Phase Transitions, Chaos and Joint Action in the Life Space Foam

TL;DR

This paper extends the Life Space Foam model to include phase transitions and chaos, providing a rigorous mathematical framework for understanding joint action and dynamic changes in motivated cognitive systems.

Contribution

It introduces a novel extension of the LSF model incorporating phase transitions and chaos, enabling analysis of multi-agent joint actions on a geometrical and topological level.

Findings

LSF model can represent co-action of multiple actors.

Phase transitions are linked to topology changes in the model.

Chaotic coupling affects geometrical properties of joint actions.

Abstract

This paper extends our recently developed Life Space Foam (LSF) model of motivated cognitive dynamics \cite{IA}. LSF uses adaptive path integrals to generate Lewinian force--fields on smooth manifolds, in order to characterize the dynamics of individual goal--directed action. According to explanatory theories growing in acceptance in cognitive neuroscience, one of the key properties of this dynamics, capable of linking it to microscopic-level cortical neurodynamics, is its meta-stability and the resulting phase transitions. Our extended LSF model incorporates the notion of phase transitions and complements it with embedded geometrical chaos. To describe this LSF phase transition, a general path--integral is used, along the corresponding LSF topology change. As a result, our extended LSF model is able to rigorously represent co-action by two or more actors in the common LSF--manifold. The model yields substantial qualitative differences in geometrical properties between bilateral and multi-lateral co-action due to intrinsic chaotic coupling between $n$ actors when $n\geq 3$. Keywords: cognitive dynamics, adaptive path integrals, phase transitions, chaos, topology change, human joint action, function approximation