June 15, 2007

Hail in Ouagadougou

A late Bombay editor regularly bemoaned the incompetence of our meteorologists. Their forecasts, he would assert, are so inaccurate! And more often than not they are just plain wrong. How much better, he would also assert, are the forecasters in the USA!

Mr Editor, I wanted to write to him, why knock our weathercasters? Sure, when he was writing, TV meteorologists in the US had more technology, their forecasts filled with impressive figures and jargon. But the actual weather? There as here, impossible to predict accurately.

Now scientists can forecast a lot of things very precisely. The tides, a solar eclipse, the coming of a comet -- we are routinely told exactly when these events will happen. So routinely, in fact, that we don't even see them as predictions any more. Think of it: is the announcement of an upcoming solar eclipse a fact or a prediction?

Still. Astronomers, for example, will readily admit that their calculations of celestial motion are not perfect. But so close are they that we laymen don't know the difference. So if astronomers can forecast the motions of the planets and stars so accurately, why can't meteorologists do as well with the weather? It is a complex, intricate phenomenon, yes. But the same physical laws that govern our universe also control the weather. Isn't it possible to come up with a set of equations and calculations -- what mathematicians would call a model -- that describes the behaviour of the weather?

In the early '60s, Edward Lorenz, a mathematician and meteorologist at MIT, produced just such a set of equations. One dozen equations. This was weather stripped to the essentials, but it was a surprisingly good model. Fed with some initial values, it would spit out sequences of figures. If you read them correctly, there were winds and storms and lazy sunlit summer days in those numbers. Lorenz's equations simulated the weather very well.

Except ... Lorenz found that if he varied his initial values even slightly, the model would spit out completely different figures. To you and I, using 1.879 instead of 1.879018, say, might seem unlikely to make a difference. But in fact, it made an enormous difference. Very quickly, the sequences of figures generated by two nearly identical initial numbers looked nothing like each other.

This challenged a fundamental assumption science makes: small changes or influences can be neglected because they have small effects. For example, if you make a small error measuring the times of the tides today, you will have only a small error in predicting them for tomorrow. But Lorenz had hit on the reason weather is so unpredictable. Tiny differences in climatic conditions can produce enormous and complex differences, even days later.

And that's an idea fundamental to what's called chaos: the study of these disorders and complexities in the behaviour of systems. Chaos tells us that even simple systems -- like Lorenz's weather equations -- can behave in tremendously complicated ways. In 1972, Lorenz wrote a paper with this title: Predictability: Does the Flap of a Butterfly's Wings in Brazil set off a Tornado in Texas? That gave us the famous phrase "butterfly effect", forever linked to chaos, that describe systems that are sensitive to initial values. Like Lorenz's equations.

Think of weather like that. If I snap my fingers in Bombay today, does that mean rain in Manila tomorrow? I boiled a litre of water this afternoon; will it hail in Ouagadougou next week?

As chaos became better understood, it popped up everywhere. Economists analysed stock prices using chaos. Ecologists used it to understand the behaviour of moth populations. Meteorologists understood that their task was difficult and thankless because of the nature of chaos.

And interest in chaos has brought about a fundamental change in the scientific method. It was a tradition as old as science itself, for scientists to ignore unexpected fluctuations in observed experimental data. "Observational error", they called it.

But now, throwing out inconsistencies is not good enough, because the models we are left with don't adequately explain real phenomena. Chaos offers a fresh way to look at fluctuations. Perhaps there are, after all, explanations for them. Chaos freed researchers and their models "from the shackles of order and predictability", wrote the late Joseph Ford, who studied chaos at the Georgia Institute of Technology, and it opened up "exciting variety, richness of choice, a cornucopia of opportunity".

And also, at the heart of it all, this fascinating thought: that out of that complexity, that chaos, that disorder, comes a certain order. Close up, a phenomenon might seem terribly complicated and disorderly. But step back for the broader, more distant view. There's order there.

Again, weather best illustrates this. Yes, you can't predict it accurately from one day to the next, from one week to the next. But it doesn't take a meteorologist to tell us that on India's west coast, it will rain between June and September and a mild winter will follow in December and January. Out of the day-to-day unpredictability of weather comes the annual predictability of our seasons.

Order from disorder. Patterns from chaos. May not have satisfied the late editor. But what a seductive idea.


J. Alfred Prufrock said...

Why would I even try to understand chaos?
Takes all the zing out of it.

The real reason, of course, is that it's too much like work.


Ravi Ramanuja said...

J.A.P. take cover! I feel a big sneeze coming on! Those in India neednt worry, but do warn the innocents in Ouagadougou!!