very long-winded; but, as you see, in reading them carefully several times over, I've marked in the margin the words where the whole nerve of the demonstration lies, and it'll be enough to read those. The first argument begins here: Et primo, si opinio Copernici recipiatur, criterium naturalis philosophiae, ni prorsus tollatur, vehementer saltem labefactari videtur — First, if Copernicus's opinion is accepted, the criterion of natural philosophy, if it isn't abolished altogether, seems at the very least severely shaken. This criterion holds — according to the view of every school of philosophers — that sense and experience are our guides in philosophizing; but on Copernicus's assumption the senses come to be greatly deceived, since they plainly see, close up and in the purest media, the heaviest bodies descend straight down along the perpendicular, never deviating so much as a hair from the straight line; and yet, for Copernicus, sight is deceived in a thing so clear, and that motion is not straight at all, but mixed of straight and circular.
Salviati: This is the first argument that Aristotle and Ptolemy and all their followers put forward — to which a full answer has already been given, the paralogism exposed, and it's been made quite plain how the motion shared by us and the other moving bodies is as if it did not exist. But since true conclusions have a thousand favorable confirmations backing them up, I'd like, for this philosopher's sake, to add something more; and you, Simplicio, playing his part, answer my questions. First, tell me: what effect does that stone have on you — the one which, falling from the top of the tower, is the cause of your noticing its motion at all? For if its falling worked nothing more, nothing new, in you than its resting on top of the tower did, you surely wouldn't notice its descent, nor tell its moving apart from its standing still.
Simplicio: I grasp its descent in relation to the tower, because now I see it beside one mark on the tower, then beside a lower one, and so on in succession, until I make it out reaching the ground.
Salviati: So then, if that stone had fallen from the talons of a flying eagle and were coming down through the plain, invisible air, and you had no other visible, fixed object to set it against, you wouldn't be able to grasp its motion?
Simplicio: On the contrary, I would notice it, since, to see it while it's way up high, I'd have to raise my head, and as it came down I'd have to lower it — in short, keep continually moving either my head or my eyes, following along with its motion.
Salviati: Now you've given the true answer. So you recognize that the stone is at rest while, without moving your eye at all, you keep seeing it there in front of you; and you recognize that it's moving when, to keep from losing sight of it, you have to move the organ of sight — that is, the eye. Therefore, whenever you saw an object continuously in the same aspect without ever moving your eye, you would always judge it to be motionless.
Simplicio: I think that would necessarily have to be so.
Salviati: Now imagine you're aboard a ship, and you've fixed your eye on the tip of the yardarm: do you think that, just because the ship was moving — even very fast — you'd need to move your eye to keep your gaze always on the tip of the yardarm and follow its motion?
Simplicio: I'm sure I wouldn't need to make any change at all — and not just my gaze: even if I'd trained the aim of a harquebus on it, I'd never, for any motion of the ship whatever, need to shift it so much as a hair to keep it lined up on the mark.
Salviati: And this happens because the motion the ship imparts to the yardarm, it imparts to you and to your eye as well, so that you don't need to move it at all to keep looking at the top of the yardarm; and consequently it appears motionless to you. Now carry this reasoning over to the whirling of the Earth and to the stone set on top of the tower, in which you can't make out the motion, because the motion needed to follow it you share in common with the stone, from the Earth, and you don't need to move your eye. But when the downward motion is then added — which is the stone's own, and not yours, and which mixes with the circular — the circular part, shared by the stone and your eye, goes on being imperceptible, and only the straight part becomes perceptible, because to follow it you have to move your eye, lowering it. To cure this philosopher of his error, I'd like to be able to tell him: some time when he's out in a boat, let him set up a fairly deep vessel full of water, and fit into it a ball of wax or some other material that sinks to the bottom very slowly — so slowly that in a minute it barely drops a single braccio, an arm-length — and then, driving the boat as fast as it will go, so that in a minute it covers more than a hundred braccia, let him gently drop the ball into the water and let it sink freely, and carefully observe its motion. First of all, he'd see it heading straight toward the point at the bottom of the vessel that it would tend to if the boat were standing still, and to his eye, in relation to the vessel, this motion would look perfectly perpendicular and perfectly straight; and yet one can't say it wasn't compounded of the straight-down and the circular around the element of water. And if these things happen in motions that aren't natural, and in materials on which we can run the experiment both in their state of rest and, oppositely, in motion — and yet, as far as appearances go, no difference is to be seen, and the senses seem to be fooled — what can we hope to make out concerning the Earth, which has forever been in the same condition as regards motion or rest? And at what time do we hope to test on it whether any difference is to be seen between these effects of local motion in its different states of motion and rest, if it eternally keeps to just one of these two?
Sagredo: These discussions have settled my stomach somewhat — those fish and those snails had rather turned it; and the first of them reminded me of the correction of an error so plausible that I'm not sure one in a thousand wouldn't accept it as beyond doubt. It was this: sailing off Syria, and having with me a very good telescope, given me by our mutual friend, who had invented it not many days before, I proposed to the sailors that it would be a great help in navigation to use it up in the maintop to spot ships from far off and identify them. The benefit was granted, but they raised the difficulty of using it, because of the ship's continual pitching and rolling — especially at the top of the mast, where the tossing is so much greater — and said it would be better to use it down at the foot of the mast, where that motion is less than anywhere else on the vessel. I (I won't hide my own mistake) fell in with the same opinion, and for the moment said nothing more; but afterward — I couldn't tell you what prompted me — I went back to chewing the matter over on my own, and finally saw my own simplicity (excusable, though) in accepting as true something utterly false: false, I say, that the maintop's greater tossing, compared with the small motion at the foot of the mast, should make it harder to use the telescope to catch an object.
Salviati: I'd have sided with the sailors — and with you too — at first.
Simplicio: And I likewise would have been, and still am; nor do I think that pondering it for a hundred years I'd understand it any other way.
Sagredo: So this time I'll get to play the schoolmaster over the pair of you (as they say); and since proceeding by questions seems to me to clear things up a great deal — quite apart from the pleasure of tripping up your companion, drawing out of his mouth what he didn't know he knew — I'll make use of that device. First, I'll assume that the ships, galliots, or other craft we're trying to spot and identify are a good way off — say 4, 6, 10, or 20 miles — since for recognizing the ones nearby there's no need of a glass; and consequently the telescope can, at such a distance of 4 or 6 miles, comfortably pick out the whole vessel, and an even bigger hull besides. Now I ask: of what kinds, and how many in number, are the motions made at the maintop, arising from the ship's tossing?
Salviati: Let's suppose the ship is heading east. First, on a perfectly calm sea, there'd be no motion but this forward one; but once the tossing of the waves is added, there'll be one that, raising and lowering the stern and the bow by turns, makes the maintop lean forward and back; other waves, making the vessel heel over, tip the mast right and left; others can turn the ship somewhat and make it swing — by the mizzen, let's say — off the due-east point, now toward the northeast, now toward the southeast; others, heaving the keel up from below, could make the ship, without swinging off course, simply rise and fall. In sum, it seems to me that in kind these motions are two: one that changes the telescope's direction by an angle, and another that changes it — let's say — along a line, without changing the angle: that is, always keeping the tube of the instrument parallel to itself.
Sagredo: Tell me next: if we, having first trained the telescope over there on that tower of Burano, six miles off from here, were to tilt it by an angle right or left, or up or down, by only a nail's-breadth, what effect would it have on our catching that tower?
Salviati: It would make it vanish from sight at once, because such a deflection, however tiny here, can amount over there to hundreds and thousands of braccia.
Sagredo: But if, without changing the angle, always keeping the tube parallel to itself, we shifted it 10 or 12 braccia farther over — right or left, up or down — what effect would that have as regards the tower?
Salviati: Utterly imperceptible; because, since the spaces here and there are contained between parallel rays, the shifts made here and there must be equal; and since the space the instrument takes in over there could hold many of those towers, we wouldn't lose it from sight at all.
Sagredo: Coming back now to the ship, we can state beyond doubt that moving the telescope right or left, up or down, and even forward or back, by 20 or 25 braccia — while always keeping it parallel to itself — cannot throw the line of sight off the observed point on the object by more than those same 25 braccia; and since, at a distance of 8 or 10 miles, the instrument's field takes in a space much wider than the galliot or other vessel being viewed, such a small shift doesn't make me lose it from sight. The hindrance, then, and the cause of losing the object, can come only from the change made by an angle — since, for the ship's tossing, shifting the telescope up or down, right or left, cannot amount to any great number of braccia. Now suppose you have two telescopes fixed in place, one at the lower part of the ship's mast, the other at the top not just of the mast but of the very tallest yardarm — when it's peaked up steeply — and both are trained on a vessel 10 miles off: tell me whether you think that, for any tossing of the ship and leaning of the mast whatever, a greater change of angle is made in the topmost tube than in the lowest. When a wave lifts the bow, it will indeed drive the tip of the yardarm back 30 or 40 braccia more than the foot of the mast, and so will pull the upper tube back by that much space, and the lower by only a single palm; but the angle changes just as much in the one instrument as in the other. Likewise, a wave coming on the beam carries the high tube right and left a hundred times more than the low one; but the angles either don't change or change equally. And whereas the change right or left, forward or back, up or down, brings no perceptible hindrance to the sight of distant objects, the change of angle brings a very great one. So we must necessarily confess that using the telescope at the top of the mast is no harder than at the foot, seeing that the angular changes are equal in both places.
Salviati: How careful one has to be before affirming or denying any proposition! I'll say it again: hearing it stated so confidently that, because the top of the mast moves through a greater distance than its foot, everyone will be persuaded that using a telescope up high must be far harder than down low. And in the same way I'm even willing to excuse those philosophers who fall into despair and throw up their hands at people who won't grant them that a cannonball — which they plainly see coming straight down along a straight, perpendicular line — really does move that way; those people insist instead that its motion runs along an arc, and a very, very slanting and sideways one at that. But let's leave them in that fix, and listen to the other objections the author we have in hand raises against Copernicus.
Simplicio: The author goes on to show how, on Copernicus's teaching, one has to deny the senses — and the plainest sensations at that. Take this: we, who feel the stirring of the lightest little breeze, would then have to feel nothing of the force of a perpetual wind striking us at a speed of more than 2,529 miles an hour — for that is how much ground the center of the Earth covers in a single hour, with its annual motion, along the circumference of the great orb (the Earth's yearly path), as he carefully calculates. And because — as he says, still following Copernicus's own view — cum Terra movetur circumpositus aër; motus tamen eius, velocior licet ac rapidior celerrimo quocumque vento, a nobis non sentiretur, sed summa tum tranquillitas reputaretur, nisi alius motus accederet. Quid est vero decipi sensum, nisi haec esset deceptio? — that is: when the Earth moves, the air surrounding it moves too; and yet its motion, faster and swifter though it be than any wind however swift, would not be felt by us, but would rather be reckoned the deepest calm, unless some other motion were added to it. And what is it to be deceived in one's senses, if this would not be a deception?
Salviati: This philosopher must believe that the Earth Copernicus sends wheeling around — together with the surrounding air — along the circumference of the great orb is not the one we live on, but some other, separate Earth; because ours carries us along with it too, at the very same speed as itself and the air around it. And what buffeting could we possibly feel, while we flee at exactly the same pace as the thing that means to strike us? This gentleman has forgotten that we, no less than the Earth and the air, are being carried around in the turn — and that in consequence we are always in contact with the same portion of air, which therefore never strikes us at all.
Simplicio: On the contrary — here are the very words that follow immediately: Præterea nos quoque rotamur ex circumductione Terræ, etc. — that is: besides, we too are spun around by the Earth's carrying-round, and so on.
Salviati: Now I can neither help him nor excuse him any longer; you excuse him and help him, Simplicio.
Simplicio: For the moment, caught off guard like this, no defense comes to me that satisfies even myself.
Salviati: Well then, sleep on it tonight and defend him tomorrow; meanwhile, let's hear the other objections.
Simplicio: He keeps pressing the same objection, showing that on Copernicus's road we have to deny our own sensations. For this principle by which we go around with the Earth is either internal to us, or external — that is, a snatching-along by the Earth itself. And if it's the second, then, since we feel no such snatching-along, we'd have to say that the sense of touch does not feel its own proper object when that object is joined to it, nor feel the impression it makes on the sensorium. But if the principle is internal, then we won't feel a local motion arising from ourselves, and we'll never notice an inclination perpetually bound up with us.
Salviati: So this philosopher's objection comes down to this: whether the principle by which we move with the Earth is external or internal, we ought in either case to feel it; and since we don't feel it, it's neither the one nor the other; and therefore we don't move, and consequently neither does the Earth. And I say it can be either way without our feeling it. As for its possibly being external, the experiment with the boat clears away every difficulty and more — and I say "and more" because, since we can set the boat moving whenever we like, and just as well bring it to rest, and watch with great care to see whether, from some difference the sense of touch can pick up, we might learn to tell whether it's moving or not — seeing that no such knowledge has ever yet been gained, why be surprised if the same fact stays hidden from us on the Earth, which may have been carrying us along forever, without our ever being able to test it at rest? Now, Simplicio, I believe you've gone by boat to Padua a thousand times; and if you'll confess the truth, you never once felt in yourself any share in that motion — except when the boat ran aground or struck some obstacle and stopped, and you, with the other passengers, caught off guard, were nearly pitched over headlong and in danger. The terrestrial globe would have to run into some obstacle that brought it up short; and I promise you that then you would indeed become aware of the impetus lodged in you, when it flung you off toward the stars. It's true you can become aware of the boat's motion by another sense — but only with the help of reasoning — namely by sight, when you look at the trees and buildings out in the countryside, which, being separate from the boat, seem to move the opposite way. But if you'd like to rest content about the Earth's motion on the strength of such an experience, I'd tell you to look at the stars, which for that very reason appear to move the opposite way. As for being surprised at not feeling this principle, supposing it were internal to us — that's an even less reasonable thought; because if we don't feel one that comes from outside us and frequently leaves us, why should we feel it when it resides in us unchangingly and without a break? Now, is there anything more in this first argument?
Simplicio: There's this little outburst: Ex hac itaque opinione necesse est diffidere nostris sensibus, ut penitus fallacibus vel stupidis in sensibilibus, etiam coniunctissimis, diiudicandis; quam ergo veritatem sperare possumus, a facultate adeo fallaci ortum trahentem? — that is: from this opinion, then, we are bound to distrust our senses, as utterly deceptive or dull in judging sensible things, even the ones most closely joined to us. What truth, then, can we hope for, when it takes its origin from so deceptive a faculty?
Salviati: Oh, I'd rather draw more useful and more reliable lessons from it — learning to be more circumspect and less trusting about whatever the senses present to us at first glance, since they can easily deceive us. And I wish this author hadn't worn himself out so trying to make us grasp, through the senses, that the motion of falling heavy bodies is simply straight and of no other kind; nor taken offense and cried out because something so clear, plain, and obvious is called into question. For by doing so he betrays a belief that those who say such motion is not straight after all, but rather circular, seem to actually see that stone travel in an arc — since he appeals more to their senses than to their reasoning to settle the matter. And that's not so, Simplicio; because just as I, who am neutral between these opinions and only put on Copernicus's mask, actor-fashion, in these performances of ours, have never seen — nor ever thought I saw — that stone fall any way but plumb straight down, so I believe the very same thing appears to everyone else's eyes. Better, then, that we set aside the appearance, on which we all agree, and bring reasoning to bear — either to confirm that the appearance is real, or to expose it as a fallacy.
Sagredo: If I could just once meet this philosopher — who does seem to me to rise well above many other followers of the same doctrines — I'd like, as a token of affection, to remind him of something he has certainly seen a thousand times, from which, much in keeping with what we're discussing, one can grasp how easily a person can be fooled by the bare appearance — or let's say, the presentation — of the senses. And the thing is this: to people walking along a road at night, the Moon seems to follow them, keeping step with them, as they watch her come skimming the eaves of the rooftops above which she appears — exactly as a cat would do that, really walking along the roof tiles, kept pace behind them. An appearance that, if reasoning didn't step in, would only too plainly deceive the eye.
Simplicio: True enough, there's no shortage of experiences that assure us of the fallacies of the bare senses. But setting such sensations aside for now, let's hear the arguments that follow, which are drawn, as he says, ex rerum natura — from the nature of things. The first is that the Earth cannot by its own nature move with three greatly different motions, unless we're willing to reject many plain axioms — self-evident truths. The first of these is that every effect depends on some cause. The second, that nothing produces itself — from which it follows that it's impossible for the mover and the thing moved to be entirely one and the same. And this is plain not only in things moved by an external mover; from the principles laid down, the same is gathered to hold in natural motion that depends on an internal principle. Otherwise, since the mover, as mover, is cause, and the moved, as moved, is effect, the very same thing would be entirely both cause and effect. So a body does not move the whole of itself — that is, such that the whole moves and the whole is moved; rather, in the thing moved we must somehow distinguish the efficient principle of the motion from that which is moved by it. The third axiom is that, among things subject to the senses, one thing, insofar as it is one, produces a single thing only. Thus the soul in an animal does indeed produce different operations — sight, hearing, smell, generation — but with different instruments; and in short, one sees that in sensible things the different operations derive from some diversity in the cause. Now, if we put these axioms together, it will be perfectly clear that a simple body, such as the Earth, cannot by its own nature move with three greatly different motions at once. For, by the assumptions made, the whole does not move the whole of itself; we must therefore distinguish in it three principles for three motions, otherwise one and the same principle would produce several motions. But since it would then contain within itself three principles of natural motion, besides the part that is moved, it would not be a simple body, but one compounded of three moving principles and of the part moved. If, then, the Earth is a simple body, it will not move with three motions. Indeed, it won't move with any of those Copernicus assigns it, since it must move with one only — it being plain, by Aristotle's reasoning, that it moves toward its own center, as its parts show, which descend at right angles to the spherical surface of the Earth.
Salviati: Many things could be said and weighed about the fabric of this argument; but since we can settle it in a few words, I don't care to spread myself out needlessly right now — all the more since the answer is handed to me by the author himself, when he says that in an animal different operations are produced by a single principle. So for now I answer him that, in the same way, different motions derive in the Earth from a single principle.
Simplicio: The author of the objection won't be quieted in the least by this answer; on the contrary, your answer is completely knocked down by what he adds immediately afterward to shore up the attack he's made — as you're about to hear. He reinforces the argument, I say, with another axiom, which is this: that nature is neither deficient nor excessive in things necessary. This is plain to observers of natural things, and above all of animals, in which, because they had to move with many motions, nature has given them many joints, and there has aptly bound the parts together for movement — as at the knees and the hips, for the walking of animals and for lying down at their pleasure; and further, in man, she has built many bends and articulations at the elbow and the hand, so as to be able to carry out many motions. From these things the argument against the Earth's triple motion is drawn: either a single, continuous body, without being articulated by any joint, can carry out different motions, or it cannot without having joints. If it can without them, then nature made the joints in animals in vain, which is against the axiom; but if it cannot without them, then the Earth, a single continuous body devoid of joints and articulations, cannot by its own nature move with several motions. Now see how shrewdly he goes to meet your answer — almost as if he'd foreseen it.
Salviati: Are you speaking in earnest, or ironically?
Simplicio: I'm speaking with the best sense I've got.
Salviati: Then you must feel you have such a good hand that you can even keep up this philosopher's defense against some further reply that might be made against him. So do me the kindness, please, of answering me on his behalf, since we can't have him here in person. First, you grant it as true that nature made the joints, bends, and articulations in animals so that they could move with many and various motions; and I deny you this proposition. I say the joints were made so that the animal can move one or more of its parts while the rest stays still; and I say that as for the kinds and differences of motion, they are all of one sort only — that is, all circular. And this is why you see that all the heads of the movable bones are either rounded or hollowed: of these, some are spherical, namely those that have to move every which way — as the standard-bearer's arm does at the shoulder joint when he handles the flag, and the falconer's when he calls back the falcon with the lure; and such is the bend of the elbow, on which the hand turns when boring with an auger. Others are circular in one direction only, and nearly cylindrical, serving the limbs that bend in a single way — like the sections of the fingers, one upon another, and so on. But without going through more particular cases, a single general argument can make this truth known: namely, that when a solid body moves while one of its ends stays in place without shifting, the motion can only be circular; and since, when the animal moves one of its limbs, it does not separate it from the neighboring limb, therefore that motion is of necessity circular.
Simplicio: I don't understand it that way; on the contrary, I see the animal move with a hundred non-circular motions, all utterly different from one another — running and jumping and climbing and descending and swimming and many more.
Salviati: Fair enough — but those are secondary motions, depending on the primary ones, which belong to the joints and bends. From the bending of the legs at the knees and the thighs at the hips, which are circular motions of the parts, there follows the jump or the run, which are motions of the whole body, and these can be non-circular. Now, since in the terrestrial globe there's no need to move one part over another that stays still — the motion being of the whole body — there's no need for joints.
Simplicio: This (the other side will say) could hold when the motion is just one; but their being three, and utterly different from one another — it's impossible that they be accommodated in an unjointed body.
Salviati: That, I truly believe, would be the philosopher's reply; and against it I rise from another quarter, and ask you whether you think the terrestrial globe could be fitted, by way of joints and bends, to share in three different circular motions. You don't answer? Since you keep silent, I'll answer for the philosopher, who would absolutely say yes — because otherwise it would have been pointless and beside the case to bring up that nature makes joints so that a movable body can move with different motions, and that therefore, the terrestrial globe having no joints, it cannot have the three motions assigned to it. For if he had judged that not even by way of joints could it be made fit for such motions, he'd have freely declared that the globe cannot move with three motions at all. Now, this being so, I beg you — and through you, if it were possible, the philosopher who authored the argument — to be so kind as to teach me in what manner the joints would have to be arranged so that the three motions could be comfortably carried out; and I'll allow you four, or even six, months for your answer. Meanwhile it seems to me that a single principle can cause several motions in the terrestrial globe, in exactly the way I answered before — that a single principle, by means of various instruments, produces multiple and different motions in an animal. And as for jointing, there's no need of it, since the motions must be of the whole and not of some parts; and because they have to be circular, the simple spherical shape is the finest jointing one could ask for.
Simplicio: The most that could be granted you would be that this might happen with a single motion; but with three different ones, in my opinion and the author's, it's not possible — as he goes on, still reinforcing the objection, writing: "Let us imagine, with Copernicus, that the Earth moves, by its own faculty and from an internal principle, from west to east in the plane of the ecliptic; and beyond that, that it turns, also from an internal principle, about its own center from east to west; and, for the third motion, that by its own inclination it tilts from north to south and back again. Since it is a continuous body, not linked by bends and joints, can our estimation and our judgment ever grasp that one and the same natural, undivided principle — that is, one and the same propensity — should split itself at once into different and almost contrary motions? I cannot believe that anyone would say such a thing, except one who had set himself, rightly or wrongly, to uphold this position."
Salviati: Hold on a moment, and find me this passage in the book; show me. Fingamus modo cum Copernico, Terram aliqua sua vi et ab indito principio impelli ab occasu ad ortum in eclipticæ plano, tum rursus revolvi ab indito etiam principio circa suimet centrum ab ortu in occasum, tertio deflecti rursus suopte nutu a septentrione in austrum et vicissim — that is: let us suppose, with Copernicus, that the Earth is driven by some force of its own, and from an inborn principle, from west to east in the plane of the ecliptic; then again turned, also by an inborn principle, about its own center from east to west; and, third, deflected once more, by its own nod, from north to south and back again. I had my doubts, Simplicio, that you might have made a slip in reporting the author's words to us; but I see that he himself, and all too gravely, is mistaken — and to my regret I realize he has set out to attack a position he hasn't properly understood; for these are not the motions Copernicus assigns to the Earth. And where does he get the idea that Copernicus makes the annual motion along the ecliptic run contrary to the motion about its own center? He can't have read Copernicus's book, which in a hundred places — and even in the opening chapters — writes that both these motions go toward the same quarter, that is, from west to east. But even without hearing it from anyone else, shouldn't he have grasped on his own that, when you assign to the Earth the motions taken away one from the Sun and the other from the primum mobile, they'd necessarily have to be made in the same direction?
Simplicio: Just take care that you don't go wrong yourself — and Copernicus along with you. Isn't the daily motion of the primum mobile from east to west? And isn't the Sun's annual motion along the ecliptic, on the contrary, from west to east? How, then, do you expect these same motions, transferred to the Earth, to turn from contrary into concordant?
Sagredo: Simplicio has certainly uncovered for us the source of this philosopher's error: he too must have reasoned in just this way.
Salviati: Well, while we can, let's at least clear Simplicio of his error. Seeing the stars rise above the eastern horizon at their rising, he'll have no trouble understanding that, if that motion did not belong to the stars, one would necessarily have to say that the horizon sank with a contrary motion — and consequently that the Earth turned upon itself the opposite way from how the stars seem to move to us, that is, from west to east, which is the order of the signs of the zodiac. As for the other motion: since the Sun is fixed at the center of the zodiac and the Earth moves along its circumference, then for the Sun to appear to us to move through that zodiac in the order of the signs, the Earth must travel in that same order — seeing that the Sun always appears to us to occupy the degree of the zodiac opposite the degree in which the Earth is found. And so, while the Earth runs through, say, Aries, the Sun will appear to run through Libra; and as the Earth passes through the sign of Taurus, the Sun will run through Scorpio; the Earth through Gemini, the Sun through Sagittarius. But this is for both to move in the same direction — that is, according to the order of the signs — just as the Earth's revolution about its own center was too.
Simplicio: I understand perfectly, and I couldn't produce a single thing to excuse so great a blunder.
Salviati: But gently, Simplicio — there's another mistake bigger than this one. He has the Earth turn with its daily rotation about its own center from east to west, and he doesn't grasp that if that were so, the twenty-four-hour motion of the universe would appear to us to run from west to east — exactly the opposite of what we actually see.
Simplicio: Oh, I — who've barely glimpsed the first elements of the sphere — I'm certain I wouldn't have gone so badly wrong.
Salviati: Judge for yourself, then, how much study you can credit this critic with having put into Copernicus's books, if he takes backwards the one principal, supreme hypothesis on which rests the whole sum of the matters where Copernicus parts company with Aristotle and Ptolemy. As for this third motion that the author — again claiming to speak Copernicus's own mind — assigns to the terrestrial globe, I don't know which one he thinks he means. It's certainly not the one Copernicus gives it alongside the other two, the annual motion and the daily rotation, and which has nothing to do with any tilting toward north or south, but serves only to keep the axis of the daily revolution perpetually parallel to itself. So we have to say either that the critic didn't understand this, or that he pretended not to. And though this one grave failing would be enough to release us from any duty to keep occupying ourselves with his objections, still I want to hold them in esteem — for they truly deserve to be valued far more than a thousand others from other empty critics. Coming back, then, to his challenge: I say that the two motions, the annual and the daily, are not in the least contrary; on the contrary, they run the same way, and so can spring from one and the same principle. And the third follows so naturally from the annual, of itself and spontaneously, that there's no need to summon any principle, inner or outer (as I'll show in its proper place), to produce it as a cause.
Sagredo: I'd like to add a word of my own to this critic, guided by plain common sense. He wants to condemn Copernicus if I can't resolve, point by point, every doubt and answer every objection he raises — as though the falsity of Copernicus's doctrine followed necessarily from my ignorance. But if this way of condemning writers strikes him as sound legal procedure, then he shouldn't find it unreasonable that I withhold my approval of Aristotle and Ptolemy, so long as he can't resolve, any better than I can, the very same difficulties I raise against their doctrine. He asks me what principles move the terrestrial globe through its annual motion in the zodiac, and its daily rotation on itself along the equinoctial. I tell him they're much like the principles by which Saturn moves through the zodiac in thirty years, and turns on itself in a far shorter time along its own equinoctial — as the appearing and vanishing of its flanking globes shows us. And much like the principle by which he himself would concede, without a qualm, that the Sun runs along the ecliptic in a year and turns on its own axis, parallel to the equinoctial, in less than a month — as its spots plainly show. And much like the principle by which the Medicean Stars — Jupiter's four little moons — run through the zodiac in twelve years, and meanwhile wheel in tiny circles and very short times around Jupiter itself.
Simplicio: This author will deny you all these things — as illusions of eyesight, produced by the crystals of the telescope.
Sagredo: Oh, that would be claiming far too much for himself. He insists the naked eye can't be fooled when it judges the straight downward motion of falling weights, and yet he wants that same eye fooled when it takes in these other motions — even with its power perfected and multiplied thirtyfold. So let's tell him instead that the Earth shares in a plurality of motions in a way much like — perhaps exactly like — the way the lodestone moves downward as a heavy body and also has two circular motions, one horizontal and the other vertical, beneath the meridian. But what more? Tell me, Simplicio: which do you think this author would judge more different from each other — straight motion and circular, or motion and rest?
Simplicio: Motion and rest, surely. And that's obvious, because for Aristotle circular motion is not contrary to straight motion — he even grants that the two can be mixed — whereas that's impossible for motion and rest.
Sagredo: Then it's the less improbable proposition to lodge in one natural body two inner principles, one for straight and the other for circular motion, than to lodge two — also inner — one for motion and the other for rest. Now, as for the natural inclination that resides in the parts of the Earth, to return to their whole when they're forcibly torn away from it, both positions agree; they part company only over what the whole does. The one wants the whole to stand still by an inner principle; the other credits it with circular motion. But by your own admission and this philosopher's, two principles — one for motion, the other for rest — are mutually incompatible, since their effects are incompatible. Whereas that doesn't happen with the two motions, straight and circular, which have no quarrel between them at all.
Salviati: Add to this that, very probably, the motion made by a piece of the Earth as it works its way back to its whole may itself be circular too, as we've already stated. So that on every count, as far as the present case goes, mobility seems more acceptable than rest. Now go on, Simplicio, with whatever's left.
Simplicio: The author reinforces his challenge by pointing out another absurdity — namely, that the very same motions belong to natures utterly different from one another. But observation teaches us that the operations and motions of different natures are themselves different; and reason confirms it, for otherwise we'd have no way in to knowing and distinguishing natures, if they didn't have their own motions and operations to guide us to a knowledge of the substances.
Sagredo: Two or three times now I've noticed, in this author's arguments, that to prove a thing stands in such-and-such a way, he falls back on saying that in that way it fits our intelligence, or that otherwise we'd have no access to the knowledge of this or that particular, or that the whole standard of philosophy would be ruined — as if nature first made the brains in men, and only afterward arranged things to suit the capacity of their intellects. But I'd sooner reckon that nature first made things her own way, and only afterward fashioned human reasoning capable of grasping (though with great effort) some little part of her secrets.
Salviati: I'm of the same opinion. But tell me, Simplicio: which are these different natures to which Copernicus, against observation and reason, assigns the same motions and operations?
Simplicio: Here they are: water and air (which are, after all, natures different from earth), and everything found in those elements, will each have those three motions that Copernicus invents for the terrestrial globe. And he goes on to demonstrate geometrically how, on Copernicus's scheme, a cloud that hangs in the air and stays a long while over our heads without changing place must necessarily have all three of the motions the terrestrial globe has. Here's the demonstration — you can read it for yourself, for I couldn't repeat it from memory.
Salviati: I won't trouble to read it. In fact I think it was pointless to include it, because I'm sure not one of those who hold the Earth to move will deny it to him. So, granting him the demonstration, let's talk about the challenge itself — which doesn't seem to me to have much force to conclude anything against Copernicus's position, since it takes nothing away from those motions and operations by which we come to know natures, and so on. Answer me, if you'd be so kind, Simplicio: those properties in which certain things agree most exactly — can they serve to make us recognize the different natures of those things?
Simplicio: No, sir — quite the opposite, because from an identity of operations and properties you can argue nothing except an identity of natures.
Salviati: So the different natures of water, of earth, of air, and of the other things scattered through these elements — you don't infer them from the operations in which all these elements and their contents agree, but from other operations. Is that right?
Simplicio: That's how it stands, in fact.
Salviati: So that anyone who left the elements all those motions, operations, and other properties by which their natures are distinguished would not deprive us of the power to come to know them — even if he then removed the one operation in which they all agree together, and which therefore does nothing to distinguish such natures.
Simplicio: I believe the argument runs very well.
Salviati: But that earth, water, and air are by nature equally constituted to be motionless around the center — isn't that your opinion, and the author's, and Aristotle's, and Ptolemy's, and all their followers'?
Simplicio: It's accepted as an irrefutable truth.
Salviati: Then from this common natural condition — resting around the center — you can draw no argument about the different natures of these elements and elemental things; such knowledge has to be gathered from other, non-shared qualities. And so anyone who stripped from the elements only this shared rest, and left them all their other operations, would in no way block the road that leads us to knowledge of their essences. But Copernicus strips from them nothing except this shared rest, and transmutes it into a most thoroughly shared motion — leaving them their heaviness, their lightness, their motions up and down, slower and faster, their rarity, their density, the qualities of hot, cold, dry, wet, and in short everything else. So the absurdity this author imagines simply isn't there in the Copernican position; nor does agreeing in an identity of motion count for any more or less than agreeing in an identity of rest, as far as diversifying natures — or not — is concerned. Now tell me if there's any other argument on the other side.
Simplicio: A fourth challenge follows, again drawn from natural observation: that bodies of the same kind have motions that agree in kind, or else agree in rest. But on Copernicus's position, bodies that agree in kind, and are extremely alike, would as to their motion be in supreme disagreement — indeed in flat, diametrical opposition. For stars so alike among themselves would nonetheless be so unlike in motion, since six planets would revolve forever, while the Sun and all the fixed stars would forever stay still.
Salviati: The form of the argument seems conclusive to me; but I strongly suspect the application, or the subject matter, is defective — and provided the author insists on his assumption, the conclusion will come out flatly against him. The argument runs like this. Among the bodies of the world there are six that move perpetually, and these are the six planets. Of the rest — that is, the Earth, the Sun, and the fixed stars — it's in doubt which of them moves and which stands still; for necessarily, if the Earth stands still, the Sun and the fixed stars move, and it could equally be that the Sun and the fixed stars stand motionless while the Earth moves. So the question, with the fact in doubt, is to whom motion can more fittingly be assigned, and to whom rest. Natural reasoning dictates that the motion should be reckoned to belong to whatever agrees most, in kind and in essence, with the bodies that indisputably move, and rest to whatever differs from them most. And since eternal rest and perpetual motion are properties as unlike as can be, it's plain that the nature of the ever-moving body must be utterly unlike the nature of the ever-still one. Let's search, then — while we're still undecided between motion and rest — to see whether, by way of some other telling condition, we might discover which agrees more with the surely moving bodies: the Earth, or the Sun and fixed stars. And behold, nature, kind to our need and desire, furnishes us two striking conditions, no less different than motion and rest: light and darkness — that is, being by nature most brilliant, and being dark and stripped of all light. Utterly unlike in essence, then, are the bodies adorned with an inner and eternal splendor and the bodies deprived of all light. The Earth is deprived of light; the Sun is most brilliant of itself, and no less the fixed stars; the six moving planets wholly lack light, like the Earth. Therefore their essence agrees with the Earth and differs from the Sun and fixed stars. So the Earth is a moving body; the Sun and the starry sphere are motionless.
Simplicio: But the author won't concede that the six planets are dark, and he'll dig in on that denial — or else he'll argue the great likeness of nature between the six planets and the Sun and fixed stars, and their unlikeness to the Earth, from conditions other than darkness and light. In fact, now that it strikes me, in the fifth challenge that comes next he sets out the supreme disparity between the Earth and the heavenly bodies. There he writes that great confusion and disorder would be introduced into the system of the universe and among its parts on Copernicus's hypothesis. For among heavenly bodies immutable and incorruptible — according to Aristotle and Tycho and others — among bodies, I say, of such nobility (as everyone confesses, and Copernicus himself, who declares them ordered and arranged in the finest constitution and clears them of every inconstancy of power) — among bodies, I say, so pure, that is, between Venus and Mars, to plant the sink of all corruptible matter: the Earth, the water, the air, and all the mixed bodies! Whereas how much finer a distribution, and more befitting nature — indeed befitting God himself as architect — to sequester the pure from the impure, the mortal from the immortal, as the other schools teach; schools that show us how these impure and perishable materials are confined within the narrow concave of the lunar orb, above which the heavenly things then rise in an unbroken series!
Salviati: It's true that the Copernican system throws Aristotle's universe into turmoil; but we're dealing with our universe, the true and real one. Now, when this author wants to infer the disparity of essence between the Earth and the heavenly bodies from the incorruptibility of the latter and the corruptibility of the former — in Aristotle's manner — and from that disparity to conclude that motion must belong to the Sun and fixed stars and immobility to the Earth, he goes wandering into the paralogism of assuming the very thing in question. For Aristotle infers the incorruptibility of the heavenly bodies from motion — and it's precisely that motion whose ownership is in dispute, whether it's theirs or the Earth's. As for the emptiness of these rhetorical inferences, enough has been said. And what could be more foolish than to say the Earth and the elements are banished and cut off from the heavenly spheres, penned up inside the lunar orb? But isn't the lunar orb one of the heavenly spheres — and, by their own agreement, set in the very middle of all the rest? A fine new way to separate the pure from the impure and the plague-stricken from the healthy: to lodge the infected in the heart of the city! I'd have thought the pest-house ought to be pushed as far off as possible. Copernicus admires the arrangement of the parts of the universe precisely because God set the great lamp, which was to pour its supreme splendor over all his temple, at the center of it, and not off to one side. As for the terrestrial globe standing between Venus and Mars, we'll deal with that shortly — and you yourself, for this author's sake, will try your hand at moving it out from there. But please, let's not weave these rhetorical posies together with the solidity of demonstrations; let's leave them to the orators, or rather to the poets, who've known how, with their charms, to lift up with praise the vilest things — and sometimes even harmful ones. And if anything else is left, let's dispatch it as quickly as we can.
Simplicio: There's the sixth and last argument, in which he sets it down as most unlikely that a corruptible, dissipable body could move with a perpetual, regular motion; and he backs this with the example of animals, which, though they move with a motion natural to them, still grow tired, and need rest to restore their strength. But what has such movement to do with that of the Earth, which is immense by comparison with theirs? And, worse, to make it move with three motions running and pulling in different directions? Who could ever assert such things, except men who'd sworn themselves its defenders? Nor does it help in this case what Copernicus brings forward — that because this motion is natural to the Earth, and not violent, it produces effects contrary to those of violent motions; and that the things to which force is applied do indeed dissolve, and can't last long, whereas the things made by nature are preserved in their best condition. This answer, I say, is no help, for it's overthrown by our own. Because the animal is, after all, a natural body, not built by art, and its movement is natural, deriving from the soul — that is, from an inner principle; while violent motion is the kind whose principle lies outside, and to which the thing moved contributes nothing. And yet, if the animal keeps up its motion a long time, it grows tired, and even dies, if it stubbornly tries to force itself. See, then, how in nature one meets, on every side, traces that run counter to Copernicus's position, and never a single one in its favor. And so as not to have to take up this critic's part yet again, hear what he brings forward against Kepler (with whom he's arguing), concerning the point Kepler pressed against those who find it awkward — indeed impossible — to enlarge the starry sphere immensely, as Copernicus's position requires. Kepler presses them, then, saying: Difficilius est accidens praeter modulum subiecti intendere, quam subiectum sine accidente augere — it is harder to stretch a property beyond the scale of its subject than to enlarge the subject without the property. Copernicus igitur verisimilius facit, qui auget orbem stellarum fixarum absque motu, quam Ptolemaeus, qui auget motum fixarum immensa velocitate — Copernicus, then, does the more plausible thing, who enlarges the sphere of the fixed stars without motion, than Ptolemy, who enlarges the motion of the fixed stars to an immense velocity. This challenge the author dissolves, marveling at how badly Kepler deceives himself in saying that on Ptolemy's hypothesis the motion is stretched beyond the scale of its subject. For to him it seems the motion is stretched only in keeping with the scale, and that as the scale grows the velocity of the motion grows with it. He proves this by imagining a millstone that makes one revolution in twenty-four hours — a motion we'd call extremely slow. Now suppose its radius stretched out to the distance of the Sun: its far end would match the velocity of the Sun. Stretched to the starry sphere, it would match the velocity of the fixed stars — even though at the rim of the millstone the motion is extremely slow. Now apply this consideration of the millstone to the starry sphere: take a point on its radius, as near the center as the millstone's radius is short. That same motion, which out at the starry sphere is exceedingly swift, will at that point be exceedingly slow. It's the size of the body that turns the exceedingly slow into the exceedingly swift, even while the motion stays one and the same. And so the velocity grows not beyond the scale of the subject, but in keeping with it and with its size — quite differently from what Kepler supposes.
Salviati: I don't believe this author has formed so thin and low an opinion of Kepler that he could persuade himself Kepler failed to understand that the topmost end of a line drawn from the center out to the starry orb moves faster than a point on that same line only a couple of arm-lengths from the center. So he's bound to grasp and understand that Kepler's meaning and intention was to say this: it is the smaller drawback to enlarge a motionless body to an enormous size than to attribute an enormous velocity to a body already vast — bearing in mind the scale, that is, the norm and the example, of the other natural bodies, in which we see that as the distance from the center increases, the velocity decreases; that is, that the periods of their revolutions require longer times. Whereas in rest — which can't be made greater or smaller — the largeness or smallness of the body makes no difference at all. So that, if the author's reply is really to meet Kepler's argument, the author must be reckoning that it's all the same to the moving principle whether it moves, in the same span of time, a tiny body or an immense one — since on his view the increase of velocity follows, without more ado, from the increase of the bulk. But that runs against the architectural rules of nature, which, in the pattern of the smaller spheres — as we see in the planets, and most plainly in the Medicean Stars — makes the smaller orbs revolve in shorter times; so that Saturn's period of revolution is longer than all the periods of the other, smaller spheres, being thirty years. Now to jump from this to a vastly greater sphere and make it turn in twenty-four hours may well, and reasonably, be called going outside the rules of the pattern. So that, if we consider carefully, the author's reply goes not against the concept and sense of the argument, but only against its wording and manner of expression — where, moreover, the author is in the wrong, and can't deny having deliberately feigned not to understand the words, so as to saddle Kepler with a too-gross ignorance. But the fraud has been so crude that, for all so large a discount, it couldn't knock down the opinion of his doctrine that Kepler has stamped on the minds of learned men. Then, as for the challenge against the perpetual motion of the Earth, drawn from its being impossible for the Earth to keep it up without tiring — seeing that the very animals, which do move naturally and from an inner principle, grow tired and need rest to relax their limbs...
Sagredo: I seem to hear Kepler answering him that, after all, there are animals that refresh themselves from weariness by rolling about on the ground, and that we needn't fear the terrestrial globe wearing itself out — on the contrary, one might reasonably say it enjoys a perpetual and utterly tranquil rest, keeping itself in an eternal rolling-about.
Salviati: Sagredo, you're too clever by half, and too fond of satire. But let's set the jokes aside while we're dealing with serious matters.
Sagredo: Forgive me, Salviati, but what I'm saying isn't so far beside the point as you perhaps make it out to be. A motion that serves as rest and removes the weariness from a body worn out by travel can far more easily serve to keep that weariness from ever setting in — since preventive remedies are easier than curative ones. And I hold it for certain that if the motion of animals proceeded like this one attributed to the Earth, they wouldn't tire at all; for a body's growing tired derives, to my mind, from employing a single part to move both itself and all the rest of the body. To walk, for instance, we use only the thighs and legs, which have to carry themselves and everything else besides; whereas you'll notice the motion of the heart is, as it were, tireless, because it moves itself alone. What's more, I don't know how true it is that an animal's motion is natural rather than violent — indeed I think one can truly say that the soul moves the animal's limbs naturally by a preternatural motion, a motion beyond their own nature. For if upward motion is preternatural to heavy bodies, then raising the legs and thighs, which are heavy bodies, in order to walk, can't be done without violence, and therefore not without effort on the mover's part. Climbing a staircase carries the heavy body upward, against its natural inclination, and from that follows weariness, by way of gravity's natural resistance to such motion. But to move a movable body with a motion to which it has no resistance whatever — what tiring, what draining of power and force, is there to fear in the mover? And why should force be spent where none is exercised at all?
Simplicio: It's the contrary motions — the ones the terrestrial globe is imagined to move by — that the author builds his objection on.
Sagredo: We've already said they aren't contrary at all, and that on this point the author badly deceived himself, so that the whole force of the objection turns back against the objector himself — once he wants the primum mobile to sweep all the lower spheres along, against the very motion those spheres are exercising at the same time and continuously. So it's the primum mobile that ought to get tired, since, on top of moving itself, it has to drag along so many other spheres — spheres that, what's more, fight back against it with a contrary motion. And so that final conclusion the author drew — that when you run through the effects of nature you always meet things favorable to the opinion of Aristotle and Ptolemy, and never anything that doesn't tell against Copernicus — needs a great deal of rethinking. Better to say that, since one of these two positions is true and the other necessarily false, it's impossible for any reason, experience, or sound argument ever to be found in favor of the false one, just as none of these things can be repugnant to the true one. So there's bound to be a great difference between the arguments and reasons produced on the one side and the other, for and against these two opinions — and I'll leave you yourself to judge their force, Simplicio.
