Macro-microscopic self-similarity in socio-cognio-physical dynamics

  • Vladimir G. Ivancevic
  • W.T. Johnson


A nonlinear, complex, Hamiltonian description of socio-cognio-physical dynamics at the macroscopic, classical, inter-personal crowd level and microscopic, quantum, intra-personal agent level, is presented in the unique form of the open Liouville equation. At the microscopic level, this can be considered as a nonlinear extension of the linear correlation and factor dynamics. This implies the arrow of time in both microscopic and macroscopic processes and shows the existence of the formal crowd-agent space-time self-similarity. This in itself shows the existence of a unique control law, which acts on different scales of agent functioning. This self-similar socio-cognio-physical control law enables us to use the crowd dynamics simulator (CDS), previously developed at Defence Science and Technology Organisation, Australia, for recursive simulation of individual agents' representation spaces, or Lewinian life-spaces, on a cluster of computers.