Guardian review: Ubiquity by Mark Buchanan | Books | The Guardian

Guardian review: Ubiquity by Mark Buchanan | Books | The Guardian
Science and nature books

Catastrophe juice
Chris Lavers sees the world in a grain of rice, in Ubiquity by Mark Buchanan
Buy it at BOL


Sat 14 Oct 2000


Ubiquity
Mark Buchanan
230pp, Weidenfeld, £20

Why are physics textbooks full of mathematics and biology books full of words? Because, as the great Richard Feynman once pointed out, physics is simple. Classical physics deals with inanimate objects performing relatively simple behaviours that can be described adequately using straightforward equations. The motion of heavenly bodies, the jiggling of atoms within molecules, even relativistic behaviours and the strange shenanigans of the quantum world - they can all be described using the general sort of equations with which most of us struggled at school.

Raise the level of complexity, however, and mathematicians begin to struggle. Notice, for example, how often the weather forecast is wrong. The atmosphere is complicated, and its description requires equations that are exquisitely sensitive to input errors. By the time we reach the irredeemably complex world of living things, traditional maths is virtually useless. Master all the mathematics in all the textbooks of classical physics in the world, and you would not be in a position even to begin to describe the internal workings of an ant.

At least, this was the situation until recently. In the last few decades, mathematicians have started grappling with more complex areas of science. First came the analysis of non-linear systems, beautifully explained by James Gleick in his 1988 bestseller Chaos . Then came complexity theory, outlined in Roger Lewin's Complexity . Now we have Mark Buchanan's Ubiquity , a book explaining the behaviour of systems in the "critical state", a concept described by the author as "the first really solid discovery of complexity theory" (to give a flavour of the intellectual lineage).

The basic principle is that certain systems, under certain circumstances, behave in rather curious yet mathematically similar ways. For a practical illustration of the idea, take a handful of rice and drop the grains one by one on to a table top. Soon you will have a pile of rice. But the pile will not grow taller for ever: eventually the addition of one more grain will cause an avalanche. Keep a tally of the magnitudes of these avalanches and a characteristic pattern emerges, one that can be described mathematically using a power function. The important point about this in the present context is that the power-function description implies something profound about our ability to predict the behaviour of the rice pile. The addition of a single grain may have no discernible effect, or it may precipitate a small avalanche, or a big one, or a series of avalanches resulting in a catastrophic collapse of the whole structure. Because of the particular mathematical distribution of avalanche magnitudes, predicting which of these consequences will ensue is, for all practical purposes, impossible.


Having established this underlying principle, Buchanan goes on to explain how it might be extended to shed light on the behaviour of more complex systems. Perhaps the most interesting concerns earthquake prediction. If fault systems in the earth's crust are in a critical state, and if the magnitude and timing of slippages along the faults follow a power law, then predicting when earthquakes will strike, and how destructive they will be, should prove virtually impossible. Historical records of the timing and magnitudes of earthquakes do seem to follow a power law, which suggests, among other things, that seismologists around the world may be wasting their own time and large amounts of our money banging their heads against an insoluble problem. To be fair to the profession, many seismologists had already come to this conclusion without the aid of rice.

Moreover, many earth scientists believe that critical-state theorists are overreaching somewhat when they try to liken the behaviour of something as complicated as the earth's crust to a pile of grain. And when essentially the same technique is employed to explain everything (note the book's title) from forest fires to stock market fluctuations, from extinctions in the fossil record to upheavals in human history, many feel that they are not so much overreaching as hurling themselves into the wide blue yonder. Perhaps because of this attitude of intellectual derring-do, most historians, economists and historical scientists at the present time seem willing to do little more than look on, often in bewilderment, as the mathematicians fly past. This is a shame because the whole project is refreshingly courageous and potentially very important. However, the theorists' cause is not helped by the extreme simplification of reality inevitably required by their analyses, nor by their sometimes shocking ignorance of the problems under investigation. The best that can be said about Buchanan's treatment of extinctions, for example, in particular the Permian mass extinction, is that the many factual errors do not greatly affect the conclusion.

Ubiquity represents an audacious attempt to explain an equally audacious ongoing programme of research, and herein lies its great strength and weakness. Any author who risks stretching ideas across numerous academic disciplines and well beyond the boundaries of knowledge is sure to receive both admiration and criticism; only time will tell which forms the greater part of the response in this case. For my part, I wish there were more juicy, thought-provoking books like Buchanan's on the now-groaning popular-science shelves of the nation's bookstores.

Topics