Deterministic Dynamics and Chaos: Epistemology and Interdisciplinary Methodology

TL;DR

This paper explores the reciprocal relationship between mathematics and psychology through the lens of deterministic dynamical systems and chaos theory, emphasizing interdisciplinary insights and the emergence of new mathematical problems from psychological research.

Contribution

It introduces a novel bidirectional framework linking mathematical chaos theory with psychological processes, highlighting interdisciplinary methodological advances.

Findings

Mathematics informs psychological modeling of complex systems.

Psychological phenomena inspire new mathematical problems.

Interdisciplinary approach bridges social sciences and pure mathematics.

Abstract

We analyze, from a theoretical viewpoint, the bidirectional interdisciplinary relation between mathematics and psychology, focused on the mathematical theory of deterministic dynamical systems, and in particular, on the theory of chaos. On one hand, there is the direct classic relation: the application of mathematics to psychology. On the other hand, we propose the converse relation which consists in the formulation of new abstract mathematical problems appearing from processes and structures under research of psychology. The bidirectional multidisciplinary relation from-to pure mathematics, largely holds with the "hard" sciences, typically physics and astronomy. But it is rather new, from the social and human sciences, towards pure mathematics.