Blindspots of empiricism in the discovery of chaos theory

Abstract

Chaos theory is a branch of classical physics, founded in the 1960s-70s, that studies systems whose solutions are sensitively dependent on their initial conditions. For many, it is surprising that chaos theory arrived so late. However, through the work of Henri Poincar\'e, we know that much of the math of chaos was understood by some 70 years prior. Furthermore, through the writings of Poincar\'e's colleagues -- Jacques Hadamard and Pierre Duhem -- we also see a detailed understanding of the chaos found in his work. They also have explicit reasons of why the math of chaos was to be ignored. It was a strict form of empiricism -- positivism -- causing them to label chaos as ``useless'' and ``meaningless'' mathematics because it was thought to be ungrounded in experience. In this paper, I describe how the empiricist tenets of positivism exiled chaos from physics following Poincar\'e.