From Divine Order to Human Approximation: Mathematics in Baroque Science
The Inverse Square Law (ISL) of Universal Gravitation is the epitome of the great achievement of mathematical natural philosophy. But what exactly was this achievement? Newton and his followers presented it as the discovery of the simple, perfect laws und
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From Divine Order to Human Approximation: Mathematics in Baroque Science Ofer Gal
Abstract The Inverse Square Law (ISL) of Universal Gravitation is the epitome of the great achievement of mathematical natural philosophy. But what exactly was this achievement? Newton and his followers presented it as the discovery of the simple, perfect laws underlying all seemingly-unruly phenomena. For Kepler, the first to introduce the ISL into natural philosophy (as the law of the decline of light with distance), mathematics was indeed the human means to decipher God’s perfect harmonies, but through the seventeenth century this belief gradually eroded. For Newton, the ISL became a tool of approximation, rooted in, and gaining its authority from, human practice: the mathematization of nature required relinquishing the certainty and perfection that mathematical knowledge was expected to provide.
Kepler and Newton “… Here ponder too the Laws which God / Framing the universe, set not aside / But made the fixed foundations of His work” (Halley’s Ode to Newton, Newton 1687, p. xiii) “A catechist announces God to children, and a Newton demonstrates Him to the learned.” (Voltaire 1901, 7:80)
This is the way in which Newton and his disciples wanted his great achievement to be remembered: as the submission of all phenomena to a small set of exact mathematical laws. These laws, Halley and Voltaire avowed, constituted a simple, perfect and harmonious structure underlying all seemingly unruly phenomena, a structure which was the divine blue print for the universe. They had to be mathematical because mathematics was the way the catechism was revealed to the sages;
O. Gal (*) Unit for History and Philosophy of Science, University of Sydney, Australia e-mail: [email protected] O. Gal and R. Chen-Morris (eds.), Science in the Age of Baroque, International Archives of the History of Ideas 208, DOI 10.1007/978-94-007-4807-1_4, © Springer Science+Business Media Dordrecht 2013
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the science of simple, perfect structures, human reason in its closest approximation of the divine.1 The two diagrams below suggest that this self presentation was not completely unfounded. They suggest that the assumption that simplicity of causes must underlie the complexity of phenomena, and that deciphering this simplicity is the role of mathematics, were not only philosophical afterthoughts for Newton and the Newtonians. Rather, they were working principles that he picked up from the tradition of mathematized natural philosophy developed through the seventeenth century and which Kepler was instrumental in shaping. Seventy year separate these diagrams and they are different in audience and goal. Kepler’s (Fig. 4.1) is public and in print—it opens the 1609 Astronomia Nova. Newton’s (Fig. 4.2) is private and hand-drawn—part of a 1679 letter to Robert Hooke (Newton 1960, 2:308). Kepler is aiming to convince the general astronomical public that the geostatic system, whether in its Ptolemaic or Tychonic version, is untenable. Newton is suggesting to h
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