The mathematical concept of catastrophe theory was proposed by René Thom in 1968 and was presented in his Structural Stability and Morphogenesis (1972/1989). Thom's "Elementary catastrophes" refer to the seven dynamic configurations that a form, being sufficiently stable to be recognized in ordinary space-time, adopts in order to appear, subsist, and change.
René Thom introduced his work as follows:
This work aims to provide a formal structure that can be used to attack any morphogenetic problem in general. Based on a consideration of the mechanisms at work in embryological development, this formal structure leads to a universal method that can be used to associate any morphological appearance with a local dynamic situation that engenders it, in a way that is independent of the substrateaterial or immaterial, living or non-livinghat supports it. In this way we introduce the notion of 'catastrophe,' whose applications range from physics ...to linguistics . . . and biology. This book provides the first systematic attempt to consider problems of biological control in geometric and topological terms as well as those associated with the structural stability of shapes (1989).
The research on which catastrophe theory depends, as undertaken by Alexandre Liapounov (1857-1918), in Russia, on structural stability, and by Henri Poincaré (1854-1912), in France, on qualitative dynamics, has continued (differential topology, dynamic systems, and so on). Structural stability treats shapes and phenomena according to an intrinsic variability that their persistence in time imposes on them, and not as if they remained strictly identical to them-selvesthe simple stability" that classical science requires. In this way the energy a being expends to persist can be taken into account, and consideration given to the stylization of structurally stable shapes, according to a dynamic that is qualitative because it indicates "state trajectories," possible histories and events, without measuring quantities. Catastrophe theory resolves the following problems: Given a structurally stable dynamic situation dependent on an unknown (or even infinite) number of parameters, it describes all the possible variations and changes in the situation with the help of a finite and minimal number of parameters. If the situation can be represented in conventional space-time, the theory provides for seven kinds of change, the seven elementary catastrophes, depending on at most four parameters.
Determining psychic forms, constructing a dynamic that creates them, then making the problems associated with the stability and regulation of these forms intelligibleheir possible historiesas the work of Freud. Psychoanalysis is psychic morphodynamics. That a theory addressing conditions of possibility and constraints can serve to make Freud's work more intelligible goes without saying. A standard case involves the coexistence of primary narcissism and a primary object relation that one of the catastrophes, the "cusp," can be used to model. Similarly, one of the aspects of the duality of the life and death drives can be described as the necessary co-presence of structural and simple stabilities.
The application of the "exact sciences," even the geometrization of a part of thermodynamics, to any nonmathematico-physical domain is complex. But René Thom began to work out the epistemological implications of catastrophe theory. In his Semiophysics: a sketch (1988/1990), he developed a phusis of meaning. He shows how these mathematics subvert the Galilean subdivision of the world and respond to Aristotle'snd Freud'suestions by treating form and dynamic together in their subjection to time. He then restores the emergence and instrumental value of these mathematics within the framework of natural philosophy, where, by means of "pregnance"rives according to Freudignification becomes a process immanent in a vital dynamic. These analyses, which overturn epistemologies in force since the Galilean revolution, provide access to "laws of nature that are vaster and of greater scope" (1914d) than Freud had hoped.
See also: Dualism; Strata/stratification.
Freud, Sigmund. (1914d). On the history of the psychoanalytic movement. SE, 14: 1-66.
Porte, Michéle. (1994). La dynamique qualitative en psychanalyse. Paris: Presses Universitaires de France.
Porte, Michéle. (Ed.). (1994). Passion des formes. Dynamique qualitative, sémiophysique et intelligibilité.René Thom. Paris: E.N.S. Fontenay-Saint Cloud.
Thom, René. (1989). Structural stability and morphogenesis: an outline of a general theory of models. (D. H. Fowler, Trans.). Reading, MA: Addison-Wesley Pub. (Original work published 1972)
. (1990). Semiophysics: a sketch. (Vendla Meyer, Trans.). Redwood City, CA: Addison-Wesley Pub. Co., Advanced Book Program. (Original work published 1988)
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