“It may be”, said US sociologist George Lundberg in 1939, “that the next great developments in the social sciences will come not from professed social scientists, but from people trained in other fields.” Take a look at any issue of a physical-sciences journal in the past five years and you will see one such field staking its claim vigorously. Physics is muscling its way into social science. Not content with explaining the behaviour of atoms and electrons, semiconductors, sand and space-time, physicists are now setting out to understand the behaviour of people.

Lundberg would have approved. He was part of a tradition that sought to establish a scientific grounding for sociology that would make it every bit as quantitative and deterministic as the natural sciences. The title of Lundberg’s 1947 book – Can Science Save Us? – says it all. This positivistic approach to social science can be traced to the French philosopher Auguste Comte (1798-1857), who called for a “social physics” that could claim its place alongside celestial, terrestrial, mechanical and chemical physics. But the impulse to identify natural laws of society is, in fact, much older. Plato may have been the first to hint at it, and the Roman writer Cicero in the second century BC believed in laws that transcended the customs and particularities of individual nations and which would apply to societies everywhere at all times.

Social statistics

The physicists today who seek rules that govern traffic or market economies have inherited this tradition – whether they know it or not. Implicit in their models and equations is the assumption that despite the quirks and caprice of individual human nature, there are emergent universal properties and laws that describe these complex systems.

It is no coincidence that this echoes the notion of universality in statistical physics. Phenomena that appear at first to be unconnected, such as magnetism and the phase changes of liquids and gases, share some identical features. This universal behaviour pays no heed to whether, say, the fluid is argon or carbon dioxide. All that matters are broad-brush characteristics such as whether the system is one-, two- or three-dimensional and whether its component elements interact via long- or short-range forces (see Physics World August 2003 pp23-27). Universality says that sometimes the details do not matter.

Physicists believe this is true of many social phenomena too. It is irrelevant whether traffic is driving down the A36 to Salisbury or the A5 autobahn to Basle because the same flow phases will appear for similar traffic densities. Such invariant properties are statistical: the peculiarities of individual drivers are subsumed within the average behaviour. That is precisely why the fashion for applying physics to social science has arisen largely within the community of statistical physicists, who have developed sophisticated tools for studying the behaviour of systems with a large number of components.

Attempts to understand systems like this are often ushered under the umbrella of complexity theory, which holds that simple rules often underlie complex behaviour. But this is not a new idea. The English philosopher John Stuart Mill said as much about society in the 19th century: “The complexity does not arise from the number of the laws themselves, which is not remarkably great, but from the extraordinary number and variety of the data or elements – of the agents which, in obedience to that small number of laws, co-operate towards the effect.”

On the other hand, a multitude of simultaneous interactions does not necessarily generate complexity. Indeed, statistical physicists often find quite the reverse. While the behaviours of the individual components are too numerous and complicated to follow in detail, the emergent effects are remarkably simple. No two water molecules, for example, are doing the same thing, but a large number of them reliably conspire to produce a freezing transition at 0 °C. The real surprise that emerges from the physics of society is that social behaviour is sometimes extremely simple and, moreover, governed by mathematical laws.

Yet physics might not seem the most obvious discipline from which to build a true science of society. Sociobiologists have long argued that this privilege belongs to evolutionary biology. They say that only by understanding the evolutionary origins of human motivations can we hope to deduce how cultures acquire their shape and form. There is undoubtedly some truth in this assertion. However, sociobiologists sometimes make the dangerous assumption that social behaviour is a straightforward extrapolation of individual behaviour.

The key element that sociobiologists neglect, and which social, economic and political scientists have also tended to overlook, is interaction. “Society”, said the German sociologist Georg Simmel in 1908, “is merely the name for a number of individuals, connected by interaction.” This is why statistical physics has such a central role to play. In its earliest days – in the kinetic theory of gases devised by James Clerk Maxwell and Ludwig Boltzmann – interactions between particles were neglected. But once they were added by Johann Diderik van der Waals in the late 19th century, out came all the characteristic motifs of condensed-matter physics: phase transitions, critical points, fluctuations, scaling laws and universality. All of these things are now appearing in studies of social phenomena too.

People as particles

The basic idea is simple: we replace the atoms of conventional statistical mechanics by people. Of course, while atoms interact via well defined forces of attraction and repulsion, people are seldom so straightforward. But in some situations human interactions do not amount to very much more than this basic concept. For example, by avoiding collisions and not encroaching on one another’s “personal space”, we act just as though there was a repulsive force between us.