Salviati: Sagredo, carried away by the quickness of your wit, you cut off my train of thought a moment ago, just as I was about to say something in reply to this last argument of the author's. And even though you've answered him more than sufficiently, I'd still like to add a little something I had in mind at the time. He sets it down as highly improbable that a dissipable, corruptible body like the Earth could move perpetually with a regular motion — especially since we see that animals, in the end, tire and need rest; and he heightens the improbability by insisting that such a motion would have to be of incomparable and immense speed, compared with an animal's. Now, I can't see why the Earth's speed should trouble him at present, when the speed of the starry sphere — so very much greater — gives him no more concern than that of a millstone making a single revolution in 24 hours. If, because the speed of the Earth's turning is on the model of the millstone's, nothing of greater consequence follows than that, then let the author stop fearing that the Earth will tire — for not even the feeblest, laziest animal you please, I mean not even a chameleon, would wear itself out by moving no more than five or six arm-lengths in 24 hours. But if he wants to consider the speed not on the millstone's model, but in absolute terms — inasmuch as in 24 hours the moving body has to pass through an enormous space — then he ought to be far more reluctant to grant that speed to the starry sphere, which, at a speed incomparably greater than the Earth's, has to carry along with it thousands of bodies, each one vastly larger than the terrestrial globe.
It would remain now for us to look at the proofs by which the author concludes that the new stars of 1572 and 1604 were sublunar, and not celestial, as the astronomers of those times generally persuaded themselves — a truly great undertaking. But since this piece of writing is new to me, and long, with all its calculations, I've thought it would be more practical for me to look over as much of it as I can between this evening and tomorrow morning, and then tomorrow, returning to our usual discussions, to report what I've gathered. And if we have time left over, we'll come to discuss the annual motion attributed to the Earth. Meanwhile, if you have anything to say — and Simplicio in particular — about matters bearing on the daily rotation, which I've now examined at such length, we still have a little time left to talk it over.
Simplicio: I've nothing left to say, except that the discussions we've had today have struck me as full of very sharp and ingenious thoughts, brought forward on Copernicus's side to confirm the Earth's motion — but I don't feel persuaded to believe it. Because, in the end, what's been said comes to nothing more than that the reasons for the Earth's stability aren't conclusive; and yet no demonstration whatever has been produced on the other side that necessarily proves and clinches the Earth's mobility.
Salviati: I never undertook, Simplicio, to move you from your opinion, and I'd hardly dare to hand down a final verdict on so great a dispute. It has only been my intention — and it will be in the discussions to come as well — to make plain to you that those who have believed this extremely swift 24-hour motion belongs to the Earth alone, and not to the whole universe with the Earth alone left out, didn't persuade themselves it could and should be so blindly, as the saying goes. Rather, they had thoroughly seen, heard, and weighed the reasons for the contrary opinion, and answered them, too, not lightly. With this same intention — whenever it suits you and Sagredo — we can move on to consider that other motion, attributed to the same terrestrial globe first by Aristarchus of Samos and then by Nicholas Copernicus: a motion which, as I believe you've already heard, is made beneath the zodiac, within the space of a year, around the Sun, set motionless at the center of that zodiac.
Simplicio: The question is so great and so noble that I'll listen to it discussed with the keenest curiosity, expecting to hear everything that can be said on the subject. Afterward I'll go on, at my own leisure, reflecting more deeply on the things I've heard and have yet to hear; and even if I gain nothing else, it'll be no small thing to be able to discuss the matter on firmer ground.
Sagredo: Then, so as not to tire Salviati any further, let's put a full stop to today's discussions, and tomorrow we'll take up the conversation again as usual, in the hope of hearing some great new things.
Simplicio: I'll leave the book on the new stars behind, but I'll carry this one of conclusions back with me, to look over what's written in it against the annual motion — which is to be the subject of tomorrow's discussions.
Sagredo: The great eagerness with which I've been awaiting your arrival — to hear the fresh thinking about the annual motion, our globe's yearly circuit around the Sun — made the hours of the night seem endless to me, and these morning ones too. Though I didn't waste them: I spent a good part of the night awake, going back over yesterday's discussions in my mind, weighing the arguments each side brought forward for the two opposing positions — that of Aristotle and Ptolemy on the one hand, and that of Aristarchus and Copernicus on the other. And truly it seems to me that whichever of these has gone wrong deserves to be forgiven; so plausible, on the face of it, are the reasons that could have won them over — at least so long as we stick to the ones the great original authors themselves put forward. But since the Peripatetic view, by its sheer antiquity, has had many followers and cultivators, while the other has had very few — first because of its obscurity, then because of its novelty — I seem to notice that among all those many, and the moderns in particular, there are some who, to prop up the opinion they take for true, have brought in other arguments so childish I hardly dare call them anything but ridiculous.
Salviati: The same thing has happened to me — and even more so than to you, since I've heard such things produced that I'd be ashamed to repeat them. Not, I'll admit, to spare the reputations of their authors, whose names can always be kept quiet, but so as not to drag down the honor of the human race itself. In the end, from watching them, I've become convinced that among men there are some who reason backwards: they first plant the conclusion in their heads, and — whether because it's their own or belongs to someone they hold in high esteem — they fix it there so firmly that it becomes utterly impossible to root it out. To any argument that occurs to them, or that they hear others produce in support of their settled notion — however simple and insipid it may be — they instantly give their assent and applause; while to any brought against it, however ingenious and conclusive, they react not merely with distaste but with disdain and the bitterest anger. And some of them, driven by fury, would not even hold back from attempting any contrivance to suppress their opponent and shut him up. I've seen a little of that firsthand.
Sagredo: So these men don't draw their conclusion from their premises, nor establish it by reasons — instead they fit, or rather force and twist, the premises and reasons to fit conclusions they've already settled and nailed down. It's just as well, then, not to test ourselves against such people; all the less so given that their company is not only unpleasant but downright dangerous. So we'll carry on with our own Simplicio, whom I've known for ages as a man of the greatest candor, wholly stripped of any malice. Besides, he's so well versed in Peripatetic doctrine that I can be sure whatever won't occur to him in support of Aristotle's opinion won't easily occur to anyone else. But here he is now, out of breath — the fellow's kept us waiting a good long while today. We were just speaking ill of you.
Simplicio: Don't blame me — blame Neptune for my long delay. This morning's ebb tide pulled the waters back so far that the gondola carrying me, having turned into a certain canal not far from here where there are no foundations along the bank, ran aground on the mud, and I had to sit there more than a solid hour waiting for the sea to come back. And while I was stuck there, unable to step out of the boat, which grounded almost all at once, I found myself watching a detail that struck me as quite marvelous. As the waters fell, you could see them fleeing away very fast through various little channels, the mud already showing in several places; and while I'm busy taking this in, all of a sudden I see the motion stop — and, without a single instant's pause, the very same water begins to run back the other way, the ebb turning straight into flow, without staying still for even a moment. It's an effect I've never happened to see once in all my time in Venice.
Sagredo: You must not have run aground very often among such tiny channels. Since they have so little slope, a fall or rise of even a paper's thickness in the surface of the open sea is enough to send the water racing back and forth through them for quite long stretches — just as, on certain seacoasts, a rise of only four or six braccia — arm-lengths — spreads the water across those flats for many hundreds and thousands of pertiche, the old land-rods.
Simplicio: That much I understand perfectly. But I'd have thought that between the last point of the fall and the first beginning of the rise there had to be some noticeable interval of rest.
Sagredo: That will look true to you when you fix your eyes on the walls or the pilings, where these changes happen straight up and down; but there's no genuine rest in it at all.
Simplicio: It seemed to me that since these are two contrary motions, there had to be some rest in between them — in keeping with Aristotle's doctrine, too, which proves that in puncto regressus mediat quies, that at the turning point a moment of rest steps in.
Sagredo: I remember that passage very well. But I also remember that when I was studying philosophy I wasn't persuaded by Aristotle's demonstration — indeed, I had a good many experiences pointing the other way, which I could lay out for you. But I don't want us wading off into other deep waters, since we've gathered here to discuss our own subject, if it's at all possible, without breaking it off the way we did these past days.
Simplicio: And yet we'll have to — if not break it off, then at least stretch it out considerably. Because when I got home last night I set about rereading the little book of theses, where I find some very conclusive demonstrations against this annual motion attributed to the Earth; and since I didn't trust myself to report them so precisely, I decided to bring the book along with me.
Sagredo: You did well. But if we want to take up our discussion according to yesterday's arrangement, we'll need to hear first what Salviati has to report about the book on the new stars, and then, with no further interruptions, we'll come to the annual motion. Now — what does Salviati have to say about these stars? Were they really carried down from the heavens into these lower regions by the power of the calculations of that author Simplicio brought us?
Salviati: Last night I set about reading through his line of argument, and this morning I gave it another once-over, just to be sure that what I thought I'd read in the evening was actually written there — or whether it had been phantoms and fantastic night-imaginings of mine. And in the end I find, to my great sorrow, that what I'd never have wished to see, for this philosopher's own reputation, is really written and printed there. That he doesn't recognize the emptiness of his whole undertaking seems impossible to me — both because it's far too plain to miss, and because I remember hearing him named with praise by our friend the Academician. It also seems far too unlikely that, to please someone else, he could have brought himself to hold his own reputation so cheap as to publish a work from which he could expect nothing but blame from anyone who knows the subject.
Sagredo: Add that those will amount to fewer than one in a hundred, compared with the crowd who'll celebrate and exalt him above every greatest mind that is or ever was. A man who's known how to defend the Peripatetic unchangeableness of the heavens against a whole army of astronomers — and, to their greater shame, floored them with their own weapons! What can four or six per province, who see through his frivolities, do against the countless multitude who, being unable to detect or grasp them, are swept along by the shouting and applaud him all the louder the less they understand? Add, too, that even those few who do understand will decline to answer writings so shabby and so empty of any real conclusion — and rightly so, for the knowledgeable have no need of it, and for those who don't understand, it's effort thrown away.
Salviati: The punishment best fitted to what they deserve really would be silence — if there weren't other reasons that make speaking up almost necessary. One of them is that we Italians get ourselves passed off, one and all, as ignorant, and give the foreigners north of the Alps something to laugh at — especially those cut off from our religion. I could point you to some quite famous ones who mock our Academician, and every mathematician in Italy, for having let the nonsense of a certain Lorenzini against the astronomers come out into the open and stand there unchallenged. But even that could be let go, compared with a still greater occasion for laughter we might hand them — one that comes precisely from the knowledgeable holding their tongues about the frivolities of opponents like these, who attack doctrines they don't understand.
Sagredo: I want no better example of the sheer insolence of these people — and of the misfortune of a man like Copernicus, exposed to being attacked by someone who doesn't even understand the basic position he's making war on.
Salviati: You'll be no less astonished at the way he sets about refuting the astronomers who maintain that the new stars were higher than the orbs of the planets — and perhaps in the firmament itself.
Sagredo: But how could you, in such a short time, have gone through that whole book? It's a big volume, and the demonstrations must be very many.
Salviati: I stopped at these first refutations of his. In them, with twelve demonstrations founded on the observations of twelve astronomers — all of whom judged that the new star of '72, the one that appeared in Cassiopeia, was in the firmament — he proves the opposite: that it was sublunar, below the Moon. He does it by comparing, two at a time, the meridian altitudes taken by different observers in places of different latitude, proceeding in the manner you'll understand shortly. And since it seems to me, examining this first stretch of his, that I've found this author a very long way from being able to conclude anything against the astronomers in favor of the Peripatetic philosophers — and that, on the contrary, the astronomers' opinion comes out far, far more firmly confirmed — I didn't bother applying the same patience to his other methods, but gave them only a superficial glance, confident that whatever ineffectiveness is in these first attacks runs through the rest as well. And as you'll see, in fact, very few words are enough to demolish this whole work, for all that it's built up with so very many laborious calculations, as you can see. So listen to how I proceed. To transfix his opponents, as I said, with their own weapons, this author takes a great many observations made by the astronomers themselves — there are twelve or thirteen of them in all — and on some part of these he makes his calculations, and concludes that these stars were below the Moon. Now, since I'm quite fond of proceeding by questions, and the author himself isn't here, let Simplicio answer the questions I put with whatever he believes the author would answer. Supposing we're dealing with that star of '72 I mentioned, the one that appeared in Cassiopeia — tell me, Simplicio: do you believe it could have been in several places at once? That is, among the elements, and also among the orbs of the planets, and also above those and among the fixed stars, and also infinitely higher still?
Simplicio: There's no doubt one has to say it was in a single place, at one single, determinate distance from the Earth.
Salviati: Then, if the observations made by the astronomers were correct, and the calculations made by this author weren't in error, it would necessarily follow that from all of the former and all of the latter you'd always gather one and the same distance, exactly. Isn't that so?
Simplicio: My reasoning gets this far — that it would have to be so of necessity; nor do I believe the author would contradict it.
Salviati: But if, out of the many, many computations made, not even two came out agreeing with each other, what would you make of that?
Simplicio: I'd judge that all of them were faulty, either through the fault of the one doing the computing or the failing of the observers. At most I could say that one — one only, and no more — was correct, but I wouldn't be able to pick which one.
Salviati: So would you want to deduce and establish a doubtful conclusion as true, from false foundations? Certainly not. Now, this author's calculations are such that no one of them agrees with another — so you can see how much faith they deserve.
Simplicio: Truly, if the matter stands like that, it's a notable failing.
Sagredo: Let me lend a hand to Simplicio and the author, and say to Salviati that his point would follow of strict necessity only if the author had set out to determine precisely how far the star was from the Earth. But I don't think that was his aim — only to show that from those observations one drew the result that the star was sublunar. So that if, from those observations and from all the computations made on them, the star's altitude always comes out less than the Moon's, that's enough for the author to convict of the crassest ignorance all those astronomers who, through some failing of geometry or arithmetic, hadn't known how to draw true conclusions from their own observations.
Salviati: Then it'll be fitting for me to turn to you, Sagredo, since you're defending this author's doctrine so shrewdly. And to try to make even Simplicio — inexperienced though he is in calculations and demonstrations — at least able to see how inconclusive this author's demonstrations are, let me first point out that both he and all the astronomers he's quarreling with agree on this: the new star had no motion of its own, and only went around with the daily motion of the primum mobile. Where they disagree is over its location. The astronomers put it in the celestial region — that is, above the Moon, and perhaps among the fixed stars — while he judges it near the Earth, that is, below the concave of the lunar orb. Now, since the new star in question stood toward the north and not far from the pole, so that for us northerners it never set, it was an easy matter to take its meridian altitudes with astronomical instruments — both the lowest, below the pole, and the highest, above it. From the comparison of these altitudes, taken from different places on Earth set at various distances from the north — that is, differing from one another in their polar altitudes — one could work out the star's distance. For if the star had been up in the firmament among the other fixed stars, its meridian altitudes, taken at different pole-elevations, would have to differ from one another by the very same differences found among those pole-elevations. For example: if the star's height above the horizon was 30 degrees when taken in the place where the pole's altitude was, say, 45 degrees, then the same star's height would have to have grown by 4 or 5 degrees in those more northerly countries where the pole stood 4 or 5 degrees higher. But if the star's distance from the Earth was quite small compared with that of the firmament, then its meridian altitudes must, as we move north, grow noticeably more than the polar altitudes do. And from that extra growth — that is, from the excess of the increase in the star's height over the increase in the pole's altitude (this is what's called the parallax difference) — one calculates promptly, by a clear and reliable method, the star's distance from the center of the Earth. Now, this author takes the observations made by 13 astronomers at different pole-elevations, and, comparing a small selection of them of his own choosing, he calculates, through twelve pairings, that the new star's altitude was always below the Moon. But he pulls this off only by counting on such crass ignorance in everyone into whose hands his book might fall that it honestly turned my stomach. And I sit here wondering how the other astronomers — and Kepler in particular, against whom this author chiefly rails — can keep so silent, when the tongue doesn't usually die in his mouth. Unless, that is, he judged such an undertaking too low to bother with. Now, to put you in the picture, I've copied out onto this sheet the conclusions he draws from his twelve investigations. Of these, the first is from the two observations —
These, then, are twelve investigations the author made at his own choosing, out of the very many that, as he says, could be made from the combinations of the observations of these thirteen observers. And it's fair to assume these twelve are the ones most favorable to proving his case.
Sagredo: But I'd like to know whether, among all the other investigations the author passed over, there are any that told against him — that is, from which, calculating, one would gather that the new star was above the Moon. It seems to me, at first glance, that I can reasonably suspect as much, when I see the ones he did produce differing so wildly among themselves: some give me the new star's distance from the Earth as 4, 6, 10, 100, even a thousand and fifteen hundred times greater than others. So I can well suspect that among the ones he left uncalculated there was some in favor of the opposing side — and I'm all the more inclined to believe it since I don't imagine those observing astronomers lacked the skill and practice for these computations, which I don't think depend on the most abstruse things in the world. In fact it'll strike me as more than miraculous if, when even these twelve investigations alone include some that put the star just a few miles from the Earth, and others that put it below the Moon by a tiny margin, not a single one turns out that, in favor of the other side, puts it even 20 braccia above the lunar orb — and, what would be stranger still, that all those astronomers were so blind they failed to spot a fallacy so glaring.
Salviati: Start bracing your ears now, to hear with boundless amazement the excesses of confidence — in one's own authority and in everyone else's stupidity — to which a man can be carried by the itch to contradict and to show himself cleverer than others. Among the investigations the author left out, there are some that put the new star not merely above the Moon, but above the fixed stars as well; and these aren't a few — they're the majority, as you'll see on this other sheet, where I've written them down.
Sagredo: But what does the author say about these? Perhaps he hasn't taken them into account?
Salviati: He's taken them into account all too well. But he says that the observations on which the calculations put the star infinitely far off are erroneous, and can't be combined with one another.
Simplicio: Oh, that strikes me as a feeble retreat — because the other side could say, with just as much reason, that the erroneous ones are the very observations he's drawing on to place the star down in the elemental region.
Salviati: Oh, Simplicio — if I manage to make you see through the trick of this author, unremarkable as the trick really is, I mean to stir up wonder in you, and even indignation. For then you'd see how he, cloaking his cunning behind the veil of your good faith and that of the other honest philosophers, tries to worm his way into your favor by tickling your ears and puffing up your ambition — parading how he's supposedly convinced and struck dumb these little astronomers who dared to assault the impregnable unchangeableness of the Peripatetic heaven, and, what's more, silenced and beaten them with their own weapons. I mean to give it my best effort. And in the meantime, let Sagredo forgive Simplicio and me for wearying him perhaps a bit too much, while, with a longer circuit of words than his own very quick grasp really needs, I go about laying plain something it's well he shouldn't be left in the dark about.
Sagredo: Not only without boredom — I'll listen to your discussions with real pleasure. And I only wish all the Peripatetic philosophers could sit in on them too, so they might grasp how much they owe to this protector of theirs.
Salviati: Tell me, Simplicio, whether you've thoroughly taken in this: since the new star is located on the meridian circle up toward the north, then for someone traveling from the south toward the north, that same new star would climb above the horizon by exactly as much as the pole does — provided it were truly located among the fixed stars; but that if it were notably lower, that is, nearer the Earth, it would appear to rise more than the pole itself, and ever more so the greater its nearness.
Simplicio: I think I've grasped it perfectly, and to show it I'll try my hand at a mathematical figure. In this large circle I'll mark the pole P, and in these two lower circles I'll mark two stars seen from a point on Earth — call it A — and let the two stars be these, B and C, seen along the one line ABC against a fixed star D. Then, traveling on Earth as far as the point E, the two stars will appear to me separated from the fixed star D and drawn nearer the pole P — the lower one, B, more so, appearing at G, and C less so, appearing at F; but the fixed star D will have kept the same distance from the pole.
Salviati: I see you understand it very well. I believe you also see how, because star B is lower than C, the angle formed by the sightlines that set out from the two places A and E and meet at C — that is, this angle ACE — is narrower, or we might say more acute, than the angle formed at B by the lines AB, EB.
Simplicio: That's plain to the eye.
Salviati: And likewise, since the Earth is exceedingly small and all but imperceptible next to the firmament, and since in consequence the distance AE — as far as one can travel on Earth — is very short compared with the immense length of the lines EG, EF stretching from Earth up to the firmament, you come to understand that star C could be raised and carried so very far from the Earth that the angle formed at it by the rays setting out from those same points A and E would become extremely acute, and virtually null and imperceptible altogether.
Simplicio: This too I understand perfectly.
Salviati: Now know, Simplicio, that astronomers and mathematicians have found infallible rules, by way of geometry and arithmetic, whereby — from the size of these angles B and C and their differences, joined with knowledge of the distance between the two places A and E — they can find the distance of these lofty things to within a hand's breadth, provided always that the distance and the angles are taken correctly.
Simplicio: So then, if the rules that depend on geometry and arithmetic are sound, all the fallacies and errors one might meet in trying to investigate such heights — of new stars, or comets, or anything else — must come down to the distance AE and the angles B, C not being well measured. And so all the discrepancies one sees in these twelve investigations depend not on any defect in the rules of calculation, but on errors committed in investigating those angles and those distances by means of instrumental observations.
Salviati: Just so, and no difficulty arises there. Now you must carefully note how, as the star is carried farther from B toward C — so that the angle grows ever more acute — the ray EBG keeps drawing away from the ray ABD on the lower side of the angle, as the line ECF shows, whose lower part EC is more remote from the part AC than EB is. But it can never happen, however immense the removal, that the lines AD, EF part company altogether, since in the end they must meet at the star; one could only say they separate and become parallel if the removal were infinite, and that case cannot occur. But because — note this well — the firmament's distance, set against the smallness of the Earth, is reckoned (as already said) as infinite, the angle enclosed by the rays that, drawn from points A and E, would end at a fixed star is judged to be null, and those rays are taken as two parallel lines. And so one concludes that only then may it be affirmed that the new star was in the firmament, when a collation of observations made in different places yields, by calculation, that this angle is imperceptible and the lines as good as parallel. But when the angle is of notable size, the new star must necessarily be lower than the fixed stars, and lower even than the Moon — that is, whenever the angle ABE were greater than the one that would be formed at the center of the Moon.
Simplicio: So then the Moon's distance is not so great that a similar angle at it stays imperceptible?
Salviati: No, sir. On the contrary, it is perceptible not only at the Moon, but at the Sun as well.
Simplicio: But if that's so, it could also be that such an angle is observable in the new star without its being lower than the Sun — let alone lower than the Moon.
Salviati: That can be, and it is indeed so in the present cases, as you'll see in due place — that is, once I've smoothed the road enough that you too, though no expert in astronomical calculations, can grasp and touch with your own hand how far this author has aimed at writing to please the Peripatetics, by cloaking and disguising various things, rather than at establishing the truth by bringing them forward with naked honesty. But let's press on. From what's been laid out so far, I believe you're fully able to see how the new star's distance can never be made so immense that the angle we've named so often entirely vanishes, and the two observers' rays from points A and E become parallel lines. And in consequence you come to understand perfectly that, if the calculation drew from the observations that this angle is totally null, or the lines truly parallel, we would be certain the observations were — by at least some tiny amount — in error; but if the calculation gave us those lines separated not merely to equidistance, that is, to being parallel, but past that point, and spread wider at the top than at the bottom, then we must firmly conclude that the observations were made with too little accuracy — in short, that they are erroneous, as leading us to a manifest impossibility. Then you must believe me, and take it for absolutely certain, that two straight lines setting out from two points marked on another straight line are wider at the top than at the bottom whenever the angles they enclose upon that straight line are greater than two right angles; and when those angles equal two right angles, the lines are parallel; but if they are less than two right angles, the lines converge, and extended far enough would beyond all doubt close up into a triangle.
Simplicio: Without taking it on your word, I have the science of it, and I'm not so bare of geometry that I don't know a proposition I've had occasion to read a thousand times in Aristotle — namely, that the three angles of every triangle equal two right angles. So that if I take, in my figure, the triangle ABE — granting the line EA to be straight — I understand very well how its three angles A, E, B equal two right angles, and that in consequence the two alone, E and A, fall short of two right angles by exactly the amount of the angle B; whence, by opening the lines AB, EB (while keeping them fixed at points A and E) until the angle they contain toward the B side vanishes, the two below will come to equal two right angles, and those lines will be reduced to being parallel; and if one went on opening them further, the angles at points E and A would become greater than two right angles.
Salviati: You're an Archimedes, and you've spared me spending more words to explain to you how, whenever the calculations turn up the two angles A and E as greater than two right angles, the observations are without question in error. This is exactly what I wanted you to understand perfectly, and what I feared I might not manage to explain in a way that a pure Peripatetic philosopher could take in with any certainty. Now let's carry on with what's left. And picking up again what you granted me a moment ago — namely, that since the new star cannot be in several places, but in one only, then whenever the calculations made upon these astronomers' observations don't give it back to us in the same place, there must be error in the observations: either in taking the polar altitudes, or in taking the star's elevations, or in both operations at once — now, since among the many investigations, made by combining the observations two by two, very few come out placing the star in the same spot, then those very few alone could be the ones not in error, while all the rest are absolutely erroneous.
Sagredo: Then we'll have to trust these very few alone rather than all the others together. And since you say the ones that agree are very few, and I see among these twelve two that both make the star's distance from the Earth's center 4 semidiameters — four Earth-radii — this fifth and the sixth, then it's more probable that the new star was elemental than celestial.
Salviati: It's not so; for if you look carefully, it isn't written that the distance was exactly 4 semidiameters, but about 4 semidiameters — and yet you'll see that those two distances differed from each other by many hundreds of miles. Here they are: you see that this fifth, which is 13,389 miles, exceeds the sixth, which is 13,100 miles, by nearly 300 miles.
Sagredo: Which, then, are these few that agree in placing the star in the same spot?
Salviati: They are, to this author's misfortune, five investigations, all of which lodge it in the firmament — as you'll see in this other note, where I record many further combinations. But I'll grant the author more than he'd perhaps ask of me: namely, that in each combination of observations there is some error. Which I believe is absolutely unavoidable; for since the observations that serve for a single investigation are 4 in number — that is, two different polar altitudes and two different star elevations, made by different observers, in different places and with different instruments — anyone with any knowledge of the practice will say it can't be that among all 4 no error slipped in, especially when we see that in taking a single polar altitude — with the same instrument, in the same place, and by the same observer, who could have done it a thousand times — one still wavers by some minutes, and often by many, as you can see in various places in this very book. These things granted, I ask you, Simplicio: do you believe this author holds his 13 observers to be shrewd, intelligent, and skilled in handling such instruments, or rather crude and inexpert men?
Simplicio: It can't be that he reckons them anything but very careful and intelligent. For if he judged them unfit for the work, he might as well throw out his own book as proving nothing, being founded on suppositions full of errors; and he'd be writing us off as too simple, if he thought he could use their inexperience to persuade us that a false proposition of his was true.
Salviati: Then, since these observers are such, and yet for all that have erred — so that their errors must be amended in order to draw from their observations what further knowledge is possible — the fitting thing is to apply to them the smallest and closest amendments and corrections we can, so long as these suffice to draw the observations out of impossibility and into possibility. So that, for instance, if a manifest error and a patent impossibility in one of their observations can be eased by adding or subtracting 2 or 3 minutes, and by that amendment brought within the possible, one shouldn't insist on adjusting it by adding or subtracting 15 or 20 or 50.
Simplicio: I don't believe the author would contradict this; for, granted that they're judicious and expert men, one should sooner believe they erred by a little than by a lot.
Salviati: Now note what follows. Of the places where the new star might be lodged, some are manifestly impossible, others possible. Absolutely impossible is that it lay an infinite interval beyond the fixed stars, for no such site exists in the world — and if it did, the star set there would have been invisible to us. It's also impossible that it went creeping over the Earth's surface, and still more that it lay inside the terrestrial globe itself. The possible places are these ones under dispute, since it doesn't offend our intellect that a visible object, with the look of a star, could be above the Moon no less than below it. Now, while we try to draw out — by way of observations and calculations made with all the certainty human diligence can reach — where its place truly was, we find that most of these calculations set it more than an infinite interval above the firmament, others set it close to the Earth's surface, and some even below that surface; and of the rest, which lodge it in not-impossible places, none agree with one another. So that we're forced to say all the observations are necessarily fallacious; and thus, if we still mean to draw some fruit from so much labor, we must resort to corrections, amending all the observations.
Simplicio: But the author will say that of the observations which set the star in impossible places, no account should be taken, being infinitely erroneous and fallacious; and one should accept only those that place it in not-impossible places, and among these alone go searching, by way of the more probable and more numerous agreements, for — if not the particular and exact site, that is, its true distance from the Earth's center — at least the knowledge of whether it was among the elements or among the celestial bodies.
Salviati: The reasoning you now make is the very one the author has made on behalf of his own cause — but with too unreasonable a disadvantage to the other side. And this is the chief point that has made me marvel beyond measure at the excessive confidence he's taken — no less in his own authority than in the blindness and heedlessness of the astronomers. I'll speak for them, and you'll answer for the author. And first I ask you: when the astronomers observe with their instruments, seeking, say, how great a star's elevation above the horizon is, can they stray from the truth as much toward the more as toward the less — that is, err by making it sometimes higher than the truth and sometimes lower — or can the error only ever be of one kind: that in erring they always sin toward excess and never toward the less, or always toward the less and never toward excess?
Simplicio: I've no doubt it's equally easy to err in the one way as in the other.
Salviati: I believe the author would answer the same. Now, of these two kinds of error — which are contrary, and into which the observers of the new star may equally have fallen — when applied to the calculation, one kind will make the star higher than the truth, and the other lower. And since we already agree that all the observations are erroneous, on what grounds does this author want us to accept as more in keeping with the truth those that show the star to have been near, rather than the others that show it excessively far?
Simplicio: From what I seem to have gathered from what's been said so far, I don't see that the author refuses those observations and investigations that would set the star farther than the Moon, or even farther than the Sun — but only those that make it remote (as you yourself have said) by more than an infinite interval. And since you too refuse that distance as impossible, he passes over such observations as infinitely convicted of falsity and impossibility. It seems to me, then, that if you want to convince the author, you ought to produce investigations more exact, or more numerous, or by more diligent observers, which set the star at such-and-such a distance above the Moon or above the Sun — in a place, in short, where it could possibly be — just as he produces these twelve, all of which set the star below the Moon, in places that exist in the world and where it could have been.
Salviati: Now — now, Simplicio, here is where the misunderstanding lies, yours and the author's: yours in one respect, and the author's in another. I gather from your talk that you've formed the notion that the wildly exaggerated figures one arrives at in fixing the star's distance grow in proportion to the errors made on the instrument in taking the observations; and that, conversely, from the size of those wild figures one can argue the size of the errors; and that therefore, on hearing it said that a given observation yields the star's distance as infinite, the error in observing must necessarily have been infinite too, and hence beyond amending and so to be refused. But the business, my dear Simplicio, doesn't run that way. And for not having grasped how this matter stands, I excuse you, as inexperienced in such dealings — but I cannot cloak the author's error under a like mantle. For he, disguising his understanding of it (having persuaded himself that we truly weren't going to understand), has hoped to make use of our ignorance in order to lend his doctrine more credit among the crowd of the little-understanding. So, as a warning to those who are more credulous than discerning, and to draw you out of your error, know this: it may be — and most of the time it will happen — that an observation which gives you the star, for example, at the distance of Saturn, will, by adding or subtracting a single minute from the elevation taken with the instrument, make it come out at an infinite distance, and so turn it from possible to impossible; and conversely, those calculations built on such observations that render the star infinitely far, many a time may, by adding or shaving off a single minute, pull it back to a possible site. And what I say of one minute can happen with a correction of a half, or a sixth, or less. Now fix it well in your mind that at the very highest distances — such as, for example, the altitude of Saturn or that of the fixed stars — the very tiniest errors made by the observer on the instrument turn the site from determinate and possible into infinite and impossible. It doesn't work that way with the sublunar distances near the Earth, where it can happen that an observation from which the star was gathered to be, say, 4 terrestrial semidiameters away, can be increased or diminished not merely by a minute, but by ten, and a hundred, and much more, without the calculation rendering it even higher than the Moon, let alone infinitely remote. Understand from this that the size of the errors — the instrumental errors, so to speak — is not to be judged from the outcome of the calculation, but from the very quantity of the degrees and minutes counted off on the instrument. And those observations are to be called more correct, or less erroneous, which, with the addition or subtraction of fewer minutes, restore the star to a possible place; and among the possible places, the true site must be believed to be the one around which the greater number of the distances concur, as calculated upon the more correct observations.
Simplicio: I can't quite get hold of what you're saying, nor make out on my own how it can be that at the very greatest distances a wilder exaggeration should spring from an error of a single minute than at small distances from an error of 10 or of 100; and so I'd be glad to have it explained.
Salviati: You'll see it — if not by theory, at least by practice — from this short summary I've drawn up of all the combinations, and of some of the investigations the author left out, which I've calculated and noted down on this very sheet.
Sagredo: So it must be that from yesterday to now — and it's not been more than 18 hours — you've done nothing but calculate, taking neither food nor sleep.
Salviati: On the contrary, I've had both those refreshments: but I run through such calculations very quickly; and, to tell the truth, I've been more than a little amazed that this author should go on at such length, larding it with so many computations that have nothing to do with the question being asked. And so that this may be fully understood, and also so that one may quickly see how much more probably it follows, from the observations of the astronomers the author himself relies on, that the new star could have been above the Moon — and even above all the planets, and higher still, among the fixed stars — I have copied onto this sheet all the observations recorded by that same author, made by 13 astronomers, where the polar elevations and the star's altitudes on the meridian are noted, both the lowest under the pole and the highest above: and here they are.
Now, to see my whole procedure, we can begin with these calculations — 5 of them the author passed over, perhaps because they tell against him, seeing that they set the star above the Moon by many terrestrial semidiameters. The first of them is this one, worked from the observations of the Landgrave of Hesse and of Tycho, who are, even by the author's own admission, among the most exact observers: and in this first one I'll spell out the order I keep in the investigation, and that knowledge will serve you for all the rest, since they go by the same rule, differing only in the quantity of the data — that is, in the number of degrees of the polar altitudes and of the elevations of the new star above the horizon, whose distance from the Earth's center we seek in proportion to the semidiameter of the terrestrial globe. And in this case it doesn't matter in the least to know how many miles that semidiameter is, so that working out that figure, and the distance between the places where the observations were made — as this author does — is labor and time thrown away, nor do I know why he did it, especially since in the end he turns the miles he found back into semidiameters of the terrestrial globe.
Simplicio: Perhaps he does this to find, by such smaller measures and their fractions, the star's distance pinned down to the last 4 fingerbreadths; because we others, who don't understand your rules of arithmetic, are struck dumb on hearing the conclusions, when we read, for instance: "Therefore the comet, or the new star, was distant from the Earth's center three hundred seventy-three thousand eight hundred and seven miles, plus two hundred eleven four-thousand-ninety-sevenths, 373807 211/4097" — and over such precise exactitudes, where these tiny fractions are set down, we form the notion that it's impossible that you, who in your calculations take account of a single finger, could in the end deceive us by 100 miles.
Salviati: This reasoning of yours, and this excuse, would be acceptable if, over a distance of thousands of miles, an arm's length more or less were of great weight, and if the suppositions we take for true were so certain that they assured us we'd draw out an indubitable truth in the end: but here you see, in the author's 12 investigations, that the star's distances gathered from them differ one from another — and therefore stray from the truth — by many hundreds and thousands of miles. Now, since I'm more than sure that what I'm looking for must necessarily differ from the right figure by hundreds of miles, why torment myself over the calculation out of a jealous fear of slipping by a single finger? But let's come at last to the operation, which I work out in this way.
Tycho, as you see in the note, observed the star at the polar altitude of 55° 58′; and the Landgrave's polar altitude was 51° 18′: the star's altitude on the meridian, taken by Tycho, was 27° 45′; the Landgrave found it at 23° 3′: which altitudes are the ones noted here below, as you see:
...the quantity for the star, which here is 62° 15′, gives us the size of angle BDC, 154° 45′; which — together with its sine, taken from the table, which is 42657 — I note down; and beneath it I note the angle of the parallax, BCD, 0° 2′, with its sine, 58. And since in triangle BCD side DB is to side BC as the sine of the opposite angle BCD is to the sine of the opposite angle BDC, therefore when line BD is 58, BC would be 42657; and since the chord DB is 8142, of which the radius BA is 100000, and we want to know how many of those same parts BC amounts to, we'll say, by the rule of three: if when BD is 58, BC is 42657, then when that same DB is 8142, how much would BC be? So I multiply the second term by the third; I get 347313294, which must be divided by the first — that is, by 58 — and the quotient would be the number of parts of line BC of which the radius AB is 100000: and to know how many radii BA that same line BC contains, we'd have again to divide that quotient by 100000, and we'd have the number of semidiameters comprised in BC. Now, the number 347313294 divided by 58 gives 5988160¼, as you see here:
and this, divided by 100000, gives us 59 and 88160/100000.
But we can greatly shorten the operation by dividing the first product we found — that is, 347313294 — by the product of multiplying the two numbers 58 and 100000, which is 5,800,000;
and it likewise comes out 59 and 5113294/5800000.
And that many semidiameters are contained in line BC, to which, adding one for line AB, we'll have a little less than 61 semidiameters for the two lines ABC together, and so the straight distance from the center A to the star C will be more than 60 semidiameters; therefore it comes out above the Moon — by Ptolemy's reckoning more than 27 semidiameters, and by Copernicus's more than 8, granting that the Moon's distance from the Earth's center, by Copernicus's account, is, as the author says, 52 semidiameters.
By this same kind of investigation I find, from the observations of Camerarius and Muñoz, that the star comes out set at a like distance — this one too more than 60 semidiameters: and these are the observations, and here following is the calculation.
The next investigation is made upon two observations of Tycho and Muñoz, from which one calculates that the star was distant from the Earth's center 478 semidiameters and more.
From this other investigation the star is found to be distant from the center more than 716 semidiameters.
These, as you see, are five investigations that render the star well above the Moon; and here I want you to weigh that particular point I mentioned to you a little while ago — namely, that at the great distances the changing, or say the correcting, of very few minutes shifts the star through enormous stretches. As, for example, in the first of these investigations, where the calculation made the star 60 semidiameters remote from the center with a parallax of 2 minutes, anyone who wanted to maintain that it was in the firmament has only to correct, in the observations, 2 minutes and even less — for then the parallax ceases, or grows so small that it puts the star at an immense distance, such as everyone grants the firmament's to be. In the second investigation an amendment of less than 4′ does the same. In the third and the fourth, again just as in the first, a mere 2 minutes lift the star even above the fixed stars. In the previous one a quarter of a minute — that is, 15 seconds — gives us the same. But it won't go this way at the sublunar heights: for imagine whatever distance you please, and try to correct the investigations the author made and adjust them so that they all answer to that same fixed distance; you'll see how much larger the amendments you'll need to make.
Sagredo: It can only do us good, for our full understanding, to see some example of what you say.
Salviati: Fix, at your own pleasure, whatever determined sublunar distance you like, where the star is to be set; for with little trouble we'll be able to satisfy ourselves whether corrections like these — which we've seen suffice to bring it among the fixed stars — will bring it to the place you've fixed.
Sagredo: To take the most favorable distance for the author, let's set it at the greatest of all those he investigated in his 12 investigations; because, while the astronomers and he are in controversy — they saying the star was above the Moon, and he that it was below — every little space by which he proves it to have been below gives him the victory.
Salviati: Let's take, then, the seventh investigation, made upon the observations of Tycho and Thaddeus Hagecius, from which the author finds the star to have been distant from the center 32 semidiameters — the site most favorable to his side; and to give him every advantage, I want us, on top of this, to set it at the least favorable distance for the astronomers, which is to place it even above the firmament. That granted, then, let's go looking for what corrections would be needed to apply to his other 11 investigations, so as to raise the star up to the distance of 32 semidiameters; and let's begin with the first, calculated upon the observations of Hainzel and Maurolyco, in which the author finds the distance from the center to be about 3 semidiameters, with a parallax of 4° 42′ 30″: let's see now whether, by pulling it back to just 20′, it rises to 32 semidiameters. Here is the operation, very brief and exact: I multiply the sine of angle BDC by the chord BD, and divide the result — dropping the last 5 figures — by the sine of the parallax; out comes 28½ semidiameters: so that not even with a correction of 4° 22′ 30″, taken away from 4° 42′ 30″, does the star rise to the height of 32 semidiameters; which correction, for Simplicio's understanding, amounts to 262½ minutes.
In the second operation, made upon the observations of Hainzel and Schuler, with a parallax of 0° 8′ 30″, the star is found at a height of about 25 semidiameters, as you see in the following operation.
And pulling the parallax of 0° 8′ 30″ back to 7′, whose sine is 204, the star rises to about 30 semidiameters: so a correction of 1′ 30″ isn't enough.
Now let's see what correction is needed for the third investigation, made upon the observations of Hainzel and Tycho, which renders the star at a height of about 19 semidiameters, with a parallax of 10′. The usual angles, and their sines and chord, found by the author, are these; and they render (as also in the author's own operation) the star distant about 19 semidiameters; so, to raise it, we must shrink the parallax, following the rule he himself observes in the ninth investigation: let's put the parallax, then, at 6′, whose sine is 175; and, the division done, one finds still less than 31 semidiameters for the star's distance. So a correction of 4′ is too little for the author's need.
Let's come to the fourth investigation, and to the rest, by the same rule, and with the chords and sines the author himself found. In this one the parallax is 14′, and the height found less than 10 semidiameters; and diminishing the parallax from 14′ to 4′, you see all the same how the star doesn't rise even to 31 semidiameters: so a correction of 10′ out of 14′ isn't enough.
In the author's fifth operation we have the sines and the chord as you see:
and the parallax is 0° 42′ 30″, which renders the star's height about 4 semidiameters; and correcting the parallax by reducing it from 42′ 30″ to just 5′ isn't enough to raise it even to 28 semidiameters: so an amendment of 37′ 30″ is too little.
In the sixth operation the chord, the sines, and the parallax are these,
and the star is found to be at a height of about 4 semidiameters: let's see where it's brought by lowering the parallax from 8′ to a single 1′. Here is the operation, and the star is raised no higher than to about 27 semidiameters: so a correction of 7′ out of 8′ isn't enough. In the eighth operation the chord, the sines, and the parallax, as you see, are these:
and from these the author calculates the star's height at 1½ semidiameters, with a parallax of 43′; which, reduced to 1′, still leaves the star distant less than 24 semidiameters: so a correction of 42′ isn't enough. Now let's see the ninth. Here is the chord, the sines, and the parallax, which is 15′: from which the author calculates the star's distance from the Earth's surface to be less than a forty-seventh of a semidiameter. But this is a calculation error; for it truly comes out, as we shall see right now, more than a fifth: here it comes to about 90/436, which is more than a fifth.
What the author then adds by way of amending the observations — namely, that it isn't enough to draw the parallax difference back even to a single minute, nor even to an eighth of 1′ — is true. But I say that not even a tenth of 1′ will reduce the star's height to 32 semidiameters: for the sine of a tenth of 1′, that is, of 6 seconds, is 3; by which, if in our rule we divide 90 — or rather, if we divide 9058672 by 300000 — it will come to 30 and 58672/100000, that is, a little more than 30½ semidiameters. The tenth gives the star's height at a fifth of a semidiameter, with this angle, sines, and parallax, which is 4° 30′: and I see that, reduced from 4° 30′ to 2′, it still doesn't advance the star to 29 semidiameters.
The eleventh renders the star, for the author, remote about 13 semidiameters, with a parallax of 55′: let's see, reducing it to 20′, how high it will lift the star. Here is the calculation: it raises it to a little less than 33 semidiameters: so the correction is of a little less than 35, out of 55′.
The twelfth, with a parallax of 1° 36′, renders the star at a height of less than 6 semidiameters: pulling the parallax back to 20′ brings the star to less than 30 semidiameters of distance: so a correction of 1° 16′ isn't enough.
From this it is seen (as I have noted here on the back) that if the author decided to accept, as the true site of the new star, the distance of 32 semidiameters, then correcting his other 10 investigations (and I say 10, because the second, being quite high already, is brought to the height of 32 semidiameters with a 2′ correction) so as to make them all restore the said star to that distance would require such a drawing-back of the parallaxes that all the subtractions together would amount to more than 756′: whereas in the 5 I calculated, which render the star above the Moon, to correct them so that they set it in the firmament, a correction of only 10¼ minutes suffices. Now add to these 5 others that render the star precisely in the firmament with no need of any correction at all, and we'll have 10 investigations agreeing to set it in the firmament, with only 5 of them corrected (as we've seen) by 10¼ minutes: whereas to correct the author's other 10, so as to bring the star to a height of 32 semidiameters, you'll need amendments of 756′ out of 836′; that is, from the sum of 836 one must subtract 756 if the star is to rise to the height of 32 semidiameters — and even that correction isn't enough.
