Hari Seldon devised psychohistory by modeling it upon the kinetic theory of gases. Each atom or molecule in a gas moves randomly so that we can't know the position or velocity of any one of them. Nevertheless, using statistics, we can work out the rules governing their overall behavior with great precision. In the same way, Seldon intended to work out the overall behavior of human societies even though the solutions would not apply to the behavior of individual human beings.7
In other words, put enough people together and the laws of human interaction will produce predictable patterns—just as the interactions and motion of molecules determine the temperature and pressure of a gas. And describing people as though they were molecules is just what many physicists are doing today—in effect, they're taking the temperature of society.
One of the best ways to take that temperature, it turns out, is to view society in terms of networks. In much the same way that "temperature" captures an essential property of a jumble of gas molecules, network math quantifies how "connected" the members of a social group are. Today's new network math applies statistical mechanics to all sorts of social phenomena, from fashion trends and voting behavior to the growth of terrorist cells. So just as Asimov envisioned, statistical physics has been enlisted to describe human society in a mathematically precise way.
For the most part, this merger of network math and statistical mechanics has been exploring human behavior without recourse to the modern views of game theory built on Nash's math. After all, Nash's original formulation had its limits; what works on paper does not always play out the way his math predicts in real-world games. But the latest research has begun to show ways that game theory can help make sense out of the intricate pattern of links in complicated networks. The game theory approach may be able to induce the world of complex networks to more readily surrender its secrets.
Wolpert's insight suggests that game theory itself can be elevated to a new level by exploiting its link to statistical mechanics. His work shows that the math of game theory can be recast in equations that mimic those used by statistical physicists to describe all sorts of physical systems. In other words, at some deep level statistical mechanics and game theory are, in a sense, two versions of the same underlying idea. And that may end up making game theory an especially sensitive social thermometer.
This new realization—that game theory and statistical mechanics share a deep mathematical unity—enhances game theory's status as the preferred tool for merging the life sciences and physical sciences into a unified description of nature. After all, there's a reason why game theory has been embraced by so many disciplines. Game theory could someday become the glue that holds all of science's puzzle pieces together.
Some people (particularly many physicists) will scoff at this contention. But pause to consider how much sense it makes. Nature encompasses so many complex networks for a reason: complexity evolves. "Intelligent" design produces simple, predictable systems that are easy to understand. The complex systems that baffle science—like bodies, brains, and societies—arise not from any plan, but from interactions among agents like cells or people, all (more or less) out for themselves. And such competitive interaction is precisely what game theory is all about.
So it should not be surprising that game theory has been so useful in evolutionary biology. Game theory is about competition, and evolution is the ultimate never-ending Olympic event. And if evolution followed game theory's rules in generating complicated life, it no doubt also observed the same rules in developing the human brain. So it's perfectly natural that game theory has become popular today in efforts to understand how the brain works, as brain scientists explore the neural physiology behind economic choices.
In turn, the brain underlies all the rest of human behavior—personal and interpersonal, social and political, as well as economic. All that behavior directs the evolution of all those networks of personal, social, political, or economic activity. Just as the complexities of life arose through eons of survival of the fittest, human culture evolves as societies or governments rise and fall; economies evolve as companies are founded and go bankrupt; even the World Wide Web evolves as pages are added and links expire. So Nash's math does seem capable of catalyzing a merger of methods for understanding individual behavior, biology, and society.
What about chemistry and physics? At first glance there doesn't seem to be any struggle for survival among the molecules engaged in chemical reactions. But in a way there is, and the connections between game theory and statistical mechanics promise to reveal ways in which game theory still applies. Reacting molecules, for instance, always seek a stable condition, in which their energy is at a minimum. The "desire" for minimum energy in molecules is not so different from the "desire" for maximum fitness in organisms. They can be treated mathematically in a similar way.
True, there's much more to physics than statistical mechanics. At first glance, game theory does not seem to touch some of the grander arenas of physical science, such as astrophysics and cosmology, or the subatomic realm ruled by quantum physics. But guess what? In the past few years physicists and mathematicians have developed quantum versions of game theory. So far, quantum theory seems to be enriching game theory, but that enrichment just might turn out to be mutual.8
Furthermore, Wolpert forges the link between statistical mechanics and game theory with help from the mathematical theory of information. As I wrote in my book The Bit and the Pendulum (Wiley, 2000), modern science has become enamored of information theory, using both its math and its metaphor to describe all sorts of science, from the contents of black holes to the computational activity in the brain. Quantum physics itself has been illuminated over the past decade by new insights emerging from quantum information theory. And some theorists have pursued the notion that information ideas hold the key to unifying quantum physics with gravity, perhaps paving the way to the ultimate "theory of everything." It's possible, Wolpert speculates, that game theory is the ingredient that could enhance the prospects for success in finding such a theory.
