Look at war by using math

Mathematical formulas that incorporate ancient wars helped researchers to figure out how complex societies came about. Picutred is "Mongol Archer on Horseback," an early 15th century illustration from the Diez Albums. (LACMA)

How did human societies ever manage to evolve from small, tightknit groups into vast, organized states?

Researchers, using computers and math, show it was the result of some very antisocial behavior. New findings, published in the journal PNAS, used mathematical formulas and computers to simulate warfare in ancient Europe, Asia and Africa.

Researchers concluded that an increase in the intensity of armed combat -- and the spread of military technology -- spurred the rise of large, complex societies.

"The story of our past is not just a case of 'one dammed thing after another,' " wrote lead author Peter Turchin, a University of Connecticut professor. "There are general mechanisms at play in shaping the broad patterns of history."

Turchin, who teaches in the department of ecology and evolutionary biology, specializes in a field he calls cliodynamics -- the study of cyclical patterns in human history, such as the rise and fall of empires. The field is named for Clio, the Greek muse of history.  

In the PNAS study, Turchin and his colleagues hypothesized that a key mechanism in the formation of ancient empires was the use of horses by nomadic steppe dwellers to attack agricultural communities.

"Steppe nomads influenced the dynamics of agrarian societies both directly, by eliminating weaker and less cohesive states, and indirectly,  by innovating and spreading technologies that intensified warfare -- most notably chariots, horse-riding, the stirrup and heavy cavalry," the authors wrote.

To test their hypothesis, researchers built an elaborate mathematical war game that divided the ancient world into grid squares of 60 square miles each. The squares were given numerical values to designate their elevation -- high elevations were easier to defend than low ones. Numerical designations were also used to distinguish between agricultural lands and desert.

At the same time, historical records were consulted for the simulation of population groups. Again, numerical designations were used to describe the group's cohesiveness, ethnicity and level of military technology, among other things.

Researchers then let their mathematical world get down to brawling, like a big computerized game of "Dungeons and Dragons."

The simulation was intended to replicate the period of history between 1500 BC and AD 1500. When researchers compared their model results with the growth and density of actual empires during that period, the warfare model was 65% accurate.

Meanwhile, a second, alternative simulation that did not account for the spread of military technology was only 16% accurate.

"The model developed here does well at predicting the broad outlines of where and when such societies have traditionally formed and persisted," the researchers concluded.

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