The investigations that, at once and without any further correction, render the star with no parallax, and therefore in the firmament, and even in its most remote parts — in short, as high as the pole itself — are these 5 noted here:
As for the rest of the pairings that can be made from the observations of all these astronomers, those that render the star sublime by an infinite interval are far more numerous — about 30 more — than the others that, by calculation, place the star below the Moon; and since (as we've agreed) it's to be believed the observers erred by a little sooner than by a lot, it is plain that the corrections to be applied to the observations that place the star infinitely high, in drawing it back down, will bring it to the firmament sooner, and with a smaller amendment, than below the Moon: so that all of these applaud the opinion of those who set it among the fixed stars. Add to this that the corrections required for such amendments are far smaller than those by which the star can be brought from its improbable nearness up to the height most favorable to this author, as we've seen in the past examples: among which impossible nearnesses there are 3 that seem to move the star from the Earth's center by less than a semidiameter's distance, making it in a certain way go wheeling under the Earth; and these are the combinations in which, the polar altitude of one of the observers being greater than the polar altitude of the other, the star's elevation taken by the former is less than the star's elevation by the latter. And such are the combinations noted here below. This first is the Landgrave's with Gemma: where the Landgrave's polar altitude, 51° 18′, is greater than Gemma's polar altitude, which is 50° 50′; but the Landgrave's star altitude, 79° 30′, is less than that of Gemma's star, 79° 45′.
The other two are these below:
From what I've shown you up to now, you can grasp how unfavorable to his own cause is this first method of investigating the star's distance and proving it sublunar, introduced by the author — and how much more probably and clearly one gathers that its distance was among the most remote fixed stars.
Simplicio: Up to this point it seems to me that the small force of the author's demonstrations has been quite plainly uncovered; but I see that all this is contained in not many pages of the book, and it could be that other arguments of his are more conclusive than these first ones.
Salviati: On the contrary, they can only be less valid, if we let the past ones be our sample for the rest; for (as is manifest) the uncertainty and inconclusiveness of those plainly derives from the errors committed in the instrumental observations, from which the polar altitudes and the star's altitudes were believed to have been correctly taken, when in fact they're all easily in error; and yet for finding the altitudes of the pole the astronomers have had centuries of time to spend on it at their leisure, and the star's meridian altitudes are the easiest to observe, being very sharply defined and allowing the observer some room to keep at them, since they don't change appreciably in a very short time, as do those far from the meridian: and if this is so — as it most truly is — what faith shall we place in calculations founded on observations more numerous, harder to make, more momentary in their variation, with the added burden of more awkward and more fallacious instruments? From a single glance I've given at the demonstrations that follow, the computations are made upon altitudes of the star taken in various vertical circles, which they call by the Arabic word azimuths: in which observations movable instruments are used, not only on the vertical circles but on the horizon as well, at the same time; so that at the very moment one takes the altitude, one must also have observed on the horizon the distance of the vertical circle in which the star lies from the meridian; besides which, after a notable interval of time, one must repeat the operation and keep close account of the elapsed time, trusting either to clocks or to other observations of stars: such a tangle of observations is then compared with another like it, made by a different observer, in a different country, with a different instrument and at a different time; and from this the author tries to draw out what the star's altitudes and horizontal latitudes would have been at the time and hour of those other, first observations, and upon such an adjustment he finally builds his calculation. I leave it now to you to judge how much faith is to be placed in what is drawn from such investigations. Besides, I've no doubt at all that if anyone chose to martyr himself over such enormously long computations, he'd find, as in the past ones, more that favored the opposing side than the author: but it doesn't seem to me worth the trouble of taking on such a labor for a thing that isn't among the primary matters we have in view.
Sagredo: I'm with you on this point; but since this whole business is hemmed in by so much confusion, uncertainty, and error, on what confidence did so many astronomers so positively declare that the new star was very high up?
Salviati: On two kinds of observation, both of them utterly simple, easy, and reliable — and either one alone is more than enough to assure us that the star was set in the firmament, or at least a very long way above the Moon. The first is drawn from the equality, or the very slight inequality, of its distances from the pole, whether it stood in the lowest part of the meridian or in the highest. The second is that it kept, permanently, the very same distances from certain fixed stars near it — in particular from the eleventh star of Cassiopeia, from which it was never more than a degree and a half away. From these two facts one gathers, beyond any doubt, either that there was no parallax at all, or else a parallax so small that a very quick calculation assures us of the star's great distance from the Earth.
Sagredo: But didn't this author take these things into account? And if he did see them, how does he defend himself?
Salviati: We have a saying: that when a man, finding no dodge that will hold up against his own blunders, comes out with the feeblest of excuses, he's trying to catch hold of the ropes of the sky. Well, this author reaches not for the ropes but for the threads of the sky's cobwebs — as you'll plainly see once we go through the two points I just mentioned. First, what the polar distances of each observer show us I've set down in these short calculations. To follow them fully, I must first point out this: whenever the new star, or any other phenomenon, is near the Earth, then as it wheels with the daily rotation around the pole, it will appear farther from the pole when it lies in the lower part of the meridian than when it is in the upper part — as this figure shows. In it, the point T marks the center of the Earth, O the place of the observer, the firmament the arc VPC, and P the pole. The phenomenon, moving along the circle FS, is seen now below the pole, along the ray OFC, and now above it, along the ray OSD, so that the places seen in the firmament are D and C; but the true places, reckoned from the center T, are B and A, equally distant from the pole. Now it is already clear that the apparent place of the phenomenon at S — that is, the point D — is nearer the pole than the other apparent place, C, seen along the ray OFC. That's the first thing to note.
In the second place, you should note that the amount by which the apparent lower distance from the pole exceeds the apparent upper distance from the pole is greater than the lower parallax of the phenomenon. What I mean is that the excess of arc CP (the apparent lower distance) over arc PD (the apparent upper distance) is greater than arc CA (which is the lower parallax). This is easy to gather: for CP exceeds PD by more than it exceeds PB, since PB is greater than PD; but PB equals PA, and the excess of CP over PA is the arc CA; therefore the excess of arc CP over arc PD is greater than arc CA, which is the parallax of the phenomenon placed at F. That's what we needed to know. And to give the author every advantage, let's suppose that the parallax of the star at F is the whole excess of arc CP (the lower distance from the pole) over arc PD (the upper distance).
Now I come to examine what the observations of all the astronomers cited by the author give us — and among them there isn't a single one that doesn't work against him and run contrary to his aim. Let's begin with Busch's. He found the star's distance from the pole, when it was above the pole, to be 28° 10′, and the lower to be 28° 30′, so the excess is 0° 20′, which I'll take (in the author's favor) as if it were all the parallax of the star at F — that is, the angle TFO. The distance from the point overhead, that is arc CV, is 67° 20′. Once these two things are found, extend the line CO, and onto it drop the perpendicular TI, and consider the triangle TOI, in which the angle I is a right angle and the angle IOT is known (being at the tip of the angle VOC, the star's distance from the point overhead). Moreover, in the triangle TIF, also right-angled, the angle F is known, taken as the parallax. So set aside the two angles IOT and IFT, and take their sines, as you see noted. And since in the triangle IOT, of the parts of which the whole sine TO is 100000, the sine TI is 92276, and since in the triangle IFT, of the parts of which the whole sine TF is 100000, the sine TI is 582 — then to find out how many parts TF is, of those of which TO is 100000, we'll say, by the rule of three: when TI is 582, TF is 100000; but when TI is 92276, how much would TF be? Multiply 92276 by 100000; that gives 9227600000; and this must be divided by 582, which yields, as you see, 15854982 — and TF will contain that many parts of those of which TO holds 100000. So, to learn how many lengths TO there are in TF, we'll divide 15854982 by 100000; that gives roughly 158½; and that many semidiameters is the distance of the star F from the center T. And to shorten the operation: seeing that the product of 92276 multiplied by 100000 must first be divided by 582 and then the quotient by 100000, we can reach the same result at once, without multiplying 92276 by 100000, by a single division of the sine 92276 by the sine 582, as you see below — where 92276 divided by 582 gives us that same 158½ or so. So let's keep in mind that simply dividing the sine TI, as the sine of the angle TOI, by the sine TI, as the sine of the angle IFT, gives us the distance we're after, TF, in that many semidiameters TO.
Now see what Peucer's observations give us: his lower distance from the pole is 28° 21′, the upper 28° 2′, the difference 0° 19′, and the distance from the point overhead 66° 27′; from all of which the star's distance from the center comes out at nearly 166 semidiameters.
Here is what Tycho's observation shows us, taking the one most favorable to our opponent: the lower distance from the pole, 28° 13′, and the upper, 28° 2′, leaving the difference, which is 0° 11′, as if it were all parallax; the distance from the point overhead, 62° 15′. Here below is the operation, with the star's distance from the center found to be 276 9/16 semidiameters.
Reinhold's observation, which follows, gives us the star's distance from the center as 793 semidiameters.
From the Landgrave's next observation, the star's distance from the center comes out at 1057 semidiameters.
Taking two of Camerarius's observations most favorable to the author, the star's distance from the center is found to be 3143 semidiameters.
Muñoz's observation gives no parallax, and so puts the new star among the fixed stars, very high up. Hainzel's makes it infinitely far off, but with a correction of half a minute it sets it among the fixed stars; and the same follows from Ursinus, with a correction of 12′. As for the other astronomers, we don't have their distances above and below the pole, so nothing can be drawn from them. Now see how all the observations, of every one of them, agree — against the author — in placing the star in the high celestial regions.
Sagredo: But what defense does he find against such open contradictions?
Salviati: One of those flimsiest of threads. He says the parallaxes are reduced by refraction, which, working in the opposite direction, lifts the phenomenon up, whereas the parallaxes push it down. Now, judge how much this wretched refuge is worth from this: even if the effect of refraction were as powerful as some astronomers have lately claimed, the most it could do to raise a phenomenon higher than its true place above the horizon — when the object is already 23 or 24 degrees up — would be to shave off about 3 minutes of parallax; and that allowance is far too meager to drag the star down below the Moon. In some cases it's even smaller than the advantage we've already granted, in admitting that the excess of the lower distance from the pole over the upper is entirely parallax — an advantage that is far clearer and more palpable than the effect of refraction, whose size I doubt, and not without reason. But there's more. I ask this author whether he believes that the astronomers whose observations he uses knew about these effects of refraction and took them into account, or not. If they knew and reckoned with them, it's reasonable to think they allowed for them in fixing the star's true elevations — making, from the degrees of altitude their instruments showed, the corrections that were fitting on account of the alterations of refraction, so that the distances they announced were then the corrected and true ones, not the apparent and false ones. But if he believes those authors gave no thought to refraction, then he must confess that they likewise erred in determining all the things that can't be perfectly adjusted without correcting for refraction — among which is the precise finding of the polar altitudes, which are commonly taken from the two meridian altitudes of some fixed star that is always visible. Those altitudes will be altered by refraction in exactly the same way as the new star's, so that the polar altitude deduced from them will come out defective, sharing the very same flaw the author ascribes to the altitudes assigned to the new star — that is, both the one and the others are set, with equal error, higher than the truth. But such an error, as far as our present business goes, does no harm at all; for since we need to know nothing beyond the difference between the two distances of the new star from the pole, when it was below and then above the pole, it's clear that those distances will be the same once the alteration of refraction is applied in common to both the star and the pole, being commonly corrected for the one and for the other. The author's argument would carry some weight, however feeble, if he had assured us that the height of the pole had been fixed precisely, corrected for the error due to refraction, while the same astronomers had then failed to guard against that error in fixing the new star's altitudes for us. But of this he has given us no assurance — nor perhaps could he — and perhaps (and this is the likelier case) the observers left out that very precaution.
Sagredo: This objection seems to me more than thoroughly demolished; but tell me now, in what fashion does he then free himself from the star's having always kept the same distance from the fixed stars near it?
Salviati: By clinging, in the same way, to two threads even weaker than the last. One of them is again tied to refraction, but this time even less firmly. He says that refraction, working on the new star and lifting it above its true place, makes the distances we see differ from the true ones when the star is compared with the fixed stars near it. And I can't marvel enough at how he pretends not to notice that the very same refraction will work the same way on the new star as on the old one beside it, lifting them both equally — so that from such an accident the interval between them stays unchanged. The other refuge is even more hapless, and has a good deal of the ridiculous about it. It rests on the error that can arise in the very handling of the instrument, when the observer — unable to set the center of the pupil of his eye at the center of the sextant (the instrument used for observing the intervals between two stars), but holding it raised above that center by the distance of the pupil from some cheekbone or other, against which the head of the instrument is propped — comes to form in his eye an angle sharper than the one made by the sides of the sextant; and this angle of the rays also differs from itself, depending on whether one looks at stars low over the horizon or the same stars set at a great height. Such an angle, he says, comes out different as one raises the instrument while keeping the head still; but if, in lifting the sextant, one bent the neck back and raised the head along with the instrument, the angle would then stay the same. The author's answer therefore supposes that the observers, in using the instrument, did not raise their heads as they needed to — which has no likelihood about it. But even granting it happened so, I'll leave it to you to judge what difference there can be between the two sharp angles of two isosceles triangles, the sides of one being four arm-lengths each, and those of the other four arm-lengths less the diameter of a lens. For the difference between the lengths of the two lines of sight can be no greater than that: when the line is drawn perpendicularly from the center of the pupil onto the plane of the sextant's bar (a line no longer than the thickness of a thumb), and the length of those same rays when, the sextant being raised without lifting the head with it, that line no longer falls perpendicular onto the plane but slants, making the angle toward the circumference somewhat sharp. But to free this author, once and for all, from these most miserable beggaries, let him know (since it's plain he hasn't much practice in the use of astronomical instruments) that on the sides of the sextant or quadrant two sights are fitted, one at the center and the other at the opposite end, raised a finger or more above the plane of the bar; and the ray from the eye is made to pass over the tops of these sights, the eye itself being held a hand's breadth or two, or even more, away from the instrument — so that neither pupil, nor cheekbone, nor any part of the person touches or leans against the instrument. Nor is the instrument even held up or raised in the arms — least of all if it's one of the big ones, as is customary, which, weighing tens and hundreds and even thousands of pounds, are supported on the firmest of bases. So the whole objection vanishes. These are this author's subterfuges, which, even were they made all of steel, couldn't lift him a hundredth of a minute; and with these he flatters himself that he can make us believe he has made up for that difference of more than a hundred minutes — I mean the fact that no notable variation was observed in the distances between a fixed star and the new star throughout their whole circuit, which, had the star been close to the Moon, would have had to grow greatly conspicuous even to the naked eye, without any instrument at all — especially when set against the eleventh star of Cassiopeia, its neighbor at a degree and a half, from which it would have had to vary by more than two diameters of the Moon, as the more intelligent astronomers of those days rightly noted.
Sagredo: I seem to be looking at that unlucky farmer who, after the hail has beaten down and destroyed his whole expected harvest, goes about with a drooping, downcast face, scraping together leavings so scanty they won't be enough to feed even a single chick for a single day.
Salviati: Truly this author has taken the field against the champions of the heavens' unchangeableness with too poor a stock of weapons, and has tried, with chains too fragile, to haul the new star of Cassiopeia down out of the highest regions into these low and elemental ones of ours. And since it seems to me we've shown quite clearly the great difference between the reasoning of those astronomers and that of their opponent here, it will be well to leave this part and return to our main matter. Next in it comes the consideration of the annual motion, commonly attributed to the Sun, but then — first by Aristarchus of Samos, and afterward by Copernicus — taken away from the Sun and transferred to the Earth. Against that position I hear Simplicio come stoutly armed, and in particular with the rapier and the shield of the little book of mathematical conclusions, or disquisitions — whose attacks it will be well to begin laying out.
Simplicio: If it's all the same to you, I'd like to hold those back for the end, since they're the latest to have been thought up.
Salviati: Then it will be necessary that you, following the method we've kept to so far, set out in orderly fashion the arguments to the contrary, both Aristotle's and those of other ancients — which I too intend to do, so that nothing is left behind without being carefully weighed and examined. And likewise Signor Sagredo, with the liveliness of his wit, will offer up his thoughts as they stir in him.
Sagredo: I'll do it with my usual freedom; and since you command it, you'll also be obliged to excuse it.
Salviati: The favor will oblige me to thank you, not to excuse you. But let Simplicio begin now to bring forward the difficulties that hold him back from being able to believe that the Earth, like the other planets, can move in a circle around a fixed center.
Simplicio: The first and greatest difficulty is the repugnance and incompatibility between being at the center and being far from it. For if the terrestrial globe is to move for a year along the circumference of a circle — that is, under the zodiac — it's impossible that it should at the same time be at the center of the zodiac; but that the Earth is at that center is proved in many ways by Aristotle, by Ptolemy, and by others.
Salviati: You reason very well; and there's no doubt that whoever wants to make the Earth move along the circumference of a circle must first prove that it isn't at the center of that circle. So it now follows that we should see whether the Earth is, or is not, at that center around which I say it turns and where you say it's placed. And before that, we must also make clear whether you and I have the same idea of this center or not. So tell me: what and where is this center you have in mind?
Simplicio: By center I mean the center of the universe, of the world, of the starry sphere, of the heavens.
Salviati: Though with very good reason I might set up a dispute with you over whether there is any such center in nature — since neither you nor anyone else has ever proved whether the world is finite and shaped, or else infinite and boundless — nevertheless, granting you for now that it's finite and bounded in a spherical figure, and that it therefore has its center, it will be worth seeing how believable it is that the Earth, rather than some other body, is to be found at that center.
Simplicio: That the world is finite, bounded, and spherical, Aristotle proves with a hundred demonstrations.
Salviati: Which then all reduce to a single one, and that single one to nothing; for if I deny him his premise — namely, that the universe is in motion — all his demonstrations collapse, since he proves nothing to be finite and bounded except the part of the universe that is in motion. But so as not to multiply disputes, let's grant for now that the world is finite, spherical, and has its center; and since that figure and center were argued from its mobility, it will be nothing but reasonable if, from those same circular motions of the world's bodies, we go on to the particular investigation of the proper site of that center. Indeed, Aristotle himself reasoned and settled the matter in just this way, making the center of the universe that very point around which all the celestial spheres turn, and in which he believed the terrestrial globe to be placed. Now tell me, Simplicio: if Aristotle found himself forced by the most obvious experiences to alter this arrangement and order of the universe in part, and to confess he had been mistaken in one of these two propositions — either in putting the Earth at the center, or in saying that the celestial spheres move around that center — which of the two confessions do you think he would choose?
Simplicio: I believe that if the case arose, the Peripatetics—
Salviati: I'm not asking about the Peripatetics; I'm asking about Aristotle himself. As for them, I know perfectly well what they'd say. They, as Aristotle's most reverent and most humble bondsmen, would deny every experiment and every observation in the world—they'd even refuse to look, so as not to have to admit them—and they'd insist the world stands as Aristotle wrote it, not as nature will have it. For once you strip away the prop of that authority, with what would you have them take the field? So tell me, rather, what you think Aristotle himself would have done.
Simplicio: Honestly, I couldn't decide which of the two drawbacks he'd have judged the lesser.
Salviati: Please don't use that word "drawback" for something that might necessarily have to be the case. It was a drawback to want to put the Earth at the center of the heavenly revolutions. But since you don't know which way he'd have leaned—and since I take him for a man of great intelligence—let's examine which of the two choices is the more reasonable, and reckon that one to be the position Aristotle would have adopted. So, picking up our reasoning from the beginning, and granting, for Aristotle's sake, that the world (of whose size we have no sense-based knowledge beyond the fixed stars) is spherical in shape and moves in a circle, and therefore necessarily has a center, both with respect to its shape and with respect to its motion; and being further sure that inside the starry sphere there are many orbs, one within another, each with its stars, that likewise move in circles—we ask what it is more reasonable to believe and to say: that these contained orbs move around the very center of the world, or else around some other point far removed from it. Now tell me, Simplicio, your opinion on this particular point.
Simplicio: If we could rest on this single assumption alone, and were sure we'd meet nothing else to trouble us, I'd say it's far more reasonable to hold that the container and the parts it contains all move around one common center, rather than around different ones.
Salviati: Now, if it's true that the center of the world is the same as the point around which the orbs of the world's bodies—that is, of the planets—move, then it's absolutely certain that not the Earth but rather the Sun is the thing situated at the center of the world; so that, as far as this first simple and general grasp of things goes, the middle place belongs to the Sun, and the Earth is as far from the center as it is from the Sun itself.
Simplicio: But from what do you argue that it's the Sun, not the Earth, that lies at the center of the planets' revolutions?
Salviati: It's concluded from the plainest observations—observations that therefore compel the conclusion. The most palpable of them, for excluding the Earth from that center and putting the Sun there, is that all the planets are found now nearer and now farther from the Earth, and by differences so great that, for example, Venus at her farthest is six times more remote from us than when she's nearest, and Mars rises to almost eight times as far in one state as in another. Judge, meanwhile, whether Aristotle was off by a little in believing they were always equally distant from us.
Simplicio: And what are the signs that their motions are around the Sun?
Salviati: For the three outer planets—Mars, Jupiter, and Saturn—the argument comes from their always being nearest the Earth when they're at opposition to the Sun, and farthest when they're toward conjunction; and this approaching and receding matters so much that Mars, when near, looks fully 60 times bigger than when it's at its farthest. As for Venus and Mercury, we're certain they revolve around the Sun from the fact that they never stray far from it, and that they're seen now above it and now below—as the change of phases in Venus necessarily proves. As for the Moon, it's true that she can't in any way be separated from the Earth, for reasons that will be brought out more distinctly as we go on.
Sagredo: I expect I'm about to hear things even more marvelous, following from this annual motion of the Earth, than the ones that followed from the daily rotation.
Salviati: You're not deceived in the least. As for what the daily rotation does to the heavenly bodies, it was nothing—and could be nothing—but to make the universe appear to go rushing past us the other way; but this annual motion, mingling with the particular motions of all the planets, produces a great many strange effects, which have so far made all the greatest men in the world lose their fencing-guard. But coming back to those first general notions, I repeat that the center of the heavenly revolutions of the five planets—Saturn, Jupiter, Mars, Venus, and Mercury—is the Sun; and it will be the center of the Earth's motion too, if we manage to set her in the heavens. As for the Moon, she has a circular motion around the Earth, from which (as I've already said) she can in no way be separated; but that doesn't stop her from going around the Sun along with the Earth, by the annual motion.
Simplicio: I still don't quite have a grip on this arrangement; perhaps making a little drawing of it would help me understand it better, and we could discuss it more easily.
Salviati: So be it—indeed, for your greater satisfaction and wonder both, I want you to draw it yourself, and to see how, while thinking you don't understand it, you understand it perfectly; just by answering my questions you'll lay it out exactly. So take a sheet of paper and a compass: let this blank page be the immense expanse of the universe, in which you're to distribute and arrange its parts as reason dictates to you. And first, since without any teaching from me you hold it firm that the Earth is placed in this universe, mark a point wherever you like, around which you take her to be positioned, and label it with some letter.
Simplicio: Let this point, marked A, be the place of the terrestrial globe.
Salviati: Good. Second, I know you know perfectly well that the Earth is not inside the body of the Sun, nor even next to it, but a certain distance away; so assign the Sun whatever other place you please, as far from the Earth as you like, and label that too.
Simplicio: There, done: let the place of the Sun's body be this one, marked O.
Salviati: With these two settled, I want us to think about fitting in the body of Venus in such a way that her position and motion can satisfy what the observed appearances show us about them; so call to mind what, whether from our earlier discussions or from your own observations, you've gathered happens with that star; and then assign her the position you judge suits her.
Simplicio: Granting that the appearances you've described are true—the ones I've also read in the little book of conclusions—namely that this star never departs from the Sun beyond a certain fixed interval of forty-odd degrees, so that she never reaches opposition to the Sun, nor even quadrature, nor so much as the sextile aspect; and further, that at one time she appears nearly forty times bigger than at another—that is, largest when, moving in retrograde, she goes toward her evening conjunction with the Sun, and smallest when, in direct motion, she goes toward her morning conjunction; and moreover, it being true that when she appears largest she shows herself crescent-shaped, and when she appears smallest she's seen perfectly round—granting, I say, that these appearances are true, I don't see how one can avoid asserting that this star circles around the Sun. For that circle can in no way be said to embrace the Earth and hold it inside itself, nor to lie below the Sun—that is, between it and the Earth—nor above the Sun either. The circle can't embrace the Earth, because then Venus would sometimes come to opposition with the Sun; it can't lie below, because around both of her conjunctions with the Sun Venus would show herself sickle-shaped; and it can't lie above, because she'd always show herself round and never crescent. And so, for her lodging, I'll mark the circle CH around the Sun, without its embracing the Earth.
Salviati: Venus settled, you'd do well to think about Mercury, which, as you know, always keeps around the Sun and strays much less far from it than Venus does; so consider what place it's fitting to assign him.
Simplicio: No doubt that, since it imitates Venus, the most fitting quarters for it will be a smaller circle inside this one of Venus, and likewise around the Sun—the liveliness of its brilliance over that of Venus and the other planets being a quite conclusive argument and sign, above all, of its nearness to the Sun. So on that basis we can mark its circle, labeling it with the letters B G.
Salviati: And where shall we put Mars?
Simplicio: Mars, because it comes to opposition with the Sun, must with its circle embrace the Earth; but I see that it necessarily must embrace the Sun as well. For, coming to conjunction with the Sun, if it didn't pass above it but were below it, it would appear crescent, as Venus and the Moon do; yet it always shows itself round. So it must enclose within its circle the Sun no less than the Earth. And since I recall you saying that when it's at opposition to the Sun it shows itself 60 times bigger than when it's toward conjunction, it seems to me that these appearances will be very well satisfied by a circle around the center of the Sun that embraces the Earth—which I now draw and mark D I: where Mars at point D is nearest the Earth and is opposite the Sun; but when it's at point I, it's in conjunction with the Sun and farthest from the Earth. And since the same appearances are observed in Jupiter and Saturn—though with far less variation in Jupiter than in Mars, and less still in Saturn than in Jupiter—it seems to me we'll very neatly satisfy these two planets too with two circles, likewise around the Sun: this first one for Jupiter, marking it E L, and another outer one for Saturn, labeled F M.
Salviati: You've acquitted yourself splendidly so far. And since (as you see) the approaching and receding of the three outer planets is measured by twice the distance between the Earth and the Sun, this makes a greater variation in Mars than in Jupiter, because Mars's circle D I is smaller than Jupiter's circle E L; and likewise, because this E L is smaller than Saturn's circle F M, the same variation is smaller still in Saturn than in Jupiter—and that answers exactly to the appearances. It remains now for you to think about assigning the Moon her place.
Simplicio: Following the same method, which strikes me as thoroughly conclusive: since we see that the Moon comes to conjunction and opposition with the Sun, we must say her circle embraces the Earth; but it need not embrace the Sun, because if she were toward conjunction she wouldn't show herself sickle-shaped, but always round and full of light—besides which she could never give us, as she often does, an eclipse of the Sun by interposing herself between it and us. So we must assign her a circle around the Earth, which would be this one, N P, such that when she's set at P she appears to us from the Earth, A, joined with the Sun—so that she can sometimes eclipse it—and when placed at N she's seen opposite the Sun, and in that state can fall into the Earth's shadow and be darkened.
Salviati: Now what shall we do, Simplicio, with the fixed stars? Do we want to set them scattered through the immense depths of the universe, at various distances from any given point, or else placed on a surface spread out spherically around a center of its own, so that each of them is equally distant from that same center?
Simplicio: I'd rather take a middle road, and assign them an orb drawn around a fixed center and enclosed between two spherical surfaces—one very high and concave, the other lower and convex—between which I'd set the innumerable multitude of the stars, but at various heights; and this could be called the sphere of the universe, containing within itself the orbs of the planets we've already drawn.
Salviati: So then, Simplicio, we've now arranged the bodies of the world exactly according to Copernicus's distribution—and it's been done by your own hand. What's more, you've assigned proper motions to all of them except the Sun, the Earth, and the starry sphere; you've given Mercury and Venus a circular motion around the Sun without embracing the Earth; around the same Sun you make the three outer planets—Mars, Jupiter, and Saturn—move, taking the Earth inside their circles; and the Moon can't move any other way than around the Earth, without embracing the Sun. And in all these motions you agree, once again, with Copernicus himself. What remains to be decided, among the Sun, the Earth, and the starry sphere, are three things: namely rest, which appears to belong to the Earth; the annual motion under the zodiac, which appears to belong to the Sun; and the daily rotation, which appears to belong to the starry sphere, sharing it out to all the rest of the universe except the Earth. And since it's true that all the orbs of the planets—I mean Mercury, Venus, Mars, Jupiter, and Saturn—move around the Sun as their center, it seems all the more reasonable that rest belongs to the Sun than to the Earth, inasmuch as, for moving spheres, it's more reasonable that the center should stand still than any other place remote from that center. To the Earth, then, which is left set in the midst of moving parts—I mean between Venus and Mars, one of which makes its revolution in nine months and the other in two years—we can very neatly attribute the motion of a year, leaving rest to the Sun. And once that's so, it follows by necessary consequence that the daily rotation belongs to the Earth as well: for if, with the Sun standing still, the Earth did not turn on itself but only had the annual motion around the Sun, our year would be nothing but a single day and a single night—that is, six months of day and six months of night, as was said before. See, then, how neatly the headlong motion of 24 hours is lifted away from the universe, and how the fixed stars, which are so many Suns, enjoy—like our own Sun—a perpetual rest. See, moreover, how much ease there is in this first sketch for giving the reasons behind such great appearances in the heavenly bodies.
Sagredo: I see it very well. But just as you gather from this simplicity a great probability for the truth of such a system, someone else might, on the contrary, draw the opposite conclusions—doubting, not without reason, how it is that a construction so ancient, held by the Pythagoreans and fitted so well to the appearances, should nonetheless in the course of thousands of years have had so few followers, and should have been rejected by Aristotle himself, and even after Copernicus should go on meeting the same fate.
Salviati: If you, Sagredo, had ever happened—as I have, many and many a time—to hear what sort of nonsense is enough to make the common crowd stubborn and unpersuadable, unwilling even to lend an ear, let alone their assent, to these new ideas, I think your wonder at finding so few followers of this opinion would shrink considerably. But little esteem, in my view, should be given to minds for whom, to confirm them and hold them fixed in the immobility of the Earth, the most conclusive demonstration is to observe that they won't be dining in Constantinople this morning nor supping in Japan this evening, and that they're certain the Earth, being so very heavy, can't climb up above the Sun and then come tumbling headlong back down. Of such people, whose number is infinite, there's no need to take account, nor to record their silly notions, nor to try to win over men whose definition includes only the genus and lacks the difference, just to have them as companions in opinions of the utmost subtlety and delicacy. Besides, what gain would you ever expect to make, with all the demonstrations in the world, upon minds so dull that they can't by themselves recognize their own most extreme follies? But my wonder, Sagredo, is very different from yours: you wonder that so few are followers of the Pythagoreans' opinion; I, for my part, am astonished that anyone has ever, up to now, been found who embraced and followed it. Nor can I sufficiently admire the towering genius of those who received it and held it true, and who, by the sheer liveliness of their intellect, did such violence to their own senses that they were able to prefer what reason dictated to them over what sense experience showed them, plainly and to the contrary. That the arguments against the Earth's daily whirling, which you've already examined, have a great show of truth, we've seen already; and that the Ptolemaics, the Aristotelians, and all their followers took them as thoroughly conclusive is itself a very strong sign of their force. But those experiences that openly contradict the annual motion carry so much greater an apparent repugnance that—I say it again—I can find no limit to my admiration at how reason could, in Aristarchus and in Copernicus, do such violence to sense as to make herself, against sense, the mistress of their belief.
Sagredo: So we're going to have other vigorous objections against this annual motion as well?
Salviati: We are; and ones so evident and so sensory that, if a higher and more excellent sense than the common and natural ones hadn't kept company with reason, I greatly suspect that I too would have been far more reluctant to accept the Copernican system than I've been ever since a brighter lamp than the usual one gave me light.
Sagredo: Well then, Salviati, let's come, as they say, to grips—because every word spent on anything else seems to me thrown away.
Salviati: Here I am, at your service. I've already drawn you the form of the Copernican system. Against its truth, the first and fiercest assault is launched by Mars itself. For if it were true that Mars varied its distances from the Earth so much that between its least and greatest remove there were a difference equal to twice the distance from the Earth to the Sun, then it would necessarily follow that when it's nearest to us its disk should show itself more than 60 times bigger than it shows when it's farthest away. Yet no such difference in apparent size is to be seen; on the contrary, at opposition to the Sun, when it's near the Earth, it doesn't show itself even 4 or 5 times bigger than when, toward conjunction, it's hidden away beneath the Sun's rays. Venus gives us another and greater difficulty. For if, circling around the Sun as Copernicus asserts, it were now above the Sun and now below—receding from and approaching us by as much as the diameter of the circle it describes—then when it was below the Sun and nearest to us, its disk ought to show itself a little less than 40 times bigger than when it's above the Sun, near its other conjunction; yet the difference is almost imperceptible. Add another difficulty: since the body of Venus is dark in itself, and shines only, like the Moon, by the Sun's illumination—as seems reasonable—then when she's below the Sun she ought to show herself sickle-shaped, as the Moon does when she too is near the Sun; an occurrence that doesn't appear in her. On account of which, Copernicus declared that either she was luminous by herself, or her matter was such that it could soak up the Sun's light and transmit it through her whole depth, so that she could always show herself shining; and in this way Copernicus excused Venus's not changing shape. But of her little-varied size he said nothing at all, and of Mars far less than the case required—I believe because he couldn't, to his own satisfaction, save an appearance so repugnant to his position; and yet, persuaded by so many other correspondences, he held to it and took it for true. Beyond these things, making all the planets, together with the Earth, move around the Sun as the center of their revolutions, while the Moon alone disturbs that order and has its own proper motion around the Earth, and while it, the Earth, and the whole elemental sphere all together move in a year around the Sun—this seems to alter the order in such a way as to render it unlikely and false. These are the difficulties that make me marvel that Aristarchus and Copernicus—who can't possibly have failed to notice them, and who couldn't then resolve them—nevertheless, on the strength of other marvelous correspondences, trusted so much in what reason dictated to them that they confidently affirmed the structure of the universe could have no other form than the one they'd drawn. There are, besides, other very grave and very beautiful difficulties, not so easily resolved by middling minds, but penetrated and set forth by Copernicus, which we'll put off until later, after we've answered other objections raised by others against this position. Now, coming to the explanations and replies to the three grave objections brought forward, I say that the first two not only don't contradict the Copernican system but strongly and absolutely favor it; for both Mars and Venus do show themselves unequal to themselves, according to the proportions assigned, and Venus below the Sun shows herself sickle-shaped, and goes on changing her phases in exactly the same way the Moon does.
Sagredo: But how did this stay hidden from Copernicus, and yet be plain to you?
Salviati: These things can't be grasped except through the sense of sight, which nature hasn't granted to human beings perfect enough to make out such differences; indeed, the very instrument of seeing gets in its own way. But after it pleased God, in our own age, to grant human ingenuity so marvelous an invention — the power to perfect our sight by magnifying it 4, 6, 10, 20, 30, and 40 times — countless objects that were invisible to us, whether because of their distance or their extreme smallness, have, by means of the telescope, been made perfectly visible.
Sagredo: But Venus and Mars aren't objects invisible for their distance or smallness — we take them in perfectly well with plain, natural eyesight. So why can't we make out the differences in their sizes and shapes?
Salviati: A big part of this comes from the interference of our own eye, as I just hinted: because of it, bright, distant objects aren't presented to us plain and clean, but handed to us wreathed in stray, foreign rays, so long and thick that the naked little body shows up magnified 10, 20, 100, even a thousand times more than it would look if you stripped away that radiant head of hair that isn't its own.
Sagredo: Now I recall having read something or other on this subject — I'm not sure whether in the Letters on Sunspots or in The Assayer, by our mutual friend. But it would do no harm — both to refresh my own memory and for Simplicio's benefit, since he perhaps hasn't seen those writings — to set out for us more distinctly how this business stands. Understanding it, I think, is quite necessary to keep proper hold of what we're now discussing.
Simplicio: Honestly, everything Salviati is now bringing forward is new to me; for, to tell the truth, I've had no curiosity to read those books, nor have I so far put much faith in the newly introduced spyglass. In fact, following in the footsteps of my fellow Peripatetic philosophers, I've believed that what others have admired as stupendous feats were really just the tricks and deceptions of the lenses. So if I've been in error up to now, I'll be glad to be drawn out of it; and, tempted by the other novelties I've heard from you, I'll listen more attentively to the rest.
Salviati: The confidence such men have in their own discernment is no less unreasonable than the low regard they hold for other people's judgment; and it's a remarkable thing that they should think themselves fit to judge such an instrument better, without ever having tried it, than those who have made — and make every day — thousands upon thousands of trials with it. But let's leave aside, if you please, this breed of stubborn men, who can't even be reproached without honoring them more than they deserve. Returning to our subject, I say that bright objects — whether because their light is refracted in the moisture on the surface of the pupils, or reflected off the edges of the eyelids, scattering its reflected rays across those same pupils, or for some other reason — show themselves to our eye ringed with extra rays, and hence far larger than their bodies would look stripped of that irradiation. And this enlargement grows in ever greater proportion the smaller and smaller those luminous objects are. Just so — suppose the growth of the radiant hair were, say, four fingers: added around a circle four fingers in diameter, it would increase its apparent size ninefold, but—
Simplicio: I suspect you meant to say three times; because adding four fingers on one side and four on the other to the diameter of a circle that's itself four fingers, you triple its size — you don't increase it ninefold.
Salviati: A little geometry, Simplicio. It's true the diameter grows three times, but the surface — which is what we're talking about — grows nine times. Because, Simplicio, the surfaces of circles are to one another as the squares of their diameters, and a circle four fingers in diameter has to one twelve fingers across the same proportion the square of four has to the square of twelve — that is, 16 to 144 — and so it will be nine times greater, not three. Let that be a caution to you, Simplicio. And to go on: if we add that same head of hair, four fingers, to a circle only two fingers in diameter, the diameter of the wreath is now ten fingers, and the area of the whole disk to the area of the naked little body is as 100 to 4, since those are the squares of 10 and 2; so the enlargement would be 25 times over. And finally, the 4 fingers of hair added to a little circle one finger in diameter would enlarge it 81 times. And so, continually, the growths happen in ever greater proportion, the smaller and smaller the real objects being enlarged.
Sagredo: The difficulty that troubled Simplicio hasn't troubled me; but there are indeed some other things I'd like to understand more clearly — in particular, I'd like to know on what grounds you claim that this growth is always the same in all visible objects.
Salviati: I've already partly explained myself, when I said that only luminous objects grow, and not dark ones. Now let me add the rest: among bright objects, those with a livelier light produce a bigger, stronger reflection on our pupil, and so appear to enlarge much more than the less bright ones. And, so as not to dwell on this point any longer, let's turn to what the true schoolmistress — experience — teaches us. This evening, once the air has grown good and dark, let's look at the star of Jupiter: we'll see it very radiant and very big. Then let's pass our gaze through a little tube — or even through a small chink left between the palm and the fingers when we clench a fist and hold it up to the eye, or through a hole made with a fine needle in a sheet of paper. We'll see the disk of that same Jupiter stripped of its rays, but so small that we'll judge it less than a sixtieth part of what its great torch appears when seen with the free eye. Then we can look at the Dog Star, that most beautiful star, biggest of all the fixed stars, which to the naked eye shows up not much smaller than Jupiter; but once its hair is stripped away in the manner described, its disk will be seen so small that it won't be judged even a twentieth part of Jupiter's — indeed, anyone without perfect eyesight will barely make it out at all. From which one may reasonably conclude that this star, having a far livelier light than Jupiter's, makes its irradiation greater than Jupiter makes his. As for the irradiation of the Sun and the Moon, it's as good as nothing, on account of their size, which by itself takes up so much room in our eye that it leaves no space for stray rays; so their disks are seen sheared and sharply bounded.
We can assure ourselves of the same truth by another experiment I've made many times — assure ourselves, I mean, that bodies shining with a livelier light irradiate far more than those of a fainter light. I've often seen Jupiter and Venus together, 25 or 30 degrees from the Sun, and with the air well darkened, Venus looked a good 8 or even 10 times bigger than Jupiter — so long, that is, as they were viewed with the free eye. But looked at then through the telescope, Jupiter's disk was seen to be truly four times and more the size of Venus's; yet the liveliness of Venus's splendor was incomparably greater than Jupiter's very faint light. And this came from nothing but the fact that Jupiter is very far from the Sun and from us, while Venus is near to us and to the Sun.
With these things explained, it won't be hard to understand how it can be that Mars, when it's at opposition to the Sun — and therefore seven times and more nearer to the Earth than when it's toward conjunction — barely shows itself 4 or 5 times bigger in the one state than in the other, when we ought to see it more than 50 times as big. And the sole cause of this is irradiation: for if we strip it of the stray rays, we'll find it enlarged precisely in the proper proportion. And to remove its mane, the telescope is the one and best means: by magnifying its disk 900 or a thousand times, it lets us see it naked and sharply bounded like the Moon's, and differing from itself in the two positions according to the proper proportion, exactly to a hair.
As for Venus: in its evening conjunction, when it's below the Sun, it ought to show itself almost 40 times bigger than in the other, morning conjunction — and yet it isn't even seen doubled. What happens here, beyond the effect of irradiation, is that it's crescent-shaped, and its horns, besides being thin, receive the Sun's light obliquely, and so quite faintly; so that, being little and weak, its irradiation is less broad and lively than when it shows us its whole lit hemisphere. But the telescope plainly shows us its horns as sharply bounded and distinct as the Moon's, and they're seen as belonging to a very large circle — proportionally almost 40 times bigger than its own disk when it's above the Sun in its last morning appearance.
Sagredo: Oh, Nicolaus Copernicus, what delight would have been yours, to see this part of your system confirmed by such clear experiments!
Salviati: Yes — but how much less would be the fame of the sublimity of his genius among those who understand! For, as I said a moment ago, we see that he steadily went on affirming, led by reason, the very thing whose opposite the evidence of the senses displayed. I can't get over my astonishment that he should so steadfastly have insisted on saying that Venus revolves around the Sun and is at one time more than six times farther from us than at another, and yet always shows itself the same size, when it ought to appear forty times bigger.
Sagredo: In Jupiter, Saturn, and Mercury too, I believe the differences in their apparent sizes must be seen to answer punctually to their varying distances.
Salviati: In the two upper ones I've observed them precisely, almost every year, for twenty-two years now. With Mercury no observation of any weight can be made, since it lets itself be seen only at its greatest elongations from the Sun — its widest swings out from it — where its distances from the Earth are imperceptibly unequal, so that such differences are unobservable, as are the changes of shape, which absolutely must occur, just as in Venus. When we do see it, it ought to show itself in the shape of a half-circle, as Venus too does at its greatest elongations; but its disk is so small and its splendor so lively, being so close to the Sun, that the telescope's power isn't enough to shave off its hair and make it appear fully sheared. That leaves us to clear away what seemed a great impropriety in the motion of the Earth: namely, that while all the planets revolve around the Sun, the Earth alone should go around the Sun in a year not solitary like the others, but in the company of the Moon, together with the whole sphere of the elements — and that at the same time the Moon itself should move every month around the Earth. Here we're forced to exclaim once more, and to exalt the admirable sharp-sightedness of Copernicus, and at the same time to grieve his misfortune, since he doesn't live in our time — when, to take away the apparent absurdity of the Earth and Moon traveling in convoy, we see Jupiter, almost another Earth, going around the Sun in 12 years not in convoy with one Moon, but accompanied by four Moons, along with everything that may be contained within the orbits of the four Medicean stars.
Sagredo: For what reason do you call the four Jovian planets Moons?
Salviati: That's how they'd appear to anyone looking at them from Jupiter. For in themselves they're dark, and they receive their light from the Sun — which is plain from their becoming eclipsed when they enter the cone of Jupiter's shadow; and since only the hemisphere facing the Sun is lit, to us — who are outside their orbits and nearer the Sun — they always show up fully bright. But to someone on Jupiter they'd show fully bright when they were in the upper parts of their circles, while in the lower parts — that is, between Jupiter and the Sun — they'd be seen from Jupiter as crescents. In short, they'd go through, for the Jovians, the very same changes of shape that the Moon goes through for us Earthlings. Now you see how marvelously these first three strings harmonize with the Copernican system, that at the start seemed so dissonant. From this, meanwhile, Simplicio can see with what probability one may conclude that not the Earth, but the Sun, is at the center of the planets' revolutions. And since the Earth is placed among the worldly bodies that undoubtedly move around the Sun — that is, above Mercury and Venus, and below Saturn, Jupiter, and Mars — won't it likewise be highly probable, and perhaps necessary, to grant that it too goes around the Sun?
Simplicio: These occurrences are so great and conspicuous that it's not possible Ptolemy and his other followers had no knowledge of them; and having had it, they must surely also have found a way to give a sufficient account of such striking appearances — and one quite fitting and plausible, too, since for so long it's been accepted by so very many.
Salviati: You reason very well; but you must know that the chief aim of the pure astronomers is only to give an account of the appearances in the heavenly bodies, and to fit to them, and to the motions of the stars, such structures and arrangements of circles that the motions calculated from them answer to those same appearances — caring little about admitting some extravagance that, in fact, on other grounds, might be hard to swallow. And Copernicus himself writes that in his early studies he had restored the science of astronomy on those same suppositions of Ptolemy, and had corrected the motions of the planets so well that the computations answered very neatly to the appearances and the appearances to the calculations — so long, that is, as each planet was taken separately. But he adds that when he then tried to put together the whole structure out of the particular constructions, what resulted was a monster and a chimera made of limbs utterly out of proportion to one another and altogether incompatible; so that, however well the part of the pure calculating astronomer was satisfied, there was still no satisfaction and repose for the philosophical astronomer. And because he understood very well that if the celestial appearances could be saved by assumptions false in nature, it could be done far better from true suppositions, he set himself to search diligently whether any of the distinguished men of antiquity had attributed to the world a structure other than the commonly received one of Ptolemy. And finding that certain Pythagoreans had in particular attributed to the Earth the daily rotation, and others the annual motion as well, he began to check against these two new suppositions the appearances and the particulars of the planets' motions — all of which he had readily at hand — and seeing the whole correspond with its parts with marvelous ease, he embraced this new arrangement and found his repose in it.
