The Physics of Miniature Worlds

Abstract

This chapter describes discussions by scientists in Wittgenstein’s milieu relevant to problems Wittgenstein was pondering after he had decided to devote himself to solving the problems of logic. The chapter opens just after his father has died, and Wittgenstein’s investigations into logic were bringing him to examine notions of mirroring and corresponding. It discusses Ludwig Boltzmann’s views on differential equations, mental models, experimental models, and debates with Ostwald on the use of models in the kinetic theory of gases. Work on similarity by various scientists (James Thomson, D’Arcy Thompson, Helmholtz, van der Waals, Onnes, Reynolds, Rayleigh, Tolman, Stanton and Pannell) developed from insights by Newton and Galileo is surveyed. Questions about equations analogous to those Wittgenstein was pondering about propositions in early 1914 would receive an answer by the end of 1914—by a physicist who had studied thermodynamics with Ostwald (Edgar Buckingham), and formalized the concept of “physically similar systems.”