What Is Chaos Theory?

One meteorologist remarked that if the theory were correct, one flap of a sea gull's wings would be enough to alter the course of the weather forever. The controversy has not yet been settled, but the most recent evidence seems to favor the sea gulls.

- Edward Lorenz, Deterministic Nonperiodic Flow

Podcast of the Day

Melvyn Bragg examines whether world is a fundamentally chaotic or orderly place. When Newton published his Principia Mathematica in 1687 his work was founded on one simple message: Nature has laws and we can find them. His explanation of the movements of the planets, and of gravity, was rooted in the principle that the universe functions like a machine and its patterns are predictable. Newton’s equations not only explained why night follows day but, importantly, predicted that night would continue to follow day for evermore. Three hundred years later Newton’s principles were thrown into question by a dread word that represented the antithesis of his vision of order: that word was Chaos. According to Chaos Theory, the world is far more complicated than was previously thought. Instead of the future of the universe being irredeemably fixed, we are, in fact, subject to the whims of random unpredictability. Tiny actions can change the world by setting off an infinite chain of reactions: famously, if a butterfly flaps its wings in Brazil - it could cause a tornado in Berlin. So what’s the answer? Is the universe chaotic or orderly? If it’s all so complicated, why does night still follow day? And what is going on in that most complex machine of all - the brain - to filter and construct our perception of the world?

Listen to the In Our Time episode on Chaos Theory

Video of the Day

Short Article of the Day

Chaos Theory is a delicious contradiction - a science of predicting the behaviour of “inherently unpredictable” systems. It is a mathematical toolkit that allows us to extract beautifully ordered structures from a sea of chaos - a window into the complex workings of such diverse natural systems as the beating of the human heart and the trajectories of asteroids.

Welcome to one of the most marvellous fields of modern mathematics.

At the centre of Chaos Theory is the fascinating idea that order and chaos are not always diametrically opposed. Chaotic systems are an intimate mix of the two: from the outside they display unpredictable and chaotic behaviour, but expose the inner workings and you discover a perfectly deterministic set of equations ticking like clockwork...

Continue reading Borwein & Rose's article: What is chaos theory?

Further Reading

The big news about chaos is supposed to be that the smallest of changes in a system can result in very large differences in that system’s behavior. The so-called butterfly effect has become one of the most popular images of chaos. The idea is that the flapping of a butterfly’s wings in Argentina could cause a tornado in Texas three weeks later. By contrast, in an identical copy of the world sans the Argentinian butterfly, no such storm would have arisen in Texas. The mathematical version of this property is known as sensitive dependence. However, it turns out that sensitive dependence is somewhat old news, so some of the implications flowing from it are perhaps not such “big news” after all. Still, chaos studies have highlighted these implications in fresh ways and led to thinking about other implications as well...

Continue reading the Stanford Encyclopedia of Philosophy article on Chaos by Robert Bishop

Related Topics

If you’re interested in chaos theory, check out some of the following related topics for more resources:

 Laws of Nature | Mathematics | Randomness

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