Cliodynamics: Modeling Complex Societies Mathematically

A mathematical model that describes the instability of large complex societies has been developed by a team lead by 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.

The research has been 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.

(Modeling complex societies)
This image shows a hexagonal array of initially autonomous
local communities or villages, which is part of a polity.
Polities grow, decrease in size, or disappear as a result of
conquest with the winner absorbing all of part of the loser.

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.

The wealthiest of polities does not necessarily win a conflict, however. There are many other factors besides wealth that can affect the outcome of a conflict, the authors write. The model also suggests that the rapid collapse of a polity can occur even without environmental disturbances, such as drought or overpopulation.

By using a mathematical model, the researchers were able to capture the dynamical processes that cause chiefdoms, states and empires to emerge, persist and collapse at the scale of decades to centuries.

"In the last several decades, mathematical models have been traditionally important in the physical, life and economic sciences, but now they are also becoming important for explaining historical data," said Gavrilets. "Our model provides theoretical support for the view that cultural, demographic and ecological conditions can predict the emergence and dynamics of complex societies."

Old school science fiction fans readily recall psychohistorians like Hari Seldon, who practiced the science of psychohistory; in the Foundation series, Seldon predicts the fall of the Galactic Empire mathematically (sometimes using his calculator pad) and then works with a team to reduce the period during which civilization falls into barbarism to a single millenium.

Here is how Isaac Asimov defines psychohistory in the novel:

PSYCHOHISTORY–...Gaal Dornick, using nonmathematical concepts, has defined psychohistory to be that branch of mathematics which deals with the reactions of human conglomerates to fixed social and economic stimuli....

... Implicit in all these definitions is the assumption that the human conglomerate being dealt with is sufficiently large for valid statistical treatment. The necessary size of such a conglomerate may be determined by Seldon's First Theorem which ... A further necessary assumption is that the human conglomerate be itself unaware of psychohistoric analysis in order that its reactions be truly random ...

The basis of all valid psychohistory lies in the development of the Seldon Plan. Functions which exhibit properties congruent to those of such social and economic forces as ...


One can easily imagine that the first issue of Cliodynamics could be projected on the wall, prime radiant- style. the "fine neatly printed equations in black".

Via Eurekalert and Cliodynamics.

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