I. Prigogine and P.M. Allen

I Prigogine and P.M. Allen, "The Challenge of Complexity", Self-Organization and Dissipative Structures, Austin, University of Texas Press, 1982.

It is precisely in nonlinear systems operating far from thermodynamic equilibrium that coherent self-organization phenomena can occur, characterized by some macroscopic organization or pattern, on a scale much larger than that of the individual elements in interaction. It is a structure whose characteristics are a property of the collectivity and cannot be inferred from study of the individual elements in isolation. We may say that reductionism, long a strongly criticized attitude in the social sciences, is found to be inadequate even in the physical sciences. The whole is more than the sum of the parts for such systems. [7]

Our point of view is that evolution results from the individual trial and error of different strategies by the entities composing the system, rather than from some 'global optimization' where in some way the good of the species exerts a direct influence. [32]

Evolution is the result of this very complex interplay between stochastic factors (mutation pressure, environment, small numbers) and deterministic factors (selection pressure, steady environment), and both aspects are in fact crucial. In view of all these interactions, the very existence of such complex systems as a tropical forest or a modern society poses an interesting problem from the start. Is there a limit to complexity? The more elements that enter into interaction, the higher the degree of the secular equation determining the characteristic frequencies of the system and greater the chance, therefore of having at least one positive root and hence instability. [35]

The question 'is there a limit to complexity?' may have a less clear-cut answer than those that have been considered up to the present. According to our results, an important aspect of the answer would be that complexity is limited by stability, which, in turn, is limited by the strength of the system-environment coupling. [36]

A complex system, such as the social system, is characterized by equations expressing the interdependence of the various actors of the system and that these intrinsic nonlinearities, in dialogue with fluctuations, result in the self-organization of the system, so that its structures, articulations, and hierarchies are the result, not of the operation of some 'global optimiser,' some 'collective utility function,' but of successive instabilities near bifurcation points. Such a view takes into account the collective dimension of individual actions and emphasizes the possibility that individuals acting according to their own particular criteria may find that the resulting collective vector may sweep them in an entirely unexpected direction, perhaps involving qualitative changes in the state of the system. It is not surprising then that many attempts at modeling such complex systems have been largely unsuccessful, particularly in the medium and long term. [37]