Is history just “one damned thing after another”? If not, if there are general principles shaping the broad patterns of history, we should be able to capture them with mathematical models. But would you believe that a mathematical model can predict, with startling accuracy, where and when major civilizations arose? (x)
University of Connecticut professor Dr. Peter Turchin has been leading the way on cliodynamics, a relatively new science at the intersection of marcosociology, economic history, and mathematical modeling. The idea is to use mathematical ideas to better understand how societies have risen or fallen throughout history.
Those working in cliodynamics have found consistent patterns of social instability. They often see that societies follow cycles resulting from both demographic trends (population growth, falling wages, age distribution) and violence trends. These trends form feedback loops that can be understood using differential equations in the same way predator-prey systems are understood in biology.
While Turchin claims most of the mathematics is not too advanced, this is a great example of how mathematical thought can be applied to uncover patterns in other disciplines. A full description of cliodynamics and its research can be found here.