The Essential Galileo (50 page)

Because we did not think you had said the whole truth about your intention, we deemed it necessary to proceed against you by a rigorous examination. Here you answered in a Catholic manner, though without prejudice to the above-mentioned things confessed by you and deduced against you about your intention.

Therefore, having seen and seriously considered the merits of your case, together with the above-mentioned confessions and excuses and with any other reasonable matter worth seeing and considering, we have come to the final sentence against you given below.

Therefore, invoking the Most Holy name of Our Lord Jesus Christ and of his most glorious Mother, ever Virgin Mary; and sitting as a tribunal, with the advice and counsel of the Reverend Masters of Sacred Theology and the Doctors of both laws, our consultants; in this written opinion we pronounce final judgment on the case pending before us between the Magnificent Carlo Sinceri, Doctor of both laws, and Prosecuting Attorney of this Holy Office, on one side, and you the above-mentioned Galileo Galilei, the culprit here present, examined, tried, and confessed as above, on the other side:

We say, pronounce, sentence, and declare that you, the abovementioned Galileo, because of the things deduced in the trial and confessed by you as above, have rendered yourself according to this Holy Office vehemently suspected of heresy,
¹⁶
namely of having held and believed a doctrine which is false and contrary to the divine and Holy Scripture: that the sun is the center of the world and does not move from east to west, and the earth moves and is not the center of the world, and that one may hold and defend as probable an opinion after it has been declared and defined contrary to Holy Scripture. Consequently you have incurred all the censures and penalties imposed and promulgated by the sacred canons and all particular and general laws against such delinquents. We are willing to absolve you from them provided that first, with a sincere heart and unfeigned faith, in front of us you abjure, curse, and detest the above-mentioned errors and [406] heresies, and every other error and heresy contrary to the Catholic and Apostolic Church, in the manner and form we will prescribe to you.

Furthermore, so that this serious and pernicious error and transgression of yours does not remain completely unpunished, and so that you will be more cautious in the future and an example for others to abstain from similar crimes, we order that the book
Dialogue
by Galileo Galilei be prohibited by public edict.

We condemn you to formal imprisonment in this Holy Office at our pleasure. As a salutary penance we impose on you to recite the seven penitential Psalms once a week for the next three years. And we reserve the authority to moderate, change, or condone wholly or in part the above-mentioned penalties and penances.

This we say, pronounce, sentence, declare, order, and reserve by this or any other better manner or form that we reasonably can or shall think of.

So we the undersigned
¹⁷
Cardinals pronounce: Felice Cardinal d'Ascoli; Guido Cardinal Bentivoglio; Fra Desiderio Cardinal di Cremona; Fra Antonio Cardinal di Sant'Onofrio; Berlinghiero Cardinal Gessi; Fabrizio Cardinal Verospi; Marzio Cardinal Ginetti.

§9.8 Galileo's Abjuration (22 June 1633)
¹⁸

I, Galileo, son of the late Vincenzio Galilei of Florence, seventy years of age, arraigned personally for judgment, kneeling before you Most Eminent and Most Reverend Cardinals Inquisitors-General against heretical depravity in all of Christendom, having before my eyes and touching with my hands the Holy Gospels, swear that I have always believed, I believe now, and with God's help I will believe in the future all that the Holy Catholic and Apostolic Church holds, preaches, and teaches. However, whereas, after having been judicially instructed with injunction by the Holy Office to abandon completely the false opinion that the sun is the center of the world and does not move and the earth is not the center of the world and moves, and not to hold, defend, or teach this false doctrine in any way whatever, orally or in writing; and after having been notified that this doctrine is contrary to Holy Scripture; I wrote and published a book in which I treat of this already condemned doctrine and adduce very effective reasons in its favor, without refuting them in any way; therefore, I have been judged vehemently suspected of heresy, namely of having held and believed that the sun is the center of the world and motionless and the earth is not the center and moves.

Therefore, desiring to remove from the minds of Your Eminences and every faithful [407] Christian this vehement suspicion, rightly conceived against me, with a sincere heart and unfeigned faith I abjure, curse, and detest the above-mentioned errors and heresies, and in general each and every other error, heresy, and sect contrary to the Holy Church; and I swear that in the future I will never again say or assert, orally or in writing, anything which might cause a similar suspicion about me; on the contrary, if I should come to know any heretic or anyone suspected of heresy, I will denounce him to this Holy Office, or to the Inquisitor or Ordinary of the place where I happen to be.

Furthermore, I swear and promise to comply with and observe completely all the penances which have been or will be imposed upon me by this Holy Office; and should I fail to keep any of these promises and oaths, which God forbid, I submit myself to all the penalties and punishments imposed and promulgated by the sacred canons and other particular and general laws against similar delinquents. So help me God and these Holy Gospels of His, which I touch with my hands.