Simplicio: But what extravagances are there in the Ptolemaic arrangement that aren't even greater in this Copernican one?
Salviati: In Ptolemy are the diseases, and in Copernicus their remedies. And first: won't all the sects of philosophers call it a great impropriety that a body naturally moving in a circle should move irregularly about its own center and regularly about some other point? And yet the fabric of Ptolemy is full of such misshapen motions; whereas in Copernicus every motion is uniform about its own center. In Ptolemy one must assign contrary motions to the heavenly bodies, and make them all move from east to west and, at the very same time, from west toward east; whereas in Copernicus all the celestial revolutions run one single way, from west to east. But what shall we say of the apparent motion of the planets, so irregular that not only do they now go fast and now slower, but sometimes stop altogether, and even afterward, for a good stretch, turn back? To save this appearance Ptolemy introduced enormous epicycles, fitting one after another to each planet, with certain rules of incongruent motions — all of which are done away with by a single, utterly simple motion of the Earth. And wouldn't you call it, Simplicio, a very great absurdity if, in Ptolemy's construction — where each planet is assigned its own orbits, one above another — it were often necessary to say that Mars, set above the sphere of the Sun, dropped so low that, breaking through the solar orb, it descended below it and came nearer the Earth than the body of the Sun, and a little later rose immeasurably above it again? And yet this extravagance, and others, are cured by the single, utterly simple annual motion of the Earth.
Sagredo: These stations, retrogressions, and direct motions, which have always struck me as great improbabilities, I'd like to understand better — how they come about in the Copernican system.
Salviati: You, Sagredo, will see them proceed in such a way that this single conjecture ought to be enough — for anyone not downright stubborn or past all teaching — to make him give his assent to everything else in this doctrine. So let me tell you: with nothing altered in Saturn's motion of thirty years, in Jupiter's of twelve, in Mars's of two, in Venus's of nine months, and in Mercury's of about eighty days, the Earth's annual motion alone — set between Mars and Venus — accounts for the apparent irregularities in the motions of all five of the planets I've named; and for an easy, full grasp of the whole thing I want to draw you its figure. So suppose the Sun is placed at the center O; around it we'll mark the orbit traced by the Earth with its annual motion, BGM; and let the circle traced, say, by Jupiter around the Sun in twelve years be this one, bgm; and in the starry sphere let us take the zodiac to be yus. On the Earth's yearly orbit we'll lay off some equal arcs, BC, CD, DE, EF, FG, GH, HI, IK, KL, LM; and on Jupiter's circle we'll mark other arcs, covered in the same stretches of time in which the Earth covers hers — namely bc, cd, de, ef, fg, gh, hi, ik, kl, lm — each of them proportionally smaller than those on the Earth's orbit, since Jupiter's motion under the zodiac is slower than the Earth's yearly one. Now suppose that when the Earth is at B, Jupiter is at b; drawing the straight line B‑b‑p, he'll appear to us in the zodiac at p. Now let the Earth move from B to C, and Jupiter from b to c in the same time: Jupiter will appear to have come to q in the zodiac, moved forward directly in the order of the signs, p, q. Then, as the Earth passes to D and Jupiter to d, he'll be seen in the zodiac at r; and from E, with Jupiter arrived at e, he'll appear in the zodiac at s — still moving forward directly. But once the Earth begins to slip more squarely between Jupiter and the Sun, having come to F while Jupiter is at f, he'll appear to us at t, already having begun apparently to go backward beneath the zodiac; and in the time the Earth has covered the arc EF, Jupiter will have held himself between the points s and t, showing us almost still and stationary. Then, when the Earth has come to G and Jupiter to g, at opposition to the Sun, he'll be seen in the zodiac at u, greatly gone backward through the whole arc of the zodiac t‑u — even though, still keeping his own steady course, he has really gone forward, not just in his own circle but in the zodiac too, with respect to that zodiac's center and to the Sun set there. Then, as both the Earth and Jupiter carry on their motions, once the Earth has come to H and Jupiter to h, he'll be seen greatly gone backward in the zodiac through the whole arc u‑x; and with the Earth at I and Jupiter at i, he'll have moved apparently through the small space x‑y, and there appear stationary. When, next, the Earth has come to K and Jupiter to k, he'll have passed the arc y‑n in the zodiac with direct motion; and continuing his course, the Earth from L will see Jupiter, at l, at the point z; and finally, with Jupiter at m, he'll be seen from the Earth at M passed on to a, again with direct motion. His whole apparent retrogradation in the zodiac will amount to the arc s‑y, made by Jupiter while in his own circle he passes the arc e‑i and the Earth in hers the arc EI. And what has been said of Jupiter, understand of Saturn and Mars as well: in Saturn these backward loops are somewhat more frequent than in Jupiter, since his motion is slower than Jupiter's, so that the Earth overtakes him in a shorter stretch of time; while in Mars they are rarer, because his motion is faster than Jupiter's, so the Earth spends more time catching up with him. As for Venus and Mercury, whose circles are enclosed within the Earth's, their stations and retrogradations likewise appear — caused not by any motions of theirs that are really such, but by the Earth's own annual motion, as Copernicus, following Apollonius of Perga, shrewdly demonstrates in Book Five of his Revolutions, chapter thirty‑five.
You see, gentlemen, with what ease and simplicity the annual motion — supposing it to be the Earth's — fits the case and explains the apparent oddities observed in the movements of the five planets, Saturn, Jupiter, Mars, Venus, and Mercury: it sweeps them all away and reduces them to even, regular motions. Nicolaus Copernicus was the first to make this marvelous effect's cause plain to us. But of another marvel — no less astonishing than this one, and one that binds the human mind, by a knot perhaps harder to loosen, to admit this yearly revolution and grant it to our terrestrial globe — the Sun itself brings us a new and unlooked‑for conjecture; the Sun, which shows that it would not, alone among all, dodge bearing witness to so weighty a conclusion, but rather, as a witness beyond every exception, insisted on taking its part. So hear this high, new wonder.
The first to discover and observe the sunspots — as with all the other novelties of the heavens — was our friend the Academician; he discovered them in the year 1610, while still holding the chair of Mathematics at the University of Padua, and he spoke of them there and in Venice to various people, some of whom are still living; and a year later he showed them at Rome to many gentlemen, as he states in the first of his Letters to Signor Mark Welser, Duumvir of Augsburg. He was the first, against the opinions of those too timid and too jealous of the heavens' unchangeableness, to affirm that these spots are matter produced and dissolved over short stretches of time; that, as to place, they are right up against the body of the Sun and turn around it — or rather, carried by the solar globe itself, which revolves upon its own center in the space of about a month, they finish their circuits with it. This motion he judged at first to be made by the Sun about an axis upright to the plane of the ecliptic, since the arcs the spots traced across the Sun's disk appeared to our eye as straight lines parallel to the plane of the ecliptic — lines that were, however, altered in part by certain accidental, wandering, irregular motions to which the spots are subject, and by which they keep shifting their positions among themselves, tumbling and without any order, now gathering many together, now separating, some splitting into several, and greatly changing their shapes, mostly into very outlandish ones. And though these fickle changes altered in part the primary periodic course of the spots, they didn't make our friend change his mind — as if he thought some fixed, essential cause lay behind such deviations; he went on believing that the whole apparent alteration came from those accidental changes, exactly as would happen to someone who, from far‑off regions, watched the motion of our clouds: he'd see them moving with a very swift, large, and constant motion, carried by the daily whirl of the Earth (if that motion were the Earth's) through twenty‑four hours along circles parallel to the equinoctial — yet altered in part by the accidental motions given them by the winds, which shove them here and there at random toward different quarters of the world. It happened at this time that Signor Welser sent him some letters written by a certain false Apelles on the matter of these spots, pressingly asking him to give his opinion freely on those letters, and further to make known what he himself thought about the essence of these spots. He satisfied him with three Letters, showing first how empty Apelles's notions were, and disclosing to him, second, his own opinions — and predicting, moreover, that Apelles, taking better counsel with time, would come round to his view, as afterward happened. And because it seemed to our Academician (as it seemed to others knowledgeable in the things of nature) that in those three Letters he had investigated and demonstrated, if not all that human curiosity could wish and seek, at least all that human reasoning could reach in such a matter, he set aside the continued observations for a time, busy with other studies, and only to oblige some friend would now and then make a scattered observation — until, running into me after some years, and the two of us being at my villa at Le Selve, one of the sunspots, solitary, quite large and dense, together with a most clear and unbroken calm of the sky, invited us; and at my request observations were made of that spot's whole transit, carefully marking on paper its places from day to day, at the hour when the Sun stood on the meridian. Noticing that its journey was not made along a straight line, but one somewhat curved, we took it into our heads to make further observations from time to time; and to that undertaking we were vigorously spurred by a thought that suddenly dropped into my guest's mind, which he shared with me in these words: "Filippo, it seems to me a road opens to a great consequence. For if the axis about which the Sun revolves is not set upright to the plane of the ecliptic, but tilted upon it — as this curved passage we've just observed hints to me — we'll have a conjecture about the standings of the Sun and the Earth as firm and as conclusive as any that has ever yet been supplied to us by any other line of evidence." Roused by so lofty a promise, I pressed him to lay his thought open to me plainly. And he: "If the annual motion belongs to the Earth, along the ecliptic around the Sun, and the Sun is set at the center of that ecliptic and turns upon itself there — not about the ecliptic's axis (which would be the axis of the Earth's annual motion), but about one that is tilted — then strange changes are bound to show themselves to us in the apparent motions of the sunspots, even granting that the Sun's axis stays forever and unchangeably at the same tilt and in the same direction, toward the same point of the universe. For, as the terrestrial globe walks around him in the annual motion, first of all it must happen that to us, carried by that globe, the passages of the spots will sometimes indeed appear made along straight lines — but this only twice a year, and at all other times they'll show as made along noticeably curved arcs. Second, the curvature of these arcs, for one half of the year, will appear tilted opposite to the way it shows in the other half; that is, for six months the convex side of the arcs will face the upper part of the solar disk, and for the other six months the lower. Third, since the spots begin to appear — to be born, so to speak — to our eye on the left side of the solar disk, and go to hide and set on the right, the eastern ends (that is, of the first appearances) will for six months be lower than the opposite ends of the settings, and for the other six the reverse will happen: the spots will be born from higher points and, descending from them in their courses, will come to hide themselves at lower points; and for only two days in the whole year will these ends, of the risings and settings, be level. After these balancings, the tilt of the spots' journeys will begin little by little, growing greater day by day, and in three months reach its greatest slant; then, beginning to lessen from there, in as much time again it will return to the other balance. It will happen, for the fourth wonder, that the day of the greatest slant will be the same as the day of the passage made along a straight line, and on the day of the balancing the arc of the journey will appear more curved than ever; while at other times, as the tilt lessens and heads toward the balance, the curving of the passages' arcs, on the contrary, will keep increasing."
Sagredo: My dear Salviati, I know that to break in on your discourse is bad manners; but I judge it no less bad to let you spread yourself at greater length in words while they are, as they say, tossed to the wind. For, to put it plainly, I can't form a single distinct notion of even one of the conclusions you've pronounced; yet because, taken so generally and confusedly, they strike me as things of admirable consequence, I'd very much like to be made able to grasp them somehow.
Salviati: The very thing that happens to you happened to me too, while they were brought to me by my guest in bare words; he then eased my understanding by picturing the matter for me on a material instrument — nothing but a plain sphere, using some of its circles, but for a purpose other than the one they're commonly meant for. Now, for want of the sphere, I'll make do by drawing figures on paper as needed. And to represent the first fact I put forward — that the passages of the spots could appear made along straight lines only twice a year — let's take this point O to be the center of the great orb, or say of the ecliptic, and likewise of the globe of the Sun itself, of which, thanks to the great distance between it and the Earth, we earth‑dwellers may suppose ourselves to see the half. So we'll draw this circle ABCD about that same center O, to stand for the extreme boundary that divides and separates the Sun's hemisphere that appears to us from the other, hidden one. And because our eye, no less than the center of the Earth, is understood to be in the plane of the ecliptic — where the center of the Sun also is — then, if we picture the solar body as cut by that plane, the section will appear to our eye as a straight line, say BOD; and setting the perpendicular AOC upon it, that will be the axis of the ecliptic and of the terrestrial globe's annual motion. Now understand the solar body (without changing its center) to turn upon itself, not about the axis AOC (the one upright to the plane of the ecliptic), but about one somewhat tilted, say this EOI — which axis, fixed and unchanging, keeps itself forever at the same tilt and direction toward the same points of the firmament and the universe. And because, in the revolutions of the solar globe, each point of its surface (except the poles) describes the circumference of a circle, larger or smaller according to how far it lies from those poles, take the point F equally distant from them and mark the diameter FOG, which will be perpendicular to the axis EI and will be the diameter of the greatest circle described about the poles E, I. Now suppose the Earth, and we with it, to be at such a place in the ecliptic that the Sun's hemisphere apparent to us is bounded by the circle ABCD, which, passing (as it always does) through the poles A, C, passes also through E, I: it's clear that the greatest circle whose diameter is FG will stand upright to the circle ABCD; and to that circle the ray falling from our eye upon the center O is perpendicular, so that this same ray falls in the plane of the circle whose diameter is FG, and therefore its circumference will appear to us as a straight line, the very same as FG. For this reason, whenever a spot was at the point F, then carried on by the solar rotation, it would trace on the Sun's surface the circumference of that circle which appears to us as a straight line. Straight, then, its passage will appear; and straight too will appear the motions of other spots which in the same revolution traced smaller circles, since all are parallel to the greatest and our eye is set at an immense distance from them. Now, if you'll consider how, after the Earth has run in six months through half of the great orb and stands over against the Sun's hemisphere now hidden from us — so that the boundary of the part then seen is the same circle ABCD, which will still pass through the poles E, I — you'll understand that the same will happen with the journeys of the spots: they'll all appear made along straight lines. But because this fact holds only when the boundary passes through the poles E, I, and that boundary keeps shifting from moment to moment through the Earth's annual motion, its passing through the fixed poles E, I is momentary, and consequently momentary is the time during which the spots' motions appear straight. From what has been said so far, one comes to grasp, too, that since the appearance and start of the spots' motion is from the F side, proceeding toward G, their passages run from the left, climbing toward the right; but with the Earth placed at the diametrically opposite part, the spots' appearance around G will indeed be at the observer's left, but the passage will be descending toward the right, F. Now let's picture the Earth situated a quarter away from its present standing, and mark in this other figure the boundary ABCD and the axis, as before, AC, through which the plane of our meridian would pass — a plane in which the axis of the Sun's revolution would also lie, with its poles, one toward us (that is, in the apparent hemisphere), which pole we'll represent with the point E, and the other falling in the hidden hemisphere, which I mark I. Tilting the axis EI, then, with its upper part E toward us, the greatest circle described by the Sun's turning will be this one, BFDG, whose half seen by us — that is, BFD — will no longer appear a straight line, since the poles E, I are not on the circumference ABCD, but will show itself curved, with its convex toward the lower part C; and clearly the same will appear of all the smaller circles parallel to the greatest, BFD. Understand too that when the Earth is diametrically opposite to this standing, so that it sees the Sun's other hemisphere, now hidden, it will see of that same greatest circle the part DGB curved with its convex toward the upper part A; and the courses of the spots in these positions will be first along the arc BFD and then along the other, DGB, and their first appearances and last settings, made around the points B, D, will be level, neither one more nor less raised than the other. But if we place the Earth at such a spot in the ecliptic that neither the bounding circle ABCD nor the meridian AC passes through the poles of the axis EI — as I now show you by drawing this third figure, where the apparent pole E falls between the arc of the boundary AB and the section of the meridian AC — the diameter of the greatest circle will be FOG, the apparent semicircle FNG, and the hidden one GSF: the first curved with its convex N toward the lower part, and the second bent with its crest S toward the upper part of the Sun. The entries and exits of the spots — that is, the ends F, G — won't be level like the earlier B, D, but F lower and G higher, though with less difference than in the first figure; the arc FNG will also be curved, but not as much as the earlier BFD. So in this position the passages of the spots will be ascending from the left part F toward the right G, and will be made along curved lines. And understanding the Earth to be placed in the diametrically opposite site, so that the Sun's now‑hidden hemisphere is the one seen, and bounded by the same circle ABCD, it's plainly made out that the course of the spots will be along the arc GSF, beginning from the high point G — which will likewise be at the observer's left — and going to end, descending toward the right, at the point F. Once what I've laid out so far is understood, I don't think any difficulty remains in grasping how, from the boundary of the solar hemispheres passing through the poles of the Sun's rotation, or near them, or far from them, arise all the differences in the apparent journeys of the spots: so that the farther those poles are from that boundary, the more the said journeys will be curved and the less oblique — whence at the greatest distance, which is when the poles are in the section of the meridian, the curvature is at its highest but the obliquity at its least, that is, at the balance, as the second figure shows; while on the other hand, when the poles are on the boundary, as the first figure shows, the tilt is greatest but the curvature least, reduced to straightness. And as the boundary parts from the poles, the curvature begins to become noticeable, always increasing, while the obliquity and tilt keep growing smaller.
These are the outlandish changes my guest told me would appear from time to time in the progress of the sunspots, provided it were true that the annual motion belonged to the Earth, and that the Sun, set at the center of the ecliptic, turned upon itself about an axis not upright, but tilted, to the plane of that ecliptic.
Sagredo: I'm quite satisfied that I follow these consequences, and I think I'll fix them in my mind better by checking them against a globe set at that tilt, and then looking at it from different sides. What's left now is for you to tell us what came of it all afterward — how the imagined consequences actually turned out.
Salviati: What came of it was this: as we went on for many, many months making the most careful observations, noting down with the utmost accuracy the crossings of various spots at different times of the year, the outcomes were found to answer the predictions exactly.
Sagredo: Simplicio, if what Salviati says is true — and it won't do to cast doubt on his word — then the Ptolemaics and the Aristotelians are going to need solid arguments, mighty conjectures, and rock-firm experiments to counterbalance a blow of such weight, and to keep their opinion from taking its final tumble.
Simplicio: Easy now, my good sir — perhaps you're not yet where you may fancy you've arrived. For although I haven't fully mastered the matter of Salviati's argument, my logic, when I attend to the form of it, does not teach me that this way of arguing forces me by any necessity to conclude in favor of the Copernican hypothesis — I mean the fixity of the Sun at the center of the zodiac and the mobility of the Earth beneath its circumference. For although it's true that, given such-and-such a rotation of the Sun and such-and-such a circling of the Earth, these and those oddities must necessarily be seen in the sunspots, it does not follow that, arguing the other way around, from seeing such oddities in the spots one must necessarily conclude that the Earth moves along the circumference and the Sun is placed at the center of the zodiac. For who assures me that such oddities couldn't also be seen in a Sun that moves along the ecliptic, by inhabitants of an Earth standing fixed at its center? Unless you first prove to me that no account of this appearance can be given when you make the Sun move and the Earth stand still, I won't budge from my opinion, or from my belief that the Sun moves and the Earth stays motionless.
Sagredo: Simplicio bears himself stoutly, and very shrewdly opposes and upholds the side of Aristotle and Ptolemy; and, if I'm to tell the truth, it seems to me that Salviati's company, brief as it's been, has trained him quite a bit in arguing to the point — an effect I gather it has had on others too. As for inquiring into and judging whether a competent account of the apparent extravagances in the sunspots' motions can be given while leaving the Earth motionless and keeping the Sun in motion, I'll wait for Salviati to lay out his thinking; for it's quite believable that he's reflected on it and drawn out whatever can be produced on the point.
Salviati: I've thought about it many times, and talked it over, too, with my friend and host. As for what the philosophers and astronomers will bring forward to prop up the old system: on the one side we're sure — sure, I say — that the true and pure Peripatetics, laughing at anyone who busies himself with such (to their taste) insipid trifles, will write off all these appearances as empty illusions in the glass, and in this way, with little effort, free themselves from any duty to think further. As for the philosopher-astronomers, after we'd speculated with some care on what might be brought to bear, we found no expedient enough to satisfy, at one and the same time, both the course of the spots and the reasoning of the mind. I'll set out for you what occurred to us, and you'll make of it whatever your judgment dictates.
Grant that the apparent motions of the sunspots are just as we've described above; and set the Earth motionless at the center of the ecliptic, on whose circumference the center of the Sun is placed. Then it necessarily follows that the causes of all the variations we see in those motions must reside in motions belonging to the body of the Sun itself. First, the Sun will have to rotate on its own axis, carrying the spots along with it — spots we've assumed, indeed proved, to be stuck fast to the solar surface. Second, we'll have to say that the axis of the Sun's rotation is not parallel to the axis of the ecliptic — which amounts to saying that it isn't set straight up, at right angles to the plane of the ecliptic. For if it were, the spots would appear to cross by straight lines parallel to the ecliptic; so the axis must be tilted, since the crossings mostly appear made along curved lines. Third, we'll need to say that the tilt of this axis is not fixed, forever pointing at the same point of the universe; rather, that from moment to moment it keeps changing its direction. Because if the lean pointed steadily toward the same point, the spots' crossings would never change their look, but — straight or curved, bent up or down, rising or falling — whatever they appeared once, so they would appear always. So we're forced to say that this axis shifts about: sometimes it lies in the plane of the outermost circle that bounds the visible hemisphere — I mean at those times when the spots' crossings appear made along straight lines, and steeper than ever, which happens twice a year; at other times it lies in the plane of the observer's meridian, in such a way that one of its poles falls in the Sun's visible hemisphere and the other in the hidden one, both of them far from the endpoints — the poles, if you like — of another axis of the Sun, one parallel to the axis of the ecliptic (a second axis we'll necessarily have to assign to the globe of the Sun); far from them, I mean, by exactly as much as the tilt of the axis of the spots' revolution comes to. And further, that the pole falling in the visible hemisphere is at one time in the upper part and at another in the lower; for the crossings give us necessary proof of this happening, at the times when they are balanced and at their greatest curvature — now bulging with their convex side toward the lower part of the solar disk, and now toward the upper. And because these states keep changing continuously — the tilts and the curvings growing now greater and now smaller, the tilts sometimes coming to perfect balance and the curves to perfect straightness — we're necessarily driven to lay it down that this very axis of the spots' monthly revolution has a turning of its own, by which its poles trace out two circles around the poles of yet another axis (the one we must, as I said, assign to the Sun), the radius of those circles matching the amount of that axis's tilt. And the period of this turning must be one year, since that is the time in which all the appearances and variations in the spots' crossings come back around. And that this axis makes its turn about the poles of that other axis — the one parallel to the ecliptic's — and not about any other points, is plainly shown by the greatest tilts and the greatest curvings, which are always of the same size. So that, in the end, to keep the Earth fixed at the center, we'll have to credit the Sun with two motions around its own center, on two different axes: one of them completing its turn in a year, the other in less than a month. And this supposition strikes my mind as very hard, next to impossible. And that comes on top of our having to credit the same solar body with two further motions around the Earth on different axes — with the one tracing out the ecliptic in a year, and with the other making spirals, or circles parallel to the equinoctial, one a day. So that for that third motion, the one we'd have to assign to the globe of the Sun in itself (I don't mean the roughly monthly one that carries the spots, but the other, which has to shift the axis and poles of that monthly one) — there is no reason to be seen why it should finish its period in a year, as though it depended on the annual motion along the ecliptic, rather than in twenty-four hours, as though it depended on the daily motion about the poles of the equinoctial. I know that what I'm saying is, for now, quite obscure; but it will become clear to you when we come to speak of the third motion — an annual one — that Copernicus assigns to the Earth. Now, when these four motions, so incompatible with one another (all of which would have to be credited, of necessity, to the one body of the Sun), can instead be reduced to a single, utterly simple motion, assigned to the Sun on an axis that never alters; and when, without introducing anything new into the motions already assigned to the terrestrial globe on so many other grounds, we can so easily save all these outlandish appearances in the motions of the sunspots — then it really does seem that the option is not to be refused.
This, Simplicio, is as much as has so far occurred to our friend and me that might be offered, in explaining this appearance, by the Copernicans and the Ptolemaics in support of their views. Make of it whatever your own judgment tells you.
Simplicio: I know myself unequal to entering into so weighty a decision; and as for my own opinion, I'll stay neutral — hoping, though, that a time will come when, enlightened by higher contemplations than these human discussions of ours, our minds will be unveiled, and the fog that now keeps them clouded will be lifted away.
Sagredo: Excellent and holy is the counsel Simplicio holds to, and worthy to be received and followed by everyone — for, deriving from the highest wisdom and the supreme authority, it alone can be embraced in safety. But as far as human reasoning is permitted to penetrate — keeping myself within the bounds of conjecture and probable argument — I'll say, a little more decidedly than Simplicio does, that among all the subtle arguments I've ever heard, I've never met anything that struck my mind with greater wonder, or bound my understanding more tightly (setting aside pure geometrical and arithmetical demonstrations), than these two conjectures: the one drawn from the stations and retrogradations of the five planets, the other from these strange behaviors in the motions of the sunspots. And because they seem to me to give, so easily and so lucidly, the true cause of appearances so bizarre — showing how a single simple motion, blended with many others that are likewise simple but different from one another, without raising any difficulty at all, and indeed sweeping away every difficulty that dogs the other position — I keep concluding to myself that those who stay obstinate against this doctrine must either not have heard, or not have understood, these so plainly conclusive arguments.
Salviati: I won't call them either conclusive or inconclusive; for, as I've said before, my aim has not been to settle anything on so lofty a question, but only to lay out the natural and astronomical arguments that I can bring on either side, leaving the decision to others — a decision that, in the end, ought not to be ambiguous. For since one of the two arrangements must necessarily be true and the other necessarily false, it's impossible that (staying, of course, within the bounds of human doctrine) the arguments offered for the true side should not show themselves just as conclusive as those on the other side are empty and ineffective.
Sagredo: Then it must be time we heard the objections in that little book of conclusions, or disquisitions, that Simplicio has brought along.
Simplicio: Here's the book; and here's the passage where the author first briefly describes the system of the world according to Copernicus's position, saying: Terram igitur una cum Luna totoque hoc elementari mundo Copernicus, etc. — "Copernicus, then, has the Earth, together with the Moon and this whole elemental world," and so on.
Salviati: Hold on a moment, Simplicio, for it seems to me that this author, at his very entrance, shows himself to understand very little of the position he's undertaking to refute — since he says Copernicus has the Earth, together with the Moon, trace out the great orb in a year while moving from east to west; a thing which, being false and impossible, was never once asserted by Copernicus. On the contrary, Copernicus has it go the other way — from west to east, I mean, that is, in the order of the signs — which is why the Sun's annual motion then appears as it does, the Sun set motionless at the center of the zodiac. See the overbold self-assurance of the man! — to set himself up to refute another man's doctrine, and be ignorant of its very first foundations, on which the greatest and most important part of the whole structure rests. This is a poor way to win credit with the reader. But let's go on.
Simplicio: Having set out the general system, he begins to raise his objections against this annual motion; and the first are these — which he delivers ironically, in mockery of Copernicus and his followers — writing that in this fantastical arrangement of the world one is bound to utter the most solemn absurdities: namely, that the Sun, Venus, and Mercury are below the Earth; that heavy matter naturally goes upward and light matter downward; that Christ, our Lord and Redeemer, ascended to hell and descended to heaven when he drew near the Sun; that when Joshua commanded the Sun to stand still, it was the Earth that stopped, or else the Sun moved contrary to the Earth; that when the Sun is in Cancer, the Earth runs through Capricorn; that the winter signs make summer and the summer signs make winter; that it is not the stars that rise and set to the Earth, but the Earth to the stars; that the east begins in the west and the west in the east; and, in short, that nearly the whole course of the world is turned upside down.
Salviati: It all pleases me well enough — except for his mixing passages of Holy Scripture, ever to be revered and feared, in among these childish and all-too-scurrilous jibes, and his wanting to wound with sacred things a man who, philosophizing in jest and in play, neither affirms nor denies, but, having laid down certain suppositions or hypotheses, reasons in a familiar way.
Simplicio: It scandalized me too, and not a little — above all with what he adds right after: that although the Copernicans do answer these and other such arguments (though in a very twisted way), still they'll never be able to satisfy and answer the things that follow.
Salviati: That, now, is worst of all — because it implies he has things more forceful and conclusive than the authority of Holy Writ. But please, let us revere Scripture, and pass on to natural and human arguments. Indeed, if among his natural reasons he produces nothing of better sense than what he's brought so far, we may set this whole enterprise aside — for I certainly don't mean to spend a word answering such silly trifles. And what he says, that the Copernicans reply to these objections, is utterly false; nor can anyone believe that a single man would set about wasting his time so uselessly.
Simplicio: I join in the same judgment; but let's hear the other objections, which he brings forward as much more powerful. And here, as you see, with the most exact calculations he concludes that if the great orb of the Earth — the one along which Copernicus has it run once a year around the Sun — were as good as imperceptible next to the immensity of the starry sphere (as Copernicus himself says one must suppose it to be), then one would necessarily have to say and grant that the fixed stars are at an unimaginable distance from us, and that the smallest of them are bigger than the whole great orb itself, and some others far larger than the entire sphere of Saturn — bulks truly all too vast, and incomprehensible, and incredible.
Salviati: I've seen something like this before, urged by Tycho against Copernicus; and it's not just now that I've uncovered the fallacy — or better, the fallacies — of this argument, built on utterly false assumptions and on a statement of Copernicus's own, seized by his opponents with the most pinpoint strictness, in the way those litigants do who, being in the wrong on the main merits of the case, fasten on a single little word the other side let drop in passing, and raise an endless clamor over it. And, for your clearer understanding: when Copernicus had set out those marvelous consequences that follow, in the other planets, from the Earth's annual motion — namely the forward and retrograde motions of the three upper planets in particular — he added that this apparent change (which showed up more in Mars than in Jupiter, Jupiter being farther off, and less still in Saturn, farther off than Jupiter) remained imperceptible in the fixed stars, on account of their immense distance from us compared with the distance of Jupiter or Saturn. Here the opponents of this view rise up; and taking that "imperceptibility" Copernicus spoke of as if he had laid it down for something really and absolutely equal to nothing, and adding that even one of the smaller fixed stars is nonetheless perceptible, since it falls under the sense of sight, they go on calculating — with the help of other false assumptions — and conclude that in Copernicus's doctrine one must admit that a fixed star is far bigger than the whole great orb. Now I, to expose the emptiness of this whole line of argument, will show that from supposing a fixed star of the sixth magnitude to be no bigger than the Sun, it follows by a true demonstration that the distance of those fixed stars from us comes out so great that it is enough to make the Earth's annual motion — which in the planets causes such large and observable variations — show no noticeable effect in them; and at the same time I'll show, point by point, the great fallacies in the assumptions of Copernicus's opponents.
And first, I suppose, with Copernicus himself and in agreement with the opponents, that the radius of the great orb — the half-diameter, that is, which is the distance from the Earth to the Sun — contains 1,208 radii of the Earth itself. Second, I lay down — with their assent, and with the truth — that the apparent diameter of the Sun, at its mean distance, is about half a degree, that is, 30 arcminutes, which are 1,800 seconds, that is, 108,000 thirds. And since the apparent diameter of a fixed star of the first magnitude is no more than 5 seconds, that is 300 thirds, and the diameter of a sixth-magnitude star is 50 thirds (and here lies the greatest error of Copernicus's opponents), it follows that the diameter of the Sun contains the diameter of a sixth-magnitude star 2,160 times. And so, if one supposed a sixth-magnitude star to be really equal to the Sun, and no bigger — which is the same as saying, if the Sun were moved away far enough that its diameter appeared one of the 2,160 parts of what it appears now — its distance would have to be 2,160 times greater than it actually is now; which is as much as to say that the distance of the sixth-magnitude fixed stars is 2,160 radii of the great orb. And because the distance of the Sun from the Earth contains, by common agreement, 1,208 radii of the Earth, while the distance of the fixed stars (as we've said) is 2,160 radii of the great orb, it follows that the radius of the Earth, compared with the great orb, is much larger — nearly double, in fact — than the radius of the great orb is in relation to the distance of the starry sphere. And for that reason, the difference of apparent position in the fixed stars, caused by the diameter of the great orb, can be scarcely more observable than the one we observe in the Sun that arises from the radius of the Earth.
Sagredo: That's quite a comedown for a first step.
Salviati: It truly is. A fixed star of the sixth magnitude, which on this author's reckoning had to be — if Copernicus's claim was to hold up — as big as the whole great orb: just by setting it merely equal to the Sun, and the Sun is far less than the ten-millionth part of that great orb, he makes the starry sphere so vast and so high that it's enough to dispose of the objection raised against Copernicus.
Sagredo: Do work that calculation for me, please.
Salviati: The calculation is easy and very quick. The Sun's diameter is eleven of the Earth's semidiameters, and the diameter of the great orb contains 2,416 of those same semidiameters, by the common account of these measures; so the diameter of the orb contains that of the Sun about 220 times over. And since spheres are to one another as the cubes of their diameters, let's take the cube of 220, which is 10,648,000, and we'll have the great orb bigger than the Sun ten million six hundred forty-eight thousand times over — and to this great orb this author said a star of the sixth magnitude would have to be equal.
Sagredo: So their error consists in going badly wrong when they take the apparent diameter of the fixed stars.
Salviati: That's the error, but it isn't the only one. And I'm truly amazed that so many astronomers — men of great name, too, like Alfraganus, Albategnius, and Thebit, and more recently men like Tycho and Clavius, in short all our Academician's predecessors — should have gone so badly wrong in determining the sizes of all the stars, both fixed and moving, apart from the two luminaries, and should have paid no heed to the stray radiance — that fringe of light around them — which deceptively shows them a hundred times and more larger than when they're seen without their rays. And this oversight of theirs can't be excused, because it was in their power to see the stars, whenever they liked, without that fringe; you need only look at them at their first appearance in the evening or their last vanishing at dawn. And if nothing else, Venus — which one often sees at midday so small that you really have to strain your eyes, and which then, the following night, shows up as an enormous torch — ought to have alerted them to their mistake. For I certainly won't believe they supposed the true disk to be the one that shows in deep darkness, and not the one seen in a lit setting; because our own lamps, which seen at night from far off look big but up close show their true flame small and sharply bounded, could well enough have put them on their guard. In fact, if I must speak my mind freely, I absolutely believe that none of them — not even Tycho himself, so careful in handling astronomical instruments, who built such large and exact ones sparing no expense — ever set out to take and measure the apparent diameter of a single star, apart from the Sun and the Moon; instead I think that arbitrarily, and as they say by eye, one of the older among them pronounced the thing to be so, and his followers then, without any further check, simply stuck with that first pronouncement. For had any one of them applied himself to putting it to some test, he would without doubt have caught the error.
Sagredo: But if they lacked the telescope — and you've already said our friend came to know the truth with that instrument — then the others ought to be excused, not charged with negligence.
Salviati: That would follow if the aim couldn't be achieved without the telescope. It's true that the instrument, by showing the star's disk bare and magnified a hundred and a thousand times over, makes the job much easier; but one can also, without the instrument, reach the same result — if not so exactly. And I've done it many times; the method I've used is this. I hung a fine cord toward some star — I used Lyra, which rises between north and northeast — and then, by moving closer to the cord and farther from it, with the cord placed between me and the star, I found the spot from which the thickness of the cord exactly hides the star. This done, I took the distance from my eye to the cord, which turns out to be one of the sides enclosing the angle formed at the eye and standing on the thickness of the cord — an angle similar to, indeed the very same as, the angle that at the starry sphere stands on the diameter of the star. And from the ratio of the cord's thickness to the distance from eye to cord, using the table of arcs and chords, I immediately found the size of the angle — using, of course, the usual precaution one observes in taking such sharp angles: not to place the meeting of the visual rays at the center of the eye, where they only reach after being bent, but beyond the eye, where in reality the size of the pupil sends them to converge.
Sagredo: I understand this precaution, though I have some slight doubt about it; but what troubles me more is that in this operation, when it's done in the dark of night, it seems to me one measures the diameter of the radiant disk, and not the true, bare diameter of the star.
Salviati: No, sir — because the cord, in covering the star's bare little body, strips away the hairs, which are not the star's but our own eye's, and of which it is robbed the moment its true disk is hidden. And when you make the observation, you'll see how unexpectedly that quite large torch — which seemed as though it couldn't be hidden except behind a much bigger obstacle — is covered by a thin little cord. Then, to measure most exactly and find out how many such cord-thicknesses fit into the distance to the eye, I take not a single diameter of the cord, but — laying many pieces of it side by side on a board so that they touch — I take with a compass the whole space occupied by fifteen or twenty of them, and with that measure I gauge the distance (already taken with another, finer thread) from the cord to the convergence of the visual rays. And by this quite exact operation I find that the apparent diameter of a fixed star of the first magnitude — commonly reckoned at 2 arcminutes, and even 3 by Tycho in his Astronomical Letters, page 167 — is no more than 5 arcseconds, which is a twenty-fourth or a thirty-sixth part of what they believed. Now see on what grave errors their doctrines are founded.
Sagredo: I see and understand it very well; but before we go any further, I'd like to raise the doubt that occurs to me about locating the convergence of the visual rays beyond the eye, when one looks at objects subtending very sharp angles. My difficulty comes from its seeming to me that this convergence may be now farther off and now nearer — and this not so much because of the greater or smaller size of the object looked at, as because, in looking at objects of the same size, it seems to me the convergence of the rays must, for some other reason, become more or less remote from the eye.
Salviati: I already see where Sagredo's sharp mind is heading — a most diligent observer of nature's workings. And I'd lay any bet you like that, among a thousand who have watched the pupil of a cat's eye contract and widen enormously, there aren't two — perhaps not one — who has noticed that a like effect happens in men's pupils when they look, according as the medium is much or little illuminated, and that in broad daylight the little circle of the pupil shrinks a great deal; so that in looking at the disk of the Sun it shrinks to something smaller than a grain of millet, whereas in gazing at non-shining objects, and within a dimmer medium, it widens to the size of a lentil or more. In short, this widening and narrowing varies by much more than a tenfold ratio. From which it's clear that when the pupil is much dilated, the angle where the rays converge must be more remote from the eye — which is what happens when we look at faintly lit objects. This is a lesson freshly supplied to me by Sagredo, by which, whenever a most exact observation of great consequence is to be made, we're warned that we must carry out the investigation of that convergence in the very act of the same, or a very similar, operation. But in this case, to expose the astronomers' error, so much accuracy isn't needed — because even if, in their favor, we supposed the convergence to fall right at the pupil itself, it would matter little, their error being so great. I don't know, Sagredo, whether this was the point you were driving at.
Sagredo: That's it exactly, and I'm glad it wasn't unreasonable — as I'm assured by finding I'd hit on the same thing as you. But now, while we're on it, I'd gladly hear in what way one can investigate the distance of the convergence of the visual rays.
Salviati: The method is quite easy, and it goes like this. I take two strips of paper, one black and one white, and I make the black one half as wide as the white. Then I fasten the white one to a wall, and at some distance from it I fix the other on a stick or some other support, fifteen or twenty braccia away. And moving off from this second strip, along the same straight line, by as much again, it's clear that at that distance the straight lines would converge — the lines that, setting out from the ends of the white strip's width, pass just grazing the width of the other strip set in the middle. Whence it follows that if the eye were placed at that meeting point, the black strip in the middle would hide the white one opposite exactly — provided sight took place at a single point. But if we find that the ends of the white strip appear uncovered, that will be a necessary proof that the visual rays don't issue from a single point. And to make the white strip get hidden by the black, we'll have to bring the eye closer: so, having moved it up until the middle strip covers the far one, and having noted how much closer we had to come, that amount of approach will be a sure measure of how far beyond the eye the true convergence of the visual rays falls in this operation. And we'll have besides the diameter of the pupil — or rather of that opening from which the visual rays issue. For the pupil's diameter will be the same fraction of the black paper's width as this ratio: the distance from the convergence of the lines (drawn through the ends of the papers) to the spot where the eye stood when it first saw the far paper hidden by the middle one, compared with the distance between the two papers. And so, if we wanted to measure with precision the apparent diameter of a star, once the observation had been made in the way described above, we'd need to compare the diameter of the cord with the diameter of the pupil. And having found, for instance, that the cord's diameter is four times the pupil's, and the distance from the eye to the cord is, say, 30 braccia, we'll say that the true convergence of the lines drawn from the ends of the star's diameter through the ends of the cord's diameter goes to meet at 40 braccia beyond the cord — for in this way the proportion will be duly preserved between the distance from the cord to the convergence of those lines and the distance from that convergence to the eye's position, which must be the same as the ratio between the cord's diameter and the pupil's diameter.
Sagredo: I've understood it perfectly. So let's hear what Simplicio brings forward in defense of Copernicus's opponents.
Simplicio: Even though that supreme and utterly incredible absurdity urged by these opponents of Copernicus has been much softened by Salviati's argument, it doesn't seem to me removed so completely that enough force doesn't still remain in it to bring down that opinion. For, if I've grasped the sum and final conclusion, even granting that stars of the sixth magnitude are as big as the Sun (which itself seems a lot to believe), it would still be true that the great orb ought to cause in the starry sphere a change and variation like the one the Earth's semidiameter produces in the Sun, which is observable. So, since neither such a variation nor even a smaller one is to be seen in the fixed stars, it seems to me that on this account the Earth's annual motion is left forlorn and demolished.
Salviati: You'd conclude rightly, Simplicio, if there were nothing else to produce on Copernicus's side; but many other things still remain to us. And as for your objection, nothing stands in the way of our supposing the distance of the fixed stars to be even much greater than has been assumed. And you yourself, and anyone else who won't set aside the propositions accepted by Ptolemy's followers, will have to admit it a most fitting thing to place the starry sphere still very much larger than what we've just said it must be reckoned. For, since all astronomers agree that the greater slowness of the planets' revolutions is caused by the greater size of their spheres — and that Saturn is therefore slower than Jupiter, and Jupiter than the Sun, because the one has to trace a larger circle than the other, and this one than that, and so on — considering that Saturn, for instance, the height of whose orb is nine times greater than the Sun's, and whose time for one revolution is therefore 30 times longer than that of one revolution of the Sun; seeing that in Ptolemy's doctrine one revolution of the starry sphere is completed in 36,000 years, whereas Saturn's is finished in 30 and the Sun's in one; arguing by a like proportion, and saying: if Saturn's orb, being 9 times larger than the Sun's, revolves in a time 30 times longer, then by inverse reasoning how large must that orb be which revolves 36,000 times more slowly? — it will be found that the distance of the starry sphere must be 10,800 semidiameters of the great orb, which would be exactly 5 times greater than what we calculated it to be a moment ago, on the supposition that a sixth-magnitude star was as big as the Sun. Now see how much smaller still, on this reckoning, the variation caused in the stars by the Earth's annual motion would have to be. And if by a similar relation we wanted to argue the distance of the starry sphere from Jupiter and from Mars, the one would give it to us as 15,000 and the other as 27,000 semidiameters of the great orb — that is, still larger, the one 7 and the other 12 times over, than the size of a fixed star supposed equal to the Sun gave it to us.
Simplicio: It seems to me one could answer this by saying that the motion of the starry sphere has, since Ptolemy, been observed not to be so slow as he reckoned it; indeed, I think I've heard that Copernicus himself was the observer.
Salviati: You put it very well, but you produce nothing that favors the Ptolemaics' cause in the least — for they never refused the 36,000-year motion of the starry sphere on the grounds that so great a slowness would make it too vast and immense. For if such immensity were not to be granted in nature, they ought — before now — to have denied a revolution so slow that it couldn't, by any reasonable proportion, be fitted to anything but a sphere of intolerable size.
Sagredo: Please, Salviati, let's waste no more time proceeding by such proportions with people who are content to admit the most disproportionate things — so that with them, by this road, it's absolutely impossible to gain anything. And what more disproportionate proportion can be imagined than the one these men swallow and admit? For, while writing that there's no more fitting way to order the celestial spheres than to regulate them by the differences in the lengths of their periods — placing, step by step, the slower above the faster — once they've set the starry sphere highest, as the slowest of all, they set another above it, and therefore larger, and make it move in twenty-four hours, while its lower neighbor moves in 36,000 years. But we spoke enough of these disproportions the other day.
