  We study the evolution of social clusters, in an analogy with physical spin
systems, and in detail show the importance of the concept of the "self" of each
agent with quantifiable variable attributes. We investigate the effective
influence space around each agent with respect to each attribute, which allows
the cutoff of the Hamiltonian dictating the time evolution and suggest that
equations similar to those in general relativity for geodesics in distorted
space may be relevant in such a context too. We perform in a simple small-world
toy system simulations with weight factors for different couplings between
agents and their attributes and spin-type flips in either direction from
consideration of a utility function, and observe chaotic, highly aperiodic
behavior, with also the possibility of punctuated equilibrium-like phenomena.
In a realistic large system, because of the very large number of parameters
available, we suggest that it would probably almost always be necessary to
reduce the problem to simpler systems with a manageable set of coupling
matrices, using assumptions of fuzziness or symmetry or some other
consideration.
