Some Remarks on Catastrophe Theory and Biology

In the founding article of catastrophe theory, Thom states that the sources of his theory are twofold: on the one hand his research in topology and differential analysis, on the other hand the treatises of embryology, in particular the books of Conrad Hal Waddington and his notions of “epigenetic landscape” and “chreod”AQ1. These two notions were introduced by Waddington through images, even before definitions. In this chapter I defend the idea that the relation of catastrophe theory to biology, which—by Thom’s admission—cannot be subjected to experimental control, rests on the bet of its relevance as an expression in mathematical terms of the images constituting Waddington’s epigenetic landscape. After showing in what sense the notion of structural stability allows Thom to relate his theory to the epigenetic landscape, I consider the limits of this ambition but also the perspectives opened by the Thom-Waddington dialogue in the context of the recently renewed interest in Waddington’s voice as a theorist of developmental canalization.