Peter Turchin, a professor of ecology and mathematics at the University of Connecticut, is pioneering research in a field he calls cliodynamics. In short, cliodynamics uses mathematics to analyze social and cultural patterns throughout history. Turchin uses his research to chart violence and unrest, and believes he has identified a pattern of social upheaval that occurs roughly every 50 years in the U.S. The next peak, he says, is in 2020. Turchin's research has been highlighted in an article in the August edition of the journal Nature.

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"My research, in general, focuses on investigating long-term dynamics of historical societies (I call this cliodynamics, Clio being the muse of history)," Turchin wrote in a blog post for Freakonomics.com. "One empirical result from this program is that societies tend to experience recurrent waves of violence and political instability; these waves are themselves the results of long-term social and economic trends."

Turchin has spent the last 15 years analyzing mountains of data reflecting economic activity, demographic trends and outbursts of violence in the U.S. Turchin and his colleagues use non-linear mathematics, advanced computer simulations that can model the interactions of large groups of people and new electronic tools for gathering and sorting enormous amounts of historical data to analyze and identify trends.  This includes historical databases, newspaper archives and ethnographic studies. The data is categorized according to four main variables: population numbers, social structure, state strength and political instability.

Cliodynamics isn't about searching for patterns, Turchin told Nature. Historians have already conducted great amounts of research identifying patterns in political stability using demographic, political and economic variables. Turchin stresses that cliodynamics works with far larger quantities of data than historians have ever worked with before.

"History is not 'just one damn thing after another'", said Turchin.

Turchin's Freakonomics post, from 2008, discussed the increase in mass killings in the U.S. Back then, Turchin compared the current economic climate to the 1970s, the last time the U.S. saw a peak in violent events. These events exclude violence related to criminal activity and domestic violence. Instead, it includes killing sprees and shooting rampages, like the recent killings in Aurora, Colo. The pattern that emerged, according to Turchin, is that socioeconomic factors play an important role in massacres.

"The rise in massacres began during the 1960's and shows no signs of abating. It's a long-term trend, and I think it is telling us something about fundamental ways in which our society is changing," Turchin wrote. "As their economic prospects deteriorate, many breadwinners find themselves under unendurable pressure to maintain the socially expected level of consumption. Under these conditions, people - whose psychological problems would be borderline in the gentler economic climate of the 1950's - today 'go postal.' So the harsher the economic conditions, the greater the numbers of those whose latent psychological problems develop into full-blown psychosis."

Turchin, commenting on the Nature article on his blog, says that since the 1970s a number of demographic variables have been trending in ways that indicate "a very serious crisis just around the corner." He admits that a crisis in 2020 is not inevitable, but only if the elites in American society implement reforms without threat of a revolution.

"We spend an enormous amount of resources, intellectual and material, on learning how to preserve the physical health of individuals." Turchin wrote in a recent research paper. "Shouldn't we invest a similar amount into understanding how to maintain and restore the health of whole societies?"