“A CERTAIN CORRESPONDENCE” THE UNIFICATION OF MOTION FROM GALILEO TO HUYGENS MAXIMILIAN ALEXANDER KEMENY FACULTY OF SCIENCE UNIVERSITY OF SYDNEY A THESIS SUBMITTED IN FULFILLMENT OF THE REQUIREMENTS OF MASTER OF SCIENCE 2016 Max Kemeny A Certain Correspondence Contents Introduction ......................................................................................................................... 3 Chapter 1: Galileo's Program, Harriot's Problems .......................................................... 10 Galileo, Harriot, and Correspondences ............................................................................ 11 The State of Mechanics in the 16th Century ..................................................................... 15 Guidobaldo and Galileo ................................................................................................... 16 Guidobaldo's Experiment ................................................................................................. 19 The Hanging Chain: No Coincidental Result .................................................................... 23 Another Correspondence: The Inclined Plane and the Pendulum .................................... 29 Successes out of Failures................................................................................................ 35 Thomas Harriot: The Mechanical Experiments of Galileo's Contemporary ....................... 37 The Galilean Program ..................................................................................................... 47 Chapter 2: Expérience and Correspondences in the Works of Mersenne .................... 49 The Rise and Decline of Mersenne's Interest in Galilean Mechanics ............................... 50 Mersenne's Early Works and First Interest in Mechanics ................................................. 55 Mersenne's Growing Interest in Galilean Mechanics and The Traite des Mouvemens ..... 58 Les Nouvelles Pensées de Galilée .................................................................................. 65 Pendulum Experiments in Nouvelles Pensées ................................................................. 69 Mersenne's Eventual Loss of Faith in Galilean Mechanics .............................................. 70 Descartes' Influence on Mersenne .................................................................................. 73 Mersenne's Last Thoughts on Galilean Mechanics .......................................................... 75 The Death of Expérience ................................................................................................. 78 Chapter 3: Christiaan Huygens and the Galilean Program ............................................ 80 The Horologium Oscillatorium ......................................................................................... 82 Horologium Oscillatorium: Proving Proposition 25 of Part Two ........................................ 85 Part Four of the Horologium Oscillatorium: Time of Free Fall and a Universal Unit .......... 90 De Vi Centrifuga .............................................................................................................. 93 The Crucial Proposition 5 of De Vi Centrifuga ................................................................ 102 A Crucial Correspondence ............................................................................................. 107 Conclusion ...................................................................................................................... 110 References ...................................................................................................................... 113 Primary Sources ............................................................................................................ 113 Secondary Sources ....................................................................................................... 114 Page 2 of 116 Max Kemeny A Certain Correspondence Introduction A pair of books written by Galileo Galilei in the 1630s, the Dialogo dei Due Massimi Sistemi del Mondo (Dialogue Concerning the Two Chief World Systems) and the Discorsi e Dimostrazoni Matematiche, Intorno a Due Nuove Scienze (Discourse and Mathematical Demonstrations Relating to the Two New Sciences) are typically regarded as founding documents of Modern Science. The program initiated by Galileo is often referred to as the mathematisation of the world picture; a concerted effort among academics in the 17th century to lay down a clear and well-ordered system of the world, written in the language of mathematics. Galileo is central to this narrative; possibly the most quoted paragraph from all of Early Modern Science presents this view: “Philosophy is written in this grand book — I mean the universe — which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth.”1 That Galileo chose to present his project in this way is clearly important. But the words of a polemic (as The Assayer was) must not be taken without a grain of salt. It is undeniable that Galileo was committed to describing the world mathematically. But the usual corollary of this position: that the basis of Galileo's work was a strict focus on that which was observable, and thus what could be quantified, should be rejected. In practice, Galileo frequently appealed to concepts that went beyond the observable or the mathematical; Joella Yoder described Galileo as someone “who invoked whatever argument would persuade his readers of the validity of his conclusion” 2. In this work, I focus on one of Galileo's concepts which was neither mathematically nor empirically derived, but instead based on a fundamental intuition regarding the nature of motion: that all mechanical phenomena could be treated in the same way, 1 (Galilei (1638) 1914, 237-8) 2 (Yoder 1988, 170) Page 3 of 116 Max Kemeny A Certain Correspondence using the same mathematical and conceptual apparatus. This was Galileo's concept of 'correspondence', and I will follow it from its origins at the turn of the 17th century through Marin Mersenne and ultimately to Christiaan Huygens. At the centre of Galileo's concept of correspondence was that phenomena which looked similar really were the same; they were separate instances of the same fundamental processes. Hanging chains and projectile trajectories did not form the same curve by coincidence; they formed the same curve because both were produced by the same competition between vertical and horizontal tendencies. Correspondences were one of the major motivating and legitimising factors behind Galileo's desire to treat all of nature mathematically. This conceptual structure justified Galileo's treatment of all of phenomena of mechanics as mathematically the same. Using a pendulum to analyse an inclined plane, as Galileo did, only makes sense if they are related phenomena. The search for these correspondences lay at the heart of Galileo's mechanical program, and he believed in them so strongly that he was willing to dismiss empirical or mathematical results that suggested otherwise. This work is not a comprehensive presentation of the development of mechanical thought in the 17th century. Nor is it an attempt to provide a unified understanding of how Galileo or his contemporaries viewed nature. I focus on a single strand of thought that, while crucially important to Galileo's study of motion, was one concept in a much broader understanding of the natural world. This work contains no astronomy, optics, or theology; the science of mechanics is my subject. The concept at the heart of this history, correspondence, took several different forms. Galileo viewed two phenomena as having a correspondence if their motions were in some way the same; sometimes he arrived at this conclusion through mathematics, other times through observation, or occasionally by guessing at the dynamics of the phenomena, but in no case could he be described as having a proof of the existence of a correspondence. Correspondences were always hunches or intuitions; something about the phenomena convinced Galileo that they were the same in some important respect. Most importantly, once convinced that a correspondence did exist between two different types of phenomena, Galileo was loathe to change his mind, even when the evidence that led him to this belief came under fire or even evaporated altogether. Page 4 of 116 Max Kemeny A Certain Correspondence Anyone who reads the Discorsi or the Dialogo is struck by how frequently Galileo uses analogies to explain a variety of phenomena. The key argument of this work is that Galileo's arguments were not merely analogies. Galileo used the concept of correspondences to tie his mechanical program together. The motion of a pendulum wasn't just similar to the motion of a ball on an inclined plane, they were in important respects the same. The shape of the hanging chain could not just be used as a convenient analogy to projectile trajectories, they were the same shape because they were the same kind of phenomenon. Correspondences legitimised Galileo's use of one to analyse the other. The first chapter of this thesis outlines Galileo's development of the