EXPERIMENTAL SENSE IN GALILEO’S EARLY WORKS AND ITS LIKELY SOURCES T. B. Settle I am going to start by declaring a number of assumptions, some of them quite old fashioned and musty, others accepted by some as commonplaces but rejected by others as outrageous, and all still open to considerable clar- ification, if not contention. First, something happened in Western Europe in the decades around the year 1600 which, for better or worse, we have come to know as a “scientific revolution”. Certainly there had been anticipations and premonitions of such an event in the previous centuries, even antiqui- ty. And certainly there were further, what shall we call them?, “upheavals”, secondary revolutions, later on, as the new ways of investigating and under- standing nature spread and became consolidated. But, and this is a second assumption, some constellation of attitudes towards nature, habits of inquiry, collections of acquired tools (both material and mathematical) and previously gathered knowledge became a coherent enough package to emerge (perhaps to condense), to take root and begin to flourish, in these years. Third, the components of this constellation, as I’ve called it, were not invented ex novo in the decades indicated; all had been maturing indepen- dently or semi-independently for years, in some cases for centuries. What was new was, first, the “mix”, followed by a growing awareness of the power and possibilities of that mix among a restricted but significant pub- lic. Fourth, I don’t believe that the touted “victories” of the period, the law of free fall, for instance, or the beginnings of the wide acceptance of the Copernican system in the hands of Tycho, Kepler, Galileo and Gilbert, were a cause of the revolution, so much as among its first fruits. Finally, as just hinted, that restricted public included many actors all over Europe, some 832 THOMAS SETTLE still famous today and many, if not most, obscure or forgotten (including many only known to historians of other disciplines such as art, literature and music). If we seem to concentrate on Galileo, it is because he was one of the more visible players in the event and because we are fortunate enough to have large collections of original sources which yet reward further study. My object here, then, is to reflect on one aspect of the beginnings in Galileo, the origins and development of his capacities as an experimental investigator. Galileo did not start his career with a fully mature notion of proper “experimental research”; in so far as he reflected on what we like to call methodology, that would only come later, and we only have limited access to what such reflections might have been. No, Galileo started by start- ing, using materials and tools ready at hand, off the shelf, including what was available in his Tuscan environment as he was growing up. And his “practice” only evolved or matured in the course of his investigations. So my questions then become: What can we discover in Galileo’s early works of a sense of or sensibility for empirical investigation; what can we suggest about its possible sources; and what can we say about its early maturation? * * * To start at the beginning, we know little of Galileo’s early life, except that he was the first among several children of a father, Vincenzo Galilei, who was a professional musician, a music teacher, a composer and student of musical theory, and eventually himself an experimenter in what we would call today “musical acoustics” (we will be returning to this shortly). One consequence of this was that Galileo himself became an expert lutanist. Galileo grew up first in Pisa and then in Florence and acquired some of his early education from a member of the Vallombrosan Order, either in one of the Vallombrosan Houses in Florence itself or in the Mother House of the Order in the hills near Florence. In the fall of 1580 (not, as is usually given, 1581) he enrolled in the University of Pisa1 and continued his formal stud- ies until 1585 when, having “discovered” and been captured by mathemat- ics, he left the University. Galileo spent the next four years mostly at home in Florence, studying Euclid and Archimedes and becoming proficient enough both to take occa- sional jobs teaching mathematics2 and to draft a set of theorems on the cen- ters of gravity of solids of revolution,3 thereby extending the reach of 1 Del Gratta, R., “A proposito della data d’iscrizione di Galileo Galilei all’Università di Pisa [1580 settembre 5; e non 1581!]”, Bollettino storico pisano, 46 (1977), 556-558. 2 For instance in 1588: Schiavo, A., “Notizie Riguardanti la Badia di Passignano in Val di Pesa Estratte dai fondi dell’ Archivio di Stato di Firenze”, in Benedictina, 9 (1955), 31-92, p. 44. 