Humanities Core Course Spring 2011 Instructor: Bencivenga

LECTURE NOTES

Lecture 3.

The second example of application by Galileo of his own method concerns objections to the Copernican system: if the earth moved from west to east, supporters of Ptolemy argued, we should be observing all sorts of strange phenomena. A stone dropped from a tower should not fall along the vertical, grazing the tower, but should rather be left behind the tower as the latter heads east following the earth; a projectile thrown straight upward should not return back exactly where it was launched; when “shooting a cannon ball point-blank to the east, and then another one with equal charge at the same elevation to the west … the shot toward the west ought to range a great deal farther out than the other one to the east” (p. 147); “shots to the south or north … would never hit the mark that one had aimed at, but would always slant toward the west because of the travel that would be made toward the east by the target, carried by the earth while the ball was in the air” (p. 147). Here Galileo brings up an analogy between the earth and a ship: if a stone is dropped from a ship’s mast, “the experiment shows … that the stone always falls in the same place on the ship, whether the ship is standing still or moving with any speed you please” (p. 168). As for the theory, Galileo claims that the stone on the moving ship, or cannon balls and the like on the earth, retain the force the ship or the earth impressed on them, hence their motion results from a combination of that impressed force and whatever other force is operative on them (gravity in the case of the stone, the explosion in the case of the cannon ball). And, since we all partake in the diurnal motion of the earth (and anyone on the ship partakes in the ship’s motion), all that we can ever observe is the one motion we lack: for us it is as if the diurnal motion did not even exist, and consequently the motions of cannon balls, stones, and so on appear to us much simpler than they actually are.

If the earth is fixed, the rock leaves from rest and descends vertically; but if the earth moves, the stone, being likewise moved with equal velocity, leaves not from rest but from a state of motion equal to that of the earth. With this it mixes its supervening downward motion, and compounds out of them a slanting movement.… But, good heavens, if it moves slantingly, why do I see it move straight and perpendicular? This is a bald denial of manifest sense…. With respect to the earth, the tower, and ourselves, all of which all keep moving with the diurnal motion along with the stone, the diurnal movement is as if it did not exist; it remains insensible, imperceptible, and without any effect whatever. All that remain observable is the motion which we lack, and that is the grazing drop to the base of the tower. (pp. 198-199)

But Galileo’s method is not foolproof: he too, like Aristotle and Ptolemy, made major mistakes. In the Dialogue, the two most important ones are his claim that celestial orbits are circular and his explanation of the tides (on both counts, Kepler was right, but Galileo belittles him and his views—as he typically did with the views of others). It is also not sufficient to discriminate between competing theories. Whereas the Copernican hypothesis can account for the phenomena, with enough complications added the Ptolemaic could do the same; therefore, Galileo, in countering his opponents’ preconceptions and their uncritical reliance on the naïve point of view, is ultimately forced to resort to ordinary intuitions too, and to appeal to rhetoric. There are three main elements to the rhetoric. Copernican explanations are simpler than Ptolemaic ones; they are more elegant and aesthetically pleasing, in that they allow for a more symmetrical, more orderly universe; and they show a better proportionality between causes and effects, in that they do not force one to believe that a small effect should have an extraordinarily large cause (see, for example, p. 68: “Has nature … produced and directed all these enormous, perfect, and most noble celestial bodies, invariant, eternal, and divine, for no other purpose than to serve the changeable, transitory, and mortal earth?”). All three elements come together in a list of seven “difficulties” for the geocentric view Salviati provides at the beginning of the second day. As an example, here is the first difficulty:

[L]et us consider … the immense bulk of the starry sphere in contrast with the smallness of the terrestrial globe, which is contained in the former so many millions of times. Now if we think of the velocity of motion required to make a complete rotation in a single day and night, I cannot persuade myself that anyone could be found who would think it the more reasonable and credible thing that it was the celestial sphere which did the turning, and the terrestrial globe which remained fixed. (pp. 133-134)

And here is a summary of the whole argument provided by Sagredo:

[W]hen all things can proceed in most perfect harmony without introducing other huge and unknown spheres; without other movements or imparted speedings; with every sphere having only its simple motion, unmixed with contrary movements, and with everything taking place in the same direction, as must be the case if all depend upon a single principle, why reject the means of doing this, and give assent to … outlandish things and … labored conditions?” (p. 141)

But is it legitimate to infer what the world is like from what appears reasonable, simple, or elegant to us? On p. 116, Sagredo issues a general word of caution precisely against such inferences:

It always seems to me extreme rashness on the part of some when they want to make human abilities the measure of what nature can do. On the contrary, there is not a single effect in nature, even the least that exists, such that the most ingenious theorists can arrive at a complete understanding of it. This vain presumption of understanding everything can have no other basis than never understanding anything. For anyone who had experienced just once the perfect understanding of one single thing, and had truly tasted how knowledge is accomplished, would recognize that of the infinity of other truths he understands nothing.

At times, Galileo uses the very omnipotence and incomprehensibility of God (hence, ultimately, the incomprehensibility of that nature which is supposed to be God’s creation) as an argument in his own favor:

How powerless are our senses to distinguish large distances from extremely large ones, even when the latter are in fact many thousands of times the larger! And finally I ask you, O foolish man: Does your imagination first comprehend some magnitude for the universe, which you then judge to be too vast? If it does, do you like imagining that your comprehension extends beyond the Divine power? Would you like to imagine to yourself things greater than God can accomplish? And if it does not comprehend this, then why do you pass judgment upon things you do not understand?” (p. 426).

Galileo actually thought that there was a factual, non-rhetorical way of establishing the primacy of the Copernican system, except that here the second criticism of his method (it cannot discriminate among competing explanations of the same facts) connects with the first one (it does not prevent mistakes), as this alleged decisive proof was his mistaken view of the tides. So, while there is no denying the brilliance and ingeniousness of Galileo’s theories and observations, the very evidence of this foundational text of modern science indicates that there is no method for the discovery of truth: no established system of steps by which one can rest assured that new knowledge will be acquired. New knowledge is acquired by trial and error, and is acquired most when most courage is displayed in such tries. Galileo displayed enormous courage, which means that he tried, and sometimes erred, and learned a tremendous amount from the process, and we have learned a lot from his trials and errors. A necessary condition for this playful experimentation is freedom, hence a major way in which Galileo can indeed be regarded as the father of modern science is his defense of freedom: his insistence that everyone be allowed (and ready) to think for him/herself, without blindly—that is, uncritically—deferring to any authority:

We need guides in forests and in unknown lands, but on plains and in open places only the blind need guides. It is better for such people to stay at home, but anyone with eyes in his head and his wits about him could serve as a guide for them. In saying this, I do not mean that a person should not listen to Aristotle; indeed, I applaud the reading and careful study of his works, and I reproach only those who give themselves up as slaves to him in such a way as to subscribe blindly to everything he says and take it as an inviolable decree without looking for any other reasons. (pp. 130-131)

And note that this point is emphasized by Einstein in his foreword: “The leitmotif which I recognize in Galileo’s work is the passionate fight against any kind of dogma based on authority” (p. xxviii).