Can Math Explain History?

Posted on September 23, 2013 by

One of the greatest puzzles of social science is how human societies evolved from small groups of relatives and friends to the huge, anonymous and complex societies of today.

demonstrationA peace demonstration. Today we live in huge societies of strangers, who nevertheless are capable of coming together for cooperative purposes

Ten thousand years ago everybody lived in a village. Strangers were rare, and most of them were enemies. Then the first hierarchically organized societies appeared – chiefdoms, simple and complex. Around 5,000 years ago the first states evolved and 2,500 years ago they transformed themselves into huge multiethnic empires, governing tens of millions of people.

How can we explain the rise of such large-scale societies? Archaeologists, sociologists, and political scientists proposed a multitude of theories. But the vast majority of them can be boiled down to just two general mechanisms.

Most anthropologists and archaeologists think that the driving force has been the invention of agriculture. It made possible high population densities as well as surpluses that could be appropriated by newly emerging ruling elites. In a way, this theory suggests that once agriculture created sufficient resources for the evolution of complex societies, such societies inevitably evolved.

A different theoretical perspective, one based on cultural evolution and multilevel selection theory, disagrees. Yes, intensive agriculture is a necessary condition for the evolution of complex societies. But it is not enough. Institutions of complex societies, such as bureaucracies, organized religion, and constraints on the ruling elites, which induce them to promote common good, are all costly. How can they evolve in spite of such costs? The theory of cultural multilevel selection says that this evolution is only possible when societies compete against each other, so that those that do not have the right institutions fail. Costly institutions of complex societies are spread because societies that have them destroy societies without them.

This may sound quite abstract, but it is actually possible to take this general theory and build a specific and detailed model that predicts where and when complex large-scale societies should arise, and how they spread during the Ancient and Medieval eras of human history. This is what we have done in a paper that was published today in the prestigious journal, Proceedings of the National Academy of Science.

The trick is to focus on factors that intensify intersocietal competition, which until very recently meant military competition.

In other words, warfare.


And between 1500 BC and 1500 AD the intensity of military competition in the Old World maps extremely well on the spread of military technologies based on warhorses. So we built a model around this factor, and it did an incredibly good job of predicting when and where large empires arose in Eurasia and Africa.

Here’s a press release that explains our model, written by Catherine Crawley of the National Institute for Mathematical and Biological Synthesis.

Math explains history: Simulation accurately captures the evolution of ancient complex societies

The question of how human societies evolve from small groups to the huge, anonymous and complex societies of today has been answered mathematically, accurately matching the historical record on the emergence of complex states in the ancient world.

Intense warfare is the evolutionary driver of large complex societies, according to new research from a trans-disciplinary team at the University of Connecticut, University of Exeter, and the National Institute for Mathematical and Biological Synthesis (NIMBioS) that appears this week as an open-access article in the journal Proceedings of the National Academy of Sciences.

The study’s cultural evolutionary model predicts where and when the largest-scale complex societies arose in human history.

Simulated within a realistic landscape of the Afro-Eurasian landmass during 1,500 BC to 1,500 AD, the mathematical model was tested against the historical record. During the time period, horse-related military innovations, such as chariots and cavalry, dominated warfare within Afro-Eurasia. Geography also mattered, as nomads living in the Eurasian Steppe influenced nearby agrarian societies, thereby spreading intense forms of offensive warfare out from the steppe belt. On the other hand, rugged terrain inhibited offensive warfare.

The study focuses on the interaction of ecology and geography as well as the spread of military innovations and predicts that selection for ultra-social institutions that allow for cooperation in huge groups of genetically unrelated individuals and prevent large-scale complex states from splitting apart, is greater where warfare is more intense.

While existing theories on why there is so much variation in the ability of different human populations to construct viable states are usually formulated verbally, by contrast, the authors’ work leads to sharply defined quantitative predictions, which can be tested empirically.

The model-predicted spread of large-scale societies was very similar to the observed one; the model was able to explain two-thirds of the variation in determining the rise of large-scale societies.

“What’s so exciting about this area of research is that instead of just telling stories or describing what occurred, we can now explain general historical patterns with quantitative accuracy. Explaining historical events helps us better understand the present, and ultimately may help us  predict the future,” said the study’s co-author Sergey Gavrilets, NIMBioS director for scientific activities.

Citation: Turchin P, Currie T, Turner E, Gavrilets S. 2013. War, space, and the evolution of Old World complex societies. PNAS.

Watch the movie by co-author Tom Currie showing model-predicted dynamics and actual historical data side by side.

Next blog: questions and answers about our model

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