Geometry as the Measure-Theoretic a Priori of Physics

Abstract

The modern physicist knows that geometry goes back to Greek science. Thales (ca. 600 B.C.) is regarded as being the first geometer and Euclid wrote the classic geometry textbook about 300 B.C. Modern times have brought us Descartes’ (1596-1650) analytical geometry, in which coordinate systems are used to represent geometric problems arithmetically. In the nineteenth century analytic geometry was further developed by Gauss and Riemann and by Felix Klein in the Erlangen Program (1872). Euclid’s synthetic method was subsequently brought to the level of modern mathematics by Pasch (1882) and Hilbert (1899). This method no longer plays a role in modern physics, for the analytical method is adequate for all physical theories.