Why the effectiveness of mathematics in the natural sciences is not surprising

Abstract

The source of human applications of mathematics to natural phenomena is very likely to be found in the perceptual processes necessary for most animals to survive, either as prey, predator, or forager. Much of the resources of the brain are used to transform the patterns of energy that impinge on sensory nerve endings into representations more or less isomorphic to the structure of some portion of the world. It is one of the intellectual triumphs of Ancient Greek thought, especially by Aristotle, to have recognized for the first time systematically the centrality of such isomorphisms for perception. The move from visual perception to intuitive geometry, and then to systematic Euclidean geometry seems psychologically natural. The Greek application of this geometric viewpoint to the motion of the heavens constitutes the first great work in mathematical physics. The progress from the Stone Age to Ptolemy is surely a very much bigger step than the move from Ptolemy to Newton and Einstein.