October 10, 2013 By Joseph P. Farrell

The basic premise of alchemy is the transformation of human consciousness, and the resulting alchemical transformation of society and culture. There is a kind of magic, and alchemy, at work in all social engineering schemes, and I have also blogged about the possibility that the NSA's vast electronic spying enterprise is really about two things: (1) the ultimate insider trading mechanism, and (2) the gathering of data to use for sophisticated "gaming" scenarios, a kind of "update" to the celebrated Inslaw PROMIS software scandals of the 1980s, a predecessor to the RIOT and "World Sentient Program" some believe to be the computer "brains" behind contemporary scenario gaming.

During the 1960s, however, all of this was foreseen by that science fiction genius Isaac Asimov, in his now famous Foundation trilogy. In that series, two private "foundations" are established by a mathematician - Harry Seldon is the character's name - in a decaying galactic empire. These foundations use Seldon's mathematical modeling of human social interaction of map out prior history and future scenarios.

In short, Asimov was proposing via his fiction that mathematical models, which had served physics in the real life twentieth century so well, would eventually be applied to that discipline considered to be the quintessential "soft" discipline: historiography, the "science" of history writing and the study of the premises that historians adopt and use to write and evaluate history itself. Asimov was not, of course, writing in a vacuum, being a trained scientist himself, and already in his day physicists, trained in quantum mechanics, were taking the first steps toward applying their techniques to economics, and eventually, "econophysics" was born, and is now a discipline in its own right that one can study in some universities. But by applying it to history, Asimov was taking the bold step of saying that, eventually, there would be a kind of "historiophysics," i.e., history that uses mathematical techniques and modeling to study the past.

Well, it seems that the fictional creation of Asimov's trilogy, Harry Seldon, and his "foundations" might be coming to life:

3,000 Years of Human History, Described in One Set of Mathematical Equations

Turchin began thinking about applying math to history in general about 15 years ago. “I always enjoyed history, but I realized then that it was the last major discipline which was not mathematized,” he explains. “But mathematical approaches—modeling, statistics, etc.—are an inherent part of any real science.”

In bringing these sorts of tools into the arena of world history and developing a mathematical model, his team was inspired by a theory called cultural multilevel selection, which predicts that competition between different groups is the main driver of the evolution of large-scale, complex societies. To build that into the model, they divided all of Africa and Eurasia into gridded squares which were each categorized by a few environmental variables (the type of habitat, elevation, and whether it had agriculture in 1500 B.C.E.). They then “seeded” military technology in squares adjacent to the grasslands of central Asia, because the domestication of horses—the dominant military technology of the age—likely arose there initially.

Over time, the model allowed for domesticated horses to spread between adjacent squares. It also simulated conflict between various entities, allowing squares to take over nearby squares, determining victory based on the area each entity controlled, and thus growing the sizes of empires. After plugging in these variables, they let the model simulate 3,000 years of human history, then compared its results to actual data, gleaned from a variety of historical atlases.

Although it’s not perfect, the accuracy of their model—predicting the development and spread of empires in nearly all the right places—surprised even the researchers. “To tell the truth, the success of this enterprise exceeded my wildest expectations,” Turchin says. “Who would have thought that a simple model could explain 65% of variance in a large historical database?”

To be sure, history, just like physics, will never be entirely reducible to mathematics - we can thank Kurt Goedel for pointing that out (and for the armchair physicist, consider Goedel's theorem as a theorem of applied physics) - but Turchin is correct: history remains the one human academic discipline that has avoided the extensive mathematization that has occurred in other disciplines, from biology to sociology. And if this article is any indicator, the success of his first steps in that direction can mean that it will only be a matter of time before courses in higher mathematical languages will be as much a staple of the history degree as it is now of physics or economics.
And to his credit, Turchin recognizes the Goedelian dilemma here, for regardless of all contervailing notions, humans, and human actions, are not reducible to a formal language, a formal mechanism, of mere numbers:
"Of course, there are limitations to viewing history through math—humans are more complicated than numbers. 'Differences in culture, environmental factors and thousands of other variables not included in the model all have effect,” Turchin says. “A simple general model should not be able to capture actual history in all its glorious complexity.'”

And that, too, is a very mathematical idea, so ably pointed out by another mathematician, in a brilliant, and brilliantly paradoxical treatise that, through the use of a formal calculus, pointed out that no formal calculus could capture all the relevant conceptions of any system. Asimov, and Goedel, had they been alive to read this article, would be smiling.
See you on the flip side.