SOCIOCONDEMNATION
Network math offers many obvious social uses. It's just what the doctor ordered for tracking the spread of an infectious disease, for instance, or plotting vaccination strategies. And because ideas can spread like epidemics, similar math may govern the spread of opinions and social trends, or even voting behavior.
This is not an entirely new idea, even within physics. Early attempts to apply statistical physics to such problems met with severe resistance, though, as Serge Galam has testified. Galam was a student at Tel-Aviv University during the 1970s, when statistical mechanics was the hottest topic in physics, thanks largely to some Nobel Prize–winning work by Kenneth Wilson at Cornell University. Galam pursued his education in statistical physics but with a concern—its methods were so powerful that all the important problems of inert matter might soon be solved! So he began to advocate the use of statistical physics outside physics, especially for analyzing human phenomena, and published several papers along those lines. He even published one with "sociophysics" in the title in 1982. The response from other physicists was not enthusiastic.
"Such an approach was strongly rejected by almost everyone," he wrote, "leading and non-leading physicists, young and old. To suggest humans could behave like atoms was looked upon as a blasphemy to both hard science and human complexity, a total non-sense, something to be condemned."2
My impression is that most physicists nowadays are not so hostile to such efforts (although some are) but are just mostly indifferent. There are some enthusiasts, though, and international conferences have been devoted to sociophysics and related topics. And thanks to the rapid advances in network math, the study of social networks has gained a certain respectability, diminishing the danger of instant condemnation for anyone pursuing it (although acceptance is clearly greater in Europe than in the United States).
Part of this acceptance probably stems from the growing popularity of an analogous discipline known as econophysics, a much more developed field of study. Econophysics3 studies the interacting agents in an economy using statistical physics, and some prominent physicists have been attracted to it. Many young physicists have taken their skills in this field to Wall Street, where they can make money without the constant fear of government budget cuts.
Sociophysics is much more ambitious. It should ultimately encompass econophysics within it, along with everything else in the realm of human interactions. Of course, it has a way to go. But whatever anybody thinks of this research, there is certainly now a lot of it. Galam himself remains a constant contributor to the field. Now working in France, he has studied such social topics as the spread of terrorism, for instance, trying to identify what drives the growth of terrorism networks. In other work, he has analyzed opinion transmission and voting behaviors, concluding that "hung election scenarios," like the 2000 U.S. presidential contest, "are predicted to become both inevitable and a common occurrence."4 Other researchers have produced opinion-spreading papers that try to explain whether an extreme minority view can eventually split a society into two polarized opposite camps, or even eventually become an overwhelming majority.
Most of this work is based on simple mathematical models that try to represent people and their opinions in a way that can be easily dealt with mathematically. There is no point in trying to be completely realistic—no amount of math could capture all the nuances in the process by which even a single individual formed his or her opinions, let alone an entire population. The idea is to find a simple way to represent opinions at their most basic and to identify a few factors that influence how opinions change—in a way that lends itself to mathematical manipulation. If the math then reproduces something recognizable about human behavior, it can be further refined in an attempt to inch closer to reality.
It's not hard to find people who think the whole enterprise is preposterous. Human beings are not particles—they bear not the slightest similarity to atoms or molecules. Why should you expect to learn anything about people from the math that describes molecular interactions?
On the other hand, molecules are not billiard balls—yet Maxwell made spectacular progress for physics by analyzing them as though they were. In his paper introducing statistical considerations to the study of gases, Maxwell applied his math to a system containing "small, hard and perfectly elastic spheres acting on one another only during impact." Molecules are small, to be sure, but otherwise that description is not very complete or accurate, as Maxwell knew full well. But he believed that insights into the behavior of real molecules might emerge by analyzing a simplified system.
"If the properties of such a system of bodies are found to correspond to those of gases," Maxwell wrote, "an important physical analogy will be established, which may lead to more accurate knowledge of the properties of matter."5 Today, physicists hope to find a similar analogy between particles and people that will lead to an improved knowledge of the functioning of society.
SOCIOMAGNETISM
One popular example of such an approach appeared in 2000 from Katarzyna Sznajd-Weron of the University of Wroclaw in Poland. She was interested in how opinions form and change among members of a society. She reasoned that the global distribution of opinions in a society must reflect the behavior and interactions of individuals—in physics terms, the macrostate of the system must reflect its microstate (like the overall temperature or pressure of a container of gas reflects the speed and collisions of individual molecules).6 "The question is if the laws on the microscopic scale of a social system can explain phenomena on the macroscopic scale, phenomena that sociologists deal with," she wrote.7
Sznajd-Weron was well aware that people recoil when told they are just like atoms or electrons rather than individuals with feelings and free will. "Indeed, we are individuals," she wrote, "but in many situations we behave like particles." And one of those common properties that people share with particles is a tendency to be influenced by their neighbors. Sometimes what one person does or thinks depends on what someone else is doing, just as one particle's behavior can be affected by other particles in its vicinity.
