The earth's atmosphere, which consists of familiar simple gases and water vapor, is nothing but a complicated mechanical system of a kind that should be calculable by the familiar rules of mechanics. So, since the beginning of the century, meteorologists have lavished care on the development of a system of interlocking equations with which it would be possible to calculate tomorrow's weather from a knowledge of today's. Only with the arrival of digital computers could they hope to succeed, for which reason there was great enthusiasm for numerical weather forecasting when, in the early 1960's, the competence of computers seemed to match the sheer complexity of the weather problem. But sadly, high optimism was quickly dashed. Nobody disputes that numerical weather forecasting has proved to be a valuable adjunct to traditional methods.
Weather forecasts are more accurate than they used to be.
Chaos is the answer. Mr. Gleick invokes what he calls the paradox of the butterfly's wings. There will be actual observations of the state of the earth's atmosphere at some places, and guesses made by weathermen or computers about the state of the atmosphere in between. But the maps do not say precisely where rain will fall, or for that matter where butterflies will beat their wings. This would not matter to numerical weather forecasters if they could be sure that similar starting points led always to similar end points.