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” 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.

In this lecture, we will revisit the connectivity dimensions of interaction, building upon a general theoretical framework I developed and published five years ago. That work primarily addressed the structural aspects of interaction and focused solely on the connectivity dimension of interaction itself. This year, we extend the framework by exploring the internal connectivity dimensions within each dynamic, providing a more comprehensive understanding of their fundamental nature and implications.After summarizing the original mathematical structure, we will present the four key dimensions of individual connectivity. These dimensions offer a refined perspective on the relations between discrete and continuous structures, linear and circular dynamics, and the role of invariants. While this framework remains theoretical, it opens avenues for further exploration in various scientific contexts.