The day all chaos broke loose

Meteorologist Edward Lorenz nearly talked himself out of a job when he discovered chaos theory. Ayala Ochert meets the man who made long-range weather forecasting impossible.

There's a great deal of uncertainty over central Europe, but a good deal of certainty over the United Kingdom," Edward Lorenz told an attentive audience in Reading earlier this week. But this was no eurosceptic convention, and Lorenz is no politician. He is a meteorologist and his certainty was a forecast of no rain for the British Isles on Tuesday. Lorenz's big idea - that the flap of a butterfly's wing in Brazil could set off a tornado in Texas - has become shorthand for chaos theory, capturing the public's imagination as well as revolutionising science.

The "butterfly effect" renders impossible long-range weather prediction, the holy grail of weather forecasters. Chaos theory has turned meteorologists, previously the butt of jokes, into their own strongest critics. "It has completely changed the way we forecast the weather", explains Professor Lorenz of the Massachusetts Institute of Technology. Meteorologists no longer consider it enough simply to say that it will rain, they have to put a value on the prediction itself.

"Knowing the limitations of forecasting, you can ask how best to capitalise on them," says Lorenz. "We know for example that we can forecast a big coastal storm further in advance than a local thunderstorm. And we can sometimes forecast whether a coming season will be warm or cold, even when we can't forecast which days individual storms are going to come by."

Lorenz discovered the butterfly effect as early as 1961, but the various strands that later became chaos theory did not come together until the late 1970s. Its influence was to extend into almost every sphere of human enquiry - mathematics, medicine, economics. Chaos theory cut to the very heart of what was knowable, claiming that the messiness of the world could not always be ironed out. Randomness did not always come from outside, but could be integral to even the simplest system.

The Enlightenment dream - to describe the mechanism inside our "clockwork universe", and so to predict the future with minute accuracy - was shattered one afternoon in Boston, Massachusetts. "I had a simple system of equations that was supposed to reproduce some gross features of the weather. I decided to look at one section of a particular mathematical solution in more detail. So I plugged in the intermediate conditions as printed out by my computer, to save starting from the beginning. But of course what had been printed out were rounded off numbers," remembers Lorenz.

When he returned from a coffee break to look at the new model, he found that it differed completely from the original. A shift of a few decimal places - little more than the flap of a butterfly's wing - had radically changed the weather over the equivalent of a couple of months. Lorenz soon realised the implications - forecasting more than a few days ahead would always remain impossible. What he didn't appreciate at the time was how far-reaching would be the consequences. If a system governed by the simplest of principles could manifest random behaviour, unpredictability might be found almost anywhere.

And, during the decades that followed, it was. Sir Robert May, now the government chief scientific adviser, then a population biologist, saw wild fluctuations in the number of animals in a species, even those living in the most stable habitat. Mathematician Benoit Mandelbrot saw infinite complexity at the heart of equations routinely taught to schoolchildren.

It is hard to imagine that Lorenz, now aged 70 and semi-retired, ever shouted "Eureka!", but he was not disheartened at the thought that his life's work, long-range weather forecasting, was impossible: "As far back as you can remember there have always been a lot of jokes about the weather forecast. We all knew that our forecasts weren't as good as we would have liked them to be, so it would have been nice to prove that forecasting was impossible." Others were less amused, and continued to believe that one day they would achieve precise predictions.

Lorenz's insight was to see that "chaos was something to be sought rather than avoided". But he remains resolutely modest. Although he acknowledges that chaos theory has changed thinking in many fields, he urges caution over seeing chaos where it isn't. "Chaos is neither the rule nor the exception," he says.

Ironically, Lorenz's own account of the emergence of chaos theory is thoroughly deterministic - he suspects that had he not found chaos when he did "the same thing would have come along in the next few weeks". His hero, 19th-century mathematician Henri Poincare, came tantalisingly close to what we would now call chaos, yet he failed to start a revolution. According to Lorenz, chaos theory emerged when it did, and not a hundred years earlier, because of computer technology.

Most agree that technology was a strong catalyst. It was as much the new forms of representation made possible by computers, including the fractal images that became icons of the 1980s, as their number-crunching capabilities that were crucial. Chaos does not imply mayhem or anarchy; it is not a vanilla term for disorder. Chaotic systems exhibit structure that, paradoxically, can make prediction possible where conventional methods fail. The study of chaos can tell us when to expect unpredictability, but also when we don't need to worry about it.