Discrete Dynamics in Nature and Society
Volume 3 (1999), Issue 1, Pages 1-8
doi:10.1155/S1026022699000011
Towards a theory of mind
Department of Mathematics and Statistics, Concordia University, Montreal H4B 1R6, Canada
Received 11 September 1998
Copyright © 1999 Abraham Boyarsky. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The language of nonlinear dynamical systems and ergodic theory is used to present a theoretical framework for the study of mind. The basic space X
consists of the collection of all brain images (clusters of activated neurons) that are relevant to consciousness. The dynamics of the brain is modelled by means of a discrete time transformation T
which takes a cluster of activated brain cells into another cluster of activated brain cells. The space X
is partitioned into subcollections of brain images, namely those generated by the five senses and by other processes that produce brain images relevant to consciousness. It is argued that T is a Markov transformation with respect to this partition of X. This leads to the existence of an object μ, referred to as an SRB measure which possesses properties that make it a candidate for mind: μ is ‘aware’ of the brain images in its support; μ is time-invariant and acts as an attractor into which all orbits of (conscious) brain images settle. Furthermore, the dynamical systems model for mind allows the estimation of brain information rates and provides a framework in which a number of mind related issues can be discussed.