On Meaningful Scientific Laws
The authors describe systematic methods for uncovering scientific laws a priori, on the basis of intuition, or “Gedanken Experiments”. Mathematical expressions of scientific laws are, by convention, constrained by the rule that their form must be invariant with changes of the units of their variables. This constraint makes it possible to narrow down the possible forms of the laws. It is closely related to, but different from, dimensional analysis. It is a mathematical book, largely based on solving functional equations. In fact, one chapter is an introduction to the theory of functional equations.
This book gives many examples of applicationsA "how to" book, which prepares the reader to transforming the problem of finding the scientific law relevant to a phenomenon into solving a functional equation problemClosely related to, but essentially different from, dimensional analysis