Stéphane Dugowson

Biography

Stéphane Dugowson is a former student at the École Normale Supérieure in Fontenay-aux-Roses and Lyon, and holds an agrégation in mathematics and a doctorate in the history and philosophy of science. He is a lecturer in applied mathematics at the Institut Supérieur de Mécanique in Paris. Following his thesis on three centuries of the history of non-integer order derivation, his mathematical research over the last twenty years has focused on the notions of boundaries and connectedness, leading him to develop a general theory of interactivity involving ¬’ non-deterministic open dynamics ¬ª based on temporalities defined in terms of categories. This work continues in constant dialogue not only with other mathematicians, but also with engineers, philosophers, psychoanalysts and artists.

Conference: Can we influence the timeless?

This curious, paradoxical question arose in the course of my mathematical research into the interaction of dynamic systems. Classically, there are two kinds of dynamical systems: those for which time is continuous, and those for which time is discrete, like the ticking of a clock. To develop a theory of interactions between such different systems, I first had to find a unified framework to bring them together. The idea is that the states in which these systems find themselves undergo transitions that are composed according to the succession of durations. From this follows a general conception of durations (and transitions) based on their ability to compose, which leads to durations being defined by what mathematicians call the “arrows” of a “category”. However, this framework in fact leads us to conceive of an infinite diversity of temporalities: in addition to linear temporalities (discrete or continuous), we encounter cyclical time, multi-dimensional time, parallel time, arborescent time, … Each such temporality gives rise to specific dynamics. In particular, when the temporality under consideration contains only zero duration, we obtain “timeless dynamics” that are in fact perfectly static, a priori of no interest since nothing happens. However, a certain technical difficulty led me to modify my definitions a little, which had the unexpected effect of making these timeless dynamics interesting, by making them in some way influenceable by dynamics with more classical temporalities. Involving non-trivial mathematical aspects, the questions raised by this type of influence are also proving to be a fascinating philosophical challenge, involving ideas of eternity, the absolute novelty of the instant, free will, destiny and the limits of the knowable, on the frontiers of spirituality.