Complexity science: Implications for forecasting

Abstract

The Curious Behavior of Complex Systems The most exciting development in the systems area in recent years is that of complexity science, focusing on nonlinear, dynamic, complex adaptive systems (CAS). It has clearly recognized the move beyond the constraints of traditional analysis, which, in the Introduction to this issue, we termed the technical/analytic or T perspective. The Santa Fe Institute’s John Casti observes that twentieth-century science has demonstrated the limits of scientific knowledge ([1], pp. 196–198). Godel’s Incompleteness Theorem, Turing’s Halting Theorem, and Heisenberg’s Uncertainty Principle all underscore the fact that knowledge of the real world cannot be satisfactorily attained by means of the world of mathematics as it exists today. But it does not mean that the human mind and its creative capability are necessarily subject to these constraints. Nonlinear systems may be (1) stable, that is, converging to an equilibrium; (2) oscillating stably; (3) chaotic within predictable boundaries; or (4) diverging unstably. In the chaotic state the system appears to exhibit paradoxical behavior: it is deterministic because it is fixed by equations and yet it incorporates randomness. It may be orderly and suddenly become chaotic or vice versa. The system is exceedingly sensitive to initial conditions, making the use of historical data as a basis for forecasting dubious at best [2]. Casti sees complex systems as either nonadaptive or adaptive. The former are characterized by the ability to see the whole picture, permit no rule changes, and can be described effectively by available predictive mathematical models. An example is astronomy. The latter, CAS, cannot see the whole picture, permit rule creation or change, and are adaptive. They tend to be medium-sized, that is, not describable either by few variables or by a very large number (and thus not amenable to statistical approaches). As Casti admits, there is no theory yet for such systems—“we’re not even