Institute for Mathematical Behavioral Sciences

On the Feasible Forms of Permutable Scientific Laws Jean-Claude Falmagne University of California, Irvine Abstract The focus of the talk is a vast class of scientific laws represented by a real positive valued function G of two real positive variables, satisfying the ‘permutability’ condition G(G(y, r), t) = G(G(y, t), r). This equation formalizes the idea that the second variable r of G(y, r) modifies the state of the the first one y, and that the cumulative effects of such modifications are permutable: the effect on y is the same whether r is applied first, followed by t or the other way around. This permutability constraint has a basic character and can sometimes be inferred from a ‘thought experiment.’ Yet, its consequences on the form of a law are powerful. Under empirically reasonable ‘meaningfulness’ conditions, the feasible forms of a scientific law are reduced to two special cases subsumed by the representation G(y, r) = f−1(f(y) + g(r)). These two cases are: Case 1: G(y, r) = y e g(r) Case 2: G(y, x) = y + x1 . Prominent examples are the Lorentz-FitzGerald Contraction, Beer’s Law, the Pythagorean Theorem. It also has implication on the form of psychophysical laws or models.