Dynamical Approach to Collective Brain
The concept of the collective brain has appeared recently as a subject of intensive scientific discussions from theological, biological, ecological, social, and mathematical viewpoints. It can be introduced as a set of simple units of intelligence (say, neurons) which can communicate by exchange of information without explicit global control. The objectives of each unit may be partly compatible and partly contradictory, i.e., the units can cooperate or compete. The exchanging information may be at times inconsistent, often imperfect, non-deterministic, and delayed. Nevertheless, observations of working insect colonies, social systems, and scientific communities suggest that such collectives of single units appear to be very successful in achieving global objectives, as well as in learning, memorizing, generalizing and predicting, due to their flexibility, adaptability to environmental changes, and creativity.
In this paper collective activities of a set of units of intelligence are represented by a dynamical system which imposes upon its variables different types of non-rigid constraints such as probabilistic correlations via the joint density. It is reasonable to assume that these probabilistic correlations are learned during a long-term period of performing collective tasks. Due to such correlations, each unit can predict (at least, in terms of expectations) the values of parameters characterizing the activities of its neighbors if the direct exchange of information is not available. Therefore, a set of units of intelligence possessing a “knowledge base” in the form of joint density function, is capable of performing collective purposeful tasks in the course of which the lack of information about current states of units is compensated by the predicted values characterizing these states. This means that actually in the collective brain global control is replaced by the probabilistic correlations between the units stored in the joint density functions.
The dynamical model is represented by a system of ordinary differential equations with terminal attractors and repellers, and it does not contain any “man-made” digital devices. That is why this model can be implemented only by analog elements. The last property allows us to assume that (at least, phenomenologically) the proposed dynamical architecture can simulate not only ecological and social systems, but also a single brain as a set of neurons performing collective tasks where the global coordination is combined with learned correlations between neurons.
KeywordsRandom Walk Equilibrium Point Direct Exchange Joint Density Function Probabilistic Correlation
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