In any case, it's already clear that Nash's math shows an unexpectedly powerful way of mirroring the regularities of the real world that make all science possible. As I described in my book Strange Matters (Joseph Henry, 2002), there is something strange about the human brain's ability to produce math that captures deep and true aspects of reality, enabling scientists to predict the existence of exotic things like antimatter and black holes before any observer finds them. Part of the solution to that mystery, I suggested, is the fact that the brain evolved in the physical world, its development constrained by the laws of physics as much as by the laws of biology. I failed then to realize that game theory offers a tool for describing how the laws of physics and biology are related.
It's clear now that game theory's math describes the capability of the universe to produce brains that can invent math. And math in turn, as Asimov envisioned, can be used to describe the behavior guided by those brains—including the social collective behavior that creates civilization, culture, economics, and politics.
While seeking the secrets of that math, we can along the way watch people play games as neuroscientists monitor the activity in their brains; we can follow anthropologists to the jungle where they test the game-playing strategies of different cultures; we can track the efforts of physicists to devise equations that capture the essence of human behavior. And just maybe we'll see how Nash's math can broker the merger of economics and psychology, anthropology and sociology, with biology and physics—producing a grand synthesis of the sciences of life in general, human behavior in particular, and maybe even, someday, the entire physical world. In the process, we should at least begin to appreciate the scope of a burgeoning research field, merging the insights of Nash's 1950s math with 21st-century neuroscience and 19th-century physics to pursue the realization of Asimov's 1950s science fiction dream.
It would be wrong, though, to suggest that Asimov was the first to articulate that dream. In
a very real sense, psychohistory was the reincarnation of the old Roman notion of a "Code of Nature" (fitting, since Asimov's Foundation series was modeled on the Roman Empire's decline and fall). As interpreted much later, that code supposedly captured the essence of human nature, providing a sort of rule book for behavior. It was not a rule book in the sense of prescribing behavior, but rather a book revealing how humans naturally behave. With the arrival of the Age of Reason in the 18th century, philosophers and the forerunners of social scientists sought in earnest to discover that code of codes—the key to understanding the natural order of human interaction. One of the earliest and most influential of those efforts was the economic system described in The Wealth of Nations by Adam Smith.
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Smith's Hand Searching for the Code of Nature
If in the seventeenth century natural philosophers borrowed notions of law in human affairs and applied them to the study of physical nature, in the eighteenth century it was the turn of the laws of physical nature to suggest ways forward for knowledge about human life.
—Roger Smith, The Norton History of the Human Sciences
Colin Camerer was a child prodigy, one of those kids who skipped several grades of school and enrolled in a special program for the gifted. By age 5, he was reading Time magazine (even though no one had taught him to read), and at 14 he entered Johns Hopkins University. He graduated in three years, then went to the University of Chicago to earn an M.B.A. and, for good measure, a Ph.D. He joined the faculty at Northwestern University's graduate school of management by the age of 22.
Today, he's a full-fledged adult on the faculty at Caltech, where he likes to play games. Or more accurately, he likes to analyze the behavior of other people during various game-playing experiments. Camerer is one of the nation's premier behavioral game theorists. He studies how game theory reveals the realities of human economic behavior, how people in real life depart from the purely rational choices assumed by traditional economic theory.
Though unquestionably brilliant, Camerer communicates as conversationally as a cab driver. Even in his prodigy days, he was a wrestler and a golfer, so he has a broader view of the world than some of the intellectually exalted scholars who live their lives on such a higher mental level. And he has a broader view of economics than you'll find in the old-school textbooks. But in a sense, Camerer's views on economic behavior are not so revolutionary. In fact, in some ways they were anticipated by the father of traditional economics, Adam Smith.
Smith's "invisible hand" is probably the most famous metaphor in all of economics, and his equally famous book, Wealth of Nations, remains revered by today's advocates of free-market economies more than two centuries after its publication. But Smith was not a one-dimensional thinker, and he understood a lot more about human behavior than many of his present-day disciples do. His insights foreshadowed much in current attempts to decipher the code of human conduct, in economics and other social arenas. He was not a game theorist, but his theories illuminate the links between games, economics, biology, physics, and society—which is what the book you're reading now is all about. The way I see it, Adam Smith was the premier player in the origins of this story, as he inspired belief in the merit of melding the Newtonian physics of the material world with the science of human behavior.
THE ECONOMICS OF INVISIBILITY
Adam Smith had a lot in common with Isaac Newton. Both were lifelong bachelors. Both became professors at the university they had attended (and both had reputations for being absentminded professors as well). Both were born after their fathers had died. And both became fathers themselves of a new scientific discipline. Newton built the foundation of physics; Smith authored the bible of economics.
Both men literally rewrote the book of their science, transforming the somewhat inchoate insights of their predecessors into treatises that guided modern thought. Just as modern physics descended from Newton's codification of what was then known as natural philosophy, modern economics is the offspring of Adam Smith's treatise on political economy. And though their major works were separated by nearly a century, the philosophies they articulated merged to forge a new worldview coloring virtually every aspect of European culture in the centuries that followed.
