The New Statesman Essay - Why the world is simpler than you think

Earthquakes, forest fires, wars and stock markets: do they all follow a universal law?

In 1934, the historian H A L Fisher arrived at a rather bleak conclusion on the nature of human history. "Men wiser and more learned than I," he wrote, "have discerned in history a plot, a rhythm, a predetermined pattern. These harmonies are concealed from me. I can see only one emergency following upon another . . . and only one safe rule for the historian: that he should recognise in the development of human destinies the play of the contingent and the unforeseen."

Fisher was writing during the Great Depression, just 20 years after a chauffeur had touched off the First World War by taking a wrong turn, thereby enabling an assassin in Sarajevo to kill the Austro-Hungarian Archduke Franz Ferdinand and his wife. To Fisher and his contemporaries, accidents of all sorts seemed charged with an alarming power to set the world on its head. One day in 1920, a pet monkey bit and infected the King of Greece. The king's subsequent death set off a chain of political events that led to war between Greece and Turkey. "A quarter of a million persons," as Winston Churchill later commented, "died of this monkey's bite."

Today, we may all feel that Fisher's view was needlessly pessimistic, a mere product of the times. And yet, one may still wonder: do we really know anything about the natural dynamics and rhythms of history? Can we do anything more than guess as to whether there is "a plot, a rhythm, a predetermined pattern"?

It may sound ridiculous, but it is my belief that a new perspective on these questions may be emerging from, of all places, theoretical physics. It suggests that Fisher's suspicions were indeed well placed - that the course of human affairs possesses a rather extraordinary kind of unpredictability, and may always escape our efforts to understand it in terms of general causes and effects. What's more, it may be something like a law of nature that history must, by necessity, be punctuated by inexplicable and utterly unforeseeable upheavals.

To see the roots of this unlikely connection between physics and history, imagine sprinkling grains of rice on to a table, one by one. As a pile grows larger and steeper, avalanches will occasionally carry some grains down the sides. This much is clear. But where and when should we expect the avalanches? What is their typical size? And what are the conditions that set up the really big ones? Over the past decade or so, physicists have tried to answer these questions.

What makes a rice pile interesting to physicists is that the forces at work do not find immediate release. Sprinkle droplets of water on a placid lake, and each will quickly disappear, swallowed up as the surface of the water becomes flat once more. The water level will gradually rise, and yet the history of the process is fairly boring. In the pile of grains, however, stress accumulates slowly, only to be released in sudden, spontaneous avalanches. When a grain falls in one place rather than another, this event is not washed away, but alters the entire course of the future. So the pile bears the long traces of the past and, in its workings, history matters in an important way.

In the late 1980s, physicists at the Brookhaven National Laboratory in New York State worked out the elements of the following basic picture. (They were envisioning a pile of sand, rather than rice, but this is of secondary importance.) At first, they found, before the pile has become steep, a falling grain can trigger only small avalanches. One grain may trigger another to tumble, and this may induce another to slide as well, but the chain reaction will die out quickly. As grains continue to rain down, however, many grains eventually come to be balanced uneasily on steep slopes, barely hanging on. The pile evolves naturally to a condition in which a single grain has the potential to trigger a domino-like reaction of tumbling grains that can sweep through the entire pile.

The Brookhaven physicists called this extremely unstable condition the "critical state". And we naturally ask: if we drop another grain, how big an avalanche will it trigger? Remarkably, this question has no answer - for there is simply no expected size for an avalanche. In the critical state, the next grain may stick and cause no avalanche at all, or it may trigger anything from the tumbling of a few grains to a system-wide cataclysm involving many millions of grains. Literally, anything is always just about to happen.

It may come as no surprise that big avalanches occur less frequently than small ones. What is startling is the precise pattern that emerges from the mathematics. In the critical state, something known as a "power law" comes into play. Each time you double the size of an avalanche of rice grains, it becomes twice as rare. This remarkably simple pattern holds for avalanches over a tremendous range of sizes, revealing that there is a hidden order and simplicity behind the apparent complexity of the pile.

Similar power laws have been discovered for events ranging from earthquakes and forest fires to mass extinctions and stock market crashes.

