11 - Spacetime and Geometry

Abstract

This chapter presents an attempt to resolve the fundamental question as to the actual information concerning the geometric structure of the world, that is, the structure of spacetime that is conveyed to us through the theory of general relativity. The chapter discusses the distinction between pure and applied mathematics. The controversy surrounding the problem of the relationship between mathematical theory and physical reality has had a long and varied history from the extreme realism of the Pythagoreans, the somewhat obscure epistemological dualism of Plato to the transcendentalism of Kant and finally to a certain point of view that is current among contemporary philosophers. Mathematics in the modern sense may be said to have originated in the work of Euclid. His monumental achievement was the invention of the axiomatic method. Prior to this time, the various truths of geometry had been treated as isolated or mutually independent.