Shifting Sands

Peter Lipton

  • How Nature Works: The Science of Self-Organised Criticality by Per Bak
    Oxford, 212 pp, £18.99, June 1997, ISBN 0 19 850164 1

Taken alone, the basic laws of physics suggest a bleak universe, a thin, cold soup of atoms in motion. From this point of view, the complex dynamic structures we actually find, animate and inanimate, seem a miracle, so prompting the famous argument for the existence of God, that such manifest design requires a Designer. The argument from design has serious weaknesses, but one may still wonder what to put in its place. Per Bak, a physicist at the Niels Bohr Institute in Copenhagen, thinks he has the answer: self-organised criticality.

Bak applies this idea to a stunning range of disciplines, from geology, economics, biology and neurology to the science of traffic jams. The flagship example of self-organised criticality, however, is the humble sandpile. Imagine that grains of sand are dropped one by one onto a flat surface. The situation is not exciting at first, with each grain staying pretty much where it lands, but in time a pile will form, and eventually new grains will trigger avalanches of various sizes.

What impresses Bak about the sandpile is that the grains of sand build up to their own ‘critical’ state, without external guidance. In the beginning, the system is simple, since the grains do not interact, but as they fall they build their own structure, which eventually behaves in complex ways. The resulting pattern of avalanches is also important. Unsurprisingly, there will be fewer large ones than small ones, but Bak claims that the distribution will obey a theoretically significant ‘power law’, the simplest form of which would have the number of avalanches inversely proportional to their size.

Bak discerns this pattern of behaviour emerging from effectively random processes all over the place. It is supposed to characterise earthquakes, the ‘punctuated equilibrium’ that Stephen Jay Gould and Niles Eldridge claim for biological evolution, stock prices, neural activity, and the movement of cars on the M25.

In 1987, along with Chao Tang and Kurt Wiesenfeld, Bak published a technical account of self-organised criticality which, he reports, has been cited over two thousand times, making it the most cited paper in physics of the past ten years. His attempt at popularisation is only partially successful, however. His prose is down-to-earth, but his tone is grandiose: not everyone will join him in wondering whether historians of science will come to rank self-organised criticality with Newton’s laws. He can also be difficult to follow; and the effect of the book’s many graphs, diagrams and pictures is primarily rhetorical and aesthetic.

Nevertheless, there are things we can learn from Bak’s sandpile. The point about the avalanche is not just that a single grain causes a large slide, but that if one grain had not done the job, another one would have done. The avalanche is overdetermined. Normally, when one thing causes another, if the cause had not occurred, the effect would not have occurred either. Indeed, according to some philosophers, this counterfactual describes the essence of causation. In cases of overdetermination, however, there is causation without the counterfactual. If the grain that actually caused the avalanche had not fallen, there would still have been an avalanche, set off by another grain.

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