Add to this some directional motion towards a goal, rather than the random Brownian drift of atoms, and you have a model of pedestrian behaviour like that developed in the mid-1990s by German physicist Dirk Helbing and co-workers. Helbing, who is now at the Technical University of Dresden, has shown that this model can be used to predict how people move in busy corridors and intersections, and how they create spontaneous trails over open spaces (see Helbing, Keltsch and Molnar in further reading).

If we include a degree of neighbour-following – a cohesive, attractive force – you find the “flocking” behaviour explored by physicist Tamás Vicsek and colleagues at Eötvös Loránd University in Budapest, which mimics the motion of animal swarms. In 1999 Vicsek, Helbing and co-worker Illés Farkas demonstrated how neighbour-following can lead to hazardous herding effects when a crowd becomes seized by panic in conditions of poor visibility, such as a smoke-filled room (see Helbing, Farkas and Vicsek in further reading).

The rules that govern the interaction between people (or “agents”) can be as simple or as complex as the situation demands. Between economic traders, for example, the interactions consist of buying and selling, as well as responding to the perceived market sentiments of their neighbours. Voters, on the other hand, seek to persuade nearby agents to adopt their views – just like magnetic atoms tending to align their magnetic moments.

These physics-inspired “interacting agent” models – which are typically studied using computer simulations – have been used to explore everything from the growth of businesses to the dynamics of boat trips in the Grand Canyon. One of the most complex examples is the virtual world of “Sugarscape” devised by Robert Axtell and Joshua Epstein of the Brookings Institution – a political-science think-tank in Washington DC. In this model, agents are free to move, breed, trade, fight and exchange cultural values according to simple rules. Their key objective is to acquire food (“sugar”), which is distributed patchily across the gridded landscape. They can obtain sugar by force if necessary, although some versions of the model permit civilized trading by introducing a second commodity, spice.

Interacting-agent models enjoy an increasing respectability in social sciences, but their complexity can mean that the connection with real physics becomes tenuous. Even in models as complex as Sugarscape, however, some of the properties that emerge can be interpreted and rationalized by drawing on the experience that statistical physics has with simpler systems. For example, these models often show statistical behaviour such as non-Gaussian fluctuations and power-law probability distributions, which are familiar in physics. Both of these features are generally signatures of non-equilibrium systems that are governed by strong correlations between the individual components. Such correlations typically mean that the system’s behaviour, while hard to predict in detail, is not simply random (that is, characterized by Gaussian fluctuations). Thus even in very complex systems there may be universal statistical features that remain aloof to the fine details.

Despite all of this, social scientists (and others) may feel uncomfortable with the notion that you can represent a human being by a particle – however complicated its interaction laws. Does it not imply that people are mere automata that jerk like puppets in response to the push and pull of external forces? In the face of such a mechanical view of society – which was pioneered by Comte along with French mathematician Pierre-Simon Laplace and others – the Russian novelist Fyodor Dostoevsky asserted that men will strive to exert their free will, even to the extent of making themselves act irrationally or insanely.

Free will

Yet modern physical models of social phenomena are not really imposing some deterministic tyranny on human actions. Rather, they are simply acknowledging that in reality our choices are often extremely limited. However much we treasure a belief in free will, social norms and conventions exist partly to reduce the need to make choices in the first place. People within a culture dress similarly, eat the same kinds of food and use the same words. We do not question whether drivers have free will simply because they predictably follow one another down the motorway at more or less the same speed. And in an election we do not exercise our free will by voting for our grandmother – we vote for one of the handful of names on the ballot sheet. Statistical physics does not prescribe which way our mental “compass needle” points. It merely asserts that the choice of orientations is limited, and that this choice is typically influenced by our neighbours.

The idea that mass decisions may have predictable yet counterintuitive consequences was pioneered by Harvard economist Thomas Schelling in his 1978 book Micromotives and Macrobehavior. Schelling was really writing about social physics, although he did not know it.

His book alludes to the way that social systems, like physical systems, may find equilibrium states by minimizing some global quantity. It is full of physics-based phenomena for which Schelling did not know the words, such as phase transitions and critical points. He talks about abrupt social changes that take place when a critical mass is reached, such as mass protests and “white flight” from US urban centres. The American writer Malcolm Gladwell has also dealt with these phenomena in his recent book The Tipping Point. These “tipping points” are generally equivalent, in Schelling’s models, to the nucleation of first-order phase transitions, like the appearance of a tiny ice crystal that seeds the freezing of a glass of water.

