On the Epistemic and Social Foundations of Mathematics as Tool and Instrument in Observatories, 1793–1846

Abstract

This chapter focuses on three episodes in the history of observatories between 1793 and 1846, to examine the epistemic and social foundations of the conception of mathematics as a tool. This is an interesting case because in the observatory culture sophisticated uses of mathematics have always been deployed side-by-side with tools and instruments taken in a material sense. We look at the Paris Observatory under the French Revolution to introduce crucial distinctions between tools and instruments. We then turn to the Royal Observatory Greenwich to show how specific social techniques were developed in order to improve the precision of the mathematical tool. We finally consider the case of Bessel functions developed at the Könisberg Observatory to show that astronomers also tinkered with the mathematical instrument, like they did with telescopes, to increase its precision. This chapter is intended as a contribution to the epistemological debate regarding the “unreasonable effectiveness,” or applicability of mathematics to the natural sciences. I argue that if we take seriously the analogy between mathematics and tools and instruments, this effectiveness is rather similar to that of tools and instruments; that is, the effectiveness of mathematics is the product of specific practices performed by socially diversified communities precisely to this effect.