Allen’s Evolution …
P M Allen Evolution, modelling, and design in a complex world Environment and Planning B, 1982, volume 9, pages 95-111
Allen, applying and developing the ideas of his supervisor, Prigogine, notes that:
… any mathematical model must be written in terms of certain variables which have been chosen because they characterize the structure. So, necessarily, any ‘prediction’ made by means of such a model will automatically assume implicitly that these variables remain adequate and thus that the structure remains unchanged except by purely quantitative growth or decline of its parts.
And yet innovation and metamorphosis exist!
Thus Allen describes a form of emergence where new factors have to be taken into account, and draws attention to the conditionality of any prediction on a lack of any such emergence. He goes on:
… under slowly changing conditions … a relatively sudden reorganization can occur, as the branch of solution corresponding to a given market structure becomes unstable and the pattern of consumption changes to that of some new branch of solution. In such changes very small differences, possibly of random origin can prove decisive in selecting the new structure that emerges, and also if such a change can be anticipated then it is a moment when small, weak firms can penetrate the market and become established. The image of a market system is therefore that of a ‘dynamic game’ with a varying number of players, where periods of adaptive jockeying are separated by successive crises during which major reorganization occurs.
Allen notes that this complexity tends to arise wherever one has ‘reflexivity’:
… Because of the strong feedbacks between the actions of individuals in social systems, their behaviour displays this property of bifurcation and choice. …
These complexities impact on the notion of ‘control’:
Again, the new scientific view is found to be a recognition of the limits to ‘control’ or ‘design freedom’. First, there is the unpredictability related to bifurcation phenomena, and, second, there is the fact that one must take into account the internal structures ‘accumulated’ in a system by its previous passage through bifurcations and along certain branches. … The question that must be answered … is, what exactly is this system? [I]t is necessary to know the nature of the inner structure before plans can be made. [T]he question is how will it react?
This changes the whole concept of modelling and of prediction. It moves away from the idea of building very precise descriptive models of the momentary state of a particular system towards that of exploring how the interacting elements of such a system may ‘fold’ in time, and give rise to various possible ‘types’ corresponding to the branches of an evolutionary tree. [A]ny decision, action, or design should be studied to see how it may affect the evolution of the system by making one future or another more probable.
The first quote may be what some people have in mind when they criticise mathematical modelling for ‘interesting’ systems. But, although Allen makes no reference to Whitehead, Keynes or Smuts, there seems a similarity and consistency of insights. For example, the first quote corresponds to Keynes’ concerns about factors, while the second quote can be seen as an example of Whitehead’s nested ‘epochs’ or Smuts’ evolutionary dynamics. In this sense mathematics would seem very appropriate, but may need extending beyond the conventional. Thus the notion of uncertainty required may be more like that of Whitehead and Keynes that the Bayesian probability conventionally used for mathematical modelling. The third quote corresponds to Keynes’ concerns about reflexivity, as when economic growth depends on our expectations.
The final quote can be read as saying that instead of focusing on ‘tactical’ activity, aimed at controlling the system of interest, for complex systems we need to ‘raise out game’, recognize the nature of the actual and potential systems, and develop a policy to support interventions to give us preferable systems. Because of the potential for emergence it is not possible to talk about probability in the conventional (numeric) sense, but we do aim to make the preferred outcomes ‘more probable’ in a general sense.
On a slightly pedantic note, the best strategy in a given game can often be a ‘mixed’ one, where the actual action is chosen randomly. Thus as long as actors are able to randomize, randomness occurs naturally as a consequence of normal game play, even if the situation is otherwise deterministic. Thus there is no need to add in external randomizing ‘noise’.