Salviati: I'd like you, Simplicio, to suspend for a moment the affection you bear the followers of your opinion, and tell me sincerely whether you believe they grasp in their minds that magnitude which they then judge cannot, on account of its immensity, be attributed to the universe. Because I, for my part, believe not; and it seems to me that just as, in grasping numbers, once one begins to pass those thousands of millions the imagination gets confused and can no longer form a concept, so it happens too in grasping immense sizes and distances. So that the same effect befalls the reasoning as befalls the senses: when on a clear night I look toward the stars, my senses judge their distance to be a few miles, and the fixed stars no more remote than Jupiter or Saturn — indeed, no farther than the Moon. But, without more ado, consider the past controversies between the astronomers and the Peripatetic philosophers over the distance of the new stars in Cassiopeia and in Sagittarius — the former placing them among the fixed stars, the latter believing them lower than the Moon. So powerless is our sense to distinguish great distances from the very greatest, even though the latter are in fact many thousands of times greater than the former. And finally I ask you, oh foolish man: do you grasp with your imagination that magnitude of the universe which you then judge to be too vast? If you grasp it, will you claim that your apprehension reaches further than divine power — will you say you can imagine things greater than God can bring about? But if you don't grasp it, why do you presume to pass judgment on things you don't understand?
Simplicio: These arguments all run very well, and it's not denied that the heavens may exceed our imagination in size — nor that God could have created them a thousand times larger than they are. But we mustn't grant that anything was created in vain or is idle in the universe. Now, since we see this beautiful order of planets arranged around the Earth at distances proportioned to producing their effects upon it for our benefit — to what end interpose, then, between Saturn's highest orb and the starry sphere, a vast space empty of any star, superfluous and pointless? To what end? For whose comfort and use?
Salviati: We arrogate too much to ourselves, Simplicio, it seems to me, when we insist that the care of us alone is the whole adequate work — the limit beyond which divine wisdom and power does or arranges nothing else. But I wouldn't have us so shorten His hand; rather let us be content to be sure that God and nature are so occupied with the government of human affairs that they could not attend to them more closely even if they had no other care than mankind alone. And this I think I can make clear with a most apt and noble example, drawn from the working of the Sun's light: which, while it draws up those vapors or warms that plant, draws them up and warms it as though it had nothing else to do; indeed, in ripening that cluster of grapes — nay, that single grape — it applies itself so that it could not apply itself more effectively even if the goal of all its business were the ripening of that one grape alone. Now, if this grape receives from the Sun all that can be received, and nothing is filched from it by the Sun's producing, at the same time, a thousand and a thousand other effects, then that grape would be chargeable with envy or with folly if it believed or demanded that the action of the Sun's rays should be spent for its benefit alone. I'm certain that nothing is left undone by divine Providence of what pertains to the government of human affairs; but that there cannot be other things in the universe dependent on His infinite wisdom — that, for my own part, so far as my reason dictates to me, I could not bring myself to believe. Yet, even if the fact stood otherwise, there would be no reluctance in me to believe the reasons that a higher intelligence might bring forward to me. Meanwhile, when I'm told that an immense space set between the planets' orbs and the starry sphere would be useless and pointless, empty of stars and idle — and likewise that so great an immensity, as a receptacle for the fixed stars, surpassing all our comprehension, is superfluous — I say it's rashness to try to make our feeble reasoning the judge of God's works, and to call vain or superfluous everything in the universe that doesn't serve us.
Sagredo: Say rather — and I think you'll put it better — that we don't know what purpose they serve for us. And I count it one of the greatest arrogances, one of the greatest follies, that anyone could put forward, to say: "Because I don't know what use Jupiter or Saturn is to me, therefore they're superfluous — in fact they don't even exist in nature." Why, you utter fool, I don't even know what use my arteries are to me, or my cartilage, my spleen, my gall bladder; I wouldn't so much as know I had a gall bladder, a spleen, or kidneys, if they hadn't been shown to me cut out of many corpses; and even then I could only learn what my spleen does in me at the moment it was taken out of me. To understand what this or that heavenly body does in me — since you insist that every operation of theirs is aimed at us — I'd have to remove that body for a while, and then whatever effect I felt go missing in me, I could say depended on that star. What's more, who is going to claim that the space these people call too vast and useless, between Saturn and the fixed stars, is empty of any other worldly bodies? Perhaps because we don't see them? So then the four Medicean Stars and the companions of Saturn came into the sky when we first began to see them, and not before? And the other countless fixed stars weren't there before men saw them? And the nebulae were once just little whitish patches, but then with the telescope we made them turn into throngs of many bright and beautiful stars? Presumptuous — no, reckless — ignorance of men!
Salviati: There's no need, Sagredo, to go on any further with these fruitless outbursts. Let's stick to our plan, which is to weigh the force of the reasons brought forward on the one side and the other, without settling anything, and leave the judgment then to those who know more than we do. And coming back to our natural, human discussion, I say that these terms — great, small, immense, tiny, and the rest — are not absolute but relative, so that the very same thing, compared with different things, may now be called immense and now imperceptible, let alone small. That being so, I ask: in relation to what can Copernicus's starry sphere be called too vast? In my view, it can't be compared or called such except in relation to something else of the same kind. So let's take the smallest of the same kind, which will be the lunar orb; and if the starry orb is to be judged too vast compared with the Moon's, then every other magnitude that exceeds another of the same kind by a like or greater proportion will have to be called too vast — and by this reasoning we'll also have to deny that it exists in the world at all. And so elephants and whales will surely be chimeras and poetic fancies; because the former, being too vast compared with ants, which are land animals, and the latter compared with sprats, which are fish — and ants and sprats are certainly there in rerum natura, in the real world — would be too enormous, since, absolutely speaking, the elephant and the whale exceed the ant and the sprat by a far greater proportion than the starry sphere exceeds the Moon's, if we picture that sphere just as large as it needs to be to fit the Copernican system. What's more, how large is the sphere of Jupiter, how large that of Saturn, each assigned as the housing for a single star — and a very small one, compared with a fixed star? Surely, if each fixed star had to be given such a portion of the world's space for its lodging, the orb where that countless multitude of them resides would have to be made many, many thousands of times bigger than what suffices for Copernicus's needs. Besides, don't you call a fixed star very small — I mean even the most conspicuous of them, let alone those that escape our sight? And we call them so in comparison with the space surrounding them. Now, if the whole starry sphere were a single shining body, who doesn't grasp that within infinite space one could assign a distance so great that this shining sphere would look just as small — smaller, even — than a fixed star looks to us now from the Earth? From there, then, we would judge small the very same thing that from here we now call immeasurably great.
Sagredo: Enormous, it seems to me, is the folly of those who would have God make the universe more in proportion to the small capacity of their reasoning than to His immense — indeed, infinite — power.
Simplicio: Everything you say is fine; but the point the other side presses on is having to grant that a fixed star must be not merely equal to, but so much larger than the Sun — and both, after all, are particular bodies set inside the starry orb. And it seems to me very much to the purpose that this author asks, and demands: "To what end, and for whose benefit, are machines so vast? Produced, perhaps, for the Earth — that is, for a tiny little point? And why so remote, so that they appear so slight and can do absolutely nothing on Earth? To what purpose that monstrous, immense chasm between them and Saturn? Empty and pointless are all those things not supported by probable reasons."
Salviati: From the questions this man asks, it seems to me one can gather that if we leave the heavens, the stars, and the distances at the quantities and sizes he has believed so far — even though he's never securely pictured any comprehensible size for them — he grasps perfectly well, and is quite satisfied about, the benefits that come from them upon the Earth, which would then no longer be a tiny little thing, nor they so remote as to appear so small, but big enough to be able to act upon the Earth, and the distance between them and Saturn perfectly well proportioned; and that he has very probable reasons for all these things — some of which I'd gladly have heard. But to see that in these few words he tangles himself up and contradicts himself makes me think he's very poor and short of these probable reasons, and that what he calls reasons are rather fallacies — shadows, even, of empty fancies. For I now ask him whether these heavenly bodies really do act upon the Earth, and whether it's for such an effect that they were produced at such-and-such sizes and set at such-and-such distances — or whether, on the contrary, they have nothing to do with earthly things. If they have nothing to do with the Earth, it's great foolishness for us earthlings to want to be arbiters of their sizes and regulators of their local arrangements, when we're utterly ignorant of all their affairs and concerns. But if he says they do act, and that they're directed to this end, then he comes to affirm what, from another angle, he himself denies — and to praise what he's just now condemned, when he said that heavenly bodies placed at such a distance that they appear tiny from the Earth can't act upon it at all. But, my dear man, in the starry sphere — already fixed at the distance it's at, which you judge to be well proportioned for its influences on these earthly things — a great many stars appear extremely small, and there are a hundred times as many altogether invisible to us (which is to appear smaller still than tiny). So you must either — contradicting yourself — now deny that they act upon the Earth; or else — contradicting yourself again — grant that appearing tiny takes nothing away from their action; or else — and this will be the more honest and modest concession — grant and freely confess that our judgment about their sizes and distances is a vanity, not to say a presumption or a rashness.
Simplicio: Truly, I saw it myself at once, reading this passage — the plain contradiction, in saying that the stars of Copernicus, so to speak, appearing so tiny, couldn't act upon the Earth, and yet not noticing that he'd granted action upon the Earth to those of Ptolemy and his own, which appear not merely tiny, but for the most part are invisible.
Salviati: But I come to another point. On what basis does he say that the stars appear so small? Perhaps because that's how we see them? Doesn't he know that this comes from the instrument we use in looking at them — namely, our eye? And that this is true is shown by the fact that if we change the instrument we'll see them bigger and bigger, as much as we please; and who knows whether to the Earth, which gazes at them without eyes, they don't show themselves enormous, and just as they really are? But it's time we left these trifles and came to weightier matters. So, having already proved these two things — first, how far off the firmament must be placed so that in it the diameter of the great orb makes no greater difference than the terrestrial orb makes in the distance of the Sun; and then having likewise proved how, to make a star of the firmament appear to us the size we see it, there's no need to make it bigger than the Sun — I'd like to know whether Tycho, or any of his followers, has ever tried to investigate in any way whether in the starry sphere any appearance can be detected by which one could more decisively deny, or admit, the annual motion of the Earth.
Sagredo: I'd answer no on their behalf — nor did they even have any need to; since it's Copernicus himself who says there is no such difference, and they, arguing ad hominem — against the man's own admission — grant it to him, and on this assumption they show the improbability that follows: namely, that one would have to make the sphere so immense that a fixed star, in order to appear as large as it appears to us, would in reality have to be a bulk so immense that it exceeded the size of the whole great orb — which is then, as they say, altogether incredible.
Salviati: I'm of the same opinion, and I believe precisely that they argue against the man more to defend another man than out of any longing to come to knowledge of the truth. And not only do I not believe that any of them has applied himself to making such an observation, but I'm not even sure whether any of them knows what difference the annual motion of the Earth would produce in the fixed stars, if the starry sphere were not at so great a distance that such a difference vanished in them for its smallness. For to stop short of such an inquiry and fall back on Copernicus's mere say-so may well be enough to defeat a man in argument, but not to make the fact itself clear — since it may be that the difference is there, but not looked for, or, for its smallness or for lack of exact instruments, not detected by Copernicus. This wouldn't be the first thing that he, for lack of instruments or some other shortcoming, failed to know, and yet, grounding himself on other utterly sound conjectures, affirmed something that the things he didn't grasp seemed to contradict. For, as was said before, without the telescope neither could Mars be seen to grow 60 times, nor Venus 40 times, larger in the one position than in the other — indeed, their differences appear far smaller than the truth; and yet we've since come to be certain that these changes exist exactly as the Copernican system required. So it would be well done to search out, with the greatest precision one could manage, whether such a change — which ought to be discernible in the fixed stars, granting the Earth's annual motion — is actually observed: something I absolutely believe has not so far been done by anyone, and not only not done, but perhaps (as I said) not even well understood by many, what one ought to be looking for. Nor do I say this at random; for I once saw a certain handwritten paper by one of these anti-Copernicans, who said that, if that opinion were true, there would necessarily follow a continual raising and lowering of the pole every six months, as the Earth in that span withdraws, over as much space as the diameter of the great orb, now toward the north, now toward the south; and it seemed to him reasonable — indeed, necessary — that, we following the Earth, when we were toward the north we should have the pole higher than when we're toward the south. Into this same error fell a mathematician who was otherwise quite intelligent, and likewise a follower of Copernicus, according to what Tycho reports in his Progymnasmata, on page 684: he said he'd observed the polar altitude change, and be different in summer from winter. And because Tycho denies the merit of the cause but doesn't condemn the procedure — that is, he denies that any change is seen in the polar altitude, but doesn't condemn the inquiry itself as unsuited to obtaining what's sought — he comes to declare that he too reckons the polar altitude, whether varied or unvaried from six months to six months, to be a good test for excluding or admitting the annual motion of the Earth.
Simplicio: Really, Salviati, it seems to me too that the same thing ought to follow. For I don't believe you'll deny me that if we walk only 60 miles toward the north, the pole will rise a degree for us, and drawing likewise another 60 miles nearer the north, the pole will rise another degree for us, and so on. Now, if drawing 60 miles nearer or farther makes so notable a change in the polar altitudes, what must carrying the Earth — and us with it — not 60 miles, but 60 thousand, do?
Salviati: It will have to make (if we're to follow that proportion) the pole rise a thousand degrees for us. See, Simplicio, how much an inveterate impression can do! You, for having fixed it in your imagination for so many years that it's the heavens that turn round in twenty-four hours, and not the Earth, and that consequently the poles of that revolution are in the sky and not in the terrestrial globe, can't for even an hour strip yourself of this habit and dress up in the opposite — picturing that it's the Earth that moves, just for as long as it takes to conceive what would follow if this fib were true. If the Earth, Simplicio, is what turns on itself in twenty-four hours, then in it are the poles, in it is the axis, in it is the equinoctial — that is, the great circle described by the point equally distant from the poles — in it are the infinitely many parallels, greater and smaller, described by the points of its surface more and less distant from the poles: in it are all these things, and not in the starry sphere, which, being motionless, lacks them all, and only in imagination can they be pictured there — by prolonging the Earth's axis out to where, ending, it will mark two points overhead of our poles, and the plane of the equinoctial, extended, will trace out in the sky a circle answering to it. Now, if the true axis, the true poles, the true terrestrial equinoctial don't change on Earth so long as you too stay in the same place on Earth, then carry the Earth wherever you please — you'll never change your relation, either to the poles, or to the circles, or to anything else terrestrial; and this because such a carrying is common to you and to all earthly things, and motion, where it's common, is as though it weren't there at all. And just as you won't change your relation to the earthly poles — a relation, I mean, such that they rise or fall for you — so likewise you won't change it to the poles figured in the sky, so long as by celestial poles we understand (as was already defined) those two points marked out there by the Earth's axis prolonged that far. It's true that those points in the sky change when the carrying of the Earth is done in such a way that its axis goes to strike other and other points of the motionless celestial sphere; but our relation to them doesn't change, such that the second should rise higher for us than the first. Whoever wants one of the firmament's points answering to the Earth's poles to rise, and the other to fall, for him must walk on Earth toward the one, moving away from the other; for carrying the Earth, and us with it (as I've already said), does nothing.
Sagredo: Do me the kindness, Salviati, of letting me lay this business out quite clearly with an example — a crude one, maybe, but all the more suited to the point. Imagine, Simplicio, that you're aboard a galley, and that, standing at the stern, you've trained a quadrant or some other astronomical instrument on the top of the foremast, as though you wanted to take its elevation, which was, let's say, 40 degrees. There's no doubt that if you walk along the gangway toward the mast some 25 or 30 paces, and then train the same instrument again on the same masthead, you'll find its elevation to be greater — grown, let's say, by 10 degrees. But if, instead of walking those 25 or 30 paces toward the mast, you stayed put at the stern and made the whole galley move that way, do you believe that, by the voyage it had made of those 25 or 30 paces, the elevation of the foremast would show itself increased to you by 10 degrees?
Simplicio: I believe, and understand, that it wouldn't gain so much as a single hair's breadth by a voyage of a thousand or a hundred thousand miles, let alone of 30 paces. But I do believe that if, in sighting along the top of the foremast, a fixed star happened to lie in the same line, then — I mean — keeping the quadrant fixed, after sailing 60 miles toward the star, the sight would strike the tip of the foremast just as before, but no longer the star, which would have risen a degree for me.
Sagredo: But surely you don't believe that the line of sight would fail to strike that point of the starry sphere which answers to the line of the masthead?
Simplicio: No, that it wouldn't; but the point would have changed, and would lie below the star first observed.
Sagredo: That's exactly how it is. But just as, in this example, what answers to the elevation of the masthead is not the star, but the point of the firmament that lies in line with the eye and the top of the mast, so in the case we're illustrating, what in the firmament answers to the pole of the Earth is not a star or any other fixed thing of the firmament, but that point at which the terrestrial axis, prolonged straight out that far, comes to end — a point that isn't fixed, but obeys the changes the earthly pole might make. And therefore Tycho, or the others who brought this objection, ought to have said that, given such a motion of the Earth (if it were true), one should detect and observe some difference in the rising and falling not of the pole, but of some fixed star toward that quarter which answers to our pole.
Simplicio: Now I understand perfectly the confusion these people fell into; but it still doesn't rob me of the force — which seems to me very great — of the argument brought on the other side, once it's referred to the change of the stars, and no longer of the pole. For if the galley's motion, of only 60 miles, makes a fixed star rise for me by a degree, how could a like change — and a far greater one, too — not come to me when the galley is carried toward that same star over as much space as the diameter of the great orb, which you say is twice the distance from the Earth to the Sun?
Sagredo: Here, Simplicio, there's another confusion — one you really do understand, only it doesn't occur to you to understand it; and I'll try to remind you of it. So tell me: suppose that, after adjusting your quadrant on a fixed star and finding, for instance, its elevation to be 40 degrees, you — without shifting from your place — tilted the arm of the quadrant so that the star stayed raised above that line of sight; would you say, on that account, that the star had gained a greater elevation?
Simplicio: Certainly not, because the change was made in the instrument, not in the observer — who would have had to change place by moving toward the star.
Sagredo: But when you're sailing or walking over the surface of the Earth, would you say that no change at all was made in that same quadrant — that it always kept the same elevation with respect to the sky — so long as you yourself didn't tilt it, but left it standing in its first setting?
Simplicio: Let me think about it a moment. I'd say without a doubt that it wouldn't keep it, because the journey I make isn't over a flat plane, but over the curved surface of the terrestrial globe, which step by step changes its inclination with respect to the sky, and consequently makes the instrument — which keeps its setting upon that surface — change too.
Sagredo: Very well put; and you also grasp that the larger and larger that circle was, over which you moved, the more miles you'd have to walk to make that star rise by that one degree for you; and finally, that when the motion toward the star was along a straight line, you'd have to move even farther than along the circumference of any circle, however enormous.
Salviati: Yes, because in the end the circumference of an infinite circle and a straight line are the same thing.
Sagredo: Oh, that I don't understand — nor do I think Simplicio understands it either; and there must be some hidden mystery underneath, because we know that Salviati never speaks at random, nor brings out a paradox that doesn't turn on some far-from-trivial idea. So, in due place and time, I'll remind you to explain this business of the straight line being the same as the circumference of the infinite circle — but for now I don't want us to interrupt the discussion we have in hand. And getting back to the point, I'd have Simplicio consider that the approaching and withdrawing the Earth does to that fixed star which is near the pole is done as if along a straight line — namely the diameter of the great orb; so that to try to gauge the rising and falling of the polar star by the motion along that diameter as though it were the motion over the Earth's own tiny little circle is a great sign of small understanding.
Simplicio: But we're still stuck in the same difficulties, since not even that slight difference which there ought to be is seen to be there; and if this is nil, then we have to confess that the annual motion along the great orb, attributed to the Earth, is nil as well.
Sagredo: Now here I'll let Salviati carry on — for it seems to me he wasn't dismissing as nil the rising or falling of the polar star, or of some other fixed star, even though it's grasped by no one, and even though Copernicus himself set it down not, I'd say, as nil, but as unobservable for its smallness.
Salviati: I've already said above that I don't believe anyone has set himself to observe whether, at different times of the year, any change can be detected in the fixed stars that might depend on the annual motion of the Earth; and I added, moreover, that I doubt whether anyone has even properly understood what the changes are, and among which stars they ought to appear. So it's well that we go through this point carefully. Finding it written only in general terms — that the annual motion of the Earth along the great orb ought not to be admitted, because it's not likely that no apparent change would be seen in the fixed stars on account of it — and then not hearing said what in particular such apparent changes should be, and in which stars, makes me very reasonably reckon that those who rest on that general pronouncement have not understood, nor perhaps even tried to understand, how the business of these changes actually works, nor what the things are that they say ought to be seen. And what moves me to judge so is knowing that the annual motion attributed by Copernicus to the Earth, when it has to become perceptible in the starry sphere, doesn't have to produce an apparent change equally with respect to all the stars; rather, that appearance must be greater in some, smaller in others, smaller still in others, and finally, in others, absolutely nil — however enormous the circle of this annual motion is supposed to be. Now the changes that ought to be seen are of two kinds: one is the stars' changing their apparent magnitude, and the other, their varying their meridian altitudes — from which follows, in consequence, the changing of their risings and settings, and of their distances from the point overhead, and so on.
Sagredo: It seems to me I see a whole skein of these turnings being got ready for me — God grant I'm ever able to disentangle myself from it; for, to confess my failing to you, Salviati, I've thought about this now and then, and could never find the loose end of the thread — and I don't mean so much about this that concerns the fixed stars, as about another, more terrible business that you've brought back to my mind by mentioning these meridian altitudes, rising latitudes, and distances from the point overhead, and so on. And my brain's tangle comes from what I'll tell you now. Copernicus places the starry sphere motionless, and the Sun at its center, likewise motionless; therefore every change that appears to us to occur in the Sun or in the fixed stars must necessarily belong to the Earth — that is, to us. But the Sun rises and falls in our meridian through an enormous arc, of nearly 47 degrees, and through arcs greater and greater still it varies the breadth of its risings and settings on the slanting horizons. Now how can the Earth ever tilt and rise so notably toward the Sun, and not at all toward the fixed stars — or by so little that it's an imperceptible thing? This is the knot that has never once been able to pass through my comb; and if you'll untie it for me, I'll think you more than an Alexander.
Salviati: These are difficulties worthy of Sagredo's wit; and the doubt is such that even Copernicus himself almost despaired of being able to explain it in a way that would make it intelligible — which is plain both from his own confession of its obscurity, and from his falling back on it twice, in two different ways, to explain it. And I frankly confess that I didn't grasp his explanation until, by another and different method, quite plain and clear, I made it intelligible to myself — though not without a long and laborious application of mind.
Simplicio: Aristotle saw this same difficulty and used it to refute certain ancients who wanted the Earth to be a planet: against them he argues that, if that were so, then it too, like the other planets, would have to have more than one motion, from which would follow this variation in the risings and settings of the fixed stars, and in their meridian altitudes as well. And since he raised the difficulty and didn't resolve it, it must be — if not impossible — at least hard to solve.
Salviati: The size and force of the knot make its untying all the finer and more admirable; but I don't promise it to you for today, and I beg you to excuse me until tomorrow. For now, we'll go on considering and explaining those changes and differences that ought to be detected in the fixed stars on account of the annual motion, just as we were saying — and in explaining them there come to be set out certain preparatory points for the untying of the greatest difficulty. Now, taking up again the two motions attributed to the Earth (and I say two, because the third isn't really a motion at all, as I'll explain in its place), that is, the annual and the daily: the first is to be understood as made by the center of the Earth along the circumference of the great orb — that is, of a greatest circle described in the plane of the ecliptic, fixed and unchanging; the other, the daily, is made by the globe of the Earth on itself, about its own center and its own axis — not upright, but tilted to the plane of the ecliptic, with an inclination of about 23 and a half degrees. This inclination is maintained all year long, and — what is most of all to be noted — it always keeps toward the same part of the sky, so that the axis of the daily motion stays perpetually parallel to itself. Thus, if we imagine that axis prolonged out to the fixed stars, then while the center of the Earth circles the whole ecliptic in a year, that same axis describes the surface of an oblique cylinder, which has for one of its bases the said yearly circle, and for the other a like circle imaginarily described by its extremity — or, if you like, its pole — among the fixed stars. And this cylinder is oblique to the plane of the ecliptic according to the inclination of the axis that describes it, which we've said is 23 and a half degrees; and this inclination, keeping perpetually the same (except that over many thousands of years it makes some very slight change, which matters nothing to the present business), causes the terrestrial globe never to tilt any further or to rise, but to keep itself unchanging. From which it follows that, as regards the changes to be observed in the fixed stars depending on the annual motion alone, the same will happen to any point whatever of the Earth's surface as to the very center of the Earth; and so in the present explanations we'll make use of the center, as of any point of the surface. And for easier understanding of the whole, we'll draw the line-figures; and first let's mark, in the plane of the ecliptic, the circle ANBO, and let's take the points A, B to be the extremes toward the north and toward the south — that is, the beginning of Cancer and of Capricorn — and let's prolong the diameter AB indefinitely through D and C toward the starry sphere. I say now, first, that none of the fixed stars set in the ecliptic will ever, by any change made by the Earth through that plane of the ecliptic, vary its elevation, but will always be seen in the same plane; but the Earth will indeed approach it and withdraw from it by as much space as the diameter of the great orb. This is plainly seen in the figure: for whether the Earth is at point A or at B, the star G is always seen along the same line ABC; but the distance BC has become smaller than CA by the whole diameter BA. The most, then, that can be detected in the star C — and in any other set in the ecliptic — is the increased or diminished apparent magnitude, from the Earth's approaching or withdrawing.
Sagredo: Hold on a moment, please, because I feel some scruple or other bothering me, and it's this. That the star C is seen along the same line A B C whether the Earth is at A or at B — this I understand very well; and moreover I grasp that the same would happen from all the points of the line A B, while the Earth passed from A to B along that line. But since it passes, as is supposed, along the arc A N B, it's a plain thing that when it's at point N — and at any other point except the two, A and B — it will be seen no longer along the line A B, but along other and other lines. So that if showing itself along different lines must cause an apparent change, some difference will have to be detected. What's more, I'll say — with that philosophical freedom which among friends who are philosophers ought to be allowed — it seems to me that you, contradicting yourself, are now denying what this very day you declared to us, to our wonder, to be a most true and important thing: I mean what happens with the planets, and in particular the three outer ones, which, being continually in the ecliptic or very near it, not only show themselves now near to us and now most remote, but so irregular in their otherwise regular motions that they sometimes appear to us stationary, and sometimes, by many degrees, retrograde — and all for no other cause than the annual motion of the Earth.
Salviati: Even though a thousand proofs have made me certain of Sagredo's shrewdness, I wanted, with this further trial, to reassure myself all the more of what I can promise myself from his wit — and all for my own benefit, since when my propositions can stand firm to the hammer, or to the assayer's cupel, of his judgment, I can be sure they're of good alloy under any test. I say, then, that I had deliberately disguised that objection — yet not with any intent to deceive you and persuade you of some falsehood, as could have happened if the instance I disguised, and you passed over, had really been such as it shows itself in appearance, that is, truly strong and conclusive. But it isn't such; on the contrary, I now suspect that you, to test me, are pretending not to recognize its nullity. But in this particular I mean to be craftier than you, by dragging out of your mouth by force what you were artfully trying to hide from us: so tell me, what is it by which you recognize the stations and retrogradations of the planets deriving from the annual motion — an effect so great that at least some trace of a like effect ought to be seen in the stars of the ecliptic?
Sagredo: Your question contains two queries, to which I must reply: the first concerns the charge you lay on me, of being a dissembler; the other is about what may appear in the stars, and so on. As to the first, I'll say — with your leave — that it's not true I pretended not to understand the nullity of that instance; and to reassure you of it, I tell you now that I understand that nullity perfectly well.
Salviati: But I don't understand how it can be that you weren't speaking dissemblingly when you said you didn't understand that particular fallacy — which you now confess you understand perfectly well.
Sagredo: The very confession that I understand it can assure you I wasn't dissembling when I said I didn't understand it; for if I'd wanted, and did want, to dissemble, who could stop me from continuing in the same pretense, still denying that I understood the fallacy? I say, then, that I didn't understand it then, but that I grasp it well now — thanks to your having woken up my intellect, first by telling me resolutely that it's nil, and then by beginning to question me so broadly, what that thing was by which I recognized the stations and retrogradations of the planets. And since this is recognized from the comparison one makes of them with the fixed stars — in relation to which their motions are seen to vary, now westward and now eastward, and sometimes to stay as if motionless — and since above the starry sphere there's no other, immensely more remote and still visible to us, with which we could compare our fixed stars, therefore we can detect no trace in the fixed stars answering to what appears to us in the planets. This, I think, is just what you meant to draw out of my mouth.
Salviati: That it is — with the added bonus of your very subtle wit. And if with a little hint I opened your mind, you with another make me recall that it's not altogether impossible that something might, at some time, be found observable among the fixed stars, by which one could make out in which of them the annual revolution resides — so that they too, no less than the planets and the Sun itself, might be willing to appear in court to bear witness to such a motion in the Earth's favor. For I don't believe that the stars are strewn over a spherical surface, all equally distant from a single center; rather I reckon that their distances from us are so various that some of them may be 2 and 3 times more remote than certain others. So that if there were found, with the telescope, some very tiny star quite close to one of the larger ones — and that larger one were therefore very high up — it might happen that some perceptible change would occur between them, answering to that of the outer planets. And so much be said for now about the particular of the stars set in the ecliptic. Let's come now to the fixed stars set outside the ecliptic, and let's imagine a greatest circle erect to the plane of the ecliptic — say, for example, a circle that in the starry sphere answers to the colure of the solstices — and let's mark it CEH, which will at the same time turn out to be a meridian; and in it let's take a star outside the ecliptic, such as E would be. Now this one, at the Earth's motion, will indeed vary its elevation; for from the Earth at A it will be seen along the ray AE, with the elevation of the angle EAC; but from the Earth placed at B it will be seen along the ray BE, with the elevation of the angle EBC, greater than the other EAC, since that one is exterior and this interior and opposite, in the triangle EAB. The distance of the star E from the ecliptic will thus be seen changed; and likewise its altitude in the meridian will have become greater in the position B than in the place A, according as the angle EBC exceeds the angle EAC, which is the size of the angle AEB. For, the side AB of the triangle EAB being prolonged to C, the exterior angle EBC (being equal to the two interior and opposite ones, E and A) exceeds A itself by the size of the angle E. And if we take another star in the same meridian, more remote from the ecliptic — such as, for instance, the star H would be — the difference in its being seen from the two places A and B will be greater still, according as the angle AHB becomes greater than the other, E; which angle will keep growing, the farther the observed star is from the ecliptic, until finally the greatest change will appear in that star which was set in the very pole of the ecliptic — as, for total understanding, we can demonstrate thus. Let the diameter of the great orb be AB, whose center is G, and let it be understood as prolonged out to the starry sphere at the points D, C; and from the center G let the axis of the ecliptic GF be raised up to the same sphere, in which let there be understood described a meridian DFC, which will be erect to the plane of the ecliptic; and taking in the arc FC any points you please, H, E, as places of fixed stars, let the lines FA, FB, AH, HG, HB, AE, GE, BE be joined, so that the angle of the difference — or let's say the parallax — of the star set at the pole F is AFB, that of the star set at H is the angle AHB, and that of the star at E is the angle AEB. I say that the angle of the difference of the polar star F is the greatest, and, of the others, the one nearer the greatest is greater than the more remote — that is, that the angle F is greater than the angle H, and this greater than the angle E. Let there be understood a circle described about the triangle FAB; and because the angle F is acute (its base AB being smaller than the diameter DC of the semicircle DFC), it will be set in the larger portion of the circumscribed circle cut off by the base AB; and because that AB is divided in half and at right angles by FG, the center of the circumscribed circle will be on the line FG: let it be the point I. And because, of the lines drawn from the point G — which is not the center — to the circumference of the circumscribed circle, the greatest is the one that passes through the center, GF will be greater than any other drawn from the point G to the circumference of that same circle; and therefore that circumference will cut the line GH (which is equal to the line GF), and cutting GH it will also cut AH: let it cut it at L, and let the line LB be joined. The two angles AFB, ALB will therefore be equal, being in the same portion of the circumscribed circle; but ALB, being exterior, is greater than the interior H: therefore the angle F is greater than the angle H. And by the same method we'll demonstrate that the angle H is greater than the angle E, because the center of the circle described about the triangle AHB is on the perpendicular GF, to which the line GH is nearer than GE, and therefore its circumference cuts GE, and also AE: whence the point is manifest. Let's conclude, then, that the difference of appearance (which, by a term proper to the art, we may call the parallax of the fixed stars) is greater and smaller according as the observed stars are more or less near the pole of the ecliptic; so that finally, of the stars that are in the ecliptic itself, that difference is reduced to nothing. As for the Earth's approaching or withdrawing from the stars by this motion: from those that are in the ecliptic it approaches and withdraws by as much as the whole diameter of the great orb, as we saw just now; but from the stars around the pole of the ecliptic that approach or withdrawal is almost nil, and for the others this difference grows greater according as they are nearer the ecliptic. We can, in the third place, understand how that difference of apparent position grows greater or smaller according as the observed star is nearer to us or more remote; for, if we mark another meridian less distant from the Earth — such as this DFI would be — a star set at F and seen along the same ray AFE, the Earth being at A, when it was then observed from the Earth at B, would be seen along the ray BF, and would make the angle of the difference, that is BFA, greater than the other first one AEB, being exterior to the triangle BFE.
Sagredo: I've listened to your argument with great pleasure — and profit, too; and to make sure I've followed it correctly, I'll sum up the conclusions in a few words. It seems to me you've explained that there are two distinct kinds of appearance we could observe in the fixed stars by means of the Earth's annual motion. One is the change in their apparent magnitudes, as we, carried along by the Earth, draw nearer to them or farther away. The other — which likewise depends on that same approaching and receding — is their showing up in the same meridian sometimes higher and sometimes lower. What's more, you tell me (and I understand it perfectly) that neither of these changes happens equally in all the stars, but more in some, less in others, and not at all in still others. The approach and recession by which a given star should look now larger and now smaller is imperceptible — practically nil — in the stars near the pole of the ecliptic, but greatest in the stars sitting right on the ecliptic, and middling in those in between; while the reverse holds for the other difference, that is, the raising and lowering is nil in the stars on the ecliptic, greatest in those near the pole of the ecliptic, and middling in the ones between. Beyond that, both of these differences are more noticeable in stars that happen to be closer, less noticeable in the farther ones, and finally, in the extremely distant ones, they would vanish altogether. That's my part of it; what remains, as I see it, is to satisfy Simplicio, who I don't think will readily agree to wave off as imperceptible such differences — differences springing from so vast a movement of the Earth, and from a change that carries the Earth to places twice as far apart from each other as we are from the Sun.
Simplicio: To speak freely, I do feel a great reluctance to grant that the distance of the fixed stars has to be so enormous that in them the differences we've been describing must be completely undetectable.
Salviati: Don't give yourself up entirely to despair, Simplicio — there may still be some easing of your difficulties. First of all, that the apparent size of the stars isn't seen to change noticeably shouldn't strike you as at all improbable, once you notice how badly people's estimation deceives them in this sort of thing, especially when they're looking at bright objects. Take yourself, for example, gazing at a lit torch 200 paces off: if it came 3 or 4 arm-lengths closer, would you claim to notice it, because it looked bigger? I certainly wouldn't notice, not even if it came 20 or 30 closer. In fact I've sometimes happened to watch a light like that at such a distance and couldn't make up my mind whether it was coming toward me or moving away, when in reality it was drawing nearer. But what of it? If that same approaching and receding (I mean twice the distance from the Sun to us) is almost totally imperceptible in the star of Saturn, and barely observable in Jupiter, what must it be in the fixed stars, which I don't think you'd be unwilling to place at twice the distance of Saturn? In Mars, which by coming closer to us —
Simplicio: Don't trouble yourself any further on this particular point; I'm already convinced that what's been said about the unchanged apparent size of the fixed stars could very well be the case. But what shall we say about the other difficulty — the one that arises from our not detecting any variation in the change of position?
Salviati: We may say something that could set you at ease on this side too. And to come straight to it: wouldn't you be satisfied if we actually did observe in the stars those changes which you think ought to be seen if the annual motion belonged to the Earth?
Simplicio: I'd be satisfied beyond any doubt, as far as this particular point is concerned.
Salviati: I'd like you to say that if such a difference were observed, nothing would be left that could cast doubt on the Earth's mobility, seeing that no other explanation could be assigned to such an appearance. But even supposing it doesn't show up perceptibly, that still doesn't remove the mobility, nor does it necessarily prove immobility, since it may be (as Copernicus maintains) that the immense distance of the starry sphere makes such tiny appearances impossible to observe. And those appearances, as I've already said, may be that up to now they've never even been looked for — or, if looked for, not in the way they should be, that is, with the exactness that such minute precision would require. That exactness is hard to come by, partly through the shortcomings of astronomical instruments, which are subject to many distortions, and partly through the fault of those who handle them with less care than they ought. A necessarily conclusive proof of how little such observations are to be trusted is the disagreement we find among astronomers in assigning the positions — I won't say of new stars and comets, but of the fixed stars themselves, right down to the polar altitudes, where more often than not they're at odds with one another by many arcminutes. And to tell the truth, who, working with a quadrant or a sextant whose side is at most 3 or 4 arm-lengths long, could be sure — in the seating of the plumb line, or in the cut of the sight-vane — not to be off by two or three arcminutes, which around its circumference will be no wider than a grain of millet? On top of that, it's nearly impossible for the instrument to be built and kept with absolute accuracy. Ptolemy himself shows distrust of an armillary instrument built by Archimedes for catching the Sun's entrance into the equinoctial.
Simplicio: But if the instruments are so suspect and the observations so doubtful, how can we ever put ourselves on secure ground and free ourselves from error? I'd heard great things preached about Tycho's instruments, made at immense expense, and about his singular diligence in his observations.
Salviati: All of that I grant you; but neither the one nor the other is enough to make us secure in a matter of such importance. I want us to make use of instruments far, far larger than Tycho's — supremely exact, and made at hardly any expense at all — whose side is 4, 6, 20, 30, or 50 miles, so that a degree comes out a mile wide, an arcminute 50 arm-lengths, and an arcsecond a little under an arm-length. In short, we can have them, without spending a thing, of any size we please. Staying at a villa of mine near Florence, I plainly observed the Sun's arrival at, and departure from, the summer solstice: one evening, as it set, it slipped behind a crag of the Pietrapana mountains about 60 miles off, leaving a thin sliver of itself uncovered toward the north, a sliver whose width was not the hundredth part of the Sun's diameter; and the next evening, at a similar setting, it again showed a similar uncovered sliver, but noticeably thinner — a sure sign that it had begun to pull away from the tropic. The Sun's backward shift from the first observation to the second certainly didn't amount to so much as one arcsecond on the horizon; and the observation, made with a superb telescope that magnifies the Sun's disc more than a thousand times, comes out both easy and delightful. Now, with instruments like these I want us to make our observations of the fixed stars, using one of those in which the change ought to be most conspicuous — namely, as already stated, the ones most remote from the ecliptic. Among these the Lyre, a very bright star near the pole of the ecliptic, would be well suited for very northern countries, worked in the manner I'll describe shortly; but I'll use a different star. I've already scouted out a spot quite well suited for such an observation. The place is an open plain, above which, toward the north, there rises a very lofty mountain, on whose summit is built a small church, set from west toward east, so that the ridge of its roof can cut the meridian of some dwelling down in the plain at right angles. I mean to fix a little beam parallel to that ridge, or crest of the roof, and about an arm-length away from it. Once that's set, I'll look in the plain for the spot from which one of the stars of the Wain — the Big Dipper — as it crosses the meridian, comes to be hidden behind the beam I've placed there; or else, if the beam isn't thick enough to hide the star, I'll find the spot from which that same beam is seen to cut the star's disc in half — an effect that a superb telescope brings out exquisitely. And if the spot from which this occurs happens to have some dwelling on it, so much the better; if not, I'll have a stake driven firmly into the ground, with a fixed mark to show where the eye should be placed each time one wants to repeat the observation. The first of these observations I'll make around the summer solstice, and then go on from month to month, or whenever I please, until the other solstice; with this observation one could detect the raising and lowering of the star, however slight it might be. And if, in carrying it out, we should manage to make out any change at all, what a great gain there would be for astronomy! For by such means, besides assuring ourselves of the annual motion, we could come to know the size and distance of that very star.
Sagredo: I follow the whole procedure perfectly, and the operation seems to me so easy, and so well suited to what's needed, that one might very reasonably believe Copernicus himself, or some other astronomer, had already carried it out.
Salviati: It seems to me quite the opposite, because it isn't likely that, if anyone had tried it, he wouldn't have made some mention of the outcome — whether it turned out in favor of the one opinion or the other. Besides, neither for this nor for any other purpose does one find that anyone made use of such a way of observing — which, moreover, could scarcely be carried out at all without an exact telescope.
Sagredo: I'm completely satisfied with what you've said. But since we still have plenty of time before nightfall, if you want me to pass the evening in peace, do me the kindness of laying out those problems whose explanation you asked, a little while ago, to put off until tomorrow. Give us back the leave you were granted — cash it in now — and setting all other discussions aside, come and explain to us how, once we grant the Earth the motions Copernicus assigns it, and hold the Sun and the fixed stars still, these same phenomena can follow — the Sun's rising and sinking in the sky, the changing of the seasons, the inequality of days and nights, and so on — in exactly the way they are so easily grasped in the Ptolemaic system.
Salviati: Nothing Signor Sagredo asks can be, or ought to be, refused. The delay I asked for had no other purpose than to give me time to arrange in my mind the premises needed for a full and open account of how the phenomena you name follow in the Copernican arrangement just as they do in the Ptolemaic — indeed, with far greater ease and simplicity in the one than in the other. From that it will be plain that this hypothesis is as easy for nature to carry out as it is hard for the intellect to grasp. Even so, I hope that by using a different way of laying it out than the one Copernicus used, I can also make it a good deal less obscure to follow. To do that I'll put forward a few assumptions that are self-evident and obvious in themselves, and they are these:
First. Suppose the Earth, a spherical body, turns about its own axis and poles: then each point marked on its surface traces out the circumference of a circle, larger or smaller according as the point is farther from or nearer to the poles. Of these circles, the largest is the one traced by a point equally distant from the two poles; and all these circles are parallel to one another — and "parallels" is what we'll call them.
Second. Since the Earth is spherical in shape and opaque in substance, it is continually lit by the Sun over half its surface, while the other half stays dark. And since the line that divides the lit part from the dark is a great circle, we'll call it the boundary circle of the light.
Third. When the boundary circle of the light passes through the Earth's poles, it cuts (being a great circle) all the parallels into equal parts. But when it does not pass through the poles, it cuts them all into unequal parts, except for the middle circle alone, which, being itself a great circle, is still cut into equal parts.
Fourth. As the Earth turns about its own poles, the lengths of the days and the nights are determined by the arcs of the parallels cut off by the boundary circle of the light: the arc that lies in the lit hemisphere sets the length of the day, and the remainder is the length of the night.
With these things laid down, and for a clearer grasp of what remains to be said, let's draw a figure. First we'll mark the circumference of a circle to stand for the great orb — the Earth's annual path — drawn in the plane of the ecliptic, and we'll divide it into four equal parts with two diameters, Capricorn, Cancer, Libra, and Aries, which at the same time will stand for the four cardinal points, that is, the two solstices and the two equinoxes. At the center of this circle we'll mark the Sun, O, fixed and unmoving. Now, about the four points Capricorn, Cancer, Libra, and Aries, taken as centers, let's draw four equal circles to stand for the Earth, set at those places at different times of year; and in the space of one year its center travels the whole circumference Capricorn, Aries, Cancer, and Libra, moving from west to east — that is, in the order of the signs. It's already clear that while the Earth is at Capricorn, the Sun will appear at Cancer; and as the Earth moves along the arc from Capricorn to Aries, the Sun will appear to move along the arc from Cancer to Libra, and in short to run through the zodiac in the order of the signs over the course of a year. And so this first premise alone accounts, without dispute, for the Sun's apparent annual motion along the ecliptic.
Now, coming to the other motion — the Earth's daily turning on itself — we have to fix its poles and its axis. This axis is to be understood as not standing upright at right angles to the plane of the ecliptic — that is, not parallel to the axis of the great orb — but leaning away from the right angle by about 23 and a half degrees, with its north pole tilted toward the axis of the great orb, while the Earth's center sits at the solstice point of Capricorn. Taking the terrestrial globe, then, to have its center at the point Capricorn, we'll mark its poles and its axis AB, tilted 23 and a half degrees from the perpendicular over the diameter Capricorn–Cancer, so that the angle at A over Capricorn–Cancer comes to be the complement of a quadrant, that is, 66 and a half degrees; and this tilt is to be understood as unchanging. The upper pole A we'll take to be the north, and the other, B, the south. Now imagine the Earth turning on itself about the axis AB in twenty-four hours, again from west to east: then every point marked on its surface traces circles parallel to one another. In this first position of the Earth, we'll mark the greatest of them, CD, and the two that lie 23 and a half degrees from it — EF above and GN below — and the two outermost, IK and LM, lying the same distance from the poles A and B. And just as we've marked these five, so we can imagine countless others, parallel to these, traced by the countless points of the Earth's surface. Now imagine the Earth, by the annual motion of its center, carried into the other places already marked, but passing through them under this law: that its own axis AB not only never changes its tilt with respect to the plane of the ecliptic, but also never changes its direction at all, so that, always keeping parallel to itself, it points continually toward the same part of the universe — of the firmament, we might say. If we imagine it extended that far, its uppermost tip would trace a circle parallel and equal to the great orb Libra–Capricorn–Aries–Cancer, like the upper base of a cylinder described by the axis itself in the annual motion over the lower base Libra–Capricorn–Aries–Cancer. So, given this unchanging tilt, we'll draw these other three figures about the centers Aries, Cancer, and Libra, alike in every respect to the first one drawn about the center Capricorn.