One of Schelling’s most celebrated examples concerns demographic segregation, which is most notable in the US in the way that neighbourhoods often tend to segregate by race. Schelling presented a lattice model that was populated by two kinds of agent, say, purple and blue. Agents, chosen randomly, will move to a free space if the number of near neighbours of a different colour exceeds some threshold. Schelling’s agents were not necessarily highly prejudiced; indeed, they might even be content in a slight minority and move only if the imbalance becomes too great. After only a few such moves, however, the population became highly segregated into purple and blue areas.

Schelling had to do all his simulations by hand, but the effect is more evident in the larger lattices that computers now handle with ease (figure 1). This segregation is entirely analogous to the process of phase separation of two liquid polymers, or two metals in a molten alloy. We can even see how the empty (white) spaces tend to migrate to the interfaces of purple and blue domains, like gas bubbles lowering the surface free-energy of these boundaries. Schelling’s point was that a highly segregated society is not necessarily an intolerant one: his agents do not move as soon as they have one or two neighbours of a different colour, but the society that results looks as though everyone seeks to be almost exclusively among their own kind.

Physics and marriage

In the same spirit as Schelling’s work is a model of marriage behaviour that was devised three years ago by economists Paul Ormerod and Michael Campbell of Volterra Consulting in London. What, one might wonder, could be more capricious and less susceptible to quantitative modelling than a decision to marry? Indeed, when marriage first became a subject for statistical surveys in the 19th century, the periodical Household Words, edited by Charles Dickens, carried the sceptical comment that “the savants are superseding the astrologers of old days, and the gipsies and wise women of modern ones, by finding out and revealing the hitherto hidden laws which rule that charming mystery of mysteries – that lode star of young maidens and gay bachelors – matrimony”.

But Ormerod and Campbell are convinced that there is more to marriage than love. There is, for example, surely a social element too. When unmarried cohabitation was frowned upon, the social pressure to tie the knot was almost irresistible. Arguably the pendulum has now swung the other way: marriage is seen not only as optional but as rather unfashionable. For the purposes of devising a model, it does not matter exactly which social climate you think prevails; all we need admit is that social pressures play a role in marriage, at any time encouraging it to a greater or lesser degree.

One way in which governments can, and do, try to engineer more marriage – a return, they might argue, to “family values” – is to provide financial incentives such as tax breaks. Ormerod and Campbell studied how changes in these two factors – social pressures and economic incentives – altered the proportion of married people.

In their model the population is divided into three groups: single, married and divorced. Singlehood, according to their definition, is rather like virginity: once you have left it, there is no going back. But one can switch at will between marriage and divorce (see Ormerod and Campbell in further reading).

If the strength of social attitudes is weak, the model predicts that the proportion of married people simply increases as the economic inventive to be married increases. But if social attitudes are stronger, the outcome is different (figure 2). Now two branches appear: a high-marriage and a low-marriage state of the population. In other words, the same set of social conditions can produce different proportions of married people, depending on whether we reached that situation from a starting point on the upper or the lower branch. A particular government policy could have two different outcomes, depending on the history. The two branches of the marriage curve are entirely analogous to the two fluid states – liquid and gas – in van der Waals’ theory, which are connected by a phase transition. What is more, the model even shows a vanishing of the “loop” that joins the two branches, which is equivalent to a critical point.

Business and war

A similar physics analogy appears in a model of alliance formation that was devised in the 1990s by political scientist Robert Axelrod of the University of Michigan. Axelrod and co-workers considered how companies join together to form a consortium. Rivals often aggregate into different consortia, such as the formation of the computer-manufacturing alliances Unix International Incorporated (UII) and the Open Software Foundation (OSF) in 1988. UII and OSF both hoped to establish the dominant standard format for the Unix operating system, and between them these alliances contained nine companies. Was there any way of predicting how they would apportion themselves into the two groups?

The researchers treated each firm like a particle that has different attractions and repulsions to all the others, with the magnitude of these forces being proportional to the size of the firms. Each pairwise interaction also depends on the relationship between two firms’ business interests: the repulsion is greater if the companies have strongly overlapping product profiles. Under such influences, the companies aggregate into two clusters – like tiny “droplets” containing just a few “particles” each (see Axelrod et al. in further reading).

Predicting which companies end up in each cluster then becomes a question of finding those configurations with the lowest “energy”, which is a typical minimization problem. Physicists would normally solve this kind of problem through computer simulation, but the numbers were small enough for the Michigan researchers to do it all by hand. The team calculated the complete “energy landscape” for all 256 configurations and selected the most stable of them. Clearly, the model is crude – there is no obvious way, for example, of fixing the magnitude of the forces of attraction and repulsion – but all the same, it mislocated only one company (IBM) relative to the actual alliances that formed (figure 3).

