Mersenne and Mixed Mathematics

One of the most fascinating intellectual figures of the seventeenth century, Marin Mersenne (1588–1648) is well known for his relationships with many outstanding contemporary scholars as well as for his friendship with Descartes. Moreover, his own contributions to natural philosophy have an interest of their own. Mersenne worked on the main scientific questions debated in his time, such as the law of free fall, the principles of Galileo's mechanics, the law of refraction, the propagation of light, the vacuum problem, the hydrostatic paradox, and the Copernican hypothesis.

In his Traité de l'Harmonie Universelle (1627), Mersenne listed and described the mathematical disciplines:

Geometry looks at continuous quantity, pure and deprived from matter and from everything which falls upon the senses; arithmetic contemplates discrete quantities, i.e. numbers; music concerns harmonic numbers, i.e. those numbers which are useful to the sound; cosmography contemplates the continuous quantity of the whole world; optics looks at it jointly with light rays; chronology talks about successive continuous quantity, i.e. past time; and mechanics concerns that quantity which is useful to machines, to the making of instruments and to anything that belongs to our works. Some also adds judiciary astrology. However, proofs of this discipline are borrowed either from astronomy (that I have comprised under cosmology) or from other sciences.¹

Mersenne dealt with almost every one of the mixed and pure mathematical sciences listed above. He first collected a number of treatises on geometry and mixed mathematics in the two editions of his Synopsis (Synopsis Mathematica 1626 and Universae geometriae synopsis 1644). He composed several treatises on music (Traité de l'harmonie universelle 1627; Questions harmoniques 1634; Les preludes de l'harmonie universelle 1634; Harmonie universelle 1636; Harmonicorum libri XII 1648) and optics (De Natura lucis 1623; Opticae 1644; L'Optique et la catoptrique 1651). Later on he published further collections of essays concerning mechanics, pneumatics, hydrostatics, navigation, and the techniques for establishing weights and measures (Cogitata physico-mathematica 1644; Novarum observationum physicomathematicarum tomus III 1647). Moreover, Mersenne contributed to spread Galileo's writings in France (Les nouvelles pensées de Galilée 1639; Les méchaniques de Galilée 1634) as well as the ideas of thinkers such as Hobbes and Roberval. Mersenne discussed natural philosophical issues not only in his mathematical works but also in a number of philosophical essays, in his huge correspondence, and also in writings whose content is not directly related to science. These are notably the cases of the Quaestiones caeleberrimae in Genesim, a huge commentary to St. Jerome's Vulgate that contains contributions to optics and acoustics, of La vérité des sciences, the Harmonicorum libri XII, and l'Harmonie Universelle, which contains contributions to arithmetic (Knobloch 1974).

Many years ago, Robert Lenoble's groundbreaking Mersenne ou la naissance du mécanisme portrayed the Minim friar as an early and influential advocate of the mechanization of the world picture (Lenoble 1943). Lenoble did much to establish Mersenne's reputation as a Christian thinker who, out of his concern for the attacks the Christian faith was receiving from many quarters, was willing to renounce some Aristotelian tenets in order to make room for philosophical innovations in mechanics, astronomy, music, and so on. In a move that was quite standard in his days, Lenoble could easily construct Mersenne's defense of the value of mathematics and advocacy of the mixed mathematical sciences as straightforward support for a mechanistic understanding of nature. Richard Popkin substantially refined Lenoble's picture by placing Mersenne's philosophical innovations within the emergence of modern skepticism and by characterizing them in terms of 'mitigated skepticism'. According to Popkin, while Mersenne partially accepted the skeptics' critique of the possibility of Aristotelian scientia, and consequently of the knowledge of the real nature of things, he advocated a kind of knowledge consisting "of information about appearances, and hypotheses and predictions about the connections of events and the future course of events" (Popkin 1979, p. 131). Along with the contributions of Lenoble and Popkin, the careful exegetical work of the curators of Mersenne's correspondence brought to light new...