The Physics of History

CERTAIN complex systems, under certain circumstances, have been discovered to behave in mathematically simple, similar ways. In 'critical states', there is no reason to look for specific causes of great events. The smallest force can have gigantic effects and sudden upheavals can strike seemingly out of nowhere. The approximate frequency of such upheavals can be predicted, but not when they will happen or what size they will be.

Mark Buchanan's book reviews the current work on the subject to highlight a deep similarity between the upheavals that affect our lives in both physical and human systems. The book warmly communicates this novel way of thinking without compromising scientific integrity. This is made possible because the author is not only a science writer but also a physicist.

Buchanan starts by discussing the principle of ubiquity which is that one should focus on the simplest mathematical game belonging to a same universal class. Details are not important in deciding the outcome because things in a critical state have no inherent typical scale in either time or space. The important issue which this book highlights is that in a critical state, something known as a 'power law' comes into play to reveal a hidden order and simplicity behind complexity. A power law means that there is no such thing as a normal or typical event, and that there is no qualitative difference between the larger and smaller fluctuations.

Buchanan illustrates this with the following example. If one takes a handful of rice (or sand) and drops the grains one by one on to a table top, a pile of rice is built soon. The pile will not grow taller for ever, though. Eventually the addition of one more grain will cause an avalanche. Such a grain is only special because it happened to fall in the right place at the right time. The addition of a single grain may have no effect, precipitate a small avalanche, or collapse the whole structure. One can predict the likely frequency of the avalanches, but not when they will happen or what size each will be. It may come as no surprise that big avalanches occur less frequently than small ones. What is surprising is that there is a power law: each time the size of an avalanche of rice grains is doubled, it becomes twice as rare.

The book reveals that power laws have been discovered for events ranging from forest fires and earthquakes to mass extinctions and stock market crashes. This is the power law for forest fires: when the area covered by a fire is doubled, it becomes about 2.48 times as rare. If the size of an earthquake is doubled, these quakes become four times less frequent. The bigger the quake, the rarer it is. The distribution is scale invariant, that is, what triggers small and large quakes is precisely the same. A power law for the distribution of extinction sizes (that fits the fossil record well) happens to be identical to that for earthquakes: every time the size of an extinction (as measured by the number of families of species that become extinct) is doubled, it becomes four times as rare. Interestingly for economists, a power law has been discovered in the stock market. Price fluctuations in the Standard & Poor 500 stock index were found to become about sixteen times less likely each time the size is doubled.

Not only that, but other human-influenced events come under the same 'natural' laws. Wars seem to strike with the same statistical pattern as do earthquakes or avalanches in the rice-pile game. What is more, the forest-fire game seems to capture the crucial elements of the way that conflicts spread. A war may begin in a manner similar to the ignition of a forest. Statistics over five centuries have uncovered a power law for wars. Every time the number of deaths is doubled, wars of that size become 2.62 times less common. Such a power law implies that when a war starts out no one knows how big it will become. There seem to be no special conditions to trigger a great conflict. Likewise revolutions are moments that got lucky...