I, the above mentioned Galileo Galilei, have abjured, sworn, promised, and obliged myself as above; and in witness of the truth I have signed with my own hand the present document of abjuration and have recited it word for word in Rome, at the convent of the Minerva, this twenty-second day of June 1633.

I, Galileo Galilei, have abjured as above, by my own hand.

1.
Reprinted from: Maurice A. Finocchiaro, trans. and ed.,
The Galileo Affair: A Documentary History
, © 1989 by the Regents of the University of California. Published by the University of California Press.

2.
For the historical background, see the Introduction, especially §0.9.

3.
Galilei 1890–1909, 19: 324–327; translated by Finocchiaro (1989, 218–22).

4.
Here, to avoid confusion between the two sets of numbers, the arabic numerals of the original have been replaced by roman numerals.

5.
Galilei 1890–1909, 19: 336–342; translated by Finocchiaro (1989, 256–62).

6.
Here and in other depositions, the questions are recorded as
indirect
queries, so that the letter
Q
ought to be taken to mean “He was asked,” rather than simply “Question.”

7.
The original sentence does explicitly have this double negative, suggesting an admission of some wrongdoing on Galileo's part. This is puzzling, especially in view of the denial later on the same page. Thus, the double negative may have been a slip of the tongue.

8.
From 12 to 30 April 1633, Galileo was detained at the Inquisition palace but allowed to lodge in the prosecutor's apartment.

9.
Galilei 1890–1909, 19: 342–44; translated by Finocchiaro (1989, 277–79).

10.
The only previous deposition of which we have a record is the one dated 12 April (see §9.2).

11.
Galilei 1890–1909, 19: 345; translated by Finocchiaro (1989, 279).

12.
Galilei 1890–1909, 19: 345–47; translated by Finocchiaro (1989, 279–81).

13.
Galilei 1890–1909, 19: 361–362; translated by Finocchiaro (1989, 286–87).

14.
That is, the pope's decision at the Inquisition meeting of 16 June, that Galileo be interrogated about his intention, under the formal threat of torture. Cf. Galilei 1890–1909, 19: 282–83, 360–61; Finocchiaro 2005, 247.

15.
Galilei 1890–1909, 19: 402–6; translated by Finocchiaro (1989, 287–91).

16.
“Vehement suspicion of heresy” was a technical term meaning a specific category of religious crime, second in seriousness only to “formal heresy.”

17.
Note that only seven out of the ten cardinals in the commission signed the sentence. This fact is worthy of further reflection. See, for example, Santillana 1955, 310–11; Langford 1966, 153; Redondi 1987, 260–61.

18.
Galilei 1890–1909, 19: 406–7; translated by Finocchiaro (1989, 292–93).

CHAPTER 10

From
Two New Sciences
(1638)
¹

[§10.1 Day I: The Problem of Scaling]
²

[49] S
ALV.
    The constant activity which you Venetians display in your famous shipyard suggests to the studious mind a large field of philosophizing, especially the part that involves mechanics. For in this department all types of instruments and machines are constantly being constructed by many artisans, among whom there must be some who, partly by inherited experience and partly by their own observations, have acquired the highest expertise and the most refined reasoning ability.

S
AGR.
    You are quite right. Indeed, I myself, being curious by nature, frequently visit this place for the mere pleasure of observing the work of those who, on account of their superiority over other artisans, we call “first-rank men.” Meeting with them has often helped me in the investigation of the reason for certain effects, including not only those that are striking, but also those that are recondite and almost incredible. At times also I have been put to confusion and driven to despair of ever explaining something for which I could not account, but which my senses told me to be true. And notwithstanding the fact that what the old man told us a little while ago is proverbial and commonly accepted, yet it seemed to me altogether false, like many other sayings that are current among the ignorant; for I think they say these things [50] in order to give the appearance of knowing something about matters which they do not understand.

S
ALV.
    You refer, perhaps, to that last remark of his when we asked the reason why they employed supports, scaffolding, and bracings of larger dimensions for launching a big vessel than they do for a small one. He answered that they did this in order to avoid the danger of the ship parting under the heavy weight of its great size, a danger to which small boats are not subject.

S
AGR.
    Yes, that is what I mean. I refer especially to his last assertion, which I have always regarded as a false, though popular, opinion. That is, that in dealing with these and other similar machines one cannot argue from the small to the large, because many devices that succeed on a small scale do not work on a large scale. Now, since all reasoning in mechanics has its foundation in geometry, I do not see that the properties of circles, triangles, cylinders, cones, and other solid figures will change with their size. If, therefore, a large machine be constructed in such a way that its parts bear to one another the same ratio as in a smaller one, and if the smaller is sufficiently strong for the purpose for which it was designed, I do not see why the larger also should not be able to withstand any severe and destructive tests to which it may be subjected.

