Chaos theory

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In mathematics and physics, Chaos Theory is the knowledge of systems that look like they are random, but actually follow certain rules. These rules can be quite simple, but there is no way for us to know what exactly the system will do in the future.

Many systems with simple rules act in simple ways. A pendulum is a good example of such a simple system. If connected to another pendulum at the low end of this simple pendulum, there is a double pendulum. Its rules are as simple as the rules for the simple pendulum, but the way it behaves is not simple. It looks as if it behaves in a random way.

Because the rules of the double pendulum are simple, it should know exactly what the pendulum does if known right where it is when started. If started the pendulum in the exact same position as started before, the pendulum should swing the exact same way. But it can never find the exact same position again, because it would need to be very much exact - a very small change in starting position that cannot even be seen, and the pendulum swing would quickly be different from what it was before.

Very small changes in the starting position of a chaotic system make a big difference after a while. This is the explanation why even large computers cannot tell the weather for more than a few days in the future: we simply can not know exactly enough what the weather is today! When a bird or a butterfly moves its wings, it makes a small wind, and this wind can make a difference on the weather in a few weeks. (This is called the "butterfly effect"). No computer knows about them.

Some systems might appear random at first look (like our weather, for example), but Chaos Theory says that these kinds of systems or patterns may not be so random after all if people pay close enough attention to what is really going on.

A very important part to the study of chaos is the study of math functions that are known as fractals. Fractal functions work like chaotic systems: a small change in the starting values, and the value of the function changes in ways that look random. Because they are mathematical, they are easy to study (simpler than the weather, certainly), and they make pretty pictures, too.

In the Michael Crichton book Jurassic Park, Ian Malcolm studies Chaos Theory a lot. His ideas on Chaos Theory help other people by letting him imagine things that could go wrong, and warning the right people to fix it before they happen.