Now let's look at the first figure of the Earth. In it, since the axis AB leans 23 and a half degrees from the perpendicular over the diameter Capricorn–Cancer, toward the Sun O, and since the arc AI is likewise 23 and a half degrees, the Sun's light will illuminate the hemisphere of the terrestrial globe turned toward the Sun (of which we see half here), divided from the dark part by the boundary of the light, IM. By this boundary the parallel CD, being a great circle, is divided into equal parts, but all the others into unequal parts, since the boundary of the light IM does not pass through their poles A and B. The parallel IK, together with all those drawn inside it and nearer the pole A, will remain wholly in the lit part; while, on the other side, the opposite ones toward the pole B, contained within the parallel LM, will remain in the dark. Moreover, since arc AI equals arc FD, and arc AF is shared between them, the two arcs IKF and AFD will be equal, each of them a quadrant. And because the whole arc IFM is a semicircle, the arc MF will be a quadrant, equal to the other, FKI. And so the Sun O will, in this state of the Earth, be directly overhead for anyone at the point F. But by the daily rotation about the fixed axis AB, all the points of the parallel EF pass through this same point F; and so on that day the Sun at noon will be directly overhead for everyone living on the parallel EF, and in its apparent motion it will seem to them to trace the circle we call the Tropic of Cancer. But to those living on all the parallels that lie above EF, toward the north pole A, the Sun sinks from their overhead point toward the south; and, on the other hand, to everyone living on the parallels below EF, toward the equinoctial CD and the south pole B, the noon Sun stands higher than their overhead point, toward the north pole A. It can be seen, next, how of all the parallels only the greatest, CD, is cut into equal parts by the boundary of the light IM, while the others, both below and above that greatest circle, are all cut into unequal parts. And of the upper ones, the daytime arcs — those of the part of the Earth's surface lit by the Sun — are larger than the nighttime arcs, which remain in the dark; and the opposite happens with the rest, which lie below the greatest circle CD toward the pole B, whose daytime arcs are smaller than their nighttime arcs. It can also be plainly seen that the differences between these arcs keep growing as the parallels come nearer the poles, until the parallel IK stays entirely in the lit part, and its inhabitants have a day of twenty-four hours with no night; while, on the contrary, the parallel LM, staying entirely in the dark, has a night of twenty-four hours with no day.
Now let's come to the third figure of the Earth, set with its center at the point Cancer, from which the Sun appears to be at the first point of Capricorn. It is at once plain that, because the axis AB has not changed its tilt but has kept parallel to itself, the aspect and situation of the Earth are exactly the same as in the first figure — except that the hemisphere lit by the Sun in the first is now in the dark, and the one that was dark in the first position is now lit. So what happened before about the differences between days and nights — about which were longer or shorter — now happens in reverse. First we see that where, in the first figure, the circle IK was wholly in the light, it is now wholly in the dark, and the opposite circle LM, which before was wholly dark, is now wholly in the light. On the parallels between the greatest circle CD and the pole A, the daytime arcs are now smaller than the nighttime ones, where before it was the reverse; and likewise on the others toward the pole B, the daytime arcs are now larger than the nighttime ones, the opposite of what happened in the other state of the Earth. Now we see the Sun standing directly overhead for the inhabitants of the tropic GN, and sunk toward the south for those on the parallel EF by the whole arc ECG, that is, 47 degrees — in short, it has passed from one tropic to the other, crossing the equinoctial, rising and sinking on the meridian through that span of 47 degrees. And all this change comes not from the Earth's tilting or rising, but on the contrary from its never tilting or rising at all — in short, from its keeping always the same posture with respect to the universe, merely circling the Sun, which sits in the middle of the very plane along which the Earth moves round it in a circle by the annual motion. And here we should note a marvelous thing: that just as the Earth's keeping its axis pointed in the same direction toward the universe — toward the highest sphere of the fixed stars, we might say — makes the Sun appear to us to rise and sink through so great a span, namely 47 degrees, while the fixed stars neither rise nor sink at all, so, on the contrary, if that same axis of the Earth kept continually the same tilt toward the Sun — toward the axis of the zodiac, we might say — no change would appear in the Sun as to its rising and sinking, so that the inhabitants of any given place would always have the same differences of days and nights and the same arrangement of seasons — some always winter, others always summer, others always spring, and so on — but, on the other hand, a very great change would appear in the fixed stars as to their rising and sinking for us, amounting to those same 47 degrees. To understand this, let's go back and consider the Earth's state in the first figure, where we see the axis AB, with its upper pole A, tilting toward the Sun. But in the third figure, that same axis, having kept the same direction toward the highest sphere by staying parallel to itself, no longer tilts toward the Sun with its upper pole A, but on the contrary has swung 47 degrees away from its first state and tilts toward the opposite side. So, to restore the same tilt of that pole A toward the Sun, we'd have to carry the terrestrial globe around the circumference ACBD, shifting it those same 47 degrees toward E; and by that many degrees any fixed star at all, observed on the meridian, would appear to have risen or sunk.
Now let's come to the explanation of what remains, and consider the Earth set in the fourth figure, that is, with its center at the first point of Libra, so that the Sun will appear at the beginning of Aries. In the first figure the Earth's axis is understood to lean over the diameter Capricorn–Cancer, and so to lie in the very plane that, cutting the plane of the great orb along the line Capricorn–Cancer, stands upright and perpendicular to it. Carried into the fourth figure, and kept, as we've always said, parallel to itself, it comes to lie in a plane that is likewise upright to the surface of the great orb and parallel to the plane that cuts that surface at right angles along the diameter Capricorn–Cancer. And so the line running from the Sun's center to the Earth's center — which is the line O–Libra — will be perpendicular to the axis BA. But the same line from the Sun's center to the Earth's center is always perpendicular to the boundary circle of the light as well; therefore this same circle will pass through the poles A and B in the fourth figure, and the axis AB will lie in its plane. But a great circle passing through the poles of the parallels divides them all into equal parts; therefore the arcs IK, EF, CD, GN, and LM will all be semicircles, and the lit hemisphere will be the one facing us and the Sun, and the boundary of the light will be that same circle ACBD. With the Earth in this place, it makes an equinox for all its inhabitants. And the same happens in the second figure, where the Earth, having its lit hemisphere toward the Sun, shows us the other, dark one with its nighttime arcs, which are likewise all semicircles; and so here too there is an equinox. And finally, since the line drawn from the Sun's center to the Earth's center is perpendicular to the axis AB — to which the greatest of the parallel circles, CD, is likewise upright — that same line O–Libra will necessarily pass through the very plane of the parallel CD, cutting its circumference at the midpoint of the daytime arc CD; and so the Sun will be directly overhead for whoever is found at that point of cutting. But carried by the Earth's daily turning, all the inhabitants of that parallel pass through it; therefore all of them, on that day, will have the noon Sun over their overhead point, while meanwhile, to everyone living on the Earth, the Sun will appear to trace the greatest parallel, called the equinoctial. Furthermore, since with the Earth at either solstice point one of the polar circles IK, LM stays wholly in the light and the other wholly in the dark, but when the Earth is at the equinox points half of each of those polar circles is found in the light and the rest in the dark, it shouldn't be hard to understand how, as the Earth passes, say, from Cancer (where the parallel IK is wholly in the dark) into Leo, a part of the parallel IK toward the point I begins to enter the light, and the boundary of the light IM begins to draw back toward the poles A and B, cutting the circle ACBD no longer at I and M, but at two other points falling between the ends I, A and M, B of the arcs IA and MB — so that the inhabitants of the circle IK begin to enjoy daylight, and those of the circle LM begin to feel the night. And there you have it: with two utterly simple motions, taking place in times proportioned to their sizes and not contrary to one another — indeed made, like all the other motions of the moving bodies of the world, from west to east — assigned to the terrestrial globe, we have given adequate reasons for all those same appearances. To save them by keeping the Earth still, one is forced instead — giving up that symmetry we see between the speeds and the sizes of the moving bodies — to grant one vast sphere, above all the others, an incomprehensible speed, while the other, smaller spheres move very slowly; and further to make that motion run contrary to theirs; and, to pile improbability on improbability, to make all the lower spheres be swept along, against their own tendency, by that topmost one. Here I leave it to your own judgment to decide which is the more likely.
Sagredo: For my part, as far as my own understanding goes, I see no small difference between the simplicity and ease of producing these effects by the means assigned in this new arrangement, and the multiplicity, confusion, and difficulty found in the old, commonly received one. For if the universe were ordered according to that multiplicity, we'd have to strike out of philosophy many axioms commonly accepted by all philosophers: that nature does not multiply things without necessity; that she uses the easiest and simplest means in producing her effects; that she does nothing in vain; and others like them. I confess I've never heard anything more admirable than this, nor can I believe that the human intellect has ever penetrated a subtler line of thought. I don't know how it strikes Signor Simplicio.
Simplicio: These, if I'm to speak my mind freely, seem to me some of those geometric subtleties that Aristotle faults Plato for, when he charges him with drifting away from sound philosophizing through too much study of geometry. And I've known and heard the very greatest Peripatetic philosophers advise their pupils against the study of mathematics, on the grounds that it makes the mind quibbling and unfit for good philosophizing — a program diametrically opposed to Plato's, who would admit no one to philosophy who had not first mastered geometry.
Salviati: I applaud these Peripatetics of yours for their advice to steer their pupils away from the study of geometry, since there's no art better suited for exposing their fallacies. But notice how different they are from the mathematical philosophers, who much prefer dealing with people well versed in the common Peripatetic philosophy than with those who lack that knowledge — for lacking it, they can't compare one doctrine with another. But setting that aside, tell me, please: what extravagances, or overstrained subtleties, make this Copernican arrangement less applaudable to you?
Simplicio: To be honest, I haven't fully grasped it — perhaps because I don't have ready to hand the explanations Ptolemy gives for these same effects: I mean the stations and retrogradations of the planets, their drawing nearer and moving farther off, the lengthening and shortening of the days, the changing of the seasons, and so on. But setting aside the consequences that follow from the first assumptions, I feel real difficulties — and no small ones — in those assumptions themselves; and when the assumptions are knocked down, they bring the whole edifice crashing down with them. Now, since the entire Copernican machine seems to me to rest on shaky foundations — for it leans on the mobility of the Earth — once that is taken away, there's no need to go on to any further disputes. And to take it away, Aristotle's axiom seems to me more than sufficient: that of a simple body only a single simple motion can be natural. Yet here the Earth, a simple body, is assigned three motions — if not four — and very different ones at that. For besides the straight motion downward toward the center, which, being heavy, it can't be denied, they credit it with a circular motion in a great circle around the Sun once a year, and with a spin on its own axis every twenty-four hours; and then — the most outlandish of all, and perhaps that's why you passed over it in silence — yet another turning about its own center, opposite to the first, the twenty-four-hour one, and completed once a year. To this my mind feels the very greatest resistance.
Salviati: As for the downward motion, we've already settled that it belongs in no way to the terrestrial globe as a whole, which has never moved with such a motion and never will; it belongs (if it belongs to anything) to the parts, as they rejoin their whole. As for the annual and the daily motions, since these both run the same way, they're perfectly compatible — just as, if we let a ball roll down a sloping surface, it will, in coming down of its own accord, also turn on itself. And now for the third motion Copernicus assigns to it, the yearly turn on its own axis whose sole purpose is to keep its axis tilted and pointing toward the same region of the firmament — here I'll tell you something well worth the greatest consideration. Namely, that so far from there being any resistance or difficulty in it (even though it runs contrary to the other yearly motion), this turn belongs, most naturally and without any moving cause at all, to any body whatsoever that is suspended and balanced: for if such a body is carried around the circumference of a circle, it immediately, and all by itself, takes on a turning about its own center, contrary to the one that carries it around, and of just such a speed that both complete one revolution in precisely the same time. You can see this remarkable experiment — and how neatly it fits our case — by putting a ball to float in a basin of water and holding the basin in your hands: if you turn yourself around on the soles of your feet, you'll see the ball at once begin to turn on itself with a motion contrary to the basin's, and finish its revolution just when the basin finishes its own. Now, what is the Earth but a globe hung and balanced in thin, yielding air, which, carried around once a year along the circumference of a great circle, must surely take on — with no other mover — a yearly turning about its own center, contrary to that other, likewise yearly, motion? You'll see this effect. But if you then look more carefully, you'll realize it isn't a real thing at all, but a mere appearance; and what looks to you like a turning-on-itself is in fact a not-moving, a keeping of the whole utterly unchanged with respect to everything outside you and the basin that stays still. For if you mark some spot on that ball and note which part of the wall of the room you're in — or of the countryside, or of the sky — it faces, you'll see that spot, as the basin and you turn, keep facing that same part the whole time; but compared with the basin and with yourself, which are the ones moving, it will certainly appear to change direction, and with a motion contrary to yours and the basin's it will seem to seek out every point along the basin's circuit. So that it's truer to say that you and the basin turn around the motionless ball than that the ball turns inside the basin. In just this way the Earth, hung and balanced on the circumference of the great orb, and set so that one of its marks — say, its north pole — faces toward some star or other region of the firmament, keeps itself always pointed toward that same region, even as it's carried by the annual motion around the circumference of that great orb. This alone is enough to make the wonder cease and to remove every difficulty. But what will Simplicio say if, to this needing-no-cooperating-cause, we add a marvelous power built into the terrestrial globe itself — a power of facing, with certain fixed parts of it, toward certain fixed parts of the firmament? I'm speaking of the magnetic power, shared out most constantly by every last piece of lodestone. And if every tiniest particle of that stone has such a power in it, who could doubt that the same power resides, on a far grander scale, in this whole earthly globe, which abounds in such material — and that perhaps the globe itself, in its inner and primary substance, is nothing but one immense mass of lodestone?
Simplicio: So you're one of those who subscribe to the magnetic philosophy of William Gilbert?
Salviati: I certainly am, and I believe I have as my companions everyone who has read his book with attention and checked his experiments for themselves. Nor would I give up hope that what happened to me in this matter might happen to you as well — provided a curiosity like mine, and a recognition that endless things in nature remain unknown to human minds, were to free you from bondage to this or that particular writer on natural things, loosen the reins on your reasoning, and soften the stubbornness and reluctance of your judgment, so that it wouldn't refuse, now and then, to lend an ear to voices it had never heard before. But — if I may use the word — the faint-heartedness of ordinary minds has reached such a point that they not only blindly give away, indeed pay as tribute, their own assent to everything they find written by those authors whom their teachers held up to them in the first infancy of their studies, but they refuse even to listen to — let alone examine — any new proposition or problem whatsoever, though it has not only never been refuted but never so much as examined or considered by their authors. One such question is precisely this: to investigate what is the true, proper, primary, inner, and general matter and substance of this earthly globe of ours. And although it never crossed the mind of Aristotle, or of anyone before Gilbert, to ask whether it might be lodestone — much less did Aristotle or anyone else ever refute such an opinion — nonetheless I've run into plenty of people who, at the very first mention of it, like a horse shying at a shadow, have shrunk back and dodged discussing it, dismissing the idea as an empty fantasy, indeed as sheer madness. And perhaps Gilbert's book would never have come into my hands if a Peripatetic philosopher of great reputation hadn't made me a present of it — to keep his own library safe from the contagion, I imagine.
Simplicio: I, who freely admit I've been one of these ordinary minds — and only in these last few days, since I was granted leave to take part in your discussions, do I recognize that I've stepped a little off the well-worn, popular roads — still don't feel myself so far raised up that the roughness of this new and fantastic opinion doesn't strike me as very hard and difficult to get over.
Salviati: If what Gilbert writes is true, then it isn't an opinion but a subject of science; it isn't something new but as old as the Earth itself; and (being true) it can't be harsh or hard, but smooth and perfectly easy. And I, whenever you please, will let you feel with your own hands how you frighten yourself with your own shadow, recoiling in horror from something that holds nothing dreadful in it at all — like a small child afraid of the witches' sabbath, knowing nothing of it but the name, which, apart from the name, is nothing.
Simplicio: I'll be glad to be enlightened and drawn out of my error.
Salviati: Then answer the questions I'll put to you. And first, tell me whether you believe that this globe of ours, which we live on and call Earth, consists of one single, simple material, or is rather a mixture of materials different from one another.
Simplicio: I see it as made up of very different substances and bodies. First of all, as to its largest components, I see water and earth, utterly unlike each other.
Salviati: Let's set the seas and the other waters aside for now and consider the solid parts. Tell me: do they seem to you all one and the same thing, or rather different things?
Simplicio: As to appearance, I see them as different. There are vast plains of barren sand, and others of rich, fruitful soil; there are countless mountains, sterile and rugged, full of hard rocks and stones of the most varied kinds — porphyry, alabaster, jasper, and a thousand thousand other sorts of marble; there are the enormous mines of metals of so many species; and, in short, so many different materials that a whole day wouldn't be enough merely to count them.
Salviati: Now, of all these different materials, do you believe that equal portions of each go into making up this great mass? Or that among them all there's one part that far surpasses the rest and is, as it were, the chief matter and substance of the vast bulk?
Simplicio: I believe the stones, marbles, metals, gems, and all the other varied materials are really like jewels and outward, surface ornaments of the primary globe, which in bulk I think immeasurably exceeds all these other things.
Salviati: And this chief, vast bulk — of which the things you've named are, so to speak, mere outgrowths and ornaments — what material do you believe it's made of?
Simplicio: I think it's the simple, or less impure, element of earth.
Salviati: But what do you mean by earth? Perhaps this stuff that's spread over the fields, that's broken up with spades and plows, where the grain is sown and the fruit trees planted, where great forests spring up of their own accord, and which, in short, is the dwelling place of all the animals and the womb of all the plants?
Simplicio: That, I'd say, is the primary substance of this globe of ours.
Salviati: Now that doesn't seem to me well said. For this earth that's broken up, sown, and made fruitful is one part — and a very thin one — of the globe's surface, going down only a short way compared with the distance to the center. And experience shows us that you don't dig far down before you come upon materials quite different from this outer rind: firmer ones, no good for growing plants. Besides, the innermost parts, pressed as they are by the enormous weights bearing down on them from above, must in all likelihood be packed together and as hard as the hardest crag. Add to this that fruitfulness would have been given in vain to materials that were never going to bear fruit anyway, but only to lie buried forever in the deep and gloomy abysses of the Earth.
Simplicio: And who assures us that the innermost parts, near the center, are barren? Perhaps they too have their own products — things unknown to us.
Salviati: You, as well as anyone, could be certain of this — since you can readily grasp that if the integral bodies of the universe are produced solely for the benefit of the human race, then this one above all the rest must be destined for the sole conveniences of us who live on it. But what benefit could we ever draw from materials so hidden and remote from us that we'll never be able to make any use of them? So the inner substance of this globe of ours can't be a crumbling, loose, incoherent material like this surface stuff we call earth; it has to be a body extremely dense and solid — in short, a rock of the hardest kind. And if it must be such, what reason should make you any more reluctant to believe it's lodestone than porphyry, or jasper, or some other hard marble? Perhaps if Gilbert had written that this globe is made inside of grey freestone, or of chalcedony, the paradox would have struck you as less outrageous?
Simplicio: That the inner parts of this globe are more compressed, and therefore more packed and solid — and more and more so the deeper down they lie — I grant, and so does Aristotle. But that they degenerate, and are anything other than earth of the same sort as this surface earth, I hear nothing that forces me to grant.
Salviati: I haven't taken up this discussion in order to prove to you demonstratively that the primary and real substance of this globe of ours is lodestone, but only to show you that there's no reason to be any more reluctant to grant that it's lodestone than that it's some other material. And you, if you'll think it over carefully, will find it not at all improbable that a single, bare, arbitrary name has moved people to believe it's made of earth. And that name is this: from the start we've commonly used the word earth to mean both the material that's plowed and sown and to name this whole globe of ours. If its name had instead been taken from stone — as it could just as well have been, no less than from earth — then to say that its primary substance was stone would surely have met with no reluctance or contradiction from anyone. And this is all the more likely because I hold it for certain that, if you could strip the bark off this great globe — peeling away a layer a thousand or two thousand arm-lengths thick — and then separate the stones from the earth, the heap of rock would be far, far greater than the heap of fertile soil. As for the arguments that would prove conclusively, in fact, that this globe of ours is lodestone, I've offered you none, nor is this the time to offer them — all the more since at your leisure you can find them in Gilbert. Only, to fire you up to read him, I'll lay out for you with a little comparison of my own the method he follows in his philosophizing. I know you're perfectly aware how much the knowledge of a thing's properties contributes to the investigation of its substance and essence. So I want you to take pains to inform yourself well of the many properties that are found in lodestone alone, and in no other stone or body: as, for instance, its attracting iron; its conferring on iron, merely by its presence, that same power; and likewise its imparting to iron the property of facing toward the poles, just as it holds that property in itself. And beyond this, see for yourself, by trial, how there resides in it the power to give the magnetic needle not only the settling of itself along a meridian toward the poles with a horizontal motion (a property known long ago), but a newly observed property of dipping — for when it's balanced beneath a meridian marked out on a little sphere of lodestone, it dips, I say, to definite degrees, more or less, according as the needle is held nearer to or farther from the pole; until, right over the pole, it plants itself upright and perpendicular, whereas over the middle parts it lies parallel to the axis. What's more, take pains to test how, since the power of attracting iron is far more vigorous toward the poles than around the middle parts, that force is markedly stronger in one pole than in the other — and this in every piece of lodestone, the stronger pole of which is the one that faces south. Note next that in a small lodestone this southern pole, the more powerful of the two, becomes the weaker whenever it has to hold up iron in the presence of the north pole of another, much larger lodestone. And, not to make a long speech of it, satisfy yourself by experiment of these and many other properties described by Gilbert, all of which so belong to lodestone alone that not one of them attaches to any other material. Now tell me, Simplicio: suppose you were offered a thousand pieces of different materials, each of them covered and wrapped in a cloth that hid it, and you were asked to guess, without uncovering them, the material of each from outward signs; and suppose that, in trying, you came upon one that plainly showed all the properties you already knew reside in lodestone and in no other material — what would you judge the essence of that body to be? Would you say it might be a piece of ebony, or alabaster, or tin?
Simplicio: I'd say, without the slightest hesitation, that it was a piece of lodestone.
Salviati: Then say so outright: under this covering and rind of earth, of stones, of metals, of water, and so on, there hides a great lodestone — since, for anyone who takes the trouble to observe them, all those very same properties are found in it that are seen to belong to a genuine, bare globe of lodestone. Why, if you saw nothing but that business of the dipping needle, which, carried around the Earth, tips more and more as it nears the north pole and dips less toward the equinoctial, under which it finally comes into balance — that alone ought to persuade the most stubborn judgment. I say nothing of that other marvelous effect plainly seen in every piece of lodestone: that for us, dwellers in the northern hemisphere, the southern pole of the lodestone is the stronger of the two, and the difference shows up the greater the farther one moves from the equinoctial; while under the equinoctial both parts are of equal force, but notably weaker; and in the southern regions, far from the equinoctial, nature switches, and the part that was the weaker for us gains the upper hand over the other. And all this squares with what we see a little piece of lodestone do in the presence of a large one, whose power, prevailing over the smaller, makes it obey; and depending on whether it's held on this or that side of the big stone's equinoctial, it undergoes the very same changes I've described every lodestone undergoing when carried this side or that of the Earth's equinoctial.
Sagredo: I was persuaded at my first reading of Gilbert's book; and, having come across a piece of the most excellent lodestone, I spent a long time making many observations, all of them worthy of the utmost wonder. But above all I find astounding the one about increasing its power to hold up iron so enormously by arming it in the way that same author teaches. By arming that piece of mine, I multiplied its force eightfold: whereas unarmed it could barely hold up nine ounces of iron, armed it held more than six pounds. And perhaps you'll have seen this very piece in the Gallery of your Most Serene Grand Duke (to whom I gave it up), holding up two little iron anchors.
Salviati: I saw it many times, and with great wonder — until an even greater astonishment was handed to me by a small piece that our friend the Academician has in his keeping. It weighs no more than six ounces, and unarmed it barely holds up two ounces; but armed — fitted with an iron cap — it holds up a hundred and sixty, so that it comes to support eighty times more armed than unarmed, and to bear a weight twenty-six times greater than its own. That is a marvel far greater than any Gilbert had been able to meet with, for he writes that he could never find a lodestone able to hold up four times its own weight.
Sagredo: This stone seems to me to open up a vast field for the human mind to philosophize in. I have turned it over in my own thoughts a thousand times — how can it be that it gives to the iron that arms it a force so much greater than its own? — and in the end I find nothing that sets me at rest; nor do I get much sense out of what Gilbert writes on this particular point. I don't know whether the same happens to you.
Salviati: I praise, admire, and envy this author to the highest degree, for having had so stupendous a conception fall into his mind about a thing that countless sublime intellects had handled, and none had noticed. He seems to me worthy of the greatest praise, too, for the many new and true observations he made — to the shame of so many lying and empty authors who write not only what they know, but everything they hear from the foolish crowd, without troubling to make sure of it by experiment, perhaps so as not to shrink their books. What I would have wished in Gilbert is that he had been a somewhat greater mathematician, and in particular well grounded in geometry; for the practice of it would have made him less ready to accept as conclusive demonstrations the reasons he offers as the true causes of the true conclusions he himself observed. Those reasons (speaking freely) do not knot and bind with the force that must belong, beyond all doubt, to reasons drawn from natural, necessary, and eternal conclusions. And I don't doubt that as time goes on this new science will be perfected, with further new observations, and still more with true and necessary demonstrations. Yet that should take nothing from the glory of the first observer. I esteem no less — indeed I admire far more — the first inventor of the lyre (even though one must suppose the instrument was very crudely built, and more crudely played) than the hundred other artists who in later centuries brought that craft to great refinement. And it seems to me quite reasonable that antiquity numbered the first inventors of the noble arts among the gods, since we see that the common run of human minds has so little curiosity, and cares so little for rare and refined things, that even when they see and hear them exquisitely practiced by masters, they are not moved to want to learn them. Now think whether brains of that sort would ever have set themselves to investigate the making of the lyre, or the invention of music, enticed by the whistling of the dry sinews of a tortoise, or the strokes of four hammers. To fasten upon great inventions, spurred by the tiniest beginnings, and to judge that beneath a first, childish appearance marvelous arts may lie hidden — that is not for ordinary minds; those are the conceptions and thoughts of superhuman spirits. Now, to answer your question: I say that I too have long thought about what the cause might be of this tenacious and powerful joining that we see form between the one iron that arms the lodestone and the other that clings to it. And first I made sure that the virtue and force of the stone is not increased in the least by being armed, since it neither attracts from any greater distance, nor holds up any more firmly an iron between which and the armature there is placed a very thin paper — down to a single leaf of beaten gold. On the contrary, with such a thing between, it holds more iron bare than armed. So there is no change in the virtue, and yet there is a new result in the effect; and since a new effect must have a new cause, I looked for what novelty is introduced in the act of holding with the armature, and could find no other change than in the different touching: for where before iron touched lodestone, now iron touches iron. So one must necessarily conclude that the different touchings are the cause of the difference in the effects. And this difference between the contacts, I can see no way for it to come from anything other than this: that the substance of iron is of parts finer, purer, and more tightly packed than those of the lodestone, which are coarser, less pure, and looser. From which it follows that the surfaces of the two irons that are to touch, so long as they are exquisitely flattened, polished, and burnished, join together so exactly that all the infinite points of the one meet the infinite points of the other, so that the filaments (so to speak) linking the two irons are far more numerous than those linking lodestone to iron — because the substance of the lodestone is more porous and less pure, which means that not all the points and filaments of the iron's surface find, in the surface of the lodestone, counterparts to unite with. And that the substance of iron (especially the well-purified kind, like the finest steel) is of parts far denser, finer, and purer than the matter of the lodestone, is shown by the fact that its edge can be brought to an extreme thinness, like the edge of a razor — something the edge of a piece of lodestone could never come near. The impurity of the lodestone, and its being mixed with other kinds of stone, is first seen plainly in the color of certain little specks, mostly whitish; and then in this: present to it a needle hanging from a thread, and over such little stones the needle cannot settle, but, drawn by the parts surrounding them, seems to flee them and jump onto the lodestone next to them. And since some of these foreign parts are, by their size, quite visible, we may believe that others in great abundance — too small to be seen — are scattered through the whole mass. What I say (namely, that the multitude of touchings made between iron and iron is the cause of so firm a joining) is confirmed by an experiment. It is this: if we present the sharp point of a needle to the armature of the lodestone, it will attach no more strongly than to the same lodestone bare — which can come from nothing but the two touchings being equal, that is, both being of a single point. But there's more. Take a needle and lay it on the lodestone so that one of its ends sticks out a little, and present a nail to that end: the needle will at once attach to it, so that as you draw the nail back, the needle is left hanging, held by its two ends to the lodestone and to the iron; and drawing the nail still further will pull the needle off the lodestone — provided the eye of the needle is the end joined to the nail, and the point is the end on the lodestone. But if the eye is toward the lodestone, then when you take the nail away, the needle stays stuck to the lodestone. And this (in my judgment) for no other reason than that, the needle being thicker toward the eye, it touches at many more points than the very sharp point does.
Sagredo: The whole argument has seemed to me very conclusive, and these experiments with the needle make it little inferior to a mathematical demonstration. And I frankly confess that in all of magnetic philosophy I have neither heard nor read anything else that accounts, with like force, for any other of its many marvelous behaviors — of which, if we had the causes explained with such clarity, I don't know what sweeter food our intellect could desire.
Salviati: In investigating the reasons for conclusions unknown to us, one must have the luck to steer the argument, from the very start, onto the road of truth. When a man sets out along that road, it readily happens that he meets one true proposition after another — known to be true whether by reasoning or by experience — and from their certainty the truth of his own gains force and evidence. That is exactly what happened to me with the present problem. Wishing to make sure, by some further check, whether the reason I had worked out was true — namely, that the substance of the lodestone is really far less continuous than that of iron or steel — I had one face of that very piece of lodestone that was once yours flattened by the craftsmen who work in the Gallery of the Grand Duke, my lord, and then polished and burnished as much as possible. And there, to my satisfaction, I touched with my hand what I was after. For there came to light many specks of a color different from the rest, but as bright and lustrous as any dense hard stone; the rest of the field was smooth, but only to the touch, being not at all shiny — rather, as if clouded by a haze. That dull part was the substance of the lodestone; the bright part, of other stones mixed into it — as one could plainly tell by bringing the flattened face over iron filings, which in great abundance jumped to the lodestone, but not a single grain to those specks. And the specks were many: some as large as a quarter of a fingernail, others somewhat smaller, very many quite small, and the barely visible ones almost past counting. So I was assured that my idea had been perfectly true, when I first judged that the substance of the lodestone must be not solid and closed, but porous — or better, spongy — yet with this difference: where a sponge holds air or water in its cavities and cells, the lodestone has its own filled with very hard, heavy stone, as the exquisite luster they take on shows us. And so, as I said at the start, when you apply the surface of the iron to the surface of the lodestone, the least particles of the iron — though more continuous, perhaps, than those of any other body (as its taking a finer polish than any other material shows) — meet pure lodestone not all of them, but few; and the contacts being few, the attachment is weak. But because the armature of the lodestone, besides touching a great part of the stone's surface, also clothes itself in the virtue of the neighboring parts even where they are not touched, then — that face of it being exactly flattened, and the matching face of the iron to be held being likewise well flattened — the touching is made of countless least particles, if not perhaps of the infinite points of both surfaces, so that the attachment turns out extremely strong. This point, of flattening the surfaces of the irons that are to touch, Gilbert did not notice; on the contrary, he makes his irons rounded, so that their contact is small, and the result is that far weaker is the grip with which those irons hold together.
Sagredo: As I said just now, the reason you have assigned leaves me hardly less satisfied than if it were a pure geometric demonstration; and since this is a physical problem, I judge that Simplicio too will find himself satisfied, so far as natural science allows — for he knows that in it one must not look for geometric proof.
Simplicio: It truly seems to me that Salviati, with a fine roundabout of words, has explained the cause of this effect so clearly that any middling mind, even one that is no scientist, could take it in. But we, keeping within the terms of the discipline, trace the cause of these and similar natural effects to sympathy, which is a certain agreement and mutual appetite arising between things that are alike in quality — just as, on the other hand, that hatred and enmity by which other things naturally flee one another and hold each other in horror, we call antipathy.
Sagredo: And so, with these two names, one manages to account for a great number of the happenings and effects that we see, not without wonder, produced in nature. But this way of philosophizing seems to me to have great sympathy with a certain manner of painting a friend of mine used to practice. On the canvas he would write in chalk: "Here I want the fountain to be, with Diana and her nymphs; here, some greyhounds; in this corner I want a hunter, with the head of a stag; the rest, countryside, wood, and little hills." The rest he then left to the painter to fill in with colors — and so he convinced himself that he had himself painted the tale of Actaeon, having put in nothing of his own but the names. But where have we brought ourselves, with so long a digression, against the rules we had already laid down? I've all but forgotten what the matter was that we were treating when we strayed into this magnetic talk — and yet I did have some point or other in mind to make about it.
Salviati: We were on the verge of demonstrating that the third motion Copernicus assigns to the Earth is not really a motion at all, but a rest — a keeping of itself unchangeably aimed, with its fixed parts, toward the same fixed parts of the universe; that is, a perpetual keeping of the axis of its daily rotation parallel to itself and turned toward certain fixed stars. This most constant state, we were saying, belongs naturally to every body balanced and suspended in a fluid, yielding medium, which, though carried around, does not change its direction with respect to external things, but only seems to turn upon itself with respect to whatever is carrying it, and to the vessel in which it is carried. Then, to this simple and natural behavior, we added the magnetic virtue, by which the terrestrial globe could all the more firmly hold itself unchangeable, and so on.
Sagredo: Now it all comes back to me. What was passing through my mind then, and what I wanted to bring out, was a certain thought about the difficulty and objection Simplicio had raised against the Earth's mobility — the one drawn from the multiplicity of motions, which cannot be attributed to a simple body, since, in Aristotle's teaching, only one single, simple motion can be natural to it. And what I wanted to put forward was precisely the lodestone, to which we plainly see three motions naturally belong. The first, toward the center of the Earth, as a heavy body. The second is the horizontal circular motion by which it restores and keeps its axis toward fixed parts of the universe. The third is this one, newly discovered by Gilbert: the tilting of its axis — lying in the plane of a meridian — toward the surface of the Earth, and this more or less according to how far it is from the equinoctial, beneath which its axis stays parallel to the Earth's axis. Besides these three, it is perhaps not unlikely that it may have a fourth: turning about its own axis, whenever it were balanced and suspended in air or some other fluid, yielding medium, so that all external and accidental hindrances were taken away — and to this thought Gilbert himself seems to give his applause. So you see, Simplicio, how shaky Aristotle's axiom is left.
Simplicio: This not only fails to wound the maxim, it isn't even aimed its way — since he speaks of a simple body and of what may naturally belong to it, while you bring up what happens to a mixed one. Nor are you saying anything new within Aristotle's teaching, since he too grants a compound motion to mixed bodies, and so on.
Sagredo: Hold on a moment, Simplicio, and answer the questions I'll put to you. You say the lodestone is not a simple body, but a mixed one: now I ask you, which are the simple bodies that mix together to compose the lodestone?
Simplicio: I couldn't tell you the ingredients, nor the exact proportions, but it's enough that they are elementary bodies.
Sagredo: That's enough for me as well. And of these simple, elementary bodies, which are their natural motions?
Simplicio: They are the two simple straight ones, sursum et deorsum.
Sagredo: Tell me next: do you believe that the motion which will remain natural to such a mixed body must be one that can result from compounding the two simple natural motions of the simple component bodies — or that it might also be a motion impossible to compound out of those?
Simplicio: I believe it will move with the motion resulting from the compounding of the motions of the simple component bodies, and that it is impossible for it to move with a motion that cannot be compounded from these.
Sagredo: But, Simplicio, with two simple straight motions you will never compound a circular motion — and circular are the two or three different motions the lodestone has. See, then, into what tight corners ill-founded principles lead us — or, better put, badly drawn conclusions from good principles. For now you are forced to say that the lodestone is a mixture composed of elementary and of celestial substances, if you want to maintain that straight motion belongs to the elements alone, and circular motion to the celestial bodies. So, if you want to philosophize more safely, say instead that of the integral bodies of the universe, those that are by nature mobile all move in circles, and that the lodestone, therefore, being part of the true, primary, integral substance of our globe, keeps that same nature. And notice this fallacy of yours: you call the lodestone a mixed body, and the terrestrial globe a simple one — when the globe is plainly a hundred thousand times more composite, since, besides containing a thousand and one materials utterly different from one another, it contains a great quantity of this very thing you call mixed, I mean the lodestone. This seems to me the same as if someone called bread a mixed body, and called simple that olla podrida — that Spanish hodgepodge — into which there also goes no small amount of bread, along with a hundred different sundries. A marvelous thing indeed seems to me, among others, this business of the Peripatetics. They grant (nor can they deny it) that our terrestrial globe is in fact a compound of endless different materials; they grant, next, that the motion of compound bodies must be compound; the motions that can be compounded are the straight and the circular, since the two straight ones, being contrary, are incompatible with each other; they affirm that the pure element of earth is nowhere to be found; they confess that it has never moved with any local motion. And then they want to place in nature that body which is not to be found, and make it move with a motion it has never performed and never will; while to the body that is, and always has been, they deny the very motion they first granted must naturally belong to it.
Salviati: Please, Sagredo, let's not wear ourselves out any further over these particulars — the more so since you know our aim has never been to settle firmly, or to accept as true, this or that opinion, but only to lay out, for our own enjoyment, the reasons and answers that can be brought forward on either side. And Simplicio gives this reply to ransom his Peripatetics. So let's leave the verdict hanging, and the decision in the hands of those who know more than we do. And since it seems to me that we've discoursed at quite enough length, over these three days, about the system of the universe, it will be time now to come to the greatest matter of all, the one that first set our conversations going: I mean the ebb and flow of the sea, whose cause, it seems, may quite probably be traced to the motions of the Earth. But that, if you please, we'll save for the following day. Meanwhile, so as not to let it slip my mind, let me tell you a certain point on which I would not have wished Gilbert to lend an ear — I mean his allowing that if a little sphere of lodestone could be perfectly balanced, it would spin upon itself; for there's no reason why it should. For if the whole terrestrial globe has it by nature to turn about its own center in twenty-four hours, and all its parts must do the same — I mean, turn, together with their whole, about the center of it in twenty-four hours — then they already do so, in effect, while, resting upon the Earth, they go around together with it. To assign them a rotation about their own center would be to give them a second motion, quite different from the first, so that they'd then have two: the turning about their whole's center in twenty-four hours, and the turning about their own. Now this second one is arbitrary, and there is no reason to bring it in. If, when a piece of lodestone is detached from the whole natural mass, it were robbed of following that mass — as it did while joined to it — so that it were left deprived of turning about the universal center of the terrestrial globe, then one might, perhaps, with somewhat more probability, believe that it would take on a new spin about its own particular center. But if it — no less when separated than when joined — still keeps up its first, eternal, natural course, why want to saddle another new one onto it?
Sagredo: I follow you perfectly, and it reminds me of an argument very much like this one in its emptiness, put forward by certain writers of textbooks on the sphere — among them, if I remember rightly, Sacrobosco. To prove that the element of water shapes itself, together with the Earth, into a spherical surface, so that the two of them make up this globe of ours, he writes that we have conclusive proof of it in seeing the tiniest particles of water take on a round shape — as we can see every day in droplets of dew, and on the leaves of many plants. And since, by the well-worn axiom "The same reasoning holds for the whole as for the parts," the parts crave that shape, it must be that the same shape belongs to the whole element. And really it seems to me quite an unseemly thing that men like this don't notice a bit of foolishness that's all too plain to see: they fail to consider that, if their reasoning were sound, it wouldn't just be the tiny drops, but any larger quantity of water whatsoever, once separated from the whole element, that would draw itself up into a ball — which is not at all what we see. What we can see with our senses, and grasp with our minds, is this: the element of water, loving to shape itself into a sphere around the common center of gravity toward which all heavy bodies tend (which is the center of the terrestrial globe), is in this followed by all its parts, just as the axiom says; so that all the surfaces of the seas, of the lakes, of the ponds — in short, of all the bodies of water held in their basins — spread themselves out in a spherical figure, but a sphere whose center is the center of the terrestrial globe, and they do not make little spheres of their own.
Salviati: The error really is childish, and if it were nobody's but Sacrobosco's, I'd forgive it him readily; but having to pardon it in his commentators too, and in other great men, and even in Ptolemy himself, I can't do it without some blush for their reputation. But it's time to take our leave, the hour being late by now — so that we can be here tomorrow, as usual, for the final conclusion of everything we've discussed.
Simplicio: Please, gentlemen, allow me to bring my mind back to some quiet — right now I find it much tossed about by a certain point Salviati has just touched on — so that afterward, once the waves have been smoothed, I can take in your speculations more distinctly; for images don't imprint themselves well on a rippling mirror, as the Latin poet gracefully put it:
. . . nuper me in littore vidi cum placidum ventis staret mare — I lately caught sight of myself at the shore, when the sea lay calm, stilled by the winds.
Salviati: You're quite right — so tell us your doubts.
Simplicio: A moment ago you dispatched, as equally dull-witted, both those who deny the Earth the daily rotation — because they don't find themselves carried off to Persia or Japan by it — and those who oppose the annual motion, out of the repugnance they feel at having to admit that the enormous, ponderous bulk of the terrestrial globe could lift itself up on high and then sink down low, as it would have to do while wheeling around the Sun with that motion. And I — not blushing to be counted among these fools — feel that same repugnance in my own head, at least as to this second point raised against the annual motion; all the more when I see how much resistance is put up against being moved even along a level surface, and I don't mean a mountain but a stone that's only a small chip off some alpine crag. So, not despising objections of this sort, I beg you to resolve them — and not only for my sake, but for others, to whom they seem utterly conclusive; because I find it very hard for anyone, however simple, to recognize and confess his own simplicity, moved by nothing more than hearing himself called simple.
Sagredo: On the contrary — the simpler he is, the more impossible it'll be to persuade him of his failing. And this gives me occasion to reflect that it's worth resolving this objection, and others of the same kind, not only to satisfy Simplicio but for another reason no less important: for you can see that there's no shortage of men, thoroughly versed in the common philosophy and in other sciences, who — for want of astronomy, or of mathematics, or of whatever other discipline it is that sharpens the mind for penetrating the truth — remain persuaded by discourses as empty as these. And so the plight of poor Copernicus seems to me to deserve our pity: he can't be sure that the judging of his doctrines won't happen to fall into the hands of people who, unable to grasp his most subtle reasonings (which are therefore hard to understand), but already persuaded by such empty appearances that they're false, go about preaching them as false and mistaken. So, when such people can't be brought to understand the more abstruse arguments, it's worth taking pains that they at least recognize the emptiness of these others — and from that recognition may come a more measured judgment and condemnation of the doctrine they now hold to be in error. Let me put forward, then, two more objections — but against the daily rotation — which not long ago I heard raised by persons of great learning; and afterward we'll come to the annual motion. The first was this: if it were true that the Sun and the other stars don't rise above the eastern horizon, but rather that the eastern part of the Earth drops down beneath them while they stay put, then within a few hours the mountains lying to the east, tilting downward through the turning of the terrestrial globe, would have to reach such a state that, where a little before you had to walk uphill to reach their ridge, you'd afterward have to go downhill to get up there. The other was this: if the daily motion belonged to the Earth, it would have to be so fast that a man standing at the bottom of a well could see a star directly overhead only for a single instant — able to see it only for that very brief time in which it crosses the 2 or 3 braccia of the Earth's circumference that make up the width of the well. Yet experience shows that the apparent passage of such a star, in crossing the well, takes up quite a long time; which is a necessary proof that the mouth of the well is not moving with anything like the fury the daily turning would require — and consequently that the Earth is standing still.
Simplicio: Of these two arguments, the second really does seem quite conclusive to me; but as for the first, I think I could get myself out of it on my own. For I consider that it comes to the same thing whether the terrestrial globe, turning on its own center, carries a mountain toward the east, or whether — the globe staying still — the mountain were torn up by the roots and dragged across the Earth; and carrying the mountain over the surface of the Earth is, so far as I can see, no different an operation from taking a ship across the surface of the sea. So that, whenever the mountain objection held good, it would follow just the same that, as the ship kept up its voyage and had drawn many degrees away from our ports, we'd have to climb its mast no longer by going up, but by moving along the flat and then even going down — which doesn't happen. Nor have I ever heard any sailor, even among those who've sailed clear around the globe, report any difference in that operation, or in any other task done aboard ship, on account of the vessel's being in one part of the world rather than another.
