Complex Systems

From Collective Mind to Communication Download PDF

Michail Zak
Jet Propulsion Laboratory
and
California Institute of Technology,
Ultra-computing Group
Pasadena, CA 91109

Abstract

"Collective mind" is introduced as a set of simple intelligent units (say, neurons, or interacting agents) that can communicate by exchanging information without explicit global control. Incomplete information is compensated for by a sequence of random guesses symmetrically distributed around expectations with prescribed variances. Both the expectations and variances are the invariants characterizing the whole class of agents. These invariants are stored as parameters of the collective mind, while they contribute to dynamical formalism of the agents' evolution, and in particular, to the reflective chains of their nested abstract images of the selves and nonselves. The proposed model consists of the system of stochastic differential equations in the Langevin form to represent motor dynamics, and the corresponding Fokker-Planck equation to represent mental dynamics. The main departure of this model from newtonian and statistical physics is due to feedback from the mental to the motor dynamics, which makes the Fokker-Planck equation nonlinear. Interpretations of this model from mathematical, physical, biological, and psychological viewpoints are discussed. The model is illustrated by the dynamics of a dialog.