The Elements of Catastrophe Theory or The Honing of Occam's Razor

Publisher Summary This chapter reviews the elements of catastrophe theory. Catastrophe theory, in the broadest sense, may be thought of as a new point of view for judging and comparing simplicity; this theory is most concerned with the points at which the change is sudden. Thom proposed the concept of elementary catastrophes to capture the association of geometries of equilibria with discontinuity and sudden change. Catastrophe theory has obvious bearing on any activity that uses Occam's razor in the celebrated form of all explanations that fit. The extreme of simplicity is known also as structural stability. The idea based on a system of structural stability depends crucially on what kinds of perturbations are to be considered, which of these are little, and what constitutes a change. Using particular decisions for choices for a wide range of systems, it has recently become possible to prove structural stability where it is present and to analyze the possible perturbations of less simple systems.