On Meaningful Scientific Laws / by Jean-Claude Falmagne, Christopher Doble.

Overview -- Extensive Measurement -- Functional Equations -- Abstract Axioms and their Representations -- Defining Meaningfulness -- Meaningfullness and Dimensional Invariance -- Propagating Axioms via Meaningfulness -- Meaningful Representation of Scientific Codes -- Order Invariance under Transformations -- Open Problems -- Bibliography -- Index.

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.