Which Number System Is “Best” for Describing Empirical Reality?

Matt Visser ()
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Matt Visser: School of Mathematics and Statistics, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand

Mathematics, 2022, vol. 10, issue 18, 1-10

Abstract: Eugene Wigner’s much-discussed notion of the “unreasonable effectiveness of mathematics” as applied to 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 by now taken on a life of their own, with at least some features of the mathematical superstructure greatly exceeding anything that can be directly probed or verified, or even justified, by empirical experiment. Specifically, I wish to raise the possibility that the real number system (with its nevertheless pragmatically very useful tools of real analysis and mathematically rigorous notions of differentiation and integration) may nevertheless constitute a “wrong turn” (a “sub-optimal” choice) when it comes to modelling empirical reality. Without making any definitive recommendation, I shall discuss several reasonably well-developed alternatives.

Keywords: mathematical physics; number systems; rational numbers; real numbers; integration; differentiation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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