Axelrod and colleagues put their “landscape model” to an even more stringent test by applying it to the formation of national alliances just before the onset of the Second World War. They used a more complex set of criteria to estimate the relative amicability or animosity of the 17 nations that were involved, and found that two stable configurations emerged (figure 4). One corresponded closely to the historical division into Axis and Allied powers, with only Portugal and Poland misplaced (both of which had clear political reasons for ambiguity of allegiance). But the other “energy minimum” was a curious alliance of most of Europe against the former Soviet Union. Historically speaking, this is not an utterly implausible possibility: such a grouping does arguably reflect the tensions of the late 1930s, when Britain and France feared Stalin as much as Hitler.

This anti-Soviet alliance is a metastable solution – that is, a local but not global energy minimum. And while this solution appears when the “forces” between nations are estimated according to their size and characteristics in 1936, it disappears under the circumstances of 1938. This disappearance of a metastable state is precisely what happens at a “spinodal point” in equilibrium statistical physics. In van der Waals’ theory, the spinodals are the turning points in the loops of the phase diagram where a metastable liquid or gas becomes unstable. By making this connection it becomes possible to understand, and to some extent quantify, the entire historical landscape (figure 4). Counterfactual history – the history of might-have-beens – then becomes much more than an exercise in subjective speculation.

Towards utopia

I have chosen these examples of “social physics” precisely because they come from social scientists rather than physicists. This might seem perverse, given the contention that physics has something to contribute to social sciences. But there are several motives for doing so. First, the social-science models that have been initiated by physicists – such as the study of networks, economics and traffic flow – have been well advertised before (see Physics World July 2001 pp33-38, September 1999 pp19-20, August 1999 pp25-30). Second, the present examples show that the physics in social phenomena is not simply being put in by physicists, but it emerges uncalled for, and sometimes partly unnoticed. And lastly, it helps to force the question: why are we doing this?

To many physicists, the social sciences are a treasure trove of complex systems, for which there often exists mountains of data and next to no theory. They regard society as a fabulous experiment (although economists sometimes complain that the things that “econophysicists” want to do are simply not interesting). The aim of social sciences, however, has never really been just to understand, but to improve. Social science is often regarded as an adjunct and guide to policy-making. From Thomas Hobbes to Karl Marx, moral and political philosophers have used their ideas about the way society works to argue for ways of making it better. The trouble is, of course, that they seldom agree.

Physicists are wary of making such interpretations – and with some justification, for attempts to construct a “rational” or “scientific” society have often produced ignominious results (witness Hobbes and Marx). “What has always made the state a hell on earth”, says German philosopher and poet Friedrich Hölderlin, “has been precisely that man has tried to make it his heaven.” So interpreting physical models of society in terms of social implications or policy recommendations is fraught with danger. Take Schelling’s segregation model. Does it tell us that we should shrug our shoulders and accept segregation as inevitable? Such a conclusion would certainly suit those like US Senator Daniel Patrick Moynihan, who notoriously advised Richard Nixon in the early 1970s that race relations should be treated with “benign neglect”. But it might be more useful to ask how we might want to respond to the consequences of such segregation in the first place.

It seems entirely possible that a separation of cultures will promote an increasing ignorance of, and thus fear of and hostility to, other ways of living. Mild preferences might then become transformed into strong prejudices. So it could be profitable to focus not on trying to suppress segregation but on fostering close interactions between the distinct communities. We might benefit from knowing that the introduction of choice and freedom of movement into social environments (such as schools) that have previously had cultural mixing imposed on them is likely to lead to rapid and extreme segregation. In other words, this kind of modelling may force us to think more carefully about what kind of society we consider desirable, and help us to identify realistic, as opposed to idealistic or simply naive, means of achieving it.

A physics of society cannot tell us how things should be, but it can hopefully elucidate the consequences of particular choices and policies. Physicists would be right to be wary of constructing a “utopia theory”, but historian Richard Olson explains the role social physics could serve: “One way of expressing the relationship between physical and moral laws… is to say that social systems are ‘softly’ deterministic. Left alone, they will inevitably develop along certain lines; but the possibility of changing those lines by conscious and intentional intervention does exist. The whole point of a ‘social science’, then, is to explore the opportunities for and likely consequences of intentional moral action. Without the science, morality is blind; but without the morality, science is useless, pointless, and paralytic.”

In comparison with the moral questions, the physics seems to be the easy part. As economics Nobel laureate Herbert Simon puts it: “We know that going to the Moon was a simple task indeed, compared with some others we have set for ourselves, such as creating a humane society or a peaceful world.”