Inferring Probabilities from Symmetries: Maxwell and Beyond

New York University, New York NY

Investigators

Abstract

This award will support research on the work of the Scottish physicist James Clerk Maxwell. In 1859 Maxwell proposed an important hypothesis for the foundations of statistical mechanics concerning the distribution of positions and velocities of the molecules of a gas; it is known as Maxwell distribution. He had no empirical data indicating that such a distribution existed, let alone that it took the mathematical form that he suggested. Yet his hypothesis proved to be correct, and still serves as an essential element of statistical physics. Maxwell made an enormously important and entirely correct deduction about the behavior of the physical world, then, on the basis of no evidence whatsoever. This project aims to determine how Maxwell came to formulate that hypothesis. It will do so, first, by showing that Maxwell's inference is based on hypothesized physical symmetries in molecular dynamics; second, by investigating similar apparently a priori probabilistic inferences in other branches of the sciences; and third, by uncovering a general technique, followed by Maxwell and others, for inferring physical probability distributions from physical symmetries. The methods of the project are diverse: a close reading of Maxwell's writings on the probability distribution; an investigation of nineteenth century philosophical commentary on inferences such as Maxwell's; an examination of contemporary psychological research on inferences about physical probability in everyday contexts, especially as found in young children and infants; and most important, an independent investigation of what inferential techniques might possibly succeed in inferring facts about probability from physical symmetries in the absence of corroborating statistical evidence. A successful completion of the project will provide, among other things, a better understanding of a certain kind of scientific reasoning, a better understanding of certain episodes in the history of scientific discovery (exemplified by Maxwell's great achievement), and a better understanding of certain important aspects of everyday thinking in which there is reasoning, discovery, and cognition involving the inference of probabilities from symmetries.