Catastrophe Theory

Abstract

The mathematical theory of catastrophes was developed by Rene Thom and consists of models suitable for explaining the abrupt changes of discontinuous dependent variables. Such variables are called catastrophic and have been difficult to analyze because mathematics has traditionally assumed that both the independent and dependent variables are continuous. Catastrophe theory has been highly touted as being particularly suitable for the less exact sciences, such as sociology, where measurement and conceptual difficulties make the assumption of a continuous dependent variable somewhat dubious in many cases. This paper explicates the nature of catastrophe theory in a nontechnical way, emphasizing the simplest model, the cusp. Both an inductive and deductive approach in applying the cusp model to sociological data are developed and illustrated, and the paper concludes with a discussion of how catastrophe theory might contribute to sociological understanding.