While Newton established the notion of natural law in the physical world, Smith tried to do the same in the social world of economic intercourse. Newton's unexplained law of gravity reached across space to guide the motion of planets; Smith's "invisible hand" guided individual laborers and businessmen to produce the wealth of nations. Together, Newton's and Smith's works inspired great thinkers to believe that all aspects of the world—physical and social—could be understood, and explained, by science. When Smith's Wealth of Nations was published in 1776, the Age of Reason reached its pinnacle.
Nowadays, of course, physics has moved beyond Newton, and most economists would say that their science has moved far beyond Adam Smith. But Smith's imprint on modern culture persists, and his impact on economic science remains substantial. If you look closely, you can even find echoes of Smith's ideas in various aspects of game theory.
For one thing, Smith ingrained the idea that pursuing self-interest drives economic prosperity. And it is pursuit of self-interest that game theory, at its most basic level, attempts to quantify. At a deeper level, Smith sought a system that captured the essence of human nature and behavior, a motivation shared by many modern game theorists. Game theory tries to delimit what rational behavior is; Smith helped deposit the idea in the modern mind that minds operate in a rational way.
It was one thing for Newton to assert that rational laws governed the motions of the planets or falling apples. It was much more ambitious for Smith to ascribe similar orderliness to the social behavior of humans engaging in economic activity. As Jacob Bronowski and Bruce Mazlish observed in a now old, but still insightful, book on Western thought, Smith took a bit of an intellectual leap to make his system fly. "In order to discover such a science as economics," they wrote, "Smith had to posit a faith in the orderly structure of nature, underlying appearances and accessible to man's reason."1
Viewed in these terms, Smith's book was an important thread in a fabric of thought seeking a Code of Nature, a system of rules that explained human behavior (economic and otherwise) in much the same way that Newton had explained the cosmos. First philosophers, and then later sociologists and psychologists, tried to articulate a science of human behavior based on principles "underlying appearances" but "accessible to man's reason." Smith's efforts reflected the influence of his friend and fellow Scotsman David Hume, the historian-philosopher who regarded a "science of man" as the ultimate goal of the scientific enterprise. "There is no question of importance, whose decision is not comprised in the science of man," Hume wrote, "and there is none, which can be decided with any certainty, before we become acquainted with that science."2 In the attempt "to explain the principles of human nature, we in effect propose a compleat system of the sciences."
Today, game theory's ubiquitous role in the human sciences suggests that its ambitions are woven from that same fabric. Game theory may, someday, turn out to be the foundation of a new and improved 21st-century version of the Code of Nature, fulfilling the dreams of Hume, Smith, and many others in centuries past.
That claim is enhanced, I think, with the realization that threads of Smith's thought are entangled not only in physical and social science, but biological science as well. Smith's ideas exerted a profound influence on Charles Darwin. Principles describing competition in the economic world, Darwin realized, made equal sense when applied to the battle for survival in the biological arena. And the benefits of the division of labor among workers that Smith extolled meshed nicely with the appearance of new species in nature. So it is surely no accident that, today, applying economic game theory to the study of evolution is a major intellectual industry.
LOGIC AND MORALS
All in all, Smith's economics provides a critical backdrop
for understanding the economic world that game theory conquered in the 20th century. His influence on today's world stemmed from a life spent gathering unusual insights into his own world.
Born in Scotland in 1723, Smith was a sickly weakling as a child (today we'd probably call him athletically challenged). At the age of 3, he was kidnapped from his uncle's front porch by some gypsylike vagrants known as tinkers. Apparently the uncle rescued the toddler shortly thereafter. Growing up, Adam was a bright kid, earning a reputation as a bookworm with a spectacular memory. At 14 he entered the University of Glasgow (in those days, that was not unusually young). At 17 he went to Oxford, at first with the intention of entering the clergy. But after seven years there he returned to Scotland in search of a different kind of life. His interests destined him to the academic world, as he had no acumen for business and, as one biographer noted, "a strong preference for the life of learning and literature over the professional or political life."3
After a time, Smith got the job that fit his interests and talents—professor of logic at the University of Glasgow. Soon he was also appointed to a professorship in "moral philosophy," providing a fitting combination of duties for someone planning to forge a rational understanding of human behavior. It was, in fact, moral philosophy that Smith seized on for his first significant treatise. And in it he outlined a very different view of life and government than what he is generally known for today. His book on morals won him the confidence of Charles Townsend, who employed Smith to tutor his stepson, the young Duke of Buccleuch. Smith left Glasgow for London in 1764 to assume his tutorial task. He and the duke traveled much during this tutorship, spending a lot of time in France, where Smith familiarized himself with the new economic ideas of a group known as the physiocrats.
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