Two years ago, for example, geophysicists at Cornell University gathered extensive data on forest fires in the United States and Australia over the past century. The size of a fire is sensibly measured by the area it consumes, and one can ask the question: how large is a "typical" forest fire? One might expect that the history of fires would reveal some rough stalemate between the forces of nature and the efforts of mankind. But in looking at more than 4,000 fires on US Fish and Wildlife Service lands between 1986 and 1995, for instance, the Cornell researchers found a spectacular power law almost exactly the same as that for avalanches in the rice pile: double the area covered by a fire, and it becomes about 2.48 times as rare. The statistics speak unambiguously - there is simply no way to form a sensible expectation regarding how big the next fire is likely to be.

Earthquakes are notoriously difficult to predict - indeed, nobody has ever predicted the date of a major one, even approximately. Yet in the 1950s, a pair of geophysicists looked at every type of earthquake recorded, from the tiny vibrations going on almost daily beneath our feet to the cataclysms that destroy whole cities. They found a very simple pattern: the so-called Gutenberg-Richter law reveals that, every time you double the strength of an earthquake (as measured by the amount of energy it releases), it becomes four times as rare. This simple pattern holds for quakes over a tremendous range of energies, the strongest being roughly a hundred million times more energetic than the weakest. The reason why seems fairly clear - like the rice pile, the stresses and strains within the earth's crust appear to be organised in an extremely unstable condition, very much like the critical state.

The point here is that we tend to think that a big event, such as last year's earthquake in Turkey or the 1995 quake in Kobe, Japan, must have a big cause. If we could only pinpoint the cause, we think, we could predict the event. But the earth's crust, like the forest and the rice pile, is always unstable; it lives permanently on the edge of upheaval. One more little stress, quite indistinguishable from yesterday's, may trigger the big one, just as one more grain of rice, indistinguishable from the one you dropped just before, may trigger the avalanche. Or, in either case, it may not. That is the significance of a power law.

A power law can transform our view of all sorts of processes, from the trivial to the global. If you throw a thousand or so frozen potatoes at a wall - and some physicists in Denmark have actually done this - they will break into fragments of varying size. If you collect the pieces all up, from the microscopic ones to those as large as golf balls, and put them into different piles according to weight, you will find a power law: each time you halve the weight of the fragments, you will have six times as many.

Now turn to the matter of evolution and extinction. We know that there have been at least five mass extinctions of species in the earth's history. We assume that these had big, dramatic causes, such as a collision with an asteroid. But what if they were caused by small, undramatic events? Scientists know that, as part of the normal cycle of evolution, species are all the time becoming extinct, and that the extinction of one species may quickly trigger the extinction of others. When we collate (from our admittedly inadequate fossil records) the frequency of extinctions of various sizes, we find the power law yet again. And it is identical to that for earthquakes. Every time you double the size of an extinction (as measured by the number of families of species that become extinct), it becomes four times as rare.

In other words, scientists may be making a terrific mistake by looking for dramatic and violent causes of mass extinctions; they may simply be the inevitable product of evolution's most ordinary principles.

Do these insights have anything to teach us about human affairs? In some respects, they clearly do. For example, researchers have found a power law that describes price changes on foreign exchange or stock markets. They even found one for the citation of scientific papers: a physicist at the University of Boston concluded that, every time you double the number of citations, the number of papers receiving them falls by about eight times.

What of history? It is one of our deepest beliefs that great events have correspondingly great causes - that it is sensible, for instance, to look for exceptional conditions that made the First World War take place. Could a perceptive observer in 1913 have pointed to any special conditions that were warning of impending disaster? We may feel the answer should be "yes". But we would do well to test out the idea in the conceptual proving ground of the rice pile.

In the rice world, every event begins in the very same way: when one more grain falls on the pile. Even so, because the pile is tuned to the critical state, the consequences of each grain are wildly unpredictable. If, one day, a great avalanche carries half the pile away, a historian of the rice pile might want to blame the triggering grain, but that would be erroneous - it was just like all the others. He might, instead, look back to a snapshot of the pile just before the cataclysm, and try to identify some special conditions then in existence. But this would also be a mistake, for there was absolutely nothing unusual about the condition of the pile the moment before the infamous grain fell.

So the rice-pile historian would come to a conclusion similar to H A L Fisher's - there are no easy answers as to why one avalanche is a million times greater than another. Even the greatest avalanches do not have special or exceptional causes. They are a trademark of the critical state, with its predilection for upheaval.

