Patterns of order in disorder
CHAOS: MAKING A NEW SCIENCE by James Gleick
Heinemann, £14.95, Cardinal, .15.99, pp.354
We could well be in at the beginning of a new science, as important as those of Newton and Darwin. Like the science of those revolutionaries, the new science of chaos, marvellously described in James Gleick's book, affects the way we see the world. Newton gave us the universe as a celestial machine: Darwin described a world in which the forms of life evolved by chance and survived by competition. The theorists of chaos guide us through the real world around us, show why conventional science fails so badly to predict 'real' events, and show how their new science makes the complexities of reality compre- hensible.
Chaos theory shows why, for example, we cannot hope for accurate long-range weather forecasts. It shows how the re- latively simple message that is all that our genes can carry can prescribe the barely imaginable complexity of the air passages in our lungs or the branching of our blood vessels. And the chaos theorists show that there is order, and predictability, in events whose courses seem completely baffling — Stock Exchange crashes and disease epidemics, to take two examples where we have no working theory at the moment.
What scientists do, in their highest mo- ments, is to look for rules of cause and effect Maws of Science') that apply to a wide range of occurrences, and use these rules to make predictions. Surprisingly frequently, science fails with real events. Weather forecasting is notoriously erratic, but science cannot even deal with relatively simple events. It cannot predict the annual incidence of disease after an innoculation programme: it cannot predict the changes in animal population that will occur when fertile animals are left in an isolated area.
Science works well in predicting the movement of the planets, say, and badly with these others because the events steadily change the conditions that the rules are supposed to apply to. As the fish in a pond multiply, they fill the space and reduce food supplies. As a drop of water falls from a tap, it leaves a residue bounc- ing up and down as the water for the next drop accumulates. And so on. The events are what scientists call 'non-linear' — doubling one element in the 'cause' side does not multiply in a simple way the corresponding element labelled 'effect'.
The unpredictability — the lack of any apparent pattern — is aptly described as chaos: chaos theory brings order to the seemingly confused events of the real world. This book shows in clear and fascinating detail how the chaos resear- chers found patterns of order in disorder (and a disorder in apparent order). Chaos theory is a revolution only made possible by the computer, because a com- puter can painlessly and quickly run through what computerists call iteration — seeing what happens when a process runs repeatedly in cycles, each cycle acting on the results of the previous one. (This is like, but normally more complex than, compound interest, where your princiPle for year two includes the interest earned in year one.) The results of iteration can be very surprising. In the situation of the fish in a pond, or elephants in a reservation, the progeny of the first cycle are there to breed for the second: and the available food is diminished by what the first generation ate before the food plants had seeded. Corn- monsense says that the population will rise to some number that balances the produc- tion of food, and settle there in equilib- rium. But if, on a computer, you write an equation for the change in population, putting in constants representing breeding rate and 'eating rate', you find that there are several possible outcomes, depending on the constants you use. There is the Possibility of equilibrium: but another set of values leads to a population that soars above equilibrium and then 'crashes'. This has actually happened in the elephant reservations in Tanzania, to the surprise and alarm of those who thought that the reservations would conserve the elephants. Chaos theory explains their error.
It also explains the complete failure of all long-range weather forecasting by what It called the 'butterfly effect'. Meteorolog- ists believe that with enough information, they really could get the weather forecasts right. But Gleick's book tells how Dr Edward Lorenz of the Massachusetts Insti- tute of Technology ran the elements of Climate iteratively through a computer and found that even a tiny change — the effect of the flight of a butterfly, for example — would be so multiplied by repetition that Prediction would be impossible.
Benoit Mandelbrot's discoveries, which started while he was in the pure research department of IBM, showed how chaos theory could reveal the simplicity in appa- rent complexity. His discoveries are con- nected with what mathematicians call 'frac- tals' — shapes with a fractional number of dimensions. It isn't easy to explain this idea, but it is easy to see the effects of the manipulations that produce fractal figures. If you draw an equilateral triangle, and then, a third of the way along each side, start the drawing of another triangle, each Side one third the length of the original one, and then on each of the two exposed Side of the three new triangles, draw triangles one third the size of the second batch, and so on, repeatedly, you get a Shape of striking beauty formed by a very long line that encloses an area barely larger than the original triangle. The DNA of our genes must contain some instruction of the type 'travel one third of the original distance and then split into two: repeat this a very large number of times' to generate the labyrinth of our blood vessels or of the air passages in our lungs. Good books explaining scientific re- search are rare. Gleick's is outstanding because he is a dramatic explainer and because, as a very long list of references Shows, he has assimilated enough research to be able to give a panoramic picture.