Sznajd-Weron related an anecdote about a New Yorker staring upward at the sky one morning while other New Yorkers pass by, paying no attention. Then, the next morning, four people stare skyward, and soon others stop as well, all looking up for no reason other than to join in the behavior of the crowd. Such pack behavior suggested to Sznajd-Weron an analogy for crowd behavior as described by the statistical mechanics of phase transitions, the sudden changes in condition such as the freezing of water into ice. Another sort of phase transition, of the type that attracted her attention, is the sudden appearance of magnetism in some materials cooled below a certain temperature.
It makes sense to relate society to magnetism, since society reflects the collective behavior of people, and magnetism reflects the collective behavior of atoms. A material like iron can be magnetic because its atoms possess magnetic properties, thanks to the arrangement of their electrons, the electrically charged fuzzballs that shield each atom's nucleus. Magnetism is related to the direction in which electrons spin. (You can view the spins as around an axis either pointing up or pointing down, corresponding to whether the electron spin is clockwise or counterclockwise.)
Ordinarily a bar of iron is not magnetic, because its atoms are directing their magnetism in random directions, so they cancel out. If enough atoms align themselves in one particular direction, though, others will follow—kind of like the way if enough people look up to the sky, everybody else will, too. When all the atoms line up, the iron bar becomes a magnet. It's as though each atom checks to see how its neighbor's electrons are spinning. When two atoms are sitting next to each other, their partnerless electrons want to spin in the same direction—that confers a slightly lower energy on the system, and all physical systems seek the state of lowest possible energy. Consequently the spin of one iron electron can influence the spin of its neighbor, inducing it to take on the same orientation. (In most materials
an atom's electrons are mostly paired off with opposite spins. But iron and a few other materials possess some properly positioned electrons without partners. Magnetism is a little more complicated than this crude picture, of course, but the basic idea is good enough.)
As scientists began to understand this aspect of magnetism, they wondered if such local interactions between neighbors could explain the global phase transition from the nonmagnetic to magnetic state. In the 1920s, the German physicist Ernst Ising tried to show how neighboring spins could induce a spontaneous phase transition in a system, but failed. The problem was not in the basic idea, though—it was that Ising analyzed only a one-dimensional system, like a string of spinning beads on a necklace. Soon other researchers showed that Ising's approach did turn out to work when applied to two-dimensional systems, like spinning balls arranged in a grid.
Magnetism could thus be understood as a collective phenomenon stemming from the interactions of individuals—sort of like pack journalism. When one newspaper makes a big deal about a major story, all the other media jump in and beat the story to death—all the news is taken over by something like O.J. or Michael Jackson or some Runaway Bride. Similarly, rapid large-scale changes mimicking phase transitions occur in biology or the economy, such as mass extinctions or stock market crashes. In recent years it has occurred to physicists like Galam, Sznajd-Weron, and many others that the same principle could apply to social phenomena, such as the rapid spread of popular fads.
Sznajd-Weron set out to devise an Ising-like model of social opinions, trying out a very simplified approach that would be easy to handle mathematically. Instead of up or down spins, people could take a yes or no stance with respect to some issue. If you start out with opinions at random, how would the system change over time? Sznajd-Weron proposed a model based on the idea of "social validation." Just as the behavior of the New York skywatcher spread when others did the same, identical opinions between neighbors could cause their same opinion to spread socially, in a way similar to the way magnetism develops through Ising interactions.
Sznajd-Weron's model of society was pretty simple— something like one long street with houses on only one side. Each house is identified by a number (OK, that's realistic), and each house gets one opinion (or spin): either yes (mathematically represented as +1), or no (–1).
To start out, the houses all have opinions at random. Then, every day each house checks its neighbors and modifies its opinions based on some simple mathematical rules. Based on neighboring opinions, each house may (or may not) modify its own. In Sznajd-Weron's model, you start by considering two neighbors— let's say House 10 and House 11. Each of that pair has another neighbor (House 9 and House 12). Sznajd-Weron's rules say that if houses 11 and 12 have the same opinion, then houses 9 and 12 will adjust their opinions to match the common opinion of 10 and 11. If houses 10 and 11 disagree, though, House 9 will adjust its opinion to agree with House 11, and House 12 will change to agree with House 10.
