What is complexity science? Knowledge of the limits to knowledge

In a recent article (Allen, 2000), the underlying assumptionsinvolved in the modeling of situations were systematically pre-sented. In essence, we attempt to trade the “complexity ” of thereal world for the “simplicity ” of some reduced representation. The reduction occurs through assumptions concerning: 1 The relevant “system ” boundary (exclude the less relevant). 2 The reduction of full heterogeneity to a typology of elements (agents that might be molecules, individuals, groups, etc.). 3 Individuals of average type. 4 Processes that run at their average rate. If all four assumptions can be made, our situation can be described by a set of deterministic differential equations (system dynamics) that allow clear predictions to be made and “optimizations ” to be carried out. If the first three assumptions can be made, then we have stochastic differential equations that can self-organize, as the system may jump between differ-ent basins of attraction that reflect distinct patterns of dynamical behav-ior. With only assumptions 1 and 2, our picture becomes one of adaptive evolutionary change, in which the pattern of possible attractor basins alters and a system can spontaneously evolve new types of agent, new behaviors, and new problems. In this case, naturally we cannot predict the creative response of the system to any particular action we may take, and the evaluation of the future “performance ” of a new design or actio