Systems with emergent dynamics

Evolutionary biologists often reject deterministic models of evolutionary processes because they equate 'deterministic' with 'goal-seeking', and have learned the hard way not to trust goal-seeking explanations of evolutionary adaptations. On the other hand, the general theory of dynamical systems potentially has much to offer for evolutionary biology-for example, as a resolution of the conflict between gradualism and punctuated equilibrium. The concept of a system with emergent dynamics retains the deterministic nature of dynamical systems, while eliminating any goal-seeking interpretation. Define an emergent property of a complex system to be a property whose computation from the entity-level rules of the system is intractable (in some reasonable sense). Say that a dynamical system has emergent dynamics if the computation of trajectories is intractable. Then systems with emergent dynamics are deterministic but not goal-seeking. As such, they offer a sensible way to use dynamical systems as models for evolutionary processes in biology, and in other areas. We discuss these issues and examine a few simple aspects of emergence in dynamical systems.