Communal connections

Robert May delves into the codes that govern our network society.

A central theme of Isaac Asimov's splendid Foundation novels is that, in some far future, an Einstein of sociology, Hari Selden, has bequeathed us a deterministic science of history and can therefore predict the fates not just of nations and civilisations but of galactic communities. Such Spenglerian dreams of understanding humans' collective behaviour, admittedly at a rather high level of aggregation, can be seductive.

In our own time, such ambitions take a more modest form and exploit new tools: advances in our understanding of nonlinear dynamical systems, along with computer power beyond the imagining of a previous generation, and associated vast compilations of data. Philip Ball's Critical Mass is an extraordinarily lucid and lively account of much of this recent work. It ranges from movements of economic markets, of crowds and of traffic through the patterns in networks of social contacts or of computer connections (the web and the internet), to the still-unsolved problems of how cooperative behaviour evolved and can be maintained within human and other animal societies.

Ball's historical sweep is especially good. Early thinkers are given fair regard and are connected to current work. Ball argues convincingly that the statistical physics of Maxwell, Boltzmann and others grew out of the earlier "political arithmetick" of Hobbes and contemporaries, outlining a journey from Hobbes' Leviathan (1651) to the Santa Fe Institute and "emergent phenomena". Likewise, a discussion of phase transitions and critical phenomena begins with Herschel, Boltzmann and Van der Waals, and carries us to postmodernist architecture and Malcolm Gladwell's "tipping points" in trends, fashions and voting patterns.

The chapter "On the road: The inexorable dynamics of traffic" is superb. Like much else, it is a miracle of compression, setting out the essential underlying ideas simply and clearly, then showing how they illuminate traffic phenomena we have all experienced, while avoiding inessential detail. The book is well worth buying for this chapter alone. The chapters on economic markets and trading are similarly excellent in sweep - ranging from Adam Smith to the fluctuation spectrum of Per Bak's "self-organised criticality" - and offer up-to-date appraisal of some of the dissonances between stimulating ideas and real data.

The chapters on networks lie closer to my own interests, which may be why I am a bit more critical. They begin with an excellent discussion of facts and theory about Steve Strogatz and Duncan Watts' "small-world" networks.

The early postal and other experiments showing typically "six degrees of separation" between any two inhabitants of the globe are sketched, along with more recent and extensive studies exploiting email. The networks thus exposed are small worlds (more technically, they are exponential distributions for the links connecting individuals or nodes within the network), with cliques of close acquaintances combined with connections to other cliques. The result is a network with a high degree of clustering, but with many shortcuts among clusters, so that the path length connecting any two individuals tends to scale weakly (logarithmically) with the size of the net.

More recent work suggests that many important networks - including the worldwide web, the internet, the distribution of contacts for sexually transmitted diseases and others - have "scale-free" behaviour. That is, the ratio between the number of nodes (individuals, computer terminals and so on) connected to, say, 40 other nodes and the number of nodes connected to 20 others is exactly the same as the ratio between the number connected to 100 others and those connected to 50 others, or more generally between those connected to 2n other nodes and n others. Such a network is scale free in the sense that there is no typical number of connections at which patterns of interlinking change; the distribution of relative numbers of connections among nodes looks the same at every scale. Such scale-free networks have some unusual and very interesting properties, particularly if they are assumed to be, in effect, infinitely large. In particular, if a few links are removed from a scale-free IT network, such as the web or internet, less damage is done than if they were removed from a randomly connected or from an exponentially distributed, small-world network.

Conversely, a targeted attack, focused on the most highly connected nodes, can be much more damaging for a scale-free network than for others.

In the literature on infectious diseases, particularly HIV/Aids, these phenomena, whereby effective intervention strategies can be sensitive to the nature of the network of contacts between infected and susceptible individuals, have been familiar for almost 20 years. Analogous to the observations about attacks on different kinds of IT networks is the observation that, for example, if you are seeking to eradicate an endemic infection by vaccinating within a population where the distribution of contacts among individuals is highly non-uniform, then if you vaccinate at random, you will need significantly greater coverage than would be estimated by treating the population as homogeneous (more precisely, interacting like a randomly connected network). But if you take advantage of the non-uniform contact patterns, focusing on the "super-spreaders", eradication of infection can be a lot easier.

Unfortunately, some of the recent scale-free literature on IT networks has been over-enthusiastically extended into epidemiological areas without proper acquaintance with existing work. The result is that some of the alarmist messages about sexually transmitted infections, such as HIV/Aids, having scale-free contact distributions, and consequently being extremely difficult to control, are simply misleading.

The book ends with chapters on a central problem of evolutionary biology, recognised by Darwin and still far from a solution today. How can groups maintain the advantages of cooperative behaviour that entail small costs for individuals (outweighed by the group benefits), when such systems are vulnerable to cheating by mutants who enjoy the benefits without paying their share of the costs? Concrete realisations of this abstract problem occur in many contexts, and, most important, in our own poorly understood and often fragile social structures. Here Ball, of necessity, can only indicate work in progress with no definitive answers yet.

In places, Critical Mass implicitly raises a more general and important question. Today, as the frontiers of scientific understanding continue to expand, reaching down into the molecular machinery whereby living things assemble themselves, it is ever more important to have a scientifically informed citizenry. If not, it will be difficult to conduct the democratic debates we need to have about which doors to open and which to leave closed, be they about stem-cell research or designer babies or topics yet unglimpsed. This implies an increasing need for scientists who have both the motivation and the skill to communicate with the public about what they are doing and what its implications may be. But there can be a fine line between enthusiastic and public-spirited engagement in communicating complex issues in appropriately simplified ways and hyped-up self-promotion. It is awkward to raise such questions and even more difficult to answer them.

Overall, Ball has done an exceptional job on a huge canvas. His book could be read in one go, but I would recommend dipping into it, chapter by chapter, in a leisurely way. In so far as the book gives a fair account of the current state of play - and I think it does, with appropriate mass and critical acumen - the dreams of Asimov's sociologist Hari Selden are as far off as ever.

Lord May is professor of zoology, Oxford University, and president, the Royal Society.