Salviati: You reason very well. And if it had ever crossed the mind of the author of that objection to consider that his neighboring mountain, set to his east, would — when the terrestrial globe turned — be carried in 2 hours by that motion to the place where, say, Mount Olympus or Mount Carmel now stands, he'd have realized that by his own way of arguing he was forced to believe and confess that, to reach the peak of those mountains, one must de facto go downhill. These are the sort of brains fit to deny the antipodes, on the grounds that you can't walk with your head hanging down and your feet stuck to the ceiling; men who, from true ideas — even ones they understand perfectly — still can't manage to draw the easiest solutions to their own doubts. I mean that they understand perfectly well that to gravitate and to descend is to tend toward the center of the terrestrial globe, and that to rise is to move away from it; and then they get lost when it comes to understanding that our antipodes have no trouble at all supporting themselves and walking, because they do exactly as we do — that is, they keep the soles of their feet toward the center of the Earth and their heads toward the sky.
Sagredo: And yet we know that men of lofty wit in other fields have been dazzled by matters like these; which all the more confirms what I was just saying — that it's good to clear away every objection, even the very weakest. So let's have an answer to those men of the well, too.
Salviati: This second argument does have, on the face of it, a certain something more than merely plausible; and yet I'm firmly convinced that if we could question the very man it occurred to — get him to explain himself better by stating exactly what the effect is that ought to follow, and that he thinks doesn't follow, once the daily turning is granted to be the Earth's — I believe, I say, that he'd get himself just as tangled up in laying out his difficulty and its consequences as he would in thinking his way out of it.
Simplicio: If I'm to tell the truth, I'm quite sure that's how it would go — because I too find myself, right now, in that same confusion. The argument seems to grip, at first apprehension; but on the other hand I see, as if through fog, that if the reasoning were carried through properly, that immense speed of travel we'd have to detect in the star if the motion belonged to the Earth would have to be detected in it just as much — indeed far more — if the motion belonged to the star itself, since it would have to be many thousands of times faster in the star than in the Earth. And on the other hand, having to lose sight of the star for the mere crossing of the well's mouth — which would be 2 or 3 braccia across, while the well, along with the Earth, travels no less than 2,000,000 in an hour — seems as though it would have to be something so momentary that it couldn't even be perceived; and yet from the bottom of that same well the star is seen for quite a long stretch of time. So I find myself wanting to be brought clear on this business.
Salviati: Now I'm confirmed all the more in believing the objection's author was confused, seeing that you too, Simplicio, only shadow forth — and don't really possess — what you're trying to say; which I gather chiefly from your leaving out a distinction that is a most crucial point in this whole matter. So tell me: in performing this experiment — this passage of a star over the mouth of the well, I mean — do you make any difference according to whether the well is deeper or shallower, that is, according to whether the observer is farther from the mouth or nearer to it? Because I haven't heard you make anything of that.
Simplicio: To tell the truth, I hadn't turned my thoughts to it; but your question wakes up my mind, and suggests to me that such a distinction must be absolutely necessary. And I'm already beginning to see that, in fixing the time of that passage, the depth of the well may perhaps make no less difference than its width.
Salviati: Indeed, I rather suspect the width has nothing to do with it — or next to nothing.
Simplicio: And yet it does seem to me that having to cross 10 braccia of width would take ten times as long as the passage of a single braccio; and I'm sure that a little boat 10 braccia long will pass across my line of sight sooner than a galley a hundred long.
Salviati: And still we go on clinging to that inveterate notion — that we don't move except as far as our own legs carry us. What you say, my dear Simplicio, is true when the object you see is the one moving while you stand still to watch it; but if you'll be down in the well when the well and you together are carried along by the Earth's turning, don't you see that neither in an hour, nor in a thousand, nor in all eternity will the mouth of the well pass you by? Whether the Earth is moving or not moving, whatever effect that has on you can't be detected in the mouth of the well, but only in some other object, separate from you, that doesn't share your same condition — of motion, I mean, or of rest.
Simplicio: That's all fine; but granting that I, down in the well, am carried along in company with it by the daily motion, and that the star I'm looking at is standing still — the opening of the well, which alone gives my sight a passage, being no more than three braccia out of the many millions of braccia of the rest of the Earth's surface that blocks my view — how can the time I see the star for be any perceptible fraction of the time it's hidden?
Salviati: And there you fall back into the same mix-up; you really do need someone to help you out of it. It isn't the width of the well, Simplicio, that measures how long the star is in view — for in that case you'd see it forever, since the mouth of the well gives your sight a passage forever. That measure has to be taken instead from the amount of motionless sky that stays visible to you through the opening of the well.
Simplicio: But what's uncovered to me of the sky — isn't it the same fraction of the whole celestial sphere as the mouth of the well is of the whole Earth?
Salviati: I'd like you to answer that for yourself. So tell me: is the mouth of the well always the same portion of the Earth's surface?
Simplicio: Beyond any doubt, always the same.
Salviati: And the part of the sky seen by the man down in the well — is that always the same fraction of the whole celestial sphere?
Simplicio: Now I'm beginning to clear the fog from my mind, and to understand what you hinted at a moment ago — that the depth of the well has a great deal to do with the present business. For there's no doubt that the farther the eye draws back from the mouth of the well, the smaller the part of the sky it will uncover; and that part, in consequence, will be crossed and lost from view all the sooner by the man gazing up at it from the depths of the well.
Salviati: But is there any place in the well from which one would uncover exactly that fraction of the celestial sphere which the mouth of the well is of the Earth's surface?
Simplicio: It seems to me that if the well were sunk all the way to the center of the Earth, then perhaps from there one would uncover a part of the sky that would stand to it as the well does to the Earth. But moving away from the center and rising toward the surface, one keeps uncovering an ever greater part of that sky.
Salviati: And finally, with the eye set in the plane of the well's mouth, one uncovers half the sky, or very little less — to cross which (supposing we were under the equinoctial) would take 12 hours of time.
Sagredo: I can't tell whether your return to our usual discussions really was later than usual, or whether my eagerness to hear Salviati's thoughts on so intriguing a subject only made it seem so. For a good hour I've been posted at the window, watching moment by moment for the gondola I'd sent to fetch you to come into view.
Salviati: I really do think it was your imagination, more than any lateness on our part, that stretched out the time. So as not to stretch it any further, we'd do well to come straight to the point, without more preamble, and show how nature has allowed — whether the matter in rei veritate, in actual fact, stands this way, or whether she is only playing, amusing herself at the expense of our fancies — has allowed, I say, that the very motions long ago assigned to the Earth for every purpose other than accounting for the ebb and flow of the sea should now turn out to serve that cause so exactly, and how, in return, that same ebb and flow shows up to confirm the Earth's mobility. Up to now the evidence for that mobility has been drawn from what appears in the heavens, since among the things that happen here on Earth not one had the power to settle the question either way — as we've examined at length, showing that all the terrestrial happenings by which people commonly hold the Earth to be at rest and the Sun and the firmament in motion must look exactly the same to us whether we grant the Earth its motion and those bodies their rest, or the reverse. The single element of water — being enormously vast, and not fastened and chained to the terrestrial globe the way all its solid parts are, but rather, by its fluidity, left in part its own master and free — is the one thing, among all things below the Moon, in which we can recognize some trace and sign of what the Earth is doing as to motion or rest. I, after examining over and over to myself the effects and occurrences observed in the movements of the waters — some seen, some learned from others — and after reading and hearing the great foolishness that many have put forward as the causes of such things, have felt myself drawn, and not slightly, to admit these two conclusions (granting, of course, the necessary premises): that if the terrestrial globe is motionless, the ebb and flow of the sea cannot come about naturally; and that when the same globe is granted the motions already assigned to it, the sea must be subject to an ebb and flow that matches everything observed in it.
Sagredo: That's a tremendous claim — both in itself and for everything that follows from it. All the more attentively, then, will I listen to your explanation and your proof of it.
Salviati: In questions about nature — and the one we have in hand is one of them — it's our knowledge of the effects that leads us to investigate and discover the causes. Without that knowledge, ours would be a blind man's walk — worse than blind, in fact, since a blind man at least knows where he wants to end up, while we wouldn't even know that. So before anything else we need a knowledge of the effects whose causes we're after. And of those effects, you, Sagredo, must be more fully and more reliably informed than I am. Besides having been born in Venice, and lived there a long time — where the tides are quite remarkable for their size — you've also sailed to Syria, and, being a lively and curious mind, you must have made many observations. Whereas I, who have only been able to observe for a while — and briefly at that — what happens here at this far end of the Adriatic gulf, and in our sea to the south, along the shores of the Tyrrhenian, must for many things rely on other people's reports. And those reports, being mostly not in good agreement, and so quite uncertain, can bring our speculations confusion rather than confirmation. Still, from the ones we can trust — which are also the main ones — I think I can arrive at the true and primary causes. I don't claim to be able to supply all the proper and adequate reasons for effects that might be new to me, ones I therefore couldn't have thought about beforehand. What I'm about to say I offer only as a key that opens the door to a road nobody has ever walked before, in the firm hope that minds more speculative than mine will push on and penetrate much further than I will in this first discovery of mine. And even though, in other seas remote from us, things may happen that don't happen in our Mediterranean, that won't keep the reason and cause I'll give from being true — provided it checks out and fully satisfies the things that occur in our own sea. Because in the end there has to be a single true and primary cause for effects that are of one and the same kind. So I'll tell the story of the effects I know to be real, and I'll assign the cause I believe to be the true one; and you, gentlemen, will add others known to you, beyond mine, and then we'll test whether the cause I've brought forward can satisfy those as well.
So then: there are three periods to be observed in the ebb and flow of sea water. The first and chief one is the great, well-known daily period, by which, at intervals of some hours, the waters rise and fall — and these intervals in the Mediterranean run mostly about six hours each, that is, six hours rising and another six falling. The second period is monthly, and seems to take its origin from the motion of the Moon — not that she introduces any other motions, but only that she alters the size of the ones just mentioned, with a notable difference according to whether she is full, or waning, or at quadrature with the Sun. The third period is yearly, and appears to depend on the Sun, again only altering the daily motions, making them, at the times of the solstices, different in size from what they are at the equinoxes.
We'll speak first of the daily period, as the chief one, on which the Moon and the Sun seem to exert only a secondary action, with their monthly and yearly alterations. Three differences are to be observed in these hourly changes. In some places the waters rise and fall without any forward movement; in others, without rising or falling, they move now toward the east and then run back toward the west; and in still others they vary both in height and in course, as happens here in Venice, where the waters rise as they come in and fall as they go out. This they do at the far ends of those gulfs that stretch from west to east and end in beaches, over which the water, as it rises, has room to spread; whereas if its course were cut off by mountains or by very high banks, there it would rise and fall without forward movement. They run and run back, without changing height, in the middle stretches — as happens most notably in the Strait of Messina, between Scylla and Charybdis, where the currents, because of the narrowness of the channel, are extremely swift. But in the more open seas, and around the islands out in the middle — such as the Balearics, Corsica, Sardinia, Elba, the part of Sicily toward Africa, Malta, Candia, and so on — the changes in height are very small, though the currents are quite notable, and especially so where the sea narrows between the islands, or between them and the mainland.
Now these effects alone, true and certain as they are, seem to me — even if nothing else were seen — quite likely to persuade anyone willing to stay within natural limits to grant the mobility of the Earth. For to hold the basin of the Mediterranean fixed, and yet have the water it contains do what it does, is beyond my imagination — and perhaps beyond anyone else's who looks past the surface and digs into the question.
Simplicio: These occurrences, Salviati, aren't new. They're extremely ancient, observed by countless people, and many have racked their brains to give a reason for them — one this reason, another that. Not many miles from here there's a great Peripatetic who brings forward a cause freshly fished out of a certain passage in Aristotle that his interpreters hadn't properly noticed. From that passage he gathers that the true cause of these movements comes from nothing but the differing depths of the seas: the waters of the greater depths, being larger in quantity and therefore heavier, drive out the waters of the shallower places, which, once raised up, then want to descend; and from this continual struggle comes the ebb and flow. Then there are the many who refer it to the Moon, saying she has a special dominion over water. And most recently a certain prelate has published a little treatise in which he says the Moon, wandering across the sky, draws and lifts toward herself a heap of water that keeps following after her, so that the sea is always high in whatever part lies beneath the Moon. And since, even when she's below the horizon, the rising still returns, he says the only way to save the effect is to hold that the Moon not only naturally keeps this faculty in herself, but in this case has the power to confer it on the point of the zodiac opposite her. Others — as I think you know — say that the Moon, by her mild warmth, has the power to rarefy the water, which, once rarefied, comes to rise up. Nor have we been without someone who —
Sagredo: Please, Simplicio, don't report any more of them. It doesn't seem worth spending the time to recite them, much less the words to refute them. And if you were to lend your assent to any of these trifles, or others like them, you'd be doing an injustice to your own judgment — which we know to be very well refined.
Salviati: Being a bit more phlegmatic than you, Sagredo, I'll spend fifty words for Simplicio's sake, in case he thinks there might be some probability in the things he's recounted. So here's what I say. Waters, Simplicio, whose outer surface stands higher do drive out the ones below them, the lower ones; but the waters that are greater in depth do not do this. And the higher waters, once they've driven out the lower, quickly settle and come level. This Peripatetic of yours would have to believe that all the lakes in the world that lie still, and all the seas where the ebb and flow is imperceptible, have perfectly level beds. And I was so simple-minded that I'd persuaded myself that, even if there were no other sounding, the islands rising above the waters were a pretty plain indication that the bottoms are uneven. To that prelate you might say that the Moon runs over the whole Mediterranean every day, and yet the waters don't rise except at its eastern extremities and here with us in Venice. To the people with the mild warmth strong enough to make water swell, tell them to put a fire under a cauldron full of water, keep their right hand in it until the heat raises the water by a single finger's width, and then pull it out and write about the swelling of the sea. Or at least ask them to teach you how the Moon manages to rarefy a certain part of the waters and not the rest — say, these here at Venice and not those at Ancona, Naples, or Genoa. One has to conclude that poetic minds come in two kinds: some deft and apt at inventing fables, others disposed and fitted to believing them.
Simplicio: I don't think anyone believes fables while he recognizes them as such. As for the many opinions about the causes of the ebb and flow, since I know that an effect has only a single primary and true cause, I understand perfectly well, and am certain, that at most one of them could be true, while all the rest, I know, are fabulous and false. And perhaps the true one isn't even among those brought forward so far — indeed, that's what I really believe, for it would be a strange thing if the truth could give off so little light that nothing of it showed among the darkness of so many falsehoods. But I'll say, with the freedom allowed among us, that bringing in the motion of the Earth and making it the cause of the ebb and flow seems to me, so far, a notion no less fabulous than any of the others I've heard. And if I were offered no reasons more in keeping with natural things, I'd pass without any resistance to believing this is a supernatural effect, and therefore miraculous and unfathomable to human minds — like the countless others there are that depend immediately on the omnipotent hand of God.
Salviati: You reason very prudently, and in keeping too with the doctrine of Aristotle — who, as you know, at the start of his Mechanical Questions attributes to miracle the things whose causes are hidden. But that the true cause of the ebb and flow is among the impenetrable ones — I don't think you have any greater sign of that than seeing how, among all the causes so far brought forward as the real ones, there isn't a single one by which, with whatever contrivance you employ, we can produce a like effect ourselves. For neither with the light of Moon or Sun, nor with mild heat, nor with differing depths, will anyone ever make the water contained in a motionless vessel run and run back, rise and fall, in one place and not another, by any artificial means. But if, by making the vessel move — with no contrivance at all, in the very simplest way — I can reproduce for you, point by point, all the changes observed in sea water, why would you refuse this cause and take refuge in a miracle?
Simplicio: I'll take refuge in a miracle if you don't dislodge me from it with some natural cause other than the motion of the vessels of the sea waters — because I know those vessels don't move, seeing that the whole entire terrestrial globe is naturally motionless.
Salviati: But don't you believe the terrestrial globe could be made movable supernaturally — that is, by the absolute power of God?
Simplicio: And who doubts it?
Salviati: Then, Simplicio — since to produce the ebb and flow of the sea we need to bring in a miracle — let's miraculously set the Earth in motion, and let the sea then move naturally at its motion. And this operation will be all the simpler, and I'd even say the more natural, among the miraculous ones, in that setting a globe spinning in a circle — when we see so many others moving that way — is less difficult than making an immense mass of water go forward and back, faster here and slower there, rise and fall here more and there less and elsewhere not at all, and produce all these variations in the very same vessel that contains it. Besides, these are many different miracles, and that is only one. And add to this that the miracle of making the water move drags another after it as a consequence: keeping the Earth steady against the water's impulses, which would be strong enough to make it sway now toward one side and now toward the other, unless it were held fast miraculously.
Sagredo: Please, Simplicio, let's suspend our judgment for a little while before pronouncing the new opinion Salviati means to explain to us worthless, and let's not so quickly throw it into the same bag with the old, ridiculous ones. As for the miracle, let's turn to it likewise after we've heard the reasoning that stays within natural limits — though, to speak my own mind, all the works of nature and of God look miraculous to me.
Salviati: And I judge the same. Saying that the natural cause of the ebb and flow is the movement of the Earth doesn't keep that movement from being a miraculous operation. Now, taking up our reasoning again, I repeat and affirm: it remains unknown, so far, how the waters contained within our Mediterranean gulf can make those movements we see them make, so long as that same gulf and containing vessel stays motionless. And what creates the difficulty, and makes this matter so hard to untangle, are the things I'll mention next, which are observed daily. So take note.
Here we are in Venice, where the waters are now low, the sea calm and the air still. The water begins to rise, and within five or six hours it swells ten palms and more. This rise isn't produced by the first water having rarefied; it's produced by new water that has come in — water of the same sort as the first, of the same saltiness, the same density, the same weight. Ships, Simplicio, float in it just as in the first, without sinking so much as a hair deeper; a barrel of this second water weighs not a single grain more or less than the same quantity of the other; it keeps the same coldness, not altered in the least. It is, in short, water newly and visibly come in through the cuts and mouths of the Lido. Now find me how and from where it got here. Are there perhaps chasms or channels round about, in the sea floor, through which the Earth draws in and pours back the water, breathing like some vast and boundless whale? But if that's so, how is it that in the space of six hours the water doesn't rise the same way at Ancona, at Ragusa, at Corfu, where the swelling is very small and perhaps unnoticeable? Who will find a way to pour new water into a motionless vessel, and have it rise only in one particular part of it and nowhere else? Perhaps you'll say this new water is lent to it by the Ocean, handed in through the Strait of Gibraltar? That won't remove the difficulties already mentioned; it'll bring greater ones. First, tell me what the course of that water must be, if, entering through the strait, it travels in six hours all the way to the farthest shores of the Mediterranean, a distance of two or three thousand miles, and then repasses that same distance in as much time on its way back. What would become of the ships scattered across the sea? What of those in the strait, caught in a continual headlong rush of an immense flood of waters that, entering through a channel no more than eight miles wide, has to give passage to enough water that in six hours it floods a space hundreds of miles across and thousands long? What tiger, what falcon, ever ran or flew with such speed — a speed, I mean, that would cover four hundred miles and more in an hour? There are currents, granted, along the length of the Gulf, but so slow that oared vessels outdo them, though not without loss to their own progress. Furthermore, if this water comes in through the strait, there still remains the other difficulty: how it's carried to rise so high here, in parts so remote, without first rising to a like or greater height in the parts nearer by. In short, I don't believe that either stubbornness or subtlety of wit could ever find a remedy for these difficulties, nor, in consequence, uphold against them the stability of the Earth, so long as one stays within natural limits.
Sagredo: Of this I'm now perfectly convinced, and I'm eagerly waiting to hear in what way these marvels can follow, without a hitch, from the motions already assigned to the Earth.
Salviati: For these effects to follow as consequences of the motions that naturally belong to the Earth, it is necessary not only that they meet no resistance or obstacle, but that they follow easily — and not only that they follow easily, but of necessity, so that it would be impossible for things to happen in any other way; for that is the property and condition of things natural and true. So, having established that it is impossible to account for the movements we see in the waters and at the same time keep motionless the vessel that holds them, let us go on to see whether the mobility of the container can produce the effect, under the conditions in which we observe it to occur.
Two kinds of motion can be given to a vessel, by which the water contained in it would gain the ability to run now toward one end and now toward the other, and there to rise and fall. The first would be when now one end and now the other is lowered; for then the water, running toward the tilted side, would in turn rise and fall, now on this side, now on that. But since this rising and falling is nothing other than moving away from and toward the center of the Earth, this kind of motion cannot be attributed to the hollows of the Earth itself — the vessels that hold the waters — because no matter what motion you assign to the terrestrial globe, the parts of those vessels can neither approach nor recede from its center. The other kind of motion is when the vessel moves (without tilting at all) with a forward motion that is not uniform but changes speed, now speeding up and now slowing down. From this unevenness it would follow that the water — held in the vessel, but not fixed to it like its other solid parts, indeed, by its fluidity almost separate and free and not bound to follow every change of its container — when the vessel slows down would retain part of the impetus already built up and run forward toward the leading end, where it would necessarily rise; and conversely, when new speed is added to the vessel, the water, keeping part of its own slowness and lagging somewhat behind before it grows used to the new impetus, would stay toward the trailing end, where it would rise a little. We can lay out these effects more openly, and show them plainly to the senses, with the example of one of those barges that come continually from Lizzafusina, full of fresh water for the use of the city. So let us picture such a barge coming along the Lagoon at a moderate speed, placidly carrying the water it is full of; and then, either through running aground or through some other obstacle set in its way, it is noticeably slowed. The water it holds will not, like the barge, lose the impetus already built up; keeping it, the water will run forward toward the bow, where it will rise noticeably, dropping away from the stern. But if, on the contrary, that same barge in the middle of its placid course is given a notable added burst of new speed, the water it holds, before growing used to it and keeping its own slowness, will lag behind — that is, toward the stern — where it will consequently rise, dropping away from the bow. This effect is beyond doubt and clear, and can be tried at any hour; and in it, for the moment, I want us to note three particulars. The first is that, to make the water rise at one end of the vessel, there is no need of new water, nor for it to run there leaving the other end. The second is that the water in the middle does not rise or fall noticeably — unless the barge's course were extremely fast, and the jolt or other check that stopped it very strong and sudden, in which case all the water might not only run forward but for the most part leap out of the barge; and it would do the same when, while moving slowly, it were suddenly struck by an extremely violent impetus. But when a moderate slowing or quickening overtakes a quiet motion of the barge, the middle parts (as I said) rise and fall imperceptibly, and the other parts rise less the closer they are to the middle, and more the farther off. The third is that, whereas the parts near the middle make little change in rising and falling compared with the waters at the ends, they, on the contrary, run far forward and back compared with the ends. Now, gentlemen, what the barge does with respect to the water it contains, and what the contained water does with respect to the barge that holds it, is exactly, to a hair, what the Mediterranean basin does with respect to the waters it contains, and what those waters do with respect to the Mediterranean basin that holds them. It now follows that we demonstrate how, and in what way, it is true that the Mediterranean and all other gulfs — in short, all parts of the Earth — move with a notably uneven motion, even though no motion that is not regular and uniform is assigned to the globe as a whole.
Simplicio: At first sight, to me — who am neither a mathematician nor an astronomer — this looks like a great paradox; and if it is true that, the motion of the whole being perfectly regular, the motion of the parts, while they stay always joined to their whole, can be irregular, then the paradox will destroy the axiom that states eandem esse rationem totius et partium — that the whole and its parts have one and the same character.
Salviati: I shall demonstrate my paradox, and to you, Simplicio, I'll leave the task of defending the axiom against it, or of reconciling the two; and my demonstration will be short and very easy, depending on things treated at length in our past discussions, without bringing in so much as a single syllable for the sake of the ebb and flow.
We have said there are two motions assigned to the terrestrial globe: the first, the annual, made by its center along the circumference of the great orb under the ecliptic, in the order of the signs — that is, from west to east; the other, made by the globe itself, turning about its own center in twenty-four hours, and this likewise from west to east, though about an axis somewhat tilted and not parallel to that of the annual revolution. From the compounding of these two motions, each of them uniform in itself, there results — I say — an uneven motion in the parts of the Earth. To make this more easily understood, I'll explain it by drawing the figure. First, about the center A I'll draw the circumference of the great orb, BC; on it, taking any point B, and about B as center, we'll draw this smaller circle DEFG, representing the terrestrial globe. We'll understand it to travel, with its center B, all the way around the circumference of the great orb, from west to east — that is, from the side B toward C. And beyond that, we'll understand the terrestrial globe to turn about its own center B, likewise from west to east — that is, in the succession of the points D, E, F, G — in the space of twenty-four hours. But here we must carefully note how, as a circle turns about its own center, any part of it must move at different times in contrary directions. This is clear if we consider that, while the parts of the circumference around the point D are moving to the left — that is, toward E — the opposite parts, those around F, are gaining toward the right — that is, toward G; so that when the parts at D have come to F, their motion will be contrary to what it was before, when they were at D. Moreover, in the same time that the parts at E descend, so to speak, toward F, those at G ascend toward D. Given, then, this contrariety of motions in the parts of the Earth's surface while it turns about its own center, it necessarily follows that, in coupling this daily motion with the other, annual one, there results for the parts of that terrestrial surface an absolute motion now much accelerated and now just as much retarded. This is clear if we first consider the part around D, whose absolute motion will be very fast, being born of two motions made toward the same side — that is, to the left: the first of them a part of the annual motion, common to all parts of the globe; the other belonging to the point D itself, carried likewise to the left by the daily whirl. So in this case the daily motion increases and accelerates the annual. The opposite happens to the opposite part, F, which, while it is carried by the common annual motion — together with the whole globe — toward the left, is carried by the daily turning toward the right; so that the daily motion comes to subtract from the annual, and the absolute movement resulting from the compounding of the two is greatly retarded. Around the points E and G, then, the absolute motion comes to be about equal to the simple annual, since the daily adds to it or subtracts from it nothing, or little, tending neither to the left nor to the right, but down and up. We conclude, therefore, that just as it is true that the motion of the whole globe, and of each of its parts, would be even and uniform if they moved with a single motion — whether the simple annual or the daily alone — so it is necessary that, when these two motions are mixed together, there result for the parts of the globe uneven motions, now accelerated and now retarded, through the additions or subtractions the daily rotation makes to the annual revolution. So that if it is true (as it most certainly is, and experience shows it) that the acceleration and slowing of the vessel's motion make the water it holds run and run back along its length, and rise and fall at its ends, who will make any difficulty about granting that this effect can — indeed, must of necessity — happen to the sea waters, held within their vessels, which are subject to such alterations, and above all in those that stretch lengthwise from west to east, which is the direction in which the motion of those vessels is made? Let this, then, be the principal and primary cause of the ebb and flow, without which nothing of the kind would follow. But because many and varied are the particular incidents observed in different places and times, which must depend on various other concomitant causes — though all of them must have a connection with the primary one — it is necessary to go on proposing and examining the various incidents that can be the causes of these various effects.
The first of these is that, whenever the water — thanks to a notable slowing or speeding of the motion of the vessel that holds it — has gained cause to run toward one end or the other, and has risen at one and dropped at the other, it will not stay in that state even when the primary cause ceases; but by its own weight and natural inclination to level and balance itself, it will of itself return, quickly, back again. And, being heavy and fluid, it will not only move toward equilibrium but, driven by its own impetus, will overshoot it, rising on the side where before it was lower; nor will it stop even here, but, going back once more, with ever more repeated back-and-forth surges it will show us that it will not pass at once from a speed of motion it has taken on to the loss of that motion and to a state of rest, but wants to be brought to it gradually, dying away little by little, slowly. In just the way we see a weight hanging from a cord, once it has been moved from its state of rest — that is, from the vertical — return there of itself and come to rest, but not before it has crossed it many times, this way and that, with its alternating runs and returns.
The second incident to note is that the back-and-forth surges just described are made and repeated with greater or lesser frequency — that is, in shorter or longer times — according to the different lengths of the vessels that hold the waters; so that in the shorter spaces the surges are more frequent, and rarer in the longer ones. Just as, in the same example of hanging bodies, we see the swings of those hung from longer cords to be less frequent than those of the ones hanging from shorter threads.
And here, for the third point worth knowing, it should be understood that not only the greater or lesser length of the vessel causes the water to make its surges in different times, but the greater or lesser depth does the same; and it happens that of waters held in basins of equal length but unequal depth, the one that is deeper makes its levelings in shorter times, and the surges of the shallower waters are less frequent.
Fourth, two effects the water makes in these levelings deserve to be noted and carefully observed. One is the rising and falling alternately toward one end and the other; the other is the moving and running, so to speak horizontally, forward and back. These two different motions reside differently in different parts of the water. For its end parts are the ones that rise and fall the most; those in the middle do not move up or down at all; and of the rest, step by step, those nearer the ends rise and fall proportionately more than the more distant ones. But conversely, in the other, forward-and-back progressive motion, the middle parts move a great deal, going and returning, while the waters at the very ends gain nothing of it — except insofar as, in rising, they overtop their banks and spill out of their original bed and basin; but where there is the check of banks to rein them in, they only rise and fall. Yet the middle waters do not for that reason stop running forward and back, which the other parts do too, proportionately, running more or less according as they are placed more distant from or nearer to the middle.
The fifth particular incident must be considered all the more attentively in that it is impossible for us to represent its effect by experiment and practice; and the incident is this. In the vessels we make by art, and move — like the barges named above — now faster and now slower, the acceleration and slowing are always shared in the same way by the whole vessel and by each of its parts; so that while, for example, the barge is checked in its motion, the leading part is slowed no more than the trailing one, but all share equally in the same slowing; and the same happens with acceleration — that is, when a new cause of greater speed is given to the barge, the bow and the stern accelerate in the same way. But in the immense vessels that are the very long beds of the seas — even though these too are nothing but certain hollows made in the solid body of the terrestrial globe — it marvelously happens that their ends do not increase and diminish their motion together, equally, and at the same moments of time; rather, it happens that when one of its ends finds itself, by virtue of the compounding of the two motions, the daily and the annual, greatly retarded in its speed, the other end finds itself still affected and joined with a very fast motion. This, for easier understanding, we'll explain
by taking up the figure just now drawn. In it, if we take a stretch of sea to be long, say, a quadrant — a quarter of the circle — such as the arc BC: because the parts at B are, as was explained above, in a very fast motion, through the union of the two motions, the daily and the annual, toward the same side, while the part at C is then in a retarded motion, being deprived of the advance that depends on the daily motion — if, I say, we take a gulf of sea as long as the arc BC, we shall already see how its ends move at the same time with great inequality. And the speeds would be utterly different in a stretch of sea half a circle long, placed in the position of the arc BCD, since the end B would be in a very fast motion, the other, D, in a very slow one, and the middle parts, toward C, in a moderate motion. And the shorter these stretches of sea are, the less they will share in this strange incident of having their parts, at certain hours of the day, differently affected by speed and slowness of motion. So that if, as in the first case, we see by experience that the acceleration and slowing — though shared equally by all parts of the containing vessel — are still the cause of the contained water's running forward and back, what must we suppose ought to happen in a vessel so marvelously arranged that slowing and speeding of motion are contributed to its parts very unequally? Certainly we can say nothing else but that a greater and more marvelous cause of commotions in the water — and stranger ones — must be found there. And though it may seem impossible to many that, in artificial machines and vessels, we could experiment the effects of such an incident, nonetheless it is not entirely impossible; and I have the design of a machine in which, in particular, the effect of these marvelous compoundings of motions can be discerned. But as far as concerns the present subject, what you have been able to grasp so far with your imagination is enough. For my part, I understand very well that this marvelous incident must necessarily be found in the gulfs of the seas, and above all in those that stretch over great distances from west to east — that is, along the course of the terrestrial globe's motions; and since it is in a certain way unthinkable and without parallel among the motions we can produce, so I find it not hard to believe that from it there may derive effects not imitable by our artificial experiments.
Salviati: Now that these matters are settled, it's time we turned to examining the particular phenomena — and their variety — that experience shows us in the ebb and flow of the waters. First, we should have no trouble understanding why in lakes, ponds, and even small seas there is no notable ebb and flow. There are two thoroughly conclusive reasons for this. The first is that, because the basin is short, when at different hours of the day it takes on different degrees of speed, those degrees are acquired with little difference by all its parts: the leading and the trailing parts alike — the eastern and the western — speed up and slow down in almost exactly the same way. And since this change happens gradually, and not by suddenly throwing some abrupt check and delay, or some sudden and great acceleration, against the motion of the containing vessel, the vessel and all its parts are slowly and evenly impressed with the same degrees of speed. From this uniformity it follows that the contained water, too, receives the same impressions with little stubbornness or resistance, and so gives only the faintest sign of rising or falling, of running toward one end or the other. You can see this same effect plainly in small artificial vessels, where the water within takes on the very same degrees of speed, provided the speeding up or slowing down is done in a slow and uniform proportion. But in arms of the sea that stretch a great distance from east to west, the acceleration or slowing is far more notable and uneven, since one of its ends will be in a much-retarded motion while the other is still moving very fast. The second cause is the reciprocal swinging of the water, arising from the impetus it, too, would have taken on from the motion of its container — a swinging whose oscillations, as we noted, are very frequent in small vessels. From this it results that, although the cause residing in the Earth's motions contributes motion to the water only once every twelve hours — since only once a day does the motion of the containing vessels reach its greatest slowing and its greatest speeding — nevertheless that other, second cause, depending on the weight of the water as it seeks to return to equilibrium, and having, according to the shortness of the vessel, its swings of one hour, or two, or three, and so on: this second cause, mixing with the first (which by itself, in small vessels, already stays very slight), renders it altogether imperceptible. For before the disturbance produced by the primary cause — the one with periods of twelve hours — has finished being impressed, along comes the other, secondary one, running counter to it, depending on the water's own weight, which, according to the shortness and depth of the vessel, has the time of its swings at one, two, three, or four hours, and so on; and, running counter to the first, it upsets and displaces it, without letting it reach the top, or even the middle, of its movement. And from this opposition the evidence of ebb and flow is wholly annihilated, or greatly obscured. I say nothing of the continual changes in the air, which, by troubling the water, would keep us from ever being sure of a very slight rise or fall of half a finger's breadth, or less, that might really reside in gulfs and basins of water no longer than a degree or two.
I come, in the second place, to resolving the puzzle of how — given that the primary principle contains no cause for stirring the waters except once every twelve hours (once by the greatest speed of motion, and once by the greatest slowness) — the period of ebb and flow nonetheless commonly appears to be one of six hours. To this the answer is that such a determination can in no way come from the primary cause alone; the secondary ones must be brought in — namely, the greater or lesser length of the vessels, and the greater or lesser depth of the waters they contain. These causes, though they have no action at all in the movements of the waters (that action belonging to the primary cause alone, without which nothing of ebb and flow would follow), nonetheless have the chief say in determining the times of the swings — so powerful a say that the primary cause must remain subject to them. So the six-hour period is no more proper or natural than those of other intervals of time; it is simply, perhaps, the most observed, being the one that fits our Mediterranean, which for long ages was the only sea people sailed. And even there this period is not observed in all its parts, since in certain more confined places — such as the Hellespont and the Aegean — the periods are much shorter, and very different from one another besides. This variety and its causes were beyond Aristotle; and some say that, after long observing them from certain rocks of Negroponte, he was driven to despair, threw himself into the sea, and deliberately drowned.
In the third place, we shall have very ready to hand the reason why a certain sea, though very long — such as the Red Sea — is nonetheless almost entirely free of ebb and flow. This happens because its length does not run from east to west, but rather crosswise, from the southeast toward the northwest. But since the Earth's movements are from west to east, the impulses of the waters always strike along the meridians, and do not move from parallel to parallel. Hence in seas that stretch crosswise toward the poles, and are narrow the other way, there remains no cause for ebb and flow except through the sharing of some other sea they communicate with, one that is subject to large movements.
In the fourth place, we shall very easily grasp the reason why the ebb and flow are greatest — in the rising and falling of the waters — at the far ends of gulfs, and least in the middle parts. Daily experience shows this here in Venice, set at the far end of the Adriatic, where the difference commonly amounts to five or six feet; whereas in places of the Mediterranean distant from the ends, the change is very slight — as in the islands of Corsica and Sardinia, and on the shores of Rome and Livorno, where it does not exceed half a foot. We shall also grasp how, conversely, where the risings and fallings are small, the currents' runnings-out and runnings-back are large. It is an easy matter, I say, to understand the cause of these phenomena, since we have plain confirmations of them in every sort of vessel we build by hand, in which these same effects are seen to follow naturally when we move them with an uneven motion — now sped up, now slowed down.
Moreover, considering, in the fifth place, how the same quantity of water, moved even slowly through a spacious channel, must of necessity run with great force when it then has to pass through a narrow place, we shall have no trouble understanding the cause of the great currents in the narrow channel that separates Calabria from Sicily. For all the water that, from the breadth of the island and from the Ionian gulf, is held in the eastern part of the sea, though it descends slowly toward the west through that whole expanse, nevertheless, on being squeezed into the strait between Scylla and Charybdis, drops swiftly and makes an enormous turmoil. A similar turmoil, and a far greater one, is understood to occur between Africa and the great island of St. Lawrence, when the waters of the two vast seas — the Indian and the Ethiopic — that flank it must, in flowing, squeeze into a smaller channel between the island and the coast of Ethiopia. And the currents must be very great indeed in the Strait of Magellan, which links the vast Ethiopic and South oceans.
It follows now, in the sixth place, that in order to account for some more hidden and unexpected phenomena observed in this matter, we go on to make another important consideration regarding the two principal causes of ebb and flow, and then compound and mix them together. The first and simpler of the two is (as has been said many times) the fixed acceleration and slowing of the parts of the Earth, from which the waters would have a fixed period of running toward the east and returning toward the west within a span of twenty-four hours. The other is the one that depends on the water's own weight, which, once stirred by the primary cause, then seeks to return to equilibrium with repeated swings — swings not determined by a single, set time, but having as many different times as there are different lengths and depths of the basins and arms of the seas. As far as this second principle goes, some would run out and back in one hour, others in two, in four, in six, in eight, in ten, and so on. Now, if we begin to join the primary cause — which steadily keeps its period of twelve hours — with some secondary one that had its period of, say, five hours, it will happen that at certain times the primary and the secondary cause agree in making their impulses both toward the same side; and in this conjunction, this so-to-speak unanimous conspiring together, the tides will be large. At other times it will happen that the primary impulse comes in a certain way to oppose what the secondary period would bring; and in this clash, each principle taking away what the other would give, the movements of the waters will be weakened, and the sea will be reduced to a very quiet and almost motionless state. And at still other times, according as the two principles neither wholly oppose nor wholly agree with each other, there will be other variations in the increase and decrease of the tides. It can also happen that two very large seas, communicating through some narrow channel, come — through the mixing of the two principles of motion — to have the one with a cause of rising at the very time the other has a cause of opposite movement. In that case, in the channel where those seas communicate, there arise extraordinary agitations, with opposing movements, whirlpools, and most dangerous boilings — of which there are continual reports and actual firsthand experiences. From such discordant movements, depending not only on the different positions and lengths but also, in great measure, on the different depths of the communicating seas, there will arise at certain times various disturbances in the waters, irregular and beyond observation, whose causes have greatly puzzled — and still puzzle — sailors, who meet with them without seeing that no force of winds, nor any other serious change in the air, can be their cause. Of this disturbance of the air we must, in other phenomena, take great account, and reckon it a third and incidental cause, capable of greatly altering the observation of effects that depend on the primary and more essential causes. And there is no doubt that if violent winds keep blowing — from the east, for example — they will hold up the waters, preventing their ebb; so that, when the second recurrence of the flow arrives at the appointed hours, and then the third, the waters will swell greatly; and thus, held up for several days by the force of the wind, they rise higher than usual, causing extraordinary floods.
We must further (and this will be like a seventh problem) take note of another cause of movement, depending on the great abundance of water from the rivers that empty into seas that are not very vast — where, in the channels or straits that communicate with such seas, the water is seen always to run the same way, as happens in the Thracian Bosphorus below Constantinople, where the water always runs from the Black Sea toward the Propontis. For in that Black Sea, because of its smallness, the principal causes of ebb and flow have little force; but on the other hand, since very great rivers empty into it, when all that flood of water must pass and pour out through the strait, the current there is quite notable, and always toward the south. Here, moreover, we must note that this strait and channel, though quite narrow, is not subject to the disturbances that the strait of Scylla and Charybdis is. For that one has the Black Sea above it toward the north, and the Propontis and the Aegean, along with the Mediterranean beyond, toward the south — though at a long remove. But, as we have already noted, seas that run north to south, however long, are not subject to ebb and flow. Whereas the strait of Sicily lies set between parts of the Mediterranean that stretch over great distances from west to east — that is, along the run of the ebb and flow — and so in it the agitations are very great. And they would be greater at the Pillars of Hercules, if the Strait of Gibraltar were to open less; and they report those of the Strait of Magellan to be very great indeed. This is all that occurs to me for now to tell you about the causes of this first, daily period of ebb and flow, and its various phenomena. If you have anything to propose, do so, and then we can pass on to the other two periods — the monthly and the annual.
Simplicio: I don't think it can be denied that the discourse you've made proceeds very plausibly, arguing, as we put it, ex suppositione — on a supposition — that is, granting that the Earth moves with the two movements Copernicus attributes to it. But if those movements are ruled out, the whole thing remains empty and invalid; and the ruling out of that hypothesis is pointed out to us quite plainly by your own discourse. With the supposition of the two terrestrial movements you account for the ebb and flow, and then, conversely, reasoning in a circle, from the ebb and flow you draw the indication and confirmation of those very movements. And, coming to a more specific point: you say that the water, being a fluid body and not tenaciously attached to the Earth, is not compelled to obey its every motion punctually — from which you then derive its ebb and flow. Now, following in your very footsteps, I argue the opposite, and say: the air is far more tenuous and fluid than water, and less attached to the Earth's surface — to which the water, if for no other reason, clings by its weight, pressing down upon it far more than the featherlight air does. Therefore the air ought much less to follow the Earth's movements; and so, if the Earth moved in that way, we — its inhabitants, carried along by it at the same speed — ought perpetually to feel a wind from the east striking us with intolerable force. And that this must be so, experience makes us aware of daily: for if, riding post at a speed of only eight or ten miles an hour, meeting the still air with our face makes us feel a wind that strikes us no lightly, what ought our rapid course of eight hundred or a thousand miles an hour to do, against air free of that motion? Yet we feel nothing of the sort.
Salviati: To this objection, which has much of the plausible about it, I answer that it is true the air is more tenuous and lighter, and by its lightness less adherent to the Earth, than water, which is so much heavier and more corporeal. But then the conclusion you draw from these conditions is false — namely, that because of this lightness, tenuity, and lesser adherence to the Earth, the air should exempt itself, more than water does, from following the terrestrial movements, so that to us, who share those movements entirely, its disobedience would become sensible and manifest. In fact, just the opposite happens. For, if you remember rightly, the cause of the ebb and flow of the water, as we assigned it, consists in the water's not following the unevenness of the motion of its vessel, but retaining the impetus conceived earlier, without diminishing or increasing it by the precise measure by which it is increased or diminished in its vessel. Since, then, the disobedience to a fresh increase or decrease of motion consists in preserving and maintaining the impetus conceived before, that body which is more apt at such preservation will also be the better suited to display the effect that follows from that preservation. Now, how disposed water is to maintain an agitation once conceived, even after the cause that impressed it has ceased, is shown by the experience of seas mightily stirred by violent winds: their waves, even after the air has calmed and the wind died, remain in motion a long while — as the sacred poet gracefully sang, "Like the high Aegean..." and so on. And this persistence in the agitation depends on the weight of the water; for, as has been said elsewhere, light bodies are indeed far easier to set moving than heavier ones, but they are just so much less able to preserve the motion impressed on them once the moving cause has ceased. Hence the air, being in itself most tenuous and light, is very easily moved by any least force, but is also most unfit to preserve the motion once the mover has ceased. So, as for the air surrounding the terrestrial globe, I would say that by its adherence it is carried around no less than the water is — especially the part contained within basins, those basins being the plains ringed by mountains. And of this portion we can much more reasonably affirm that it is carried around, snatched along by the roughness of the Earth, than the upper air is snatched along by the celestial motion, as you Peripatetics assert.
What I have said so far seems to me a fairly adequate answer to Simplicio's objection; nevertheless, I want, with a new objection and a new reply — founded on a marvelous experience — to satisfy him more than fully, and to confirm for Sagredo the mobility of the terrestrial globe. I said that the air — and in particular that part of it which does not rise above the summits of the highest mountains — is carried around by the roughness of the Earth's surface. From this it seems to follow that if the Earth's surface were not uneven, but smooth and polished, there would be no cause to draw the air along in its company, or at least to carry it along with such uniformity. Now, the surface of this globe of ours is not all rugged and rough: there are very great, quite smooth expanses — namely, the surfaces of the vast seas — which, being also very far from the mountain ridges that ring them, do not seem able to have the power to carry the overlying air along with them. And, not carrying it, one ought in those places to feel just what follows from that.
Simplicio: This is the very difficulty I too was about to raise, and it seems to me of great force.
Salviati: You speak very well: so that, Simplicio, from not feeling in the air what would follow as a consequence if this globe of ours went around, you argue its immobility. But if this thing, which you think one should feel by necessary consequence, were in fact and by experience felt, would you accept it as a strong enough indication and argument for the mobility of that same globe?
