MYTH 5
THAT GALILEO PUBLICLY REFUTED ARISTOTLE’S CONCLUSIONS ABOUT MOTION BY REPEATED EXPERIMENTS MADE FROM THE CAMPANILE OF PISA
John L. Heilbron
Many of Aristotle’s conclusions about motion were held to be very clear and indisputable.… [Galileo showed the contrary] by repeated experiments made from the height of the Campanile of Pisa in the presence of the other teachers and philosophers and all the students.
—Vincenzio Viviani, Vita di Galileo (1654)
The incident recorded in the epigraph refers to a demonstration that Galileo Galilei (1564–1642) may or may not have conducted when he was a young lecturer at the University of Pisa. The clear and indisputable conclusions he thus publicly sustained against the Master of Those who Know were that “the velocities of bodies of different weights made of the same material moving through the same medium do not keep the proportion of their weights … but they are all moved with equal velocities,” and that “the velocities of the same body moving through different media retain the reciprocal proportion of the resistances or densities of these media.” We know this incident from Vincenzio Viviani (1622–1703), who probably learned its ingredients from Galileo, with whom he lived as pupil and assistant during the last years of Galileo’s life. The legend first appeared in the short biography that Viviani wrote as front matter to a projected edition of Galileo’s writings, aborted under pressure from the Roman Catholic Church.1
There are several reasons for suspecting that Viviani’s story is a myth: No member of the large and literate audience supposedly present and shocked by Galileo’s disproof of received truth seems to have written a word about it. The theses ascribed to Aristotle (384–322 BCE) are taken out of context. Galileo would have been as surprised as his audience had his repeated experiments showed that all bodies fall with the same velocity. Nonetheless, much of Viviani’s story can be confirmed if we take it to apply to a group rather than to an individual. It is true and false in ways that lend themselves to pedagogy and myth. Myth mongers who have added such details as the time of day, the suspense of the expectant viewers, and the weights and materials used have made the legend the exemplar of the triumph of commonsense experiment over slavish adherence to authority—and also, perhaps, of storytelling in the history of science.2
The reason that none of the putative witnesses to Galileo’s singular performance from the campanile ever mentioned it is that it did not take place. In any case, the demonstration would not have been singular. Professors claiming to know and show the truth about motion, including Galileo’s professors when he studied at Pisa, Girolamo Borro (1512–1592) and Francesco Buonamici (1533–1603), frequently threw objects from the windows of their lecture rooms. Borro reported that as often as he dropped chunks of wood and lead balls of roughly the same weight, the wood at first fell faster than the metal, which, he said, answered the tricky question whether air has weight (tends to descend) in air. He apparently had a talent for observation. Filmed re-creations of his demonstration confirm his results, which Galileo also accepted when he taught at Pisa. The effect apparently arises from the experimenter’s unconscious tendency to release the wooden object first.3
During his tenure at Pisa, from 1589 to 1592, Galileo probably added his heavy missiles to the dangers of studying philosophy there. In a manuscript “De Motu,” unpublished in its time but known to Viviani, he refers to Borro’s experiments and adds that the lead soon overtakes the wood, “and if they are let fall from a high tower, precedes it by a large distance, and this I have often tried by experiment.”4 If Galileo did these experiments, his students probably attended them, just as he had witnessed Borro’s and Buonamici’s; and if the tower was the cathedral’s campanile, the choice was so obvious that Giorgio Coresio, one of Galileo’s philosophical opponents, “[whose] intellect could no more understand Aristotle than an anvil can fly,” used it to try to confirm the standard account of motion.5
The passages in Aristotle to which Viviani referred and in which later mythographers have spied the hidden algebra “v[elocity] = W[eight]/R[esistance]” do not concern free fall directly. Rather, they provide the hinges for an argument against the existence of a vacuum understood as a space with no properties but extension. What would happen to a moving body entering such a space? Well, it would have no idea where or what it was, no notion of up or down, no way of knowing whether it was a rock or a balloon. This is because the locomotion of a body—or, if at rest, its tendency to motion—depends on its place, which Aristotle defined, after much fuss, as the interior surface of the containing medium.6 Water in air proceeds, or has a tendency to proceed, downward because it is in air; if in sand, it would want to move upward; if in a vacuum, it would not move at all, a void “having no place to which things can move more or less than to another.” Or, rather, if set in motion, it would move ad infinitum, “for why should it stop here rather than here?”7
As further proof, Aristotle adduced this hostage to fortune: “we can see the same weight or body moving faster than another for two reasons,” either because of the nature of the medium or because of an “excess of weight or lightness.” To this he added a compromising illustration: if air is twice as “thin” as water, a body heavier than water will traverse a given distance in air twice as fast as in water. “And always, by so much as the medium is more incorporeal and less resistant and more easily divided, the faster will be the movement.” Hence a body, any body, would have an infinite velocity in vacuum, which is absurd.8 Again, since observation shows that “bodies that have a greater impulse either of weight or of lightness, if they are alike in other respects, move faster over an equal space, and in the ratio that their magnitudes bear to one another.” This is because the greater the weight, the more easily it divides the medium it penetrates. If there is nothing to divide, all bodies would move with the same speed. “But this is impossible.”9 Thus, for two good and sufficient reasons there can be no void, and therefore—here is the point of the business—we must reject the theories of the atomists.
