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Critical Mass: How One Thing Leads to Another

Ball, Philip
Arrow Books: London, 2005
ISBN 0099457865 (pb)

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Reviewed by Bruce Edmonds
Centre for Policy Modelling
Manchester Metropolitan University

Cover of book In Isaac Asimov's Foundation science fiction trilogy there is a genius called Harry Seldon who has invented a science called "Psycho-history". As it says (Asimov 1962, page 7):
"Psycho-history dealt not with man, but with man-masses. It was the science of mobs; mobs in their billions ... The reaction of one man could be forecast by no known mathematics; the reaction of a billion is something else again."

The idea is that the behaviour of many humans in aggregate can be accurately captured in a mathematical model even though this may not be possible for the behaviour of any particular individual. In other words there are clever "short cuts" that would allow us to bypass our lack of understanding of individual human behaviour as we observe it in everyday life, to obtain successful analytic models of humans en masse.

This can be thought of using an analogy with an ideal gas: the individual particles trace out intricate paths, interacting with each other and any walls (by colliding with them), but all this intricacy cancels-out to an extraordinary extent (from our perspective) allowing the aggregate properties of such a gas to be capturable by some relatively simple equations or properties. The fact that we can't trace out the individual particles is not a barrier to the description of the aggregate behaviour of the collection. The idea is that a similar approach might work with social systems composed of individuals.

This sort of idea has stalked social science for a long time – that, when looked at en masse a "physics of social phenomena" (or sociophysics[1]) is possible. It holds out the prospect of the social sciences becoming a "real" science: avoiding being mired in the context-dependent detail of complex human behaviour, and aspiring to generality and predictive power. Critical Mass narrates the story of this approach.

This book traces the development of sociophysics all the way back to Hobbes, the 17th Century philosopher who first sought to make political thought a more certain science and who sought to relate how the properties of individuals might relate to those of the society they composed. From there it takes a broad sweep through familiar areas, including: social statistics, flocking, traffic simulation, small world networks, power laws, phase transitions, the minority game, self-organised criticality and iterated prisoner dilemmas. It is, in its way, the first "popular science" book covering a substantial section of social simulation, and talks about many of the main figures up to about 1990 (it does cover later work but not so comprehensively, which is understandable). Thus the work of Thomas Schelling, Ilya Prigogine, Brian Arthur, Alan Kirman, Robert Axtell, Joshua Epstein, Robert Axelrod, Paul Omerod, Martin Nowak, Per Bak, Duncan Watts, are all discussed.

In all of this the book is quite careful as to matters of fact – in detail all its statements are cautiously worded and filled with subtle caveats. However its broad message is very different, implying that abstract physics-style models have been successful at identifying some general laws and tendencies in social phenomena. It does this in two ways: firstly, by slipping between statements about the behaviour of the models and statements about the target social phenomena, so that it is able to make definite pronouncements and establish the success and relevance of its approach; and secondly, by implying that it is as well-validated as any established physics model but, in fact, only establishing that the models can be used as sophisticated analogies – ways of thinking about social phenomena. The book particularly makes play of analogies with the phase transitions observed in fluids since this was the author's area of expertise.

This book is by no means unique in making these kinds of conflation – they are rife within the world of social simulation. The culture of physics is a complex of different attitudes, norms, procedures, tools, bodies of knowledge and social structures that are extremely effective at producing useful knowledge in some domains – it is not for nothing that physists have gained status within our society. However when this culture is transported into new domains, such as that of modelling social phenomena, the culture does not travel uniformly. Thus we have seen (and Critical Mass documents) an influx of simple, physics-style simulation models into sociology but they have arrived without the usual physists' insistence that models predict unseen data. It is part of the culture of physics to aspire to the simplest possible model of phenomena but a model which only acted as a sort of vague analogy with respect to its phenomena would get short shrift in traditional physics domains. Yet frequently one reads social simulation work which takes the form of physics-style models and yet uses only vague, hand-waving justifications to justify its relevance (and, at best, a rough fitting of known, aggregate data). Models need to be constrained by the subject matter they are supposed to be about – there are two main ways of doing this: by ensuring the model is designed to behave as we know it should do (typically the parts of the model); and by checking the resulting behaviour against corresponding observed behaviour (often in aggregate). Sociophysics models tend to avoid either: they impose over-simple behaviour onto the design and don't validate strongly against unseen data. Thus whilst such models may have interesting behaviour there is little reason to suppose that they do in fact represent observed social behaviour.

Although this book does add the occasionally warning and caveat (especially over the distinction between what we would want a society to be like and how it operates) it is basically uncritical of the work it presents, painting it in a far more favourable light than is justified. It goes beyond praising work as pioneering and exploratory so as to claim that it already does (in parts) capture general and true theories about social phenomena and is already useful as an aid to judging policy. Thus for example it says (page 560) "…there is no denying the strong implication from game theory that an unswervingly retaliatory strategy is the best way to bring about cooperation.'

