A powerful leap from chaos

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The natural world, financial crises, wars, history — all modelled in a pile of sand.

Ubiquity: Why the World Is Simpler Than We Think

Weidenfeld & Nicolson: 2000. 230 pp. £20
Credit: ALL IMAGES BY DAVID NEWTON

A few years ago, historians belatedly caught up with the fact that science had moved on somewhat since Newton and Laplace. Years had been spent down culs-de-sac named Hegel, Marx, Toynbee and Braudel, in the vain pursuit of 'laws of history' comparable with the laws of motion. Whereas some historians had reversed out of these dead ends onto the ring road of literary criticism, abandoning the notion that history might have anything to learn from the natural sciences, a few ventured down the winding lane of chaos theory.

The key insights of chaos — sensitivity to initial conditions, stochastic behaviour in deterministic systems — had an obvious relevance to historical study, not least because one of the best-known chaotic systems, the world's weather, dominated the lives of most people throughout the long pre-industrial era.

As a historian, what I liked about chaos theory was the way it reconciled the manifest unpredictability of history — its apparent chaos — with the reality of determinism, in the sense of meaningful causal relationships. History was not just an infinite number of contingencies. Rather, the multiple equations at work in history were nonlinear. So teleological philosophies of history such as that of Marx could be consigned to the rubbish bin without the need to retreat to the extreme position of the idealist philosophers of history (and of the post-modernists) — that historians are engaged in nothing more than the construction of narratives whose meaning is as dependent on literary convention as on any empirical verifiability.

History was authentically chaotic: just as the famous Amazonian butterfly's wings could indirectly unleash a storm over England's Home Counties, so a single political decision could make the difference between war and peace. And precisely for that reason it was a worthwhile exercise to contemplate what might have happened if the decision had gone the other way: if the butterfly had not flapped its wings. 'Counterfactual' history — the asking of 'what if' questions and the contemplation of parallel worlds — is a lot easier to justify in a chaotic universe than in a universe of rigidly deterministic laws.

Now comes Mark Buchanan with solace for those discomfited by historical debates conducted largely in the subjunctive. “The world,” he tells us, is “simpler than we think.” By this he means not only the natural world of earthquakes and biological evolution, but also the human world of financial crashes, scientific breakthroughs, international wars and political revolutions.

I must confess to feeling ambivalent about Buchanan's project. Part of me was not unhappy with the idea of 'chaostory', which created the opportunity to turn history into a series of subversive counter-narratives of what (to invert Ranke's dictum) did not 'actually happen'. That part was rather alarmed at the possibility of some new simplification imported from the natural sciences. But the other part of me — the part that is attracted to the empirical rigour of the social sciences, and which has spent the past two years poring over the fluctuations of the financial markets in the hope of discerning something other than a 'random walk' — was rather excited at the prospect of a return to linearity.

Buchanan is a science journalist with a PhD in theoretical physics. He does a superb job in this book of explaining a number of important related breakthroughs in the natural sciences, ranging from the incidence of earthquakes to mass extinctions. This is popular science writing at its best, translating recent research in physics and biology into language a layman — even a historian — can grasp.

The key concept — the 'ubiquitous' idea promised by his title — is the 'power law'. Nine out of 15 chapters are concerned with demonstrating the existence of this law in the natural world or, more commonly, in the simplified versions of that world constructed by ingenious physicists with the help of their computers.

Buchanan's starting point is a game played with a pile of sand (or grains of rice). Drop individual grains, one after another, onto the pile and watch what happens — sometimes not much; but every now and then the pile collapses completely.

Statistical analysis reveals that there is no 'typical' or average sand-slide. Plotted on a graph, the distribution of slides is not the familiar bell curve. Rather, if you plot the size of slides against the frequency of their occurrence, you get a straight line. To use the physicists' jargon, the pile of sand/rice was in a self-organized critical state.

Buchanan shows that this kind of pattern is remarkably common in nature, from earthquakes to extinctions, to forest fires, to the effect of heat on magnets, to the way a frozen potato smashes. Only the steepness of the line on the graph varies. In the case of earthquakes, “double the energy [released by an earthquake] and an earthquake becomes four times as rare”. In the case of fragments of frozen potato, “each time you reduce by two the weight of the pieces, their numbers increase by six”. All of these relationships are 'power laws'.

So far, so fascinating — although I am not competent to judge whether Buchanan is getting the science right. What I can address is the question raised in his final six chapters: do such power laws exist in history? I can also address a question the author does not explicitly pose: if they do, so what?

The difficulty is that, splendid science writer though he is, Buchanan is no historian, and his argument begins to creak when he moves away from natural science. This is partly because — as his references make abundantly clear — his reading of history has been somewhat selective. More seriously, I think it is because he does not really understand what history is as a discipline.

For Buchanan, it is an exciting possibility that versions of the 'power law' might exist for finance, war or politics. I have three difficulties with this. First, the quality of evidence is only good enough to sustain his argument in the case of financial markets (the data he uses for wars are just too unreliable). He needs, however, to read more: not only more of the work of Robert Shiller, but also Andrei Shleifer's research on irrationality in financial markets, to name only one of many economists who have worked on this. (Unlike most historians, economists can do maths, so this really is a big field.)

Second, the analogy between natural catastrophes and wars or revolutions — and it remains only an analogy — is not new. In the 1920s Winston Churchill likened international relations on the eve of the First World War to the interaction of planetary bodies: “If they got too near the lightnings would begin to flash, and beyond a certain point they might be attracted altogether from their orbits . . . and draw each other into collision.” David Lloyd George claimed the nations had “slid” into war — like grains of sand, perhaps. In other words, it was all inevitable. This was, of course, a convenient get-out for the politicians who had argued for war when the issue was decided on 2 August 1914.

My third quibble is that history doesn't gain much as a discipline even if it turns out that wars are just like earthquakes. Where do we go from here if, as Buchanan suggests, there really is a negative linear relationship between the size of financial crises or wars and their frequency, and if the same size of trigger can unleash anything from a 'correction' to a crash, or from a skirmish to a world war?

The author is rather scornful of traditional history, the sort that tries to apportion responsibility for the outbreak of the First World War (“The trouble began a week ago in the remote West, where in the early evening a single grain of sand fell on a portion of our pile that was already very steep”). But that is just what history is about. Ultimately, Buchanan has made the error of confusing history with social science. The reality, as the historian R. G. Collingwood pointed out long ago, is that history is our interpretation of past thoughts that happened to be written down or otherwise preserved. We do not really study the causes of wars, but what people at the time thought were the causes. And our aim in retrieving their thoughts is not so much to explain how things happened as to understand how they seemed to have happened.

If history is only a succession of economic, social, political and cultural earthquakes — usually small tremors, once in a blue moon really huge, with the timing more or less random — then we are indeed, as Shakespeare put it, “as flies to wanton boys”. That certainly delivers the coup de grâce to models of history based on regular cycles over time — and good riddance. What it does not do is make the historian's strange communion with the dead any more or less superfluous.

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