On a bounded version of Holder's Theorem and an application to the permutability equation

Abstract

The permutability equation G(G(x,y),z) = G(G(x,z),y) is satisfied by many scientific and geometric laws. A few examples among many are: The Lorentz-FitzGerald Contraction, Beer's Law, the Pythagorean Theorem, and the formula for computing the volume of a cylinder. We prove here a representation theorem for the permutability equation, which generalizes a well-known result. The proof is based on a bounded version of Holder's Theorem.

This paper will be submitted as a chapter in an edited volume honoring the 90th birthday of Patrick Suppes. The author presented the paper at a conference honoring Suppes 90th birthday at Stanford University