Abstract
The ''unreasonable effectiveness of mathematics’’ in describing the physics of empirical reality is simultaneously both trivial and profound. After all, the relevant mathematics was, (in the first instance), originally developed in order to be useful in describing empirical reality. On the other hand, certain aspects of the mathematical superstructure have now taken on a life of their own, with some features of the mathematics greatly exceeding anything that can be directly probed or verified by experiment. Specifically, I wish to raise the possibility that the real number system, (with its pragmatically very useful tools of real analysis, and mathematically rigorous notions of differentiation and integration), may nevertheless constitute a ''wrong turn’’ when it comes to modelling empirical reality. I shall discuss several alternatives.
Matt Visser