A Step Toward the Elucidation of Quantitative Laws of Nature

Abstract

When we mathematically model natural phenomena, there is an assumption concerning how the mathematics relates to the actual phenomenon in question. This assumption is that mathematics represents the world by “mapping on” to it. I argue that this assumption of mapping, or correspondence between mathematics and natural phenomena, breaks down when we ignore the fine grain of our physical concepts. I show that this is a source of trouble for the mapping account of applied mathematics, using the case of Prandtl’s Boundary Layer solution to the Navier-Stokes equations.