Mathematically, the rules look like this, with S representing a house and the subscript i representing the house number (in the above example, Si is House 10, Si+1 is House 11, etc.):
In other words, when the two neighbors (10 and 11) agree, the two outside neighbors will share that opinion. If the first two neighbors disagree, then the one on the left will agree with the second and the one on the right will agree with the first. Why should that be? No reason, it's just a model. In a variant on Sznajd-Weron's original proposal, the second rule is switched:
In the original model, Sznajd-Weron performed computer simulations on a street with 1,000 houses and watched as opinions changed over 10,000 days or so. No matter how the opinions started out, the neighborhood eventually reached one of three stable situations—either all the houses voting yes, all no, or a 50-50 split. (These conditions correspond, in Sznajd-Weron's words, to either "dictatorship" or "stalemate.")
Since not all societies are dictatorships or stalemates, the model does not reflect the true complexity of the real world. But that doesn't mean the model is dumb—it means that the model has told us something, namely that more than just local interaction between neighbors is involved in opinion formation. And you don't need to know what all those other factors are to improve the model—you just need to know that they exist. In her 2000 paper, Sznajd-Weron showed that such unknown factors (in technical terms, noise) could be described as a "social temperature" raising the probability that an individual would ignore the neighbor rules and choose an opinion apparently at random. With a sufficiently high social temperature, the system can stay in some disordered state, more like a democracy, rather than becoming a stalemate or dictatorship.
Even so, as Sznajd-Weron pointed out, her one-dimensional model is not likely to be very useful for social systems, just as Ising's one-dimensional model did not get the magnetism picture right, either. So in the years since her proposal, she and others have worked on extensions of the model. A similar model in two dimensions (with the "houses" occupying points on a grid) was developed by Dietrich Stauffer of the University of Cologne, probably today's most prominent sociophysicist. With the people aligned on a grid, everybody has four neighbors, a pair has six neighbors, and a block of four has eight neighbors. In this case, one rule might be that a block of four changes its eight neighbors only if all four in the block have the same spin (or opinion). Or two neighbors paired with the same spin can change the spins of their six neighbors. A grid model can accommodate more complications and thus reproduce more of the real properties of society.
SOCIONETWORKS
Clearly, though, the way to get more social realism is to apply such rules not to simple strings or grids but to the complex social networks discovered in the real world. And much interesting work has begun to appear along these lines. One approach examines the general idea of "contagion"—the spread of anything through a population, whether infectious disease or ideas, fads, technological innovations, or social unrest. As it turns out, fads need not always spread the same way as a disease, as different scenarios may guide the course of different contagions.
In some cases, a small starting "seed" (a literal virus, perhaps, or just a new idea) can eventually grow into an epidemic. In other cases a seed infects too few people and the disease or idea dies out. Peter Dodds and Duncan Watts (of the Watts-Strogatz network paper) of Columbia University have shown that what happens can depend on how much more likely a second exposure is to infect an individual than a first exposure. Their analysis suggests that the spread of diseases or ideas depends less on "superspreaders" or opinion leaders than on how susceptible people are—how resistant they are to disease or how adamantly they hold their current opinion. Such results imply that the best way to hamper or advance contagion would be strategies that increase or reduce the odds of infection. Better health procedures, for instance, or financial incentives to change voting preferences, could tip the future one way or another.
"Our results suggest that relatively minor manipulations … can have a dramatic impact on the ability of a small initial seed to trigger a global contagion event," Dodds and Watts declared in their paper.8 It sounds like just the sort of thing that Hari Seldon incorporated into psychohistory, so that his followers could subtly alter the course of future political events.
In real life, of course, people don't necessarily transmit opinions or viruses in the simple ways that such analyses assume. So some experts question how useful the statistical mechanics approach to society will ultimately be. "I think in some limited domains it might be pretty powerful," says Cornell's Steven Strogatz. "It really is the right language for discussing enormous systems of whatever it is, whether it's people or neurons or spins in a magnet.… But I worry that a lot of these physicist-style models of social dynamics are based on a real dopey view of human psychology."9
Of course, that is precisely where game theory comes into play. Game theory has given economists and other social scientists the tool for quantifying human psychology in ways that
Freud could only dream of. Neuroeconomics and behavioral game theory have already sculpted a much more realistic model of human psychology than the naive Homo economicus that lived only to maximize money. And once you have a better picture of human psychology—in particular, a picture that depicts the psychological variations among individuals—you need game theory to tell you what happens when those individuals interact.
SOCIOPHYSICS AND GAME THEORY
After all, when you get to really complex social behaviors—not just yes or no votes, but the whole spectrum of human cultural behavior and all its variations—the complex interactions between individuals really do matter. It is yet again similar to the situation with molecules in a gas. In his original math describing gas molecules, Maxwell considered their only interaction to be bouncing off of each other (or the container's walls), altering their direction and velocity. But atoms and molecules can interact in more complicated ways. Electrical forces can exert an attractive or repulsive force between molecules, and including those forces in the calculations can make statistical mechanical predictions more accurate.
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