S
ALV.
    The common opinion is here absolutely wrong. Indeed, it is so far wrong that precisely the opposite is true, namely, that many machines can be constructed even more perfectly on a large scale than on a small; for instance, a clock that indicates and strikes the hour can be made more accurate on a large scale than on a small. There are some intelligent people who maintain this same opinion, but on more reasonable grounds, when they cut loose from geometry and argue that the better performance of the large machine is owing to the imperfections and variations of the material. [51] Here I trust you will not charge me with arrogance if I say that imperfections in the material, even those that are great enough to invalidate the clearest mathematical proof, are not sufficient to explain the deviations observed between machines in the concrete and in the abstract. Yet I shall say it and will affirm that, even if the imperfections did not exist and matter were absolutely perfect, unalterable, and free from all accidental variations, still the mere fact that it is matter makes the larger machine, built of the same material and in the same proportion as the smaller, correspond exactly to the smaller in every respect except that it will not be so strong or so resistant against violent treatment; the larger the machine, the greater its weakness. Since I assume matter to be unchangeable and always the same, it is clear that we are no less able to treat this constant and invariable property in a rigorous manner than if it belonged to simple and pure mathematics. Therefore, Sagredo, you would do well to change the opinion which you, and perhaps also many other students of mechanics, have entertained concerning the ability of machines and structures to resist external disturbances; namely, that when they are built of the same material and maintain the same ratio between parts, they are able equally, or rather, proportionally, to resist or yield to such external disturbances and blows. For we can demonstrate by geometry that the large machine is not proportionately stronger than the small. Finally, we may say that, for every machine and structure, whether artificial or natural, there is set a necessary limit beyond which neither art nor nature can pass; it is here understood, of course, that the material is the same and the proportion is preserved.

S
AGR.
    My brain already reels. My mind, like a cloud momentarily illuminated by a lightning flash, is for an instant filled with an unusual light, which beckons to me and suddenly mingles and obscures strange and crude ideas. From what you have said it appears to me impossible to build [52] two similar structures of the same material but of different sizes, and have them proportionately strong; and if this were so, it would also not be possible to find even two poles made of the same wood that shall be alike in strength and resistance but unequal in size.

S
ALV.
    So it is, Sagredo. But let us make sure we understand each other. I say that if we take a wooden rod of a certain length and breadth, fitted into a wall at right angles, i.e., parallel to the horizon, and we reduce it to such a length that it will just support itself (so that if a hair's breadth be added to its length it will break under its own weight), then it will be the only rod of the kind in the world. Thus if, for instance, its length be a hundred times its breadth, you will not be able to find another rod whose length is also a hundred times its breadth and which, like the former, is just able to sustain its own weight and no more. Rather, all the larger ones will break, while all the smaller ones will be strong enough to support something more than their own weight. And what I have said about the ability to support itself must be understood to apply also to other cases; so that if a scantling will carry the weight of ten equal to itself, a beam having the same proportions will not be able to support ten equal beams.

Please observe, gentlemen, how facts that at first seem improbable will, even on scant explanation, drop the cloak that has hidden them and stand forth in naked and simple beauty. Who does not know that a horse falling from a height of three or four cubits will break his bones, while a dog falling from the same height or a cat from a height of eight or ten cubits will suffer no injury? Equally harmless would be the fall of a grasshopper from a tower or the fall of an ant from the distance of the moon. Do not children fall with impunity from heights that would cost their elders a broken leg or perhaps a fractured skull? And just as smaller animals are proportionately stronger and more robust than the larger, so also smaller plants are able to stand up better than larger. I am certain you both know that an oak two hundred cubits high would not be able to sustain its own branches if they were distributed as in a tree of ordinary size; and that [53] nature cannot produce a horse as large as twenty ordinary horses or a giant ten times taller than an ordinary man, unless by miracle or by greatly altering the proportions of the limbs and especially of the bones, which would have to be thickened way beyond their ordinary symmetry. Likewise the current belief that, in the case of artificial machines, the very large and the very small are equally feasible and lasting is a manifest error. Thus, for example, small spires, columns, and other solid figures can certainly be handled, laid down, and set up without danger of breaking, while the large ones will go to pieces under the slightest provocation, and that purely on account of their own weight.

