Thom

NotesReneThom

Some main points about Thom
First, keep in mind that it is a theory of models – and this is always an interesting problem, which is how it takes up a model of meaning.
The general background to this is really biology: “a system of forms in evolution constitutes a formalizable process if . . . “

At the same time, we are talking about the sciences in general, hence the quote of D’ARchy Thompson. But note how that quote institutes one of the main problems of mathematics in the modern era, which is the study of patterns, as opposed to what we previously considered mathematical, that is the treatment of numbers.
Thompson makes this distinction between form and pattern explicity.
Then, note the title of the subchapters: Succession of form; Science, and the indeterminism of pheonena, Qualitative or quantitative, etc.

In otherwords Thom is pointing to a main problem which in a sense constitutes all scientific inquiry – foresee the change of form and “if possible,” explain it.
Its important to see how Thom introduces the notion of a model to formalize the space of change. And it is also important to understand that the model has two elements: topology and calculus. It is interesting in this to see him refer to Descartes and Newton in this context, specifically since it introduces the problem of the quantitative (Descartes and Newton) but in different ways. “Descartes, with his vortices, hi hooked atoms and the like explained everything and calculated nothing; Newton, wit hthe inverse square law of gravitation, acluated eeryting and explained nothing.”

The point his is really about how to quantify quality, how do you explain transformations in quality. “With the exception of the grandiose, profound, but rather vague ideas of Anaximander and Heraclitus, the fir pre-Coscrativ philosophers, all these thoereis rely on the experience of solid bodies in three-dimensional Euclidean space.” And, according to Thom, this is insufficient to explain the intensity of phenomena.

The then goes on to justify this problem of the formal model exactly by evacuating from it the Euclidean notion of space and of objects in space (recall our initial discussions of the ontological “limits” of Euclidean geometry). Hence the introduction of another, unlimited, formalizable space, which is topological – a manifold. “We therefore endeavor to free out intuition from three-dimensional experience and to use much more general, richer, dyamical contps, which will in fact be independe of the configuration spaces.” Keep in mind how architecture problematically exploits the topological model Thom introduces by the very fact that it returns it directly to Euclidean space.

Note that the catastrophe models that he elaborates are only local models, and there is no universal model. That’s one of the important distinctions from previous models. The second is that the model accounts for change, namely catastrophic change. This is what differential analysis (calculus) could not explain. Calculus treats of dynamical systems (which are continuous) and the rate of change as long as that change is continuous. But it cannot account for a discontinuous system.

Morphogenesis just is the discontinuity of a system.

It is that which leads to change, growth, and alteration.
Note how this notion, still based in mathematical physics, though now of a qualititative rather than quantitative stance, will constrast heavily with the algorithmic notions we are about to encounter.