Theoretical physicist Mark Buchanan’s Ubiquity: The Science Of History . . . Or Why The World Is Simpler Than We Think (Phoenix, 2000), is a book whose implications are so powerful they’ve given me vertigo. Buchanan makes a very strong argument that, despite all appearances to the contrary, human history may be governed by very simple mathematical laws. Unfortunately, those laws would guarantee history’s complete unpredictability, and they would also fundamentally contradict the economic and political theories informing our decision-makers.

In 1987 three physicists named Per Bak, Chao Tang, and Kurt Wesenfeld designed a game that was to have profound effects on the scientific understanding of the way our world is organized. They used a computer program to simulate the growth and collapse of sand piles. The program would intermittently drop a single grain of virtual sand at some random location on a virtual plain. Over time, the grains would form piles. Every so often, a falling grain would trigger an avalanche. Those avalanches were usually rather small, but every so often they were catastrophically large. To the physicists’ surprise, there was no “typical” avalanche size, and no predictable interval between large avalanches. Despite this, the size of the avalanches obeyed a power law. Whenever the number of grains involved in an avalanche doubled, the avalanche became about 2.14 times less likely. Importantly, the variable that caused huge avalanches was identical to the one that caused tiny avalanches: the random fall of a single grain of sand.

The avanlanche moment

They then modified the program to reveal the height of the ridges being formed within the piles. This showed that the steeper the ridge, the more vulnerable it was to an avalanche. The more numerous the ridges, the more likely massive avalanches became. There was no way to predict in advance how the ridges would form, or what effects a falling grain would have at any given point in the pile.

The more ridges formed, the more the pile entered into what’s called a critical state. A critical state occurs when a system becomes hypersensitive to small changes. This phenomenon had been known about for some time, but was seen as a rather artificial occurrence.

Consider iron bars, for example. Every atom in an iron bar is like a tiny magnet that can point in one of two directions. When the iron is cool the atomic magnets all line up in one direction, giving the bar a significant magnetic charge. When the iron is very hot, thermal energies disrupt the atomic magnets so much that they point randomly, and the bar loses its magnetic force. If, however, the bar is heated to a point just below the threshold of complete chaos, the atomic magnets begin to configure themselves in very interesting and ever-changing factions of all sizes. Like the frequency of avalanches in the sand pile game, the sizes of these factions conform to a power law, in this case a power law of 1.19. Because they obey a power law, the factions display something called “self-similarity”: smaller factions are organized in ways very similar to larger factions, such that, regardless of the scale we use, the factions look basically the same. Of course, the critical state in this case is formed in a very artificial way, by purposefully forcing the temperature of an iron bar to remain within a very narrow range. In the sand pile game, however, the critical state forms naturally through an utterly random process.

Natual power laws

The sand pile game led the physicists to ask whether critical states could emerge naturally in other phenomena. Research in recent decades reveals that yes, critical states obeying power laws appear naturally in many phenomena, such as earthquakes, forest fires, and mass extinctions. Power laws are even found in the frequency with which research papers are cited in the Science Citation Index. This last example is very important, because it can provide an objective measurement of intellectual revolutions within the sciences: the more a paper is cited, the more influence it has over scientific paradigms. If intellectual revolutions obey power laws, then it seems reasonable to suggest that collective human behaviour is governed by critical state dynamics.

The study of non-equilibrium statistical physics shows that critical states seem to emerge whenever systems are kept far from equilibrium in conditions where the forces of chaos and order are in constant flux, and where the components of the system exert some influence on each other’s behaviour. It seems that at least some features of our collective behaviour can be reasonably explained by these concepts.

Might as well just guess

Research suggests that both stock market fluctuations and the distribution of global wealth follow power laws. This is an unnerving finding, as it flies in the face of traditional economic theory, which holds that the forces of supply and demand, governed by the rational self-interest of market participants, should keep the marketplace in a state of manageable and predictable equilibrium. If stock market fluctuations and the distribution of global wealth follow power laws, however, then our economy must exist within a critical state. If so, then its behaviour will necessarily be unpredictable. Just as the random fall of a virtual grain of sand may dislodge anywhere from a couple of grains to many thousands, the effects of a relatively minor economic variable may produce anything from unnoticeable effects to such calamities as the 1929 stock market crash and the collapse of the “tiger” economies of Southeast Asia in 1997.

This helps explain why economic forecasts are so consistently proven wrong. Buchanan writes that in 1993 the OECD “analyzed forecasts made between 1987 and 1992 by the governments of the USA, Japan, Germany, France, Italy, and Canada, as well as those of the International Monetary Fund and the OECD itself. Their conclusions? Not only were each of these organizations’ predictions abysmally inaccurate, but they would have made better predictions for inflation and gross domestic product if they had scrapped all their sophisticated economic models and simply guessed that the numbers in each year would be unchanged from the last.” Similar studies have produced the same results. This has grave implications. Given that the study of economics presupposes equilibrium, and given that our nations’ powerbrokers rely upon economists for their understanding of the world, it seems that our leaders’ most basic assumptions about the economy are dangerously wrong-headed. Mind you, neo-Liberal economists aren’t the only ones blinded by their assumptions. To the degree that they ignore the findings of non-equilibrium statistical physics, left-wing theorists are guilty of the same thing.

Any policy is irrelevant

That global wealth distribution follows a power law should certainly offer little comfort to anyone. While progressives may be grieved to learn that wealth distribution appears to follow mathematical laws that are independent of social policy, reactionaries should be equally dismayed that this distribution would hold even if everyone had exactly the same set of strengths and weaknesses, undermining the whole concept of meritocracy and the support it gives to the status quo.

Even more disturbingly, when we adjust for population growth, the number of people killed in wars also seems to obey a power law: “wars become 2.62 times less frequent every time you double the number of deaths.” If wars obey power laws, then they follow critical state dynamics and it will always be impossible to predict how large any war will become or how many people will die in it. Using the Great War as an example, Buchanan raises the possibility that the causes of small conflicts are identical to the causes of global bloodbaths, which would make those bloodbaths almost impossible to prevent.

So, where does this leave us? I’ll give the last word to Buchanan: “Today, we are still baffled by great wars and revolutions, although now we confront them without the metaphysical comfort that might be afforded by the ancients’ beliefs in the gods. We know that history is made by individuals acting as individuals, and that the potential for both war and peace lives in every person, and that somehow, out of the mysterious ocean of individual activity, great tidal waves all too frequently rise up to sweep us away. It will make no one feel any safer or happier to realize that these waves may be inevitable. But it is at least a step towards greater understanding to recognize that the tumultuous course of humanity need not be the product of some deeply malignant human madness, but of ordinary human nature and simple mathematics.”