ABSTRACT: Complexity arises at the onset of chaos. Natural systems that evolve with and learn from interaction with their immediate environment exhibit both structural order and dynamical chaos. Order is the foundation of communication between elements at any level of organization, whether that refers to a population of neurons, bees, or humans. For an organism order is the distillation of regularities abstracted from observations. An organism's very form is a functional manifestation of its ancestor's evolutionary and its own developmental memory.
A completely ordered universe, however, would be dead. Chaos is necessary for life. Behavioral diversity, to take an example, is fundamental to an organism's survival. No natural environment can be modeled in its entirety. Approximation becomes essential to any system with finite resources. Chaos, as we now understand it, is the dynamical mechanism by which nature develops constrained and useful randomness. And from it follow diversity and the ability to anticipate the uncertain future.
There is a tendency, whose laws we dimly comprehend, for natural systems to balance order and chaos, to move to the interface between structure and uncertainty. The result is increased complexity. This often appears as a change in a system's computational capability. The present state of evolutionary progress suggests that one need go even further and postulate a force that drives in time toward successively more sophisticated and qualitatively different computation. We can look back to times in which there were no systems that attempted to model themselves, as we do now. This is certainly one of the outstanding puzzles: how can lifeless and disorganized matter exhibit such a drive? And the question goes to the heart of many disciplines, ranging from philosophy and cognitive science to evolutionary and developmental biology and particle astrophysics. The dynamics of chaos, the appearance of pattern and organization, and the complexity quantified by computation will be inseparable components in it's resolution.
NOTE: Based on talks given at the International Conference on Fuzzy Logic and Neural Networks, Iizuki, Japan, 20-24 July 1990.