Meeting 43

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DATE: Tuesday, October 26

TIME: 1 PM Princeton time (ET) / 8 PM Bucharest time (UTC+2)

PANEL: Early Modern Correspondence and Open-Ended Inquiries Therein

SPEAKERS: Ovidiu Babeș (University of Bucharest) & Monica Solomon (Bilkent University)

Solid Explanations: Descartes on Mathematically Modelling the Fall of Water

Ovidiu Babeș

My presentation focuses on an episode of mixed-mathematical practice in Descartes’ correspondence: the explanation of the freefall of water. In a 1643 exchange with Constantijn Huygens and Marin Mersenne, Descartes provided a quantitative explanation of the phenomenon of water flowing out of a filled vertical tube. I argue that this episode helps delineate the precise role of mixed-mathematics and natural philosophy in Descartes’ natural scientific practice. I show that his mixed-mathematical explanation is not natural philosophically innocent, making use of many conceptual maneuvers and demonstrative strategies which transgress disciplinary boundaries.

Traditionally, such exercises belonged to mixed-mathematics, a bundle of disciplines that were subordinated mathematics and physics. Mixed-mathematics had little to do with establishing the natural causes of phenomena. One might suspect this is especially true in the case of mixed-mathematics framed as patchy problem-solving, a practice at the heart of Mersenne’s scientific activity in the 1630s and 1640s. After all, Mersenne (and Constantijn Huygens) simply wrote to Descartes asking for a mathematical explanation of the motion of water in freefall. The issue had practical outcomes, and seemed disconnected to any explanatory ambition in natural philosophy.

However, if one studies the development of Descartes’s explanation, the role of natural philosophical concepts and commitments becomes more and more salient. For instance, Descartes packed his physical account of liquidity within his mathematical treatment of the freefall of water, thereby creating important conceptual gaps between how liquid bodies and solid bodies behave in freefall. These gaps resulted in several properties of bodies of liquids which were emergent on the collection of single drops of liquid. Descartes’ systematic natural philosophy does not have the available conceptual resources to account for these emergent properties. Instead, his mixed-mathematical explanation of the flow of water navigated around this constraint by quantitative means. Even if Descartes’ explanation delves into physics as deeply as it can, it does not delve into Descartes’ own physics.

The Hooke – Newton correspondence of 1679

Monica Solomon

I will follow the Hooke-Newton correspondence of 1679 with an eye towards interpretations of the original question posed by Hooke and the follow-up exchanges. Several scholars (De Gandt 1995; Guicciardini, 2005, 2020; Gal 2002;  Marshall Miller 2014; Nauenberg 1994, 1998, 2005; Westfall 1971 to name but a few) have scrutinized this series of correspondence mainly because of the two great (and peculiar) personalities and their priority disputes.

In his first letter, Hooke asks Newton, among other things, for “[his] thoughts of that [hypothesis or opinion of his] of compounding the celestiall motions of the planets of a direct motion by the tangent & an attractive motion towards the centrall body.” Part of the question seems to be that of understanding trajectories as composed of certain motions. It is less clear at which level of generality we should try to answer the question and whether those motions have anything to do with forces (And if so, with which or what kind of forces?)

Throughout the exchange we discover that the original question, which seemed like a well-defined problem in geometry, turns out to be anything but. As we witness Hooke and Newton trying to explain trajectories of bodies under gravity as an attractive force with a center, we also see the difficulties involved in finding the right quantities that make our problems tractable in term of geometrical representations of trajectories. Instead of making Newton or Hooke the characters of this narrative, I will focus on the details of the problem, its interpretation, and possible solutions.

The methodological lesson is that the standards for judging replies as answers or solutions to a specific problem can hardly fit into disciplinary boundaries. Consequently, exchanges such as this one (and correspondence materials more broadly) reveal a far more dynamic disciplinary landscape, one in which physics and mixed-mathematics are sometimes in tension, but never far apart from each other. In particular, a consequence of this analysis is that we should probably give up on describing such processes or series as an example of “mathematization.” 

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