It is perverse to read these passages as expressions of quantitative relations intended seriously. All Aristotle wanted from his inverse proportion of speed to resistance was to put “thinness” in the denominator, and his implausible numerical example, assuming air to be twice as thin as water, could not have been meant literally. Similarly, the vague statement that bodies with “a greater impulse … of weight” move faster in proportion to their magnitudes when traversing a plenum was made not to lay down the law v ∝ W but to secure what Aristotle regarded as a reductio ad absurdum: since there is no function for weight in a vacuum, all bodies would move with the same velocity there.
It is also perverse to read the discussion, which pertains to directionless motion in a void, as an account of falling bodies. But that is precisely what Galileo did when “quoting” Aristotle to the straw-man peripatetic philosopher who is the butt of the dialogue in Two New Sciences (1638), in which Galileo first made public his definitive theories on motion. After Galileo’s spokesman admits that occasionally he exaggerates a little, he proceeds as follows:
Aristotle says, “A ball of iron of a hundred pounds falling from a height of a hundred braccia hits the ground before one weighing one pound descends a single braccio.” I say that they arrive at the same time; you [may] find when making the experiment that the larger precedes the smaller by two fingers’ breadth … will you hide Aristotle’s ninety-nine braccia behind these two fingers?10
Two fingers to Aristotle! How could he be so ignorant about the most obvious things?
Galileo had expressed himself with equal confidence about these obvious things in 1590, although the theory of motion he held then predicted experimental results significantly different from those claimed in Two New Sciences. The theory of 1590 or thereabouts anticipated that in free fall, light objects at first descend more swiftly than heavy ones, and that if the drop is high enough, a body will attain a velocity proportional to the difference between its specific gravity and that of air. “Oh subtle invention, most beautiful thought! Let all philosophers be silent who think they can philosophize without knowledge of divine mathematics!” What about the corresponding Aristotelian teachings about motion? “Oh ridiculous chimeras! Immortal gods, how, please, can anybody believe in them since the contrary is obvious to sense?”11
The longest convenient vertical drop from the Leaning Tower is about 150 feet. Ignoring air resistance, Galileo’s weights would have taken just over three seconds for their fall. He and his students would have had trouble discerning by eye or ear whether the weights reached the ground together (“within two fingers’ breadth”) or not. Hence, they could not have confirmed the law that Galileo then did not hold: that the speed of fall (absent resistance) is the same for all bodies. Nor could they disconfirm by his experiments that a body passes through different media with velocities in “reciprocal proportion to [their] resistance or densities,” since they examined only descent in air. However, they could have confirmed that the velocities of different bodies do not “keep the proportion of their weights,” since if they did, a body twice the weight of another would precede it by a second or so.
In any case, it is hard to drop weights by hand at the same instant precisely along the vertical. When Galileo’s remote successor at Pisa, Vincenzo Renieri (1606–1647), tried the experiment from the campanile in 1641, he could not confirm the results Galileo gave in his definitive treatment of the problem in Two New Sciences. The circumstances of Renieri’s failure very probably played a part in the creation of the legend. Being informed (so he wrote Galileo) that “some Jesuit” (the adept natural philosopher Niccolò Cabeo [1586–1650]) had found that unequal weights fell to the ground from the same height in the same time (in agreement with Galileo’s definitive law) and doubting the result, Renieri tried the experiment and saw the lead ball hit the ground four or five feet before the wood. Repeating it with lead balls of different weights, he confirmed that the heavier landed before the lighter. Also, it seemed to him that toward the end of its fall, a wooden object tended to swerve.
