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Philosophy, sociology and religion

Philosophy, sociology and religion

History found in a grain of sand

01 Nov 2000

Ubiquity: Why the World is Simpler than We Think
Mark Buchanan
2000 Weidenfeld and Nicolson 224pp £20.00hb

Past behaviour

Hari Seldon, the fictional creator of “psychohistory” in Isaac Asimov’s “Foundation” series of novels, predicts the imminent demise of the First Galactic Empire after a 12 millennium run and establishes the Foundation on a planet at the galaxy’s edge. In doing so, he initiates a chain of events aimed at reducing the duration of the dark ages between the first and second empires from a disastrous 30 millennia to a tolerable one. Seldon’s plan is based on psychohistory – “that branch of mathematics which deals with the reactions of human conglomerates to fixed social and economic stimuli”.

Will psychohistory always remain in the realms of science fiction, or might complex human affairs be susceptible to scientific description – and even to prediction and control? Mark Buchanan, in his new book Ubiquity: The Science of History…or Why the World is Simpler than We Think, suggests that the answer might be partly “yes”. Human history, he argues, is simpler than we think, but that very simplicity tells us that it is intrinsically unpredictable, subject to uncontrollable catastrophic events. Buchanan, who has a PhD in theoretical physics and is now a science writer after spells on Nature and New Scientist, argues that various ideas, originally developed to describe non-equilibrium many-body systems, are now being successfully applied to phenomena both inside and outside physics, and that they now await application to history.

Buchanan’s argument is based on several observations. The first is the ubiquity of “power laws” in natural systems and human affairs. According to these laws, the number of events of a certain size – such as earthquakes, forest fires or price movements in the stock market – falls off as a power of the size. So, for example, earthquakes that are n times as large as smaller ones are also rarer by a factor of 1/n2 , as was first shown by the seismologists Beno Gutenberg and Charles Richter in the 1950s. The exponent varies from one phenomenon to another, but in all cases the power law means that the events have no typical size, and it suggests that all events, large and small, have the same cause.

The second observation is that such power-law distributions seem to be a general consequence of toy models of these systems, in which “microscopic” constituents or agents – rocks, trees and investors in the examples above – interact through a simple set of rules. The system organizes itself naturally into a “critical state” in which a single microscopic occurrence – be it a microscopic slippage at a point along a fault, a single tree catching fire after a lightning strike or a single investor deciding to sell – can trigger events of all possible sizes.

The third observation is that the size of an event depends critically on the history of the system. Indeed, the critical state is dominated by “frozen accidents” of history, which determine whether an event becomes large or small.

These ideas were originally formulated in 1987 by Per Bak, Chao Tang and Kurt Wiesenfeld in an analysis of a theoretical model of a sand pile, in which grains of sand are sprinkled onto the pile, one at a time. As the pile grows, its sides become steeper, until it reaches a critical state, at which point dropping just one more grain triggers an avalanche. Bak, Tang and Wiesenfeld found that the size of these avalanches is distributed according to a power law, and they coined the phrase “self-organized criticality” to describe the pile’s natural growth to a critical state.

Buchanan believes that the notion of a self-organized critical state provides a unifying principle for understanding a variety of complex phenomena. The causes of big and small events are the same in the critical state, so one should give up the notion of finding a special cause for large events, be they catastrophic earthquakes, forest fires or collapses in the stock market. Such systems are organized in such a way that they are inherently susceptible to unpredictable events of all sizes.

One of the charms of Buchanan’s book is his description of the diverse phenomena the sizes of which are governed by power laws. The most amusing of these is the experiment that determined the power-law distribution for the sizes of the shards produced when a frozen potato shatters. The study was carried out by three Danish physicists in 1993, who counted shards ranging in size from one hundred grams down to one-thousandth of a gram and found that doubling the size of a shard makes it six times as rare.

The connection to history comes in the final chapters, where Buchanan presents evidence that power laws govern the numbers of casualties in wars and the numbers of citations garnered by scientific papers. These data invite explanation in terms of models of interacting agents, groups of people or scientists, producing a critical state in which scientific ideas or intergroup tensions operate. Buchanan is not saying that we can predict the future course of history, but that we can use the notion of a critical state to provide the context for analysing and understanding past historical events.

It is probably unnecessary to remind the reader to be cautious about buying all of Buchanan’s argument. I prefer to see this set of ideas as part of a larger enterprise to understand the behaviour of complex systems. Although the notion of a critical dynamical state might serve as one of the guiding principles in this effort, it will not be the only such principle. It is probably just one clue to the puzzle of complexity.

Physicists are good at taking advantage of even one clue, however, and an inspiring feature of Buchanan’s book is his account of physicists applying the methods of many-body physics to such diverse phenomena as earthquakes, forest fires and market movements (see “Complexity, catastrophe and physics” by Didier Sornette Physics World December 1999 p57). In doing so, they reduce a phenomenon to its constituent parts, formulate a simple model that tries to capture the interactions between parts, and then try to reproduce the essential features of the phenomenon.

Sound familiar? This is what physicists always do when faced with a new situation. What’s inspiring is to find physicists doing physics in fields far removed from their usual concerns. We need to apply our expertise to areas throughout the sciences, wherever our distinctive approach of analysis followed by synthesis can be applied. Buchanan’s book is a cheerleader in this regard. It should be required reading for physicists – especially department chairs – to teach that physics is the way we do problems, as much as the problems we’ve always done.

That models of interacting constituents lead generally to power laws means that a successful model might not teach one much about the actual interactions in a system. Yet understanding the actual interactions – instead of toy interactions in a toy model – could be important. Buchanan suggests that, since events of all sizes have the same cause in a critical state, it is hopeless to think about predicting large events. Perhaps that is giving up too easily.

However, if one understood the actual system and its interactions with other systems, one might be able to identify observable signatures of the critical organization that precedes a large event, either in the system itself or in systems with which it interacts – for example, in the density of trees or underbrush preceding a catastrophic fire, or in the tensions between nations and the attitudes of their citizens prior to a major war.

When asked how, in view of the First Galactic Empire’s evident strength, he could predict its fall, Hari Seldon said: “The appearance of strength is all about you. It would seem to last forever. However…the rotten tree-trunk, until the very moment when the storm-blast breaks it in two, has all the appearance of might it ever had. The storm-blast whistles through the branches of the Empire even now. Listen with the ears of psychohistory and you will hear the creaking.”

If Asimov were alive today, psychohistory might be the science of the critical state, and the creaking might be the tell-tale signature of collapse.

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