Galileo's Experimental Research

Thomas B. Settle GALILEO'S EXPERIMENTAL RESEARCH Contents Galileo's Experimental Research, an Experimental Approach (1996) 5 Appendix: Selcted Excerpts 29 The Pendulum and Galileo, Conjectures and Constructions (1965) 39 GALILEO'S EXPERIMENTAL RESEARCH, AN EXPERIMENTAL APPROACH* GENERAL CONSIDERATIONS What sort of an experimenter was Galileo? What were his sources and how did he begin his experimental career? How important was experimental evidence to the formulation and reformulation of his general conclusions about certain aspects of nature? How developed was his style of work and how typical was it to what would become standard later on? These and related questions have fascinated and divided Galileo scholars over the years. Historians and philosophers have been able to find justification for quite divergent views both of Galileo and of the nature of experimental research in general. Some have concluded that Galileo did no experiments at all, in any interesting sense, that is. Others have painted simplistic "inductivist" portraits. Indeed, the purely written sources, largely those published by Antonio Favaro in the National Edition of Le Opere di Galileo Galilei, while presenting invaluable material when studied closely, leave wide margins for interpretation. And it is likely, had we no other evidence to offer, that we would have resign ourselves to the lack of further clarification of these issues. Fortunately, there is another source of information to draw upon, nature itself, indeed several "natures". For instance, there is the nature constituted, in many variants, of our relatively untutored beliefs about the way the world works and our capacity to act successfully in that world (we can throw rocks at moving objects with some probability of hitting them). It has become a cliche, possibly a very misleading one, that Aristotelian and medieval physics provided a natural, if naive, rendering of the properties of motion. What is undeniably true is that today's children do construct, out of their everyday experiences, definite expectations about the material world, expectations that can differ markedly from the "truths" of Newtonian physics. Whether it was a distillation of such expectations that constituted the core of pre- Galilean physics is a problem to be investigated elsewhere, but we cannot ignore the possibility * Up to now unpublished English version of Thomas B. Settle: La rete degli esperimenti Galileiani, in: P. Bozzi, C. Maccagni, C. Olivieri, T.B. Settle: Galileo e la scienza sperimentale, a cura di M. Baldo Ceolin, Padova 1995, pp. 11- 62. Thomas Settle Galileo's Experimental Research that Galileo began his own career predisposed to one or another such "natural" belief about motion. In fact, it should be part of our interests to look for traces of what Galileo may have "known", even apart from what he may have been taught in his early schooling or as a student at the University of Pisa. Then there are our own bodily systems, which are immensely sensitive in some domains but which also have their limits. If we are tuned physiologically to the requirements of living in small groups and prospering in a hunting-gathering society, 10,000 years of cultural overlay have added both material and intellectual tools to enhance our perceptive abilities, as in the cases of the balance (allowing the making of fine distinctions in weight otherwise beyond our normal capacity) and practical geometry (permitting the precise surveying and depiction of the three dimensional world). What can we expect of Galileo's "natural" abilities? We know that he was brought up in a musical household and had both an excellent ear for distinguishing tones and harmonies and the hands of a near professional performer on the lute and organ. He was also well exposed to the Renaissance pictorial arts, including their geometrical aspects, and he must have had a keen and attentive eye. This background and training would certainly have contributed to his experimental capacities, but they may also have imposed boundaries, for example, in his ability to imagine further extensions to a particular line of investigation, or in an excessive reliance on these very abilities, unaware of their limitations. So we should also be looking for what we should be able to expect of Galileo's own system. Thirdly, there is the "world out there". From our exposure to science courses we derive an image of how some of the principal features of the world are thought to work. But that image can present a very abstracted and sanitized version of what actually happens. We are told how bodies are supposed to move down inclined planes, for instance, and when presented with a lecture demonstration we "see" what we are expected to see, ignoring all the complications that intrude in an actual physical case, disregarding circumstances that don't fit the theoretical account. While there are distinct advantages in using this summarizing mode in the teaching of the sciences, we often make the simple mistake of assuming that Galileo saw (or ought to have seen) what we have been taught to see, forgetting that the early Galileo had never read Newton or even his own later writings. If we are to understand Galileo's own words and diagrams, we should try to learn how the physical world presented itself to him. Finally, there is the nature of experimental research itself, or at least of Galileo's version of it. Let me introduce this most complex topic by describing the several levels of questions one might pose if given the opportunity of doing empirical studies of Galileo's work. At the very elementary level, one would hope to simulate, in equipment and procedures, the many experimental set-ups that Galileo described, sometimes in detail and sometimes only casually, in 6 Thomas Settle Galileo's Experimental Research his published and unpublished writings. An obvious example is the famous experiment of rolling balls down inclined planes and timing their motions with a water-timer, a device if not of Galileo's invention at least of his elaboration into a precision instrument. As we know, the validity of this experiment came under severe doubt two generations ago. It even came to be thought, in the history of science community, that Galileo could not have achieved the results he claimed with the equipment at his disposal [Koyré: 1939, 1943]. Then, in a contribution of my own in 1961, I showed that the inclined plane work, as described, was quite do-able [Settle: 1961]. There were two critical elements. One was the water-timer, not a clock meant to keep reliable time for several days, but a timing device capable of giving consistent measures of intervals as short as one second to about five or six seconds maximum and with a precision of at least 1/10th of a second. Galileo's device, a water container with a small tube through its bottom through which water was allowed to run during the interval to be timed, proved quite up to the task, as subsequently confirmed by many others besides myself. The other element was the experimenter, Galileo himself in the first instance. Since the experimenter has to close the flow of water in the small tube when he or she hears the ball striking an object at some distance down the plane, one had to wonder whether the human system was capable of responding in such a way as to obtain Galileo's results. Evidently, yes; the experimental results bear this out. This was not so unlikely, on reflection, in the light of the fact that trained pianists, violinists and lutanists must accomplish even more prodigious feats of ear-hand coordination in their daily exercises. This story shows, I think, that it is important to take Galileo's claims seriously and to attempt reasonable empirical simulations of them. At a second level, beyond just deciding whether a given experimental set-up could work, we can establish the limits or boundaries of its workability. Regarding the inclined plane, Galileo himself said, in the Third Day of the Discorsi: In un regolo ... di legno, lungo 12 braccia, ... costituito che si era il detto regolo pendente, elevando sopra il piano orizontale una delle sue estremit à un braccio o due ad arbitrio, ... [GG: VIII, 212-213]. In fact, we know that the desired results obtain quite satisfactorily over a range of inclinations from about 10 degrees to about 40 or 45 degrees. Below the lower limit the motion is not reliably uniformly accelerated; in fact, with a little care we can even make the motion quasi-uniform. And above the upper limit the ball begins to skip and slide, definitely not undergoing uniform acceleration. Interestingly, this latter was also known, in a limited sense, to Marin Mersenne in the 1630s. And my own feeling is that Galileo's precise knowledge of these limits, dating back to around 1600, was behind the very carefully crafted description of the inclined plane partially cited above. In other words, our own empirical investigations promise to help us clarify the scope and intent of important written passages. 7 Thomas Settle Galileo's Experimental Research But if they do that, they can also pose other problems. In the Discorsi Galileo used the inclined plane to justify his claim that free motions on ALL inclinations, including the vertical, were both uniformly accelerated according to his rule and related among themselves, i.e., calculable from one inclination to another. If, as I am convinced, he knew that this was not the case empirically (for the reasons I have already indicated, as well as for others beyond his ability to understand), then he must have satisfied himself that the motions that did not fit his rule of acceleration were in some sense artifacts.

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