3 Galilei, G., Theoremata circa centrum gravitatis solidorum (ms. c. 1586-87), in Favaro, A. (ed.), Le Opere di Galileo Galilei, 20 Vols, Firenze, Barbèra, 1890-1909, reissued with addi- tions: 1929-39 & 1964-66: 1, 181-208. EXPERIMENTAL SENSE IN GALILEO’S EARLY WORKS AND ITS LIKELY SOURCES 833 Archimedean techniques and (not just incidently) earning a reputation among some important contemporary mathematicians. Amid these mathematical studies he also drafted and circulated his first public work, La bilancetta, the Little Balance, in this case a balance which, he proposed, Archimedes might have used in detecting the goldsmith’s fraud in the crafting of Hiero’s crown4. [Can we think of Galileo as an experimentalist historian of science, attempt- ing to understand Archimedes by trying to simulate some of his work?] Galileo felt that the commonly told story about Archimedes in the bath could not be correct; the implied measuring technique would have been too impre- cise and certainly not worthy of the Syracusan’s real capabilities. By Galileo’s time, of course, balances had had a long history as tools: both in the abstract (at the core, for instance, of some of Archimedes’ mathematical techniques), and in the flesh as part of the kit of everyday work and trade. In this last regard, the economic health of medieval and renaissance Florence depended in part on the reliability and precision of the balances used by goldsmiths as well as those used in the Florentine Mint, the latter organization responsible since the early 13th century for the quality and content of the gold Florin. So Galileo was not really inventing a new device. What he was doing was stretch- ing his new Archimedean muscles and satisfying himself, if he bothered to worry about the issue at all, that with care and ingenuity one can, in fact, build very precise measuring instruments. The Little Balance starts by being a normal equal arm balance, a longish rod, balanced in the center, with a hook at one end and a balance pan sus- pended at the other, these at equal distances from the center. It differs from the normal balance in that one needs to be able to move the suspension of the pan from its “home” point, back and forth along its arm. And it also differs in that it requires a special, finely divided ruler along a portion of the rod with the movable pan. To create a ruler designed, say, for the Archimedean problem, testing a possible fraud and measuring the relative amounts of gold and silver in it: 1) start by hanging a sample of pure gold from the hook, and with the pan’s suspension in its “home” position bring the balance into equilibrium; 2) then immerse the gold in a container of water and slide the pan’s suspension along the rod until the balance is again in equilibrium; 3) mark the position of the suspension on the rod; this will be the “gold” point; 4) repeat these three steps with a sample of pure silver thereby establishing a “silver” point; 5) finally, install the special ruler between the two established “points”; 6) To test a suspect sample, simply repeat the first two steps using that sample; if the pan’s point of suspension then falls somewhere between the two previously established points, it is a mix, and its relative distances to those points will be in the ratio of the rel- ative amounts of each component. 4 Galilei, G., La bilancetta (ms. ca. 1586), in Favaro, A. (ed.), Le Opere..., 1, 209-220; Fermi, L. & Bernardini, G.(trs. & eds.), Galileo and the Scientific Revolution, Basic Books, New York, 1961: Appendix. 834 THOMAS SETTLE I have taken you through these details because I think that it is impor- tant to have a feel for the material aspect of the instrument. But we have not yet finished. What did Galileo use for the special rule? Here he shows some nice opportunistic ingenuity. He used a fine wire (he did not say so, but a good guess would be a standard steel lute string) which he wound tightly and compactly around the balance arm in the space between the two points. Then, since visually counting the wires to complete a measurement would have been difficult (the eyes glaze over), he recommended drawing the point of a stiletto across the wires between the points to be measured. A combi- nation of the slight sound resulting from the passing of the point of the knife from one wire to another and the tactile feel of that same jump through the handle of the knife would allow an accurate count. A nice touch for a musician. And one should say that the instrument, including the system of measurement, does work as proposed.