And here I must relate a story that is worthy of your attention, as indeed are all events that happen contrary to expectation, especially when a precautionary measure turns out to be a cause of disaster. A very large marble column was laid out so that its two ends rested each upon a piece of beam. A little later it occurred to a mechanic that, in order to be doubly sure of its not breaking in the middle by its own weight, it would be wise to lay a third support midway. This seemed to all an excellent idea. But the sequel showed that it was quite the opposite, for not many months passed before the column was found cracked and broken exactly above the new middle support.

S
IMP.
    A very remarkable and thoroughly unexpected accident, especially if caused by placing that new support in the middle.

S
ALV.
    Surely this is the explanation, and the moment the cause is known our surprise vanishes. For when the two pieces of the column were placed on level ground it was observed that one of the end beams had, after a long while, become decayed and sunken, but that the middle one remained hard and strong, thus causing one half of the column to project in the air without any support; thus, its own weight made it behave differently from what it would have done if supported only upon the first two beams, because no matter how much they might have sunk the column would have gone with them. There is no doubt that this accident would not have happened to a small column, even though made of the same stone and having a length [54] relative to its thickness preserving the ratio between length and thickness found in the large pillar.

S
AGR.
    I am quite convinced of the facts of the case, but I do not understand the reason why the strength and resistance are not multiplied in the same proportion as the size of the material. And I am the more puzzled because, on the contrary, I have noticed in other cases that the strength and resistance against breaking increase in a larger ratio than the size
³
of material. For instance, if two nails be driven into a wall, the one that is twice as big as the other will support not only twice as much weight as the other, but three or four times as much.

S
ALV.
    Indeed you will not be far wrong if you say eight times as much; nor does this phenomenon contradict the other even though in appearance they seem so different.

S
AGR.
    Will you not then, Salviati, remove these difficulties and clear away these obscurities if possible? For I imagine that this problem of resistance opens up a field of beautiful and useful ideas. And if you are willing to make this the subject of today's reasoning, you will place Simplicio and me under many obligations.

S
ALV.
    I am at your service if only I can call to mind what I learned from our Academician, who has thought much upon this subject; and according to his custom, he has demonstrated everything by geometrical methods, so that one might fairly call this a new science. For, although some of his conclusions had been reached by others, first of all by Aristotle, these are not the most beautiful, and what is more important, they had not been proven by necessary demonstrations from fundamental and indubitable principles. Now, since I wish to assure you by means of demonstrations rather than to persuade you by mere probable reasoning, I shall suppose that you are familiar with presentday mechanics so far as it is needed in our discussion.

[§10.2 Day I: Critique of Aristotle's Law of Fall]
⁴

[105] SAGR. I quite agree with the Peripatetic philosophers in denying the penetrability of matter. As to the vacuum, I should like to hear a thorough discussion of Aristotle's demonstration in which he opposes it and what you, Salviati, have to say in reply. I beg of you, Simplicio, that you give us the precise proof of the Philosopher and that you, Salviati, give us the reply.

S
IMP.
    So far as I remember, Aristotle
⁵
inveighs against the ancient view that a vacuum is a necessary prerequisite for motion and that the latter could not occur without the former. In opposition to this view Aristotle shows that it is precisely the phenomenon of motion, as we shall see, which renders untenable the idea of a vacuum. His procedure is the following. He begins with two assumptions. The first concerns bodies of different weights moving in the same medium; the second, one and the same body [106] moving in different media. In the first case he supposes bodies of different weights to move in one and the same medium with different speeds that stand to one another in the same ratio as the weights; so that, for example, a body that is ten times as heavy as another will move ten times as rapidly as the other. In the second case he assumes that the speeds of one and the same body moving in different media are in inverse ratio to the densities of these media; thus, for instance, if the density of water were ten times that of air, the speed in air would be ten times greater than in water. From this second supposition, he gives the following demonstration: since the thinness of a vacuum differs infinitely from that of any medium filled with matter however rare, any body that moves in a plenum through a certain space in a certain time ought to move through a vacuum instantaneously; but instantaneous motion is an impossibility; it is therefore impossible that the existence of a vacuum should result from the existence of motion.

S
ALV.
    The argument is, as you see, ad hominem; that is, it is directed against those who thought the vacuum a prerequisite for motion. Now if I admit the argument to be conclusive and concede also that motion cannot take place in a vacuum, the assumption of a vacuum considered absolutely and not with reference to motion is not thereby invalidated. But to tell you what the ancients might possibly have replied and in order to better understand just how conclusive Aristotle's demonstration is, we may, in my opinion, deny both of his assumptions. And as to the first, I greatly doubt that Aristotle ever tested by experiment whether it be true that two stones, one weighing ten times as much as the other, if allowed to fall at the same instant from a height of, say, one hundred cubits, would so differ in speed that when the heavier had reached the ground, the other would not have fallen more than ten cubits.