Mathematical Model Explains How Complex Societies Emerge, Collapse

The instability of large, complex societies is a predictable phenomenon, according to a new mathematical model that explores the emergence of early human societies via warfare.

Isaac Asimov predicted mathematics of psychohistory in "Foundation" series - is it becoming a reality?

ScienceDaily (Jan. 25, 2011) - The instability of large, complex societies is a predictable phenomenon, according to a new mathematical model that explores the emergence of early human societies via warfare. Capturing hundreds of years of human history, the model reveals the dynamical nature of societies, which can be difficult to uncover in archaeological data.

Communities growing and shrining

The research, led Sergey Gavrilets, associate director for scientific activities at the National Institute for Mathematical and Biological Synthesis and a professor at the University of Tennessee-Knoxville, is published in the first issue of the new journal Cliodynamics: The Journal of Theoretical and Mathematical History , the first academic journal dedicated to research from the emerging science of theoretical history and mathematics.

The numerical model focuses on both size and complexity of emerging "polities" or states as well as their longevity and settlement patterns as a result of warfare. A number of factors were measured, but unexpectedly, the largest effect on the results was due to just two factors

the scaling of a state's power to the probability of winning a conflict and
a leader's average time in power.

According to the model, the stability of large, complex polities is strongly promoted if the outcomes of conflicts are mostly determined by the polities' wealth or power, if there exist well-defined and accepted means of succession, and if control mechanisms within polities are internally specialized. The results also showed that polities experience what the authors call "chiefly cycles" or rapid cycles of growth and collapse due to warfare.

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Journal Reference:

Gavrilets, Sergey, Anderson, David G and Turchin, Peter. Cycling in the Complexity of Early Societies. Cliodynamics: The Journal of Theoretical and Mathematical History, Vol 1, Issue 1.