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. Capturing hundreds of years of human history, the model reveals the dynamical nature of societies, which can be difficult to uncover in archaeological data.

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.

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.”

Co-authors are David G. Anderson, professor of anthropology at the University of Tennessee-Knoxville and Peter Turchin, professor of ecology and evolutionary biology and mathematics at the University of Connecticut.

The National Institute for Mathematical and Biological Synthesis (NIMBioS) brings together researchers from around the world to collaborate across disciplinary boundaries to investigate solutions to basic and applied problems in the life sciences. NIMBioS is sponsored by the National Science Foundation, the U.S. Department of Homeland Security, and the U.S. Department of Agriculture with additional support from The University of Tennessee, Knoxville.

Citation: Gavrilets S, Anderson D, Turchin P. 2010. Cycling in the complexity of early societies. Cliodynamics: The Journal of Theoretical and Mathematical History. 1:1;issue=1

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2 thoughts on “Mathematical model explains how complex societies emerge, collapse”

  1. As we watch the sun set on the American Dream, and as Europe follows America in the folding, we are reminded of the great U.S.S.R.’s collapse in a single decade. People closest to the earth, the poorest of the poor, dirt farming, veggie gardening, self-reliant, sustainable, survivors will not feel as much pain as the masses, as the Western World is extracted for every last valuable by this strange new force in the world. FEMA (concentration?) camps are already set up, just in case, and by the people who can tell you for fact, who killed JFK, Why Saddam was murdered, Why Iraq was reduced to the stone age, why we are in Afghanistan, what 9/11 was really all about, why Obama’s socialized medical care never took flight, why the EV-1 was scuttled (Google, torrent the movie, “Who Stole The Electric Car” and see for yourself!), why American taxpayers were forced to finance the Chev Volt,and where America will go in the next phase of her great paradigm shift.
    The mathematical model is only part of the picture! Just suppose, Chinese intellectuals, studying complex world situations from a uniquely independent, pragmatic, cold, factual, non-propagandized, clear headed, communist government sponsored, point of view. Now, suppose this group includes economists, now look at the new battlefield of the world. Not the American preferred, WWII style “Ships, Planes and Tanks, Destroyers, and Aircraft carriers, Fire-power, and Soldiers” style battlefield, but a World’s economy battlefield. Imagine, for a moment, that America was prevented from profitably selling her manufactured products abroad! Imagine if America was unable to profitably sell food products abroad! Imagine an America that imported what they once manufactured at home, because what they once manufactured at home was replaced with better, cheaper, products from China and the rest of Asia!
    Inside the inner core of America lies the realm of the Uber-Rich. Some are internationals, some are Americans,some are Asians, some may be representative of the Chinese communist government, all have a great deal of power through money. All have the Capitalists disease – ROI at any price! Can this dangerous group of Uber Rich be led around by the nose? Yes! The Chinese economists have presented these folk with a stable, well valued Yuan, in which to play their deceitful games! Compared to the U.S. Dollar, the Yuan is relatively un-diluted, well backed, and universal.
    China does not want WWII style world war with the U.S. – they don’t need it! They already have economic wins that America will never get over! This intellectually astute group of Chinese economists, scientists, mathematicians, physicists, financiers, strategists, have already undone the American Corporatist grip on the world’s economy and will proceed to dismantle the parts of America and the Western World they see as advantageous for themselves. They will do this with impunity, they will use their financial leverage to do so! America and their Western allies lay in financial ruin as we speak! Witness: the ruins in Detroit City! When are we going to admit the folly, admit our defeat, recognize our weak under-belly, and move to remedy?
    Humility is not a strong American strength, but this time, Americans have been bought and sold and have had their greedy asses reamed good! It is time to back down, in recession and depression, in devaluation and inflation, and down-size the American Dream to tent cities, and part-time day-laborers. It is time to stop importing foreign oil Americans cannot afford, it is time to go Solar, Wind, Wave, Hydro, Tidal, Geothermal, and Nuclear/electric. It is time to adjust dreams to a much more sustainable level, It is time to invest in aquaculture and veggie gardening for the sake of feeding ourselves during the crunch. It is time to build survival shelters of sustainable, practical and depression survivable dimension. McMansions must be recognized as part of the corporatist’s propaganda for huge profits – theirs, not ours! It is time to leave the great cities before they collapse, time to steal the land back from the multi-Nationals, time to look at basic survival time to recoil from the Corporatist’s great propaganda machine’s influence on our souls, the disposable life-style, time to move away from the over-manipulated money we use, and develop immediate, tangible survival means.
    Those who feel they are crafty enough, crooked enough, mean enough, positioned well enough, smart enough, to escape the coming doom, look only as far as your Russian counter-parts. the greatest secret of the Corporatists is the plight of the well placed Russian, after the U.S.S.R. was collapsed! Look up these once self confident, cocksure, well armed, well educated, well placed, folk today, for the surprise of your life!
    The greatest sucking sound we hear in America today is the inordinately high price of Gold! Beware the sly corporatists! Gold once sold, and only in the past two decades, for less than $300.00 an ounce! Beware amassing American dollars! They are not worth the paper they are printed on and will go the way of the Zimbabwe currency and for exactly the same reason, by the same manipulation! Beware the McMansions! Some have actually been bulldozed by the Banksters, and recently, still American folks build even more?
    The rules have changed! are you up to date? Do you still have wet dreams about the American Dream of the 60’s, 70’s, 80’s 90’s? Not since America built her own Oldsmobiles have these ideas been realistic! Dark clouds on the horizons! Too many rich riders, too many unemployable ex-producers! America’s greatest crime? The wasted resource, her unemployables! They are a living, perishable resource, and the Chinese have low-balled them! Once they fail to reproduce, and die off, and this is happening fast, America will have lost the greatest labor resource the world has ever known – The Uber-Rich and the Chinese intellectuals who form the economic policies of the world are counting on this! The ass-holes in Washington are to old, to well off, to well propagandized to realize the truth! The lobbyists take the sting out of the American peon’s vote, and the Corporatist’s rule! We, in our sustainable sheds, with our veggie gardens, our wood-piles, our few goats, our well-water, our hard earned daily bread, watch from the hills, the dales, the hidden valleys, our secret sanctuaries, with great sorrow, as many good folk, who cannot see the light, face the greatest depression even by Chinese standards falls over our fair land – God help you in your suffering, in your hardening, may you not fall as chaff, in this the great winnowing, and may you eventually find pride in a more chaste self reliant sustainability. God speed.

  2. It is a bit of a dogmatic stretch to say that this model “explains” how societies evolve.

    When does a model go from simply modeling or mimicking reality to “explaining” it to actually revealing exactly all of it’s hidden machinations? Scientists (and thinking people in general) have a dogmatic and neurotic tendency to prematurely declare that they have “explained” reality just because their models coincide with what we are able to observe of it.

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