David Rand

From Waddington via Smale and Thom to a landscape conceptual framework that models real embryonic data.

David Rand

University of Warwick, UK

e-mail: marsz@live.warwick.ac.uk

In René Thom's book "Modèles Mathématique de la Morphogenèse" which I co-translated when I was a graduate student there is a fascinating account of a discussion with Waddington about the history of ideas around the notion of what we would now call multistability, and about Waddington's concept of a 'chreod' and Thom's more general notion of a 'morphogenetic field'. According to Thom his discussions with Waddington were seminal in his development of Catastrophe Theory which he saw as a general theory of models that could be used for a discussion of morphogenesis of a most general sort which spanned not just biology but also, for example, semantics and linguistics, semiotics and games. I want to trace a path from such discussions through Thom's Catastrophe Theory and Smale's contributions to topology and dynamics to current ideas in cellular decision-making and developmental biology. In this discussion my end-point will be a brief analysis of a specific biological system (the early development of the ventral neurons) using a modern version of the Waddington-Thom ideas. When I finished translating Thom's book in the 70's, I was proud that he congratulated me on not converting it to an Anglo-Saxon viewpoint. I suspect he would not say the same about the biological analysis I will present, but I think I can defend myself.