Simplicio: In this case one mustn't argue with me alone, because if it happened, and the cause of it were hidden from me, perhaps it might be known to others.
Salviati: So with you one can never win, but always stands to lose — better, then, not to play at all. Still, so as not to leave the third player in the lurch, I'll go on. We were just saying — and I'll repeat it with something added — that the air, being a tenuous and fluid body, not firmly joined to the Earth, seemed to have no need to obey its motion, except insofar as the roughness of the Earth's surface snatches up and carries along with it a portion of air contiguous to it, a portion rising not much above the greatest heights of the mountains. And this portion of air will be all the less resistant to the terrestrial turning insofar as it is full of vapors, fumes, and exhalations — all of them materials partaking of earthly qualities, and consequently born by their nature apt for the same movements. But where the causes of motion were lacking — that is, where the surface of the globe had great flat spaces, and there was less of the admixture of earthly vapors — there the cause by which the surrounding air should wholly obey the snatching of the terrestrial turning would in part cease. So in such places, while the Earth turns toward the east, one ought continually to feel a wind striking us, blowing from the east toward the west; and such a blowing ought to be more perceptible where the whirl of the globe is faster — which would be in the places most remote from the poles and nearest the greatest circle of the daily turning. But in fact experience much applauds this philosophical reasoning: for in the wide seas, in their parts far from land and lying beneath the torrid zone — that is, enclosed between the tropics, where the earthly evaporations are also lacking — one feels a perpetual breeze moving from the east, with so constant a tenor that ships sail prosperously by its grace to the West Indies; and from those same shores, casting off from the Mexican coast, they plow with the same favor across the Pacific toward the Indies that are eastern to us but western to them. Whereas, on the contrary, voyages from there toward the east are difficult and uncertain, and can by no means be made along the same routes; instead one must hug the coast more, to find other winds — accidental and unruly, so to speak — caused by other principles, such as we who dwell among the mainland continually feel by experience. Of these generations of winds the causes are many and various, which there is no occasion to produce at present; and these accidental winds are the ones that blow indifferently from every quarter of the Earth, and that disturb the seas remote from the equinoctial and surrounded by the rough surface of the Earth — which is as much as to say, subject to those disturbances of the air that confound that primary breathing-out, which, if these accidental impediments were lacking, ought perpetually to be felt, and most of all over the sea. Now see how the effects of the water and of the air seem marvelously to agree with the celestial observations in confirming the mobility of our terrestrial globe.
Sagredo: I want, as a final seal on all this, to add one detail I think you don't know, and which also confirms the very same conclusion. You, Salviati, brought up that phenomenon sailors meet with inside the tropics — I mean the perpetual steadiness of the wind that comes to them from the east; and I've had an account of it from someone who has made that voyage many times. What's more (and here's the notable part), I gather the sailors don't call it a wind at all, but by some other name I can't call to mind just now — taken, perhaps, from its being so steady and constant that, once they've fallen in with it, they lash the shrouds and the other sail ropes and, without ever needing to touch them again, can hold their course in safety even while they sleep. Now this perpetual breeze has been recognized for what it is precisely by its blowing on and on without interruption; for if it were broken up by other winds, it would never have been noticed as a single effect distinct from the rest. From which I want to infer that it might well be that our own Mediterranean shares in some such phenomenon, only unobserved, because it is so frequently disturbed by other winds coming on. And I say this not without solid grounds — indeed, with very probable evidence, which came my way from something I had occasion to learn on the voyage I made to Syria, going as consul of our merchant community in Aleppo. It is this: a particular record and register is kept of the days on which ships depart from and arrive in the ports of Alexandria, of Alexandretta, and here at Venice; and in comparing a great many of these against one another — which I did out of my own curiosity — I found that, on average, the returns homeward, that is, the voyages from east toward west across the Mediterranean, are made in less time than the opposite runs, by a good 25 percent. So you can see that, all told, the winds out of the east are stronger than those out of the west.
Salviati: I'm glad to have learned this detail; it brings no small confirmation for the mobility of the Earth. And even though one might say that all the water of the Mediterranean runs perpetually toward the Strait — being water that has to go and discharge into the Ocean the flow of the many rivers that pour into it — I don't believe such a current could be strong enough, by itself alone, to produce so notable a difference. And that's clear enough, too, from the fact that in the Faro — the Strait of Messina — you see the water run back toward the east no less than it runs toward the west.
Sagredo: I, who unlike Simplicio have no spur to satisfy anyone but myself, am content with what has been said on this first part; so, Salviati, whenever it suits you to go on, I'm ready to listen.
Salviati: I'll do as you bid me; but I'd like to hear Simplicio's opinion too, since from his judgment I can gauge how much I might promise myself, regarding these arguments of mine, from the Peripatetic schools — if ever they reached their ears.
Simplicio: I don't want my opinion to carry weight with you, or to serve you as a guess at what others will judge, because — as I've said many times — I'm one of the least in this sort of study, and something will occur to those who have penetrated into the innermost sanctuaries of philosophy that cannot occur to me, who have (as they say) barely greeted it from the doorstep. Still, just to show some sign of life, I'll say that as for the effects you've recounted, and this last one in particular, it seems to me that without the mobility of the Earth one could give a perfectly sufficient account of them by the mobility of the heavens alone, introducing no novelty whatever except the converse of the very thing you yourself put forward. The Peripatetic schools have accepted that the element of fire, and a great part of the air as well, are carried around, following the daily rotation, from east toward west by contact with the concave of the lunar orb, as by the vessel that contains them. Now, without straying from your own footsteps, let's stipulate that the quantity of air taking part in this motion reaches down almost to the tops of the highest mountains, and would reach all the way down to the Earth if the obstacle of those same mountains didn't block it. This matches what you say — for just as you affirm that the air hemmed in by the mountain ridges is carried around by the roughness of the moving Earth, we say the converse: that the whole element of air is carried around by the motion of the heavens, except the part lying below the ridges, which is held back by the roughness of the motionless Earth. And where you said that if that roughness were taken away, the air too would lose being swept along, we can say that with the same roughness removed, all the air would go on with its motion. Hence, because the surfaces of the wide seas are smooth and polished, over them the motion of the breeze carries on, blowing perpetually from the east; and this is felt more in the regions under the equinoctial and within the tropics, where the motion of the heavens is faster. And just as this celestial motion is powerful enough to carry all the free air along with it, so we may very reasonably say that the same motion also acts on the moving water, since water is fluid and not fastened to the immobility of the Earth. And we can affirm this all the more confidently in that, by your own admission, this motion must be very small compared with the cause that produces it — a cause which, circling the whole terrestrial globe in one natural day, covers many hundreds of miles an hour, especially toward the equinoctial, whereas the currents of the open sea run at very few miles an hour. And so the westward voyages come out easy and quick not only thanks to the perpetual easterly breeze, but to the course of the waters as well — a course from which the ebb and flow might perhaps also arise, by way of the different lay of the shores, where the water, going to strike against them, can turn and run back with a contrary motion. Experience shows us as much in the course of rivers: wherever the water, in the unevenness of the banks, meets some part that juts out, or some hollow below, there the water wheels around, and you plainly see it run back the other way. So it seems to me that from the very effects by which you argue for the mobility of the Earth, and which you offer as the cause of them, one can allege a cause that concludes well enough while keeping the Earth at rest and restoring the mobility to the heavens.
Salviati: There's no denying your argument is ingenious and has a good deal of the probable about it — probable, I say, in appearance, but not in fact and reality. It has two parts. In the first, it accounts for the continuous motion of the easterly breeze, and for a like motion in the water; in the second, it tries to draw from the same source the cause of the ebb and flow. The first part has, as I said, some semblance of probability, though far less than what we take from the Earth's motion; the second is not merely improbable but flatly impossible and false. Coming to the first, where it's said that the lunar concave sweeps along the element of fire and all the air up to the tops of the highest mountains, I say, to begin with, that it's doubtful whether there even is an element of fire; but granting there is, there's grave doubt about the sphere of the Moon, as about all the others — whether there really are such solid, enormous bodies, or whether, beyond the air, there extends a continuous expanse of a substance far more tenuous and pure than our air, through which the planets go wandering, as by now a good many of these same philosophers are beginning to hold. But whichever way it is, there's no reason why fire, from the mere contact of a surface you yourself judge to be perfectly polished and smooth, should be carried around throughout its whole depth by a motion foreign to its own natural bent — as has been amply proved, and demonstrated with sound experiments, in The Assayer; setting aside the further improbability of such a motion being transfused from the most subtle fire through the far denser air, and then from the air into the water. But that a body with a rough, mountainous surface, in turning upon itself, carries with it the air right next to it, against which its prominences go striking — that is not merely probable but necessary, and one can actually see it by experiment; though even without seeing it, I don't believe there's any mind that would doubt it. As for the other part: granting that the motion of the heavens did carry the air, and the water too, that motion would still have nothing to do with the ebb and flow. For since from a single, uniform cause nothing can follow but a single, uniform effect, what we ought to observe in the water would be a continuous, uniform course from east toward west — and only in that sea which, closing on itself, encircles the whole globe. But in bounded seas, like the Mediterranean, shut off on the east, there could be no such motion; because if its water could be driven westward by the course of the heavens, it would have been left dry many centuries ago. Besides which, our water doesn't run only westward but comes back the other way, toward the east, and does so on regular schedules. And though you say, with the example of the rivers, that even if the sea's course were originally the single one from east to west, still the different lay of the shores can make part of the water surge back — this I grant you. But you must take note, my dear Simplicio, that wherever the water runs back for that reason, it runs back there perpetually, and wherever it runs straight on, it always runs the same way — that's exactly what the example of the rivers shows you. Whereas in the case of the ebb and flow, you have to find and produce a reason why, in one and the same place, the water should now run one way and now the opposite; and those effects, being contrary and unlike, you'll never be able to deduce from a uniform, constant cause. And the same thing that overthrows this notion — of the sea's motion being contributed by the daily motion of the heavens — also demolishes the notion of anyone who'd want to admit only the daily motion of the Earth and thought that by that alone he could account for the ebb and flow. For since that effect is not uniform, the cause of it absolutely must be non-uniform and changeable.
Simplicio: I've nothing to say in reply — neither of my own, given the weakness of my wit, nor from anyone else, given the novelty of the opinion. But I'd well believe that, once it were put about in the schools, there'd be no shortage of philosophers who'd know how to challenge it.
Sagredo: We'll wait, then, for such an occasion; and meanwhile, if it so please you, Salviati, let's go on ahead.
Salviati: Everything said so far belongs to the daily period of the ebb and flow. First we demonstrated, in general, its primary and universal cause, without which none of this effect would follow at all; then, moving on to the particular incidents — varied, and in a way irregular — that are observed in it, we treated the secondary and attendant causes on which they depend. Now come the other two periods, the monthly and the annual, which bring no new and different incidents beyond those already considered in the daily period, but work upon those same ones by making them greater and smaller at different points of the lunar month and at different seasons of the solar year — almost as if both the Moon and the Sun had a hand in the work and in producing these effects. And that's something my mind refuses utterly; for seeing, as I do, that this business of the seas is a local, tangible motion, worked in an immense mass of water, it can't bring itself to sign on to influences, to mild warmths, to dominances by occult qualities, and to similar empty fancies — which, tantum abest, so far from being, or possibly being, the causes of the tides, that on the contrary the tides are the cause of them: the cause, that is, of their springing up in the sort of brains fitter for chatter and show than for the study and investigation of nature's more hidden works. Such men, rather than bring themselves to utter that wise, honest, modest little word "I don't know," rush to let fall from their mouths — and from their pens too — any great absurdity you please. And the mere fact that this same Moon and this same Sun don't act — not with their light, not with motion, not with heat great or mild — upon smaller bodies of water; that indeed, to make water rise by heat, you'd have to bring it very nearly to a boil; and, in short, that we can't artificially imitate the movements of the tide by any means whatever except by moving the vessel — shouldn't all this convince everyone that the other things put forward as causes of the effect are empty fantasies, wholly alien from the truth? I say, then, that if it's true that one effect has only one primary cause, and that between the cause and the effect there's a firm, constant connection, then it necessarily follows that whenever a firm, constant change is seen in the effect, there's a firm, constant change in the cause. And because the changes that come over the tides at different parts of the year and month have their own firm, constant periods, we're forced to say that a regular change occurs, at those same times, in the primary cause of the tides. Now the change found at those times in the tides consists in nothing but their magnitude — that is, in the waters rising and falling more or less, and running with greater or smaller force. Therefore what is the primary cause of the ebb and flow must, at those determined times, increase or diminish its own strength. But we've already concluded that the primary cause of the tides is the unevenness and non-uniformity in the motion of the vessels holding the water; therefore this non-uniformity must, from time to time, correspondingly grow more uneven — must, that is, become greater and smaller. Now we should recall how this non-uniformity — the varying speed of motion of the vessels, that is, of the parts of the Earth's surface — depends on their moving with the composite motion that results from coupling the two motions, annual and daily, belonging to the whole terrestrial globe. Of these, it's the daily whirl, by now adding to and now subtracting from the annual motion, that produces the non-uniformity in the composite motion; so that in the additions and subtractions the daily whirl makes to the annual motion lies the original cause of the uneven motion of the vessels, and consequently of the ebb and flow. In such a way that, if these additions and subtractions were always made in the same proportion to the annual motion, the cause of the ebb and flow would indeed persist, but so as to act perpetually in the same manner. But we need to find the cause of these same tides being made, at different times, greater and smaller; therefore we must (if we want to keep the cause the same) find some change in these additions and subtractions that makes them more and less powerful in producing the effects that depend on them. And I don't see how such power and weakness could be brought about except by making these same additions and subtractions now greater and now smaller, so that the quickening and slowing of the composite motion happens now in a greater and now in a smaller proportion.
Sagredo: I feel myself being led very gently by the hand; and although I meet no stumbling blocks along the road, still, like a blind man, I don't see where your guidance is taking me, nor can I imagine where this journey is to end.
Salviati: Great as the difference is between my slow philosophizing and your very swift reasoning, still, on this particular point we now have in hand, I won't be surprised that the sharpness of your wit is left clouded by the high, dark fog that hides from us the goal we're walking toward. And my surprise fades when I remember how many hours, how many days — and, more than that, how many nights — I spent on this speculation, and how many times, despairing of ever reaching the end of it, I struggled, to console myself, to believe, like the unhappy Orlando, that what the testimony of so many trustworthy men set before my eyes could not, after all, be true. So don't be surprised if this once, against your custom, you don't foresee the mark; and if you are surprised, I believe the outcome — quite unexpected, as far as I can judge — will put an end to your surprise.
Sagredo: I thank God, then, that He kept such despair from carrying you off to the end the tale gives the wretched Orlando — or to the one, no less fabulously reported, they tell of Aristotle — so that neither I nor anyone else should be left robbed of the discovery of a thing as hidden as it is longed for. I beg you, then, to feed my starving hunger as soon as you can.
Salviati: Here I am, ready to satisfy you. We had got as far as finding out in what way the additions and subtractions of the Earth's whirl upon the annual motion could be made now in a greater and now in a smaller proportion — a variation which, and nothing else, could be assigned as the cause of the monthly and annual changes seen in the magnitude of the tides. Now, I observe that this proportion, between the additions and subtractions of the daily whirl and the annual motion, can be made greater and smaller in three ways. The first is by increasing and diminishing the speed of the annual motion, while keeping the additions and subtractions made by the daily whirl at the same size; for since the annual motion is about three times greater — that is, faster — than the daily motion (taken even at its great circle), if we increase it further, the additions or subtractions of the daily motion will alter it less; whereas, on the contrary, if we make it slower, it will come to be altered in a greater proportion by that same daily motion. It's like adding or taking away four degrees of speed from something moving at twenty degrees: that alters its course less than the same four degrees added or subtracted would alter something moving at only 10 degrees. The second way would be to make the additions and subtractions greater or smaller while keeping the annual motion at the same speed — as easy to grasp as it's plain that a speed of, say, 20 degrees is altered more by adding or subtracting 10 degrees than by adding or subtracting 4. The third way would be when these two are joined together, diminishing the annual motion and increasing the daily additions and subtractions. Up to here, as you see, it hasn't been hard to get; but it was laborious indeed for me to find out in what way this could be brought about in nature. Yet in the end I find that she makes marvelous use of it, and by means almost past imagining — marvelous and unimaginable to us, I mean, but not to her, who works with the utmost ease and simplicity even the things that fill our intellect with boundless wonder; and what is hardest for us to understand is easiest for her to do. Going on further, then, and having shown how the proportion between the additions and subtractions of the whirl and the annual motion can be made greater and smaller in two ways (I say two, because the third is compounded of the first two), I add that nature makes use of both; and, further, I add that if she made use of only one, one of the two periodic changes would have to be taken away. That of the monthly period would cease, if the annual movement were not altered; and if the additions and subtractions of the daily whirl kept themselves continually equal, the changes of the annual period would be lacking.
Sagredo: So the monthly variation in the tides depends on the change in the Earth's annual motion? And the yearly variation in those same tides derives from the additions and subtractions of the daily whirl? Now I find myself more confused than ever, and more hopeless of ever managing to grasp how this tangle holds together — more knotted, it seems to me, than the Gordian knot. And I envy Simplicio, from whose silence I gather that he's understood the whole of it, and is free of the confusion that so clutters my imagination.
Simplicio: I do believe, Sagredo, that you find yourself confused, and I think I even know the cause of your confusion — which, to my mind, comes from this: of the things Salviati has brought up just now, part you understand and part you don't. It's also true that I'm free of confusion, but not for the reason you suppose — that is, not because I've grasped the whole of it. Quite the opposite: it comes to me from grasping nothing at all. Confusion lies in a multitude of things, not in nothing.
Sagredo: You see, Salviati, how a few little jerks of the bridle given to Simplicio these past days have made him tame, and changed him from a jumper into a gentle palfrey. But please, without any more delay, get us both out of our trouble.
Salviati: I'll strain my clumsy powers of expression as far as they'll go; their dullness will be made up for by the sharpness of your wits. There are two phenomena whose causes we have to track down. The first concerns the differences that occur in the tides over the monthly period; the other belongs to the yearly period. First we'll speak of the monthly, then treat the yearly; and we must resolve all of it according to the foundations and hypotheses already established, without introducing any novelty — not into astronomy, nor into the universe — for the sake of the tides. Instead, let's show that of all the various phenomena we observe in them, the causes reside in things already known, and accepted as true and beyond doubt.
I say, then, that it's a true, natural — indeed necessary — thing that one and the same moving body, set turning in a circle by the same moving power, should take a longer time to complete its course along a larger circle than along a smaller one. This is a truth accepted by everyone, and confirmed by every experiment, of which I'll offer a few.
In wheel-clocks, and the large ones in particular, to regulate the timekeeping the makers fit a certain rod that turns freely in the horizontal, and at its ends they hang two lead weights; and when the clock runs too slow, merely by bringing those leads a little nearer the center of the rod they make its swings more frequent; and on the other hand, to slow it down, it's enough to draw the same weights out toward the ends, because then the swings come more seldom, and consequently the intervals of the hours grow longer. Here the moving power is the same — the counterweight; the moving bodies are the same leads; and their swings are more frequent when they're nearer the center, that is, when they move along smaller circles.
Hang equal weights from unequal cords, and, drawn aside from the vertical, let them go free: we'll see the ones on shorter cords make their swings in shorter times, as being those that move along smaller circles. But more: attach such a weight to a cord that rides over a nail fixed in the ceiling, and hold the other end of the cord in your hand; having set the hanging weight going, then, while it's making its swings, pull the end of the cord you're holding so that the weight rises. You'll see, as it lifts, the frequency of its swings increase, since they're being made continually along smaller circles.
And here I want you to note two particulars, worth knowing. One is that the swings of such a pendulum are made, with such necessity, under certain determined times, that it's utterly impossible to make it swing under any other times except by lengthening or shortening the cord — of which you can even satisfy yourself right now, by experiment: tie a stone to a string, hold the other end in your hand, and try whether, by any device whatever, you can ever manage to make it go back and forth under anything but one determined time, short of lengthening or shortening the string — which you'll see is flatly impossible.
The other particular, truly marvelous, is that the same pendulum makes its swings with the same frequency — or with so slight, so nearly imperceptible a difference — whether they're made along the largest arcs or the smallest of the same circumference. I mean that if we move the pendulum from the vertical by only one, two, or three degrees, or move it 70, 80, or even a full quarter-circle, once let go it will, in the one case and the other, make its swings with the same frequency — the first, where it has to move along an arc of 4 or 6 degrees, just as much as the second, where it has to pass through arcs of 160 degrees or more. This is seen more plainly still by hanging two equal weights from two equally long threads, then drawing one aside from the vertical by a small distance and the other by a very great one; set free, they'll go and return in the same times, the one along quite small arcs, the other along very great ones.
From which follows the conclusion of a most beautiful problem: that, given a quarter-circle (I'll sketch a little figure here on the ground) — say this one AB, set upright to the horizon so that it stands on the plane, touching at the point B — and having made an arc, with a board well planed and smooth on its concave side, bent to the curve of the circumference ADB, so that a ball, well rounded and polished, can run freely inside it (the frame of a sieve suits this experiment) — I say that, put the ball wherever you like, near or far from the lowest terminus B — say, putting it at the point C, or here at D, or at E — and let go, in equal times, or times imperceptibly different, it will arrive at the terminus B, whether it starts from C or from D or from E or from any other place whatever: a phenomenon truly marvelous.
Add another phenomenon, no less beautiful than this: that along all the chords drawn from the point B to the points C, D, E, and to any other — not only taken in the quadrant BA, but in the whole circumference of the entire circle — the same moving body will descend in absolutely equal times; so that in the same time it will descend along the whole diameter erected perpendicular over the point B as it descends along BC, even if BC subtended only a single degree or a smaller arc.
Add the other marvel, which is that the motions of falling bodies made along the arcs of the quadrant AB are made in shorter times than those made along the chords of the same arcs: so that the swiftest motion, made in the shortest time, by a body going from the point A to the terminus B, will be the one made not along the straight line AB (though it's the shortest of all the lines that can be drawn between the points A and B), but along the circumference ADB. And taking, too, any point you like in that same arc — say, for instance, the point D — and drawing the two chords AD, DB, the moving body, starting from the point A, will reach B in less time coming along the two chords AD, DB than along AB alone; but the shortest time of all will be that of the fall along the arc ADB. And understand the same phenomena of all the other smaller arcs, taken from the lowest terminus B upward.
Sagredo: No more, no more! You so overwhelm me with wonder, and pull my mind in so many directions, that I fear little of it will be left free and clear to apply to the main matter we're treating — which is quite obscure and difficult enough on its own. I'll beg you, though, to do me the favor, once we've finished this speculation about the tides, of being here on other days too, to honor this house — mine and yours — and to discourse on so many other problems we've left hanging, which are perhaps no less curious and beautiful than the one we've treated on the past days and must finish today.
Salviati: I'll be at your service; but we'll need more than one or two sessions, if, on top of the other questions reserved for separate treatment, we want to add all the many that belong to local motion — of natural bodies as much as of projectiles — a subject treated at length by our friend the Academician. But coming back to our first purpose, where we were explaining how, for bodies moved in circles by a moving power that keeps itself continually the same, the times of their circuits were fixed and determined, and impossible to make longer or shorter — having given examples, and brought experiments both sensible and doable by us — we can confirm the same truth with the observed motions of the heavenly planets, in which the same rule is seen to hold: that those which move along larger circles use up more time in traversing them. A very ready observation of this we have from the Medicean Stars — Jupiter's four little moons — which in short times make their revolutions around Jupiter. So there's no room for doubt — indeed we may hold it for firm and sure — that when, for example, the Moon, continuing to be moved by the same moving power, were drawn little by little into smaller circles, she would acquire a disposition to shorten the times of her periods, just like that pendulum whose cord we were shortening in the course of its swings — that is, shortening the radius of the circumferences it passed through.
Now know that what I've offered about the Moon as an example actually happens, and holds true, in essence, in fact. Let's recall that it was already concluded by us, together with Copernicus, that it's impossible to separate the Moon from the Earth, around which — beyond dispute — she moves in a month. Let's likewise recall that the terrestrial globe, always accompanied by the Moon, travels along the circumference of the great orb around the Sun in a year, in which time the Moon revolves around the Earth nearly 13 times. From which revolving it follows that the Moon is sometimes near the Sun — that is, when she's between the Sun and the Earth — and sometimes much farther off — that is, when the Earth stands between the Moon and the Sun: near, in short, at the time of her conjunction and new moon; far, at the full moon and opposition. And the greatest distance and the greatest nearness differ by as much as the diameter of the lunar orb.
Now, if it's true that the power which moves the Earth and the Moon around the Sun keeps always the same vigor; and if it's true that the same moving body, moved by the same power but along unequal circles, passes similar arcs of the smaller circles in shorter times — then we must necessarily say that the Moon, when she's at a smaller distance from the Sun (that is, at the time of conjunction), passes greater arcs of the great orb than when she's at a greater distance (that is, at opposition and full moon). And this lunar unevenness must be shared by the Earth as well. For if we conceive a straight line drawn from the center of the Sun through the center of the terrestrial globe, and prolonged as far as the lunar orb, this will be the radius of the great orb, along which the Earth, were she alone, would move uniformly; but if along that same radius we place another body to be carried — putting it now between the Earth and the Sun, and now beyond the Earth at a greater distance from the Sun — it must be that in this second case the shared motion of the two along the circumference of the great orb, by reason of the Moon's remoteness, turns out somewhat slower than in the other case, when the Moon is between the Earth and the Sun, that is, at the smaller distance. So in this business exactly what happens in the clock happens: the Moon representing to us that lead which is fixed now farther from the center, to make the swings of the rod less frequent, and now nearer, to make them more frequent.
From here it can be plain how the Earth's annual motion along the great orb and under the ecliptic is not uniform, and how its irregularity derives from the Moon, and has its own periods and monthly returns. And since it was concluded that the periodic alterations of the tides — monthly and yearly — could derive from no cause other than the altered proportion between the annual motion and the additions and subtractions of the daily whirl; and since such alteration could come about in two ways, namely by altering the annual motion while keeping the amount of the additions fixed, or by changing the size of these while keeping the annual motion uniform — we've now found the first of these two ways, founded on the irregularity of the annual motion, which depends on the Moon and has its monthly periods. It's therefore necessary that, for this cause, the tides have a monthly period, within which they grow greater and smaller. Now you see how the cause of the monthly period resides in the annual motion, and at the same time you see what the Moon has to do with this business, and how she takes a part in it without having anything at all to do with either seas or waters.
Sagredo: If someone who had no acquaintance with any kind of stairs were shown a very tall tower, and asked whether he had the heart to reach its topmost height, I absolutely believe he'd say no, not understanding that it could be reached in any way but by flying; but if a stone no higher than half an arm-length were shown him, and he were asked whether he thought he could climb up onto that, I'm certain he'd answer yes — and wouldn't deny that not once, but 10, 20, and 100 times, he could easily climb it. So that if the stairs were then shown him, by means of which — with the ease he'd granted — one could get up to where a moment before he'd declared it impossible to arrive, I believe that, laughing at himself, he'd confess his little foresight. You, Salviati, have led me by degrees so gently that, not without wonder, I find myself arrived with the least effort at that height where I believed one could not arrive. It's quite true that, the stairway having been dark, I didn't notice I'd approached or reached the top until, coming out into the bright air, I discovered a great sea and a great countryside. And just as in climbing one step there's no effort at all, so, one by one, your propositions seemed to me so clear that, little or nothing new coming to me, the gain seemed to me little or none — whence all the more the wonder grows in me at the unexpected upshot of this discourse, which has led me to the understanding of a thing I reckoned inexplicable. Only one difficulty remains to me, from which I desire to be freed; and this is that if the motion of the Earth, together with that of the Moon under the zodiac, are irregular, that irregularity ought to have been observed and noted by the astronomers — which I don't know to have happened. So you, who are better informed than I in these matters, free me from the doubt, and tell me how the fact stands.
Salviati: Very reasonably you doubt; and, answering the objection, I say that although astronomy, in the course of many centuries, has made great progress in investigating the constitution and the motions of the heavenly bodies, it hasn't yet arrived at such a point that very many things don't remain undecided — and perhaps still many others hidden. It's to be believed that the first observers of the sky knew of nothing but a motion common to all the stars, namely this daily one. I'll readily believe that within a few days they noticed the Moon was inconstant in keeping company with the other stars; but that then many years ran on before all the planets were distinguished. And in particular I think that Saturn, for its slowness, and Mercury, for being seen only rarely, were among the last to be recognized as wanderers and rovers. Many more years, it's to be believed, passed before the stations and retrogradations of the three upper planets were observed, as also their approaches to and recessions from the Earth — occasions necessarily prompting the introduction of eccentrics and epicycles, things unknown even to Aristotle, since he makes no mention of them. Mercury and Venus, with their marvelous appearances, how long they've held the astronomers in suspense over settling — of all things — their very position! So that even the mere order of the world's bodies, and the whole structure of the parts of the universe known to us, remained in doubt until the time of Copernicus, who has at last pointed out to us the true constitution and the true system according to which those parts are ordered — so that we're certain Mercury, Venus, and the other planets revolve around the Sun, and that the Moon revolves around the Earth. But how each planet then governs itself in its particular revolution, and how the structure of its orb precisely stands — which is what's commonly called its theoric — we cannot yet resolve beyond doubt: let Mars, which so troubles the modern astronomers, be our witness; and to the Moon herself varied theorics have been assigned, after Copernicus himself changed hers a good deal from Ptolemy's.
And to come down more to our particular case — that is, to the apparent motion of the Sun and the Moon — of the Sun a certain great unevenness has been observed, by which it passes the two half-circles of the ecliptic, divided by the points of the equinoxes, in quite different times; in passing one of them it uses about nine days more than in passing the other — a difference, as you see, very great and notable. But whether, in passing small arcs — such as, for example, the 12 signs — it keeps a perfectly regular motion, or instead proceeds now somewhat faster and now slower, as must happen when the annual motion is only apparently the Sun's, but in reality the Earth's, accompanied by the Moon — this has not so far been observed, nor perhaps looked into. And of the Moon, whose returns have been investigated chiefly for the sake of eclipses — for which it's enough to have exact knowledge of her motion around the Earth — it has likewise not been investigated with full curiosity what her progress is along the particular arcs of the zodiac. That the Earth and the Moon, then, in running along the zodiac — that is, along the circumference of the great orb — speed up somewhat at the new moons and slow down at the full moons, must not be doubted just because such unevenness hasn't shown itself. This has happened for two reasons: first, because it hasn't been looked for; second, because it may be not very great.
Nor does it need to be very great to produce the effect we see in the alteration of the sizes of the tides, because not only such alterations, but the tides themselves, are a small thing compared with the size of the bodies in which they take place — even though, with respect to us and our littleness, they seem great things. For to add or take away one degree of speed where there are naturally 700 or 1000 can't be called a great alteration, either in what confers it or in what receives it. The water of our sea, carried by the daily whirl, makes about 700 miles an hour (which is the motion common to the Earth and to it, and therefore imperceptible to us); what becomes noticeable to us in the currents is not one mile an hour (I speak of the open sea, not of the straits); and this is what alters the primary, natural, and great motion. And such an alteration is a great deal with respect to us and to ships, because to a vessel that by the force of its oars would make, say, 3 miles an hour in still water, having that current in its favor rather than against it will mean double the voyage — a most notable difference in the boat's motion, but a very tiny one in the sea's motion, which is altered by its seven-hundredth part. The same I say of the rising and falling of one, two, or three feet — and barely four or five at the far end of a gulf two thousand or more miles long, and where there are depths of hundreds of feet: this alteration is far less than if, in one of the boats that carry fresh water, that water, when the boat comes to a stop, were to rise at the prow by the thickness of a sheet of paper. I conclude, then, that very tiny alterations, with respect to the immense size and the utmost speed of the seas, are enough to make in them changes that are great in relation to our littleness and to our own affairs.
Sagredo: I'm fully satisfied on that point. What remains is for you to explain how those additions and subtractions arising from the daily whirl come to be now greater and now smaller — the variation on which, as you hinted, the yearly cycle of the increases and decreases of the ebb and flow depends.
Salviati: I'll do everything I can to make myself understood; but the difficulty of the thing itself, and the great mental abstraction it takes to grasp it, daunt me. The inequality of the additions and subtractions that the daily whirl makes upon the annual motion depends on the tilt of the axis of the daily rotation with respect to the plane of the great orb — or, if you like, of the ecliptic. Because of this tilt, the equinoctial cuts the ecliptic, remaining tilted and oblique upon it by the same amount as the axis is tilted. The size of the additions comes to equal the whole diameter of that equinoctial when the center of the Earth is at the solstitial points; but away from those points it amounts to less and less, as that center approaches the equinoctial points, where these additions are smaller than anywhere else. That is the whole of it — but wrapped in the obscurity you can see.
Sagredo: In the obscurity I can't see, rather — because so far I understand nothing of it.
Salviati: I foretold as much. Still, let's try whether by drawing a bit of a figure we can gain some light — though it would be far better to represent it with solid bodies than with mere drawings. We'll help ourselves out with perspective and foreshortening. So let us mark, as before, the circumference of the great orb, in which take the point A to be one of the solstitial points, and the diameter A P to be the common section of the solstitial colure and the plane of the great orb — or, if you like, of the ecliptic — and at that point A let the center of the terrestrial globe be located, whose axis CAB, tilted upon the plane of the great orb, falls in the plane of the said colure, which passes through both axes, that of the equinoctial and that of the ecliptic. And for less confusion we'll mark only the equinoctial circle, labeling it with these letters DGEF, whose common section with the plane of the great orb is the line DE, so that the half of this equinoctial DFE will remain tilted below the plane of the great orb, and the other half DGE raised above it. Now understand the revolution of this equinoctial to run according to the sequence of the points D, G, E, F, and the motion of the center to go from A toward E. And because, with the center of the Earth at A, the axis CB (which stands upright to the diameter of the equinoctial DE) falls, as we said, in the solstitial colure — whose common section with the great orb is the diameter PA — that line PA will be perpendicular to DE, the colure being upright to the great orb, and therefore DE will be the tangent to the great orb at the point A. So that in this position the motion of the center along the arc AE, which is one degree a day, differs very little — indeed, it's as if it were made along the tangent DAE. And because, through the daily whirl, the point D carried through G to E adds to the motion of the center — moved almost along the same line DE — as much as the whole diameter DE, and on the other hand subtracts just as much in moving through the other half-circle EFD, the additions and subtractions in this place, that is at the time of the solstice, will be measured by the whole diameter DE.
Let us now go on to see whether, at the times of the equinoxes, they're of the same size. Transferring the center of the Earth to the point I, a quarter away from the point A, understand the same equinoctial GEFD, its common section with the great orb DE, the axis with the same tilt CB. But the tangent to the great orb at the point I will no longer be DE, but another that will cut it at right angles — let this be marked HIL — along which the motion of the center I will be directed, proceeding along the circumference of the great orb. Now in this position the additions and subtractions are no longer measured on the diameter DE, as before, because, since that diameter doesn't extend along the line of the annual motion HL but rather cuts it at right angles, those termini D, E neither add nor take away anything. Instead the additions and subtractions have to be taken from the diameter that falls in the plane upright to the plane of the great orb and that cuts it along the line HL — which diameter will now be this one, GF. And the additive motion, so to speak, will be the one made from the point G through the half-circle GEF, and the subtractive the remainder, made through the other half-circle FDG. Now this diameter, since it isn't in the same line HL of the annual motion but rather cuts it, as you see, at the point I — the terminus G remaining raised above and F sunk below the plane of the great orb — does not determine the additions and subtractions along its whole length. Rather, their amount must be taken from the part of the line HL intercepted between the perpendiculars dropped upon it from the termini G, F — namely these two, GS, FV — so that the measure of the additions is the line SV, smaller than GF, or than DE, which was the measure of the additions at the solstice A. Then, as the center of the Earth is set at other points of the quadrant AI, by drawing the tangents at those points and the perpendiculars falling upon them from the termini of the equinoctial's diameters — marked out by the planes upright, through those tangents, to the plane of the great orb — the parts of those tangents (which will always be smaller toward the equinoxes and greater toward the solstices) will give us the amounts of the additions and subtractions. As for how much the smallest additions differ from the greatest, that's easy to know, because between them is the same difference as between the whole axis or diameter of the sphere and the part of it that lies between the polar circles — which is smaller than the whole diameter by about a twelfth part — meaning, of course, the additions and subtractions made on the equinoctial; on the other parallels they're smaller, in proportion as their diameters shrink.
This is as much as I can tell you on this subject, and as much, perhaps, as can fall under any knowledge of ours — which, as you well know, can be had only of those conclusions that are firm and constant, such as the three cycles of the ebb and flow considered in general, depending as they do on causes invariable, single, and eternal. But because with these primary and universal causes there then mix in the secondary and particular ones, capable of producing many variations — and these secondary causes are partly unobservable and inconstant, as, for example, the shifting of the winds, and partly, though fixed and determinate, still not observed because of their multitude, such as the lengths of the gulfs, their various slopes toward this side or that, the many and so different depths of the waters — who could, except perhaps after very long observations and thoroughly reliable reports, form such ready histories of them as could serve as secure hypotheses and suppositions to anyone who wished, by combining them, to give adequate reasons for all the appearances — I'll even say the anomalies and particular irregularities — that may be discerned in the movements of the waters? I'll content myself with having pointed out that accidental causes do exist in nature, and are powerful enough to produce many variations; the minute observations I'll leave to be made by those who frequent the various seas. And only, to close this discussion of ours, I'll set down for your consideration how the precise times of the ebb and flow are altered not only by the lengths of the gulfs and the varying depths, but also — I think — how a notable alteration may come from the joining of different stretches of sea, differing in size and in position, or let's say slope. Just such a difference falls out right here in the Adriatic gulf, far smaller than the rest of the Mediterranean and set at so different a slope that, whereas the latter has its boundary closing it off on the eastern side — the shores of Syria — this one is shut in at its most western part. And because at the far ends the ebbs and flows are much greater — indeed, only there are the risings and fallings very great — it may very likely happen that the times of the floods at Venice fall during the ebbs of the other sea, which, being much larger and more directly stretched from west to east, comes in a certain way to have dominion over the Adriatic. And so it wouldn't be surprising if the effects depending on the primary causes did not verify themselves at the proper times, answering to the cycles, in the Adriatic, but rather in the rest of the Mediterranean. But these particulars call for long observations, which I have neither made up to now nor am likely to be able to make in the future.
Sagredo: It seems to me you've done a great deal in opening for us the first entrance to so lofty a speculation. Even if you'd brought us nothing beyond that first general proposition — which to me seems to admit no reply, where it's so conclusively declared that, with the vessels containing the sea-waters standing still, it would be impossible, by the common course of nature, for those movements to take place in them that we see taking place; and that, on the contrary, granting the motions attributed for other reasons by Copernicus to the terrestrial globe, similar variations must necessarily follow in the seas — even if, I say, there were nothing else, this alone seems to me to surpass by so great an interval the empty notions brought forward by so many others, that merely to think back on those turns my stomach. And I marvel greatly that among men of sublime intellect — and there've been not a few — it never crossed anyone's mind, the incompatibility there is between the back-and-forth motion of the contained water and the immobility of the containing vessel, a contradiction that now seems to me so obvious.
Salviati: More to be marveled at is that, though it did occur to some to refer the cause of the ebb and flow to the motion of the Earth — showing in that a sharper insight than the common run — when they came to pin the business down they grasped nothing, for not having noticed that a single uniform motion isn't enough — such as, for instance, the simple daily motion of the terrestrial globe — but that an uneven motion is required, now accelerated and now retarded. Because when the motion of the vessels is uniform, the contained waters get used to it and never make any change at all. To say too (as is reported of a certain ancient mathematician) that the motion of the Earth, meeting the motion of the lunar orb, causes the ebb and flow by that clash, is utterly empty — not only because it isn't explained, nor can one see how it should follow, but the manifest falsity of it is plain, seeing that the turning of the Earth isn't contrary to the motion of the Moon but goes the same way. So that all that's been said and imagined by the others up to now remains, in my opinion, entirely invalid. But of all the great men who have philosophized on this marvelous effect of nature, I marvel at Kepler more than at any of them: a man of free and acute intellect, who had in his hands the motions attributed to the Earth, and yet lent his ear and his assent to a dominion of the Moon over the water, and to occult properties, and suchlike childishness.
Sagredo: I'm of the opinion that what's happening to me at present has happened to these more speculative men too — namely, not being able to grasp the tangle of the three cycles, annual, monthly, and daily, and how their causes appear to depend on the Sun and the Moon without the Sun or the Moon having anything to do with the water. It's a business that, for full understanding, needs of me a steadier and longer application of mind, which for now is quite clouded over by the novelty and the difficulty. But I don't despair — by coming back to it on my own, in solitude and silence, to chew over what remains ill-digested in my imagination, of coming to possess it. So then, from the discussions of these four days we have great testimonies in favor of the Copernican system — among which these three, taken, the first from the stations and retrogradations of the planets and from their approaches to and retreats from the Earth; the second from the revolution of the Sun upon itself and from what is observed in its spots; the third from the ebb and flow of the sea — show themselves quite conclusive.
Salviati: To these one might perhaps shortly add a fourth, and maybe even a fifth: the fourth, I say, taken from the fixed stars, if in them, by the most exact observations, those minimal changes should appear that Copernicus takes to be imperceptible. And there's now arising a fifth novelty, from which mobility in the terrestrial globe might be argued — by means of what the most illustrious Signor Cesare, of the most noble Marsili family of Bologna, likewise a Lincean Academician, is very subtly discovering: in a most learned paper he is setting out how he has observed a continual change, though a very slow one, in the meridian line. This paper, which I lately saw with astonishment, I hope he'll make copies of for all students of the marvels of nature.
Sagredo: This isn't the first time I've heard tell of the exquisite learning of this gentleman, and of how anxious a protector he shows himself of all men of letters. And if this or any other of his works comes to light, we can be sure already that it will be something distinguished.
Salviati: Now, since it's time to put an end to our discussions, it remains for me to beg you that, if in going back over the things I've brought forward more calmly you should meet difficulties or doubts not well resolved, you'll excuse my failing — both for the novelty of the thought, and for the weakness of my wit, and for the greatness of the subject, and finally because I don't claim, and never have claimed from others, that assent which I don't give to this fancy myself — a fancy I could very easily admit to be a most empty chimera and a most solemn paradox. And you, Sagredo, though in the discussions we've had you've many times, with great applause, shown yourself contented with some of my thoughts, that, I reckon, came in part more from their novelty than from their certainty, but much more from your courtesy, which has believed, and wished by its assent to bring me that pleasure we naturally take in the approval and praise of what is our own. And just as your kindness has obliged me, so Simplicio's candor has pleased me; indeed his steadfastness in sustaining, with so much force and so intrepidly, the doctrine of his master has made me most fond of him. And as I give thanks to you, Sagredo, for your most courteous affection, so I ask Simplicio's pardon if now and then I've upset him with my too bold and resolute speech; and let him be sure that I haven't done it moved by any ill feeling, but only to give him greater occasion to bring forward lofty thoughts, so that I might make myself more learned.
Simplicio: There's no need for you to make these excuses, which are superfluous, and above all to me — who, being used to finding myself among gatherings and public disputes, have a hundred times heard the disputants not only heat up and grow angry with one another, but even break out into insulting words, and sometimes run very close to coming to blows. As for the discussions we've had, and in particular this last one concerning the cause of the ebb and flow of the sea, I truly don't remain entirely satisfied of it; yet by whatever slight idea I've formed of it, I confess your thought seems to me far more ingenious than any of the others I've heard, though even so I don't hold it for true and conclusive. Rather, keeping always before the eyes of my mind a most solid doctrine that I once learned from a most learned and eminent person, and in which one must rest, I know that both of you, if asked whether God, with His infinite power and wisdom, could confer upon the element of water the back-and-forth movement we see in it by some other means than by moving the containing vessel — I know, I say, that you'll answer that He could have, and known how to, do this in many ways, and even in ways unimaginable to our intellect. Whereupon I immediately conclude to you that, this being so, it would be excessive boldness for anyone to want to limit and confine the divine power and wisdom to one particular fancy of his own.
Salviati: An admirable and truly angelic doctrine — to which very harmoniously answers that other, likewise divine, which, while it allows us to dispute about the constitution of the world, adds to us (perhaps so that the exercise of human minds should not be cut off or grow slack) that we are not to find out the work fashioned by His hands. Let the exercise permitted and ordained to us by God, then, avail to make us recognize, and so much the more admire, His greatness, the less we find ourselves fit to penetrate the deep abysses of His infinite wisdom.
Sagredo: And let this be the last close of our four days' reasonings. After which, if it should please Salviati to take some interval of rest, our curiosity must grant it him — on condition, though, that when it's less inconvenient to him he'll come back to satisfy the desire, mine in particular, concerning the problems left behind, which I've noted down to put to him in one or two further sessions, as we agreed. And above all I'll be waiting with the utmost eagerness to hear the elements of our Academician's new science of local motions, natural and violent. And meanwhile we can, as usual, go and enjoy an hour of the cool of the evening in the gondola that awaits us.