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Cognitive Morphodynamics

Dynamical Morphological Models of Constituency in Perception and Syntax

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Jean Petitot

This book – written in collaboration with René Doursat, director of the Complex Systems Institute, Paris – adds a new dimension to Cognitive Grammars. It provides a rigorous, operational mathematical foundation, which draws from topology, geometry and dynamical systems to model iconic «image-schemas» and «conceptual archetypes». It defends the thesis that René Thom’s morphodynamics is especially well suited to the task and allows to transform the morphological structures of perception into Gestalt-like, abstract, proto-linguistic schemas that can act as inputs into higher-level specific linguistic routines.
Cognitive Grammars have drawn upon the view that the deep syntactic and semantic structures of language, such as prepositions and case roles, are grounded in perception and action. This study raises difficult problems, which thus far have not been addressed as a mathematical challenge. Cognitive Morphodynamics shows how this gap can be filled.

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Chapter 5. From Morphodynamics to Attractor Syntax 205

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CHAPTER 5 From Morphodynamics to Attractor Syntax 1. Introduction It was in the late 1960’s and early 1970’s that morphodynamics established the basis for a dynamical approach to higher level cognitive performance such as categorization and syntax. In this chapter we will give a short review of the principles, mathematical tools and results of these works. It will be only a crude summary but, even if the matter is very technical, it may help the reader to better understand the issues of morphodynamical modeling in cognitive sci- ences. 2. Christopher Zeeman’s initial move To our knowledge, it was Christopher Zeeman who introduced the first dy- namical approach to explain the links between neurology and psychology. In his seminal 1965 article Topology of the Brain [416], he introduced the key idea that brain activity must be modeled by dynamical systems (flows) Xw on configuration spaces M = IN , where I = [0, 1] is the range of activity of a neuron, N is the number of neurons of the system under consideration, and the flows Xw depend on control parameters w, micro-parameters such as synap- tic weights and macro-parameters such as behavioral or psychological values. The main novelty was to identify mental states with attractors of the flows Xw, their content with the topological structure of the attractors, and the flux of consciousness with a “slow” temporal evolution of the Xw. Consequently, the strategy for explaining mental phenomena was to use the mathematical theory of dynamical systems (global analysis)—especially theorems concerning...

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