Abstract
This chapter offers a commentary on the correspondence exchanged between René Thom and Conrad Hal Waddington in 1967, concerning the interpretation in terms of catastrophe theory of the concepts of epigenetic landscape and chreod, introduced by Conrad Hal Waddington since the 1940s. It is intended to provide some elements of reflection on the difficulties encountered in exchanges between a mathematician and a biologist on the subject of the mathematization– in this case by means of a “dynamical systems” approach– of a theoretical question in biology, expressed in images by the compound metaphor of epigenetic landscape. One interpretation of the disagreement between the two scholars is based on the difference between their mathematical cultures, making it difficult to establish a shared dictionary (this was René Thom’s view). But another aspect must be taken into account to understand the difficulties of dialogue between the two scientists: the choice of variables (and the timescale specific to each of them) used to construct a mathematical model of the epigenetic landscape.
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