This overstatement reaches its apogee in its consideration of Axelrod's model of alliances between countries as a balancing of the forces of difference and similarity between them (Axelrod and Bennett 1993). Being under-critical of the extremely limited validation this model is exposed to and the ease to which such models can be unwittingly fitted to known data, it gives the impression that this model actually correctly "predicted" the alliances of European countries in the two world wars and implies that it will predict future configurations… Thus this book does not, overall, take heed of its own advice to "…exercise great care when we are tempted to couch technical conclusions in anthropomorphic terms" (pages 508-9) but rather seems to repeat the over-optimism of earlier attempts – "When William Petty applied strict mathematical reasoning to social phenomena… some of his contemporaries found his approach ridiculously naïve. And so it was." (pages 567-8)

Oddly, it does criticise neo-classical Economics for its over-simplification and lack of validated relevance, but it does not take a step back to consider how the sociophysics it reports on might be have the same problems. Included in these criticisms are (neo-classical) Economics': assumptions of rationality, homogeneity, over-simplification of agent behaviour, assumptions of randomness, existence of equilibria, lack of validation against real data. Yet many of the models discussed in Critical Mass use these kinds of assumptions! One suspects that a large reason that these physics-like models have been given credence is that they are not quite as bad as the economics models that preceded them.

Only in the section on crowding/traffic models is it at all convincing. Here the models do seem to match individual as well as subsequent aggregate behaviour (for example where static traffic will form on motorways). Here, where human behaviour is constrained to extremely simple behaviours and actions, it is credible that a simple model may suffice to capture the consequences of the actors' interaction. This chapter actually presents some evidence of validation that goes beyond 'data fitting' or analogical credibility – evidence that is lacking elsewhere in the book.

In a sense the whole book is an elaboration of the argument summarised on page 568: "Society is complex but that does not place it beyond our ken. As we have seen complexity of form and organisation can arise from simple underlying principles if they are followed simultaneously by a great number of individuals." This is an argument that has been repeatedly made in the sciences of complexity (and particularly in ALife): that complex behaviour can result from the interaction of lots of simple parts. This is now well established, but the implied corollary that the complexity we observe is a result of lots of simple interactions (or that it is useful to model this in this way) does not, of course, follow. Grounds for hope does not make it a reality.

If sociophysics makes the same mistake of lack of relevance that economics did, it will be similarly unsuccessful at illuminating social phenomena. Physics-type models may be impressive in terms of their formal content and analysis, but vague social interpretations are insufficient to ensure that they are about social phenomena. Assumptions and modelling styles that physicists use will tend to exacerbate this problem if they are not adapted to the different demands of social phenomena. The result could be yet another retreat away from the target phenomena into the exploration of the formal properties of models – the 'inward turn' that has occurred in many fields where empirical and/or practical success has not materialised (e.g. AI or Economics).

This would be a pity, because physics has a lot to teach the social sciences. These include:

These are in sharp contrast with the situation in the social sciences which is 'top-heavy' in terms of abstract paradigms/frameworks and theories and relatively lacking in data collection and descriptive modelling. Sociophysics consists of a movement from traditional theoretical physics into the domain of the social sciences, what would be more productive is the import of some of the more mundane, but fundamental, aspects of physics.

This book is a well-written, and historically careful account of the development of sociophysics and abstract social simulation. It gives a good overview of several fields of application and an accessible, entry-level description of many simulation models that can be interpreted as forming part of the sociophysics strand. But don't be beguiled into thinking that the simple computational models presented actually represent social phenomena or are reliable models of those phenomena just because they make for attractive analogies. It may be helpful and interesting to think of the universe as a clock, but this does not mean that it is useful to model it as a clock.

As it says on page 567: "The skill lies in knowing where a mechanistic, quantitative models is appropriate for describing human behaviour, and where it is likely to produce nothing but a grotesque caricature." The weakness of this book is its lack of skill in this regard, its strength is its careful account of the scope and development of sociophysics. Read it for an education into the history of sociophysics-type modelling, but take its judgement as to the success of the results with more than a pinch of salt.

* Notes

1For the sake of brevity I will lump all the models described in this book as sociophysics, since they share most of the characteristics of physics models. However, it must be said that most of the participants mentioned in the book would not see themselves or their models in this regard, and indeed be hostile to such a clustering. I do not mean to insult them but are simply using this review to point out and discuss certain approaches and styles of modelling that have been converged upon from many directions. Having said this, I have no doubt that this kind of modelling has been inspired and influenced by the success and methods of physics.

* References

ASIMOV I (1962) Foundation and Empire. London: Panther Books.

AXELROD R and BENNET D S (1993) A Landscape Theory of Aggregation. In British Journal of Political Science, 23, pp. 211-233.


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