Dynamics of intelligent systems

Recent advances in nonlinear dynamics demonstrate a remarkable complexity o f patterns outside of equilibrium, which are derived from simple basic laws of physics. A class of mathematical models has been identified providing a variety of such patterns in the form of static, periodic, or chaotic attra ctors. These models appear to be so general that they predict not only phys ical, but also biological, economic, and social patterns of behavior. Such a phenomenological reductionism may suggest that, on the dynamical level of description, there is no difference between a solar system, a swarm of ins ects, and a stock market. However, this conclusion is wrong for a very simp le reason: Even primitive living species possess additional non-Newtonian p roperties which are not included in the laws of Newtonian or statistical me chanics. These properties follow from a privileged ability of living specie s to possess a self-image (a concept introduced in mathematical psychology) . In this paper we consider the existence of a self-image as a postulate to be added to classical physics for modeling behavior of living systems. We show that self-image can be incorporated into the mathematical formalism of a nonlinear dynamics which evolves in probability space. We demonstrate th at one of the basic invariants of living systems is their ability to predic t the future, which is associated with intelligence.