Professor Émérite, Université de Picardie Jules Verne
Approaching creative systems: insights from contemporary mathematics
Full set of keynote videos at bit.ly/mcm2015-keynotes.
Abstract: What are the general properties of a creative system? How to model the formation of its internal creative processes? How to embrace the various kinds of creativity including “transformational creativity” which Boden considered as the highest one?
These issues will be studied within the MENS framework, a mathematical integrative model drawing on a ‘dynamic’ category theory incorporating time. Without falling into simple reductionism MENS articulates both the neural and mental systems of a human (Ehresmann & Vanbremeersch).
Approaching the formation of creative processes within MENS reveals that any creative system necessitates a kind of ‘functional redundancy’, formalized by the “Multiplicity Principle”. This accounts for the emergence of specific memories which integrate various modalities and are strongly interconnected; they are named “multi-faceted” memories. In addition, as these memories can become a nexus of the global memory over time, MENS formalizes the notion of “Archetypal Core” and explains how it acts as an engine for the construction of long term conceptual spaces in which creative processes can develop, by iteration of 3 intertwined processes: retrospection, prospection and complexification. In particular the MENS approach accounts for transformational creativity by showing how it relies on the emergence, through iterated complexifications, of “change in the conditions of change” (Popper). The results extend to collective creativity.
Biosketch: Andrée Ehresmann (maiden name Bastiani) is Professeur Emérite at the Université de Picardie Jules Verne (Amiens, France) and Director of the mathematical Journal “Cahiers de Topologie et Géométrie Différentielle”. Author or Editor of several books (e.g. “Memory Evolutive Systems”, 2007 and “Integral Biomathics”, 2012), she has published more than 100 articles in various mathematical or multidisciplinary domains, in particular:
(i) functional analysis and optimal control;
(ii) category theory (in collaboration with Charles Ehresmann);
(iii) self-organized multi-scale systems: model MES, based on a ‘dynamic’ category theory, for living organisms, with applications to biology, cognition (model MENS for a neuro-cognitive system), anticipation, creativity and innovative design.
Personal website: ehres.pagesperso-orange.fr