A lost letter from Galileo must have reminded Renieri that the definitive law of free fall could be found in Two New Sciences. Renieri’s reply to the reminder is almost as hard to credit as the legend itself. He had not read Galileo’s long-awaited book! He excused himself by blaming the heavy teaching load that had kept him from it for over two years. If true, it is instructive. Did he think Two New Sciences too demanding to be read during the school year and too insignificant to have priority during vacations? It is more likely that he knew what he took to be Galileo’s views from conversations at Galileo’s home prison in Arcetri, which he visited frequently as a friend, consoler, and collaborator. He had retained from these conversations that different bodies do not fall with velocities proportional to their weights; Cabeo’s assertion that lead and a crust of bread fell together seemed to him too extravagant an application of the principle. Renieri had also retained from Galileo, “what I thought I heard or read from you,” that the larger of two weights of the same material falls faster. He closed his letter reporting his heresies by sending his most affectionate greetings to Viviani.12 Since by 1641 Galileo was totally blind, Viviani would have read him Renieri’s letters and helped with the replies. No doubt the process prompted some conversation about fall experiments at the Leaning Tower between the master and his assistant. As every oral historian knows, the dialogue would have proceeded along these lines:
Viviani: What do you say about Sig. Renieri’s experiment, maestro?
Galileo: It is not easy. I tried something of the same kind about fifty years ago, but then I knew the outcome I expected.
V: Did things work out as you expected?
G: Pretty closely. I tried the experiment several times with several people present—my students and a few other professors and philosophers. Old Buonamici came once, and also Jacopo Mazzoni, who brought some of his many students. He was working then on his famous comparison of the philosophies of Plato and Aristotle and looking for mistakes Aristotle made by neglecting mathematics.
V: And of course Aristotle would have seen the inanity of his doctrine of motion if he had followed out the logic of the proportions he set down, as you, maestro mio, have demonstrated so clearly.
G: No doubt.… Hmmm, Yes, Mazzoni must have been there. He was a family friend, and I talked with him a lot about the big problems in philosophy and helped him develop examples against Aristotle’s nonmathematical way.13
V: So fifty years ago you did experiments like Renieri’s from the campanile and showed them to a few teachers and students? And the results made clear to them that Aristotle’s pseudo-mathematics of motion was nonsense? And that all bodies fall at the same speed apart from the slowing effected by the medium?
G: That’s about right. But of course it was a long time ago, and it took me many years to perfect my ideas about motion as you find them in Two New Sciences.
In reworking his materials, Viviani combined a faithful Pisan portrait (the hail of falling bodies, the audience of students and professors, the theatrical test of Aristotle) with artistic touches that gave life to the legend (Galileo as sole performer, the campanile as test site, the test as a choice between a caricature of Aristotle’s views and a misrepresentation of Galileo’s). The maestro’s writings abound in such touches. He portrayed himself as the victim when he was the aggressor. He created and annihilated straw-men opponents. And he exaggerated the accuracy and reliability of his results to the limits of his powerful rhetoric.14 His caricature of Aristotle’s “law of falling bodies” is grosser by far than Viviani’s. Galileo told stories about the physics he invented; Viviani told lesser fibs about the manner in which the maestro’s inventions took place. The legend is an excellent piece of seventeenth-century rhetoric contrived jointly by teacher and disciple to promote themselves and the application of mathematics to physics, and to push back the date of Galileo’s definitive teaching about motion to the time of his first experiments on the subject. As the great Eusebius (ca. 275–339) understood when incorporating the Old Testament in his history of the Christian church, an orthodoxy is the more persuasive the longer its pedigree.
It appears that exploration of the origins of the legend of the Leaning Tower may help the historian identify and appreciate some of the differences in the practice of physics between Galileo’s day and ours. Further exploration will suggest other applications. An analysis of the practical difficulties of the tower experiment and of the finer details of free fall as described in Newtonian mechanics could make good pedagogy. The reasons for propagating and embellishing the legend might also repay study. Of these, the least interesting is the celebration of the triumph of one notion of motion over another. More significantly, the legend conveys answers to such fundamental questions as whether physics should be qualitative, coherent, and explanatory, or quantitative, piecemeal, and descriptive. Perhaps of most importance in the present context, the myth mongers who purvey the legend without looking into it commit the very crime that it warns against: they rely on authority, on someone else’s say-so, rather than on their own informed judgment.