ESHS/HSS Annual Meeting

The Language of the "Statistical": Contrasting Maxwell and Boltzmann on Gas Theory

• In Event: Models, Concepts and Boundaries in the 19th and Early 20th Century

English Abstract

The emergence and development of the statistical method marked an epoch in the history of science, leading to a novel view of nature and natural laws in late nineteenth-century physics, as often represented by the names of James Clerk Maxwell (1831-1879) and Ludwig Boltzmann (1844-1906). Treating the adjective "statistical" as a category employed by historical actors, I argue that the term was initially too foreign to be readily incorporated into the vocabulary of physics, as shown by the cases of these two physicists. While Maxwell introduced his velocity distribution in analogy with the error distribution in 1860, it was not until over a decade later, in _Theory of Heat_ (1871), that he explicitly described his method as "statistical," drawing an analogy with population statistics. Boltzmann was more cautious. Although he occasionally mentioned statistics for illustrative purposes, he continued to refer to his gas theory as "probabilistic." When he applied the adjective "statistical," his usages can be classified into three categories: (1) to refer to statistics as the science of states, (2) to draw analogies between a group of gas molecules and a population, and (3) to describe theories of Maxwell and Josiah Willard Gibbs (1839-1903) as statistical. Despite the shared analogy with population statistics, Boltzmann evidently avoided the adjective "statistical." I suggest that the German _Statistik_ carried a strong connotation of _Staatenkunde_ (the science of states) in Habsburg Austria, where Boltzmann spent much of his career, as reflected in contemporary university curricula and treatises on statistics.

Author

• Hajime Inaba, Meiji University / University of Copenhagen