A phenomenology of Galileo’s experiments with pendulums

The paper reports new findings about Galileo’s experiments with pendulums and discusses their significance in the context of Galileo’s writings. The methodology is based on a phenomenological approach to Galileo’s experiments, supported by computer modelling and close analysis of extant textual evidence. This methodology has allowed the author to shed light on some puzzles that Galileo’s experiments have created for scholars. The pendulum was crucial throughout Galileo’s career. Its properties, with which he was fascinated from very early in his career, especially concern time. A 1602 letter is the earliest surviving document in which Galileo discusses the hypothesis of pendulum isochronism. In this letter Galileo claims that all pendulums are isochronous, and that he has long been trying to demonstrate isochronism mechanically, but that so far he has been unable to succeed. From 1602 onwards Galileo referred to pendulum isochronism as an admirable property but failed to demonstrate it. The pendulum is the most open-ended of Galileo’s artefacts. After working on my reconstructed pendulums for some time, I became convinced that the pendulum had the potential to allow Galileo to break new ground. But I also realized that its elusive nature sometimes threatened to undermine the progress Galileo was making on other fronts. It is this ambivalent nature that, I thought, might prove invaluable in trying to understand crucial aspects of Galileo’s innovative methodology. To explore Galileo’s innovative methodology, I have repeated most of his pathbreaking experiments with pendulums. Furthermore, I have investigated the robustness * Department of History and Philosophy of Science, University of Pittsburgh, 1017 Cathedral of Learning, Pittsburgh, PA 15260, USA. Email: [email protected]. My thanks to anonymous referees for their helpful comments, and to the editor of this journal for his assistance in refining the original manuscript. There is a ‘Supporting document’ for this paper, with detailed discussions of technical issues that could only be briefly hinted at here, and a large number of videos of experiments cited below in ‘Galileo’s investigative pathways around the pendulum’. This material can be downloaded at www.exphps.org, a website devoted to experimental history and philosophy of science. Previously available English translations of Galileo’s texts concerning the pendulum are often unsatisfactory. I have furnished new translations in Reenacting Galileo’s Experiments: Rediscovering the Techniques of Seventeenth-Century Science, Lewiston, NY, 2008, to which the reader is invited to refer. 1 Galileo to Guido Ubaldo dal Monte, Padua, 29 November 1602, in Galileo, Le opere di Galileo Galilei : Edizione Nazionale (ed. A. Favaro), 20 vols., Florence, 1890–1909, x, 97–100, translated in P. Palmieri, Reenacting Galileo’s Experiments: Rediscovering the Techniques of Seventeenth-Century Science, Lewiston, NY, 2008, 257–60. ‘Isochronism’ is the property of certain physical systems to oscillate at constant frequency regardless of the oscillations’ amplitude. We now know that simple pendulums are not isochronous. ‘Isochronism’ is not a Galilean word. As the reader will see, Galileo uses other expressions to refer to this property. I will retain ‘isochronism’ since it has become common in the literature. BJHS, Page 1 of 35. f British Society for the History of Science 2009 doi:10.1017/S0007087409990033 of pendulum effects, otherwise difficult to capture, with computer simulations. This paper relates my discoveries and emphasizes their significance for our understanding of Galileo’s innovative methodology at its initial stages, especially in the context of his early writings. I am not the first to have been beguiled by Galileo’s pendulums. Ronald Naylor, who contributed most to our understanding of Galileo’s work with pendulums, long ago reconstructed Galileo’s experiments. He summarizes his findings as follows: One of Galileo’s most renowned discoveries was the isochronism of the simple pendulum. In the Discorsi, Galileo used this discovery to good effect – though his claim that the pendulum was isochronous for all arcs less than 180x has created something of a puzzle for the history of science. The question arises as to how far the evidence available to Galileo supported his claims for isochronism.3