One might fairly wonder whether the social and political fabric of our world is in something like a critical state. The statistics available suggest that it may be. In the 1920s, the British physicist Lewis Richardson studied 82 wars that had flared up between 1820 and 1929. In reckoning the size of a war, Richardson chose the simplest and grimmest statistic - the number of deaths - and found that wars, just like earthquakes, forest fires and rice piles, conformed to a power law: each time he doubled the number of deaths, the war became four times less common. In 1983, Jack Levy of the University of Kentucky extended Richardson's study to include conflicts stretching from the war of the League of Venice in 1495 to the Vietnam war in 1975. Because the world's population changes with time, Levy altered Richardson's prescription slightly and took the "size" of a war to be the fraction of the world's population killed. Again, he found an unmistakable power-law pattern.

These patterns imply that the greatest conflicts do not stand out from others as being extraordinary in the conditions that set them up. There are no such special conditions. As with the rice pile, there is no instructive way of explaining why one war is big and another small. None the less, the idea of a critical state - analogous to the rice pile with more and more grains balanced precariously on more and more expanse of slope - does explain how it is possible that sudden upheavals can rise up seemingly out of nowhere.

And some historians, without the benefit of mathematics, sense this. Norman Davies, the author of Europe: a history, has compared the First and Second World Wars to a pair of earthquakes that shook the fabric of international politics. "The years between 1914 and 1945," he wrote, "appear as the time of Europe's troubles, which filled the space between the long peace of the late 19th century and the still longer peace of the 'cold war'. They may be likened to the slipping of a continental plate, and to the resultant season of earthquakes."

Similarly, the American historian Paul Kennedy, in The Rise and Fall of the Great Powers, has argued that, as nations naturally wax and wane in economic strength, some are left clinging to a power that their economic base can no longer support, while others find new economic strength, and so seek greater influence. Tension grows until it passes some threshold and something gives way. Usually, the stress finds its release through armed conflict, after which each nation's influence falls back into line with its true economic strength. In this view, armed conflict is analogous to the avalanche of grains in the rice pile. Such conflicts, as the statistics over five centuries reveal, have no typical or expected size, and seem to arrive utterly without warning.

As a masterpiece of dynamical complexity, the rice pile stands at the forefront of theoretical physics. Perhaps historians should now add the concept to their armoury. In War and Peace, Tolstoy asked: "Why do wars and revolutions happen?" He answered: "We do not know. We only know that to produce the one or the other men form themselves into a certain combination in which all take part; and we say that this is the nature of men, that this is a law." Can theoretical physicists help historians to improve on that answer?

The writer is a former journalist for Nature and the New Scientist. This article is based on his book Ubiquity: the science of history . . . or why the world is simpler than we think, just published by Weidenfeld & Nicolson (£20)

. . . and can theoretical physics explain Labour's slump in the polls?

Can the power law of theoretical physics, as outlined above by Mark Buchanan, explain the movements of opinion polls and, in particular, the sudden and unexpected collapse of Labour support last month? Pollsters and commentators, to say nothing of ministers, admit that they are baffled. The big cause that people naturally look for seems to lie in the fuel crisis. But fuel prices had been rising for months, without any apparent effect on Labour's poll lead or ministers' personal popularity. Why did discontent come to a head at that particular moment? Why did the public give such instant support to the blockading truckers, and why did that translate into a sudden shift in the polls?

In many respects, the situation prior to the fuel crisis conforms to the "critical state" described by Buchanan. Accumulated discontents - over the health service, pensions, the Dome fiasco and rising petrol prices - created something very like the unstable rice pile that preoccupied the Brookhaven physicists. Each new grumble - another bailout for the Dome or another price rise - although small in itself, has the potential to trigger an avalanche. But there was no way that anybody could predict which of them, if any, would do so, or when.

Does the explanation stand up mathematically? The New Statesman sent Buchanan poll data from MORI and Gallup dating back to the Second World War. He concluded, as scientists will, that more data is needed. As he points out, physicists looking for a power law for the financial markets can use figures of price movements recorded every 15 seconds for 20 years. Public voting intentions are simply not tested as often or as accurately as that.

Nevertheless, Buchanan did find the bare bones of a power law, although only where party support changed by more than 5 per cent (up or down) month on month. Above this level, each time the size of the fluctuation doubled, he found that it became four times less frequent. It is possible, therefore, that all the print expended on deep explanations for Labour's slump was wasted: no such explanation may exist.

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