The everyday meaning of chaos is complete disorder and confusion. In science, chaos has a different meaning. The word relates to phenomena that are unpredictable in detail but nevertheless conform to some overall pattern - deterministic chaos.
Traditionally, chaotic behaviour in nature was thought to result from complex causes. Now we know that systems operating to simple and well-known laws can also display chaotic behaviour. In order to understand chaos, let us consider some examples of non-chaotic and chaotic behaviour.
Consider a simple pendulum, swinging to and fro in periodic motion. If you know the position of the pendulum bob at any instant, you can calculate its position at any future time. Left to its own devices, the swinging pendulum will gradually settle down to rest. Now consider the elliptical orbit of Earth around the sun. Knowing Earth's position at any time, you can predict its position as far ahead in the future as you want.
Finally, consider a spherical pendulum; that is, a pendulum free to swing in two directions, such as a ball on the end of a string. If you drive the system by periodically oscillating the pivot in one plane, the ball will swing about and probably settle into a stable and predictable elliptical path. If you change the driving frequency slightly, however, the regular motion may break down into chaos, with the bob swinging this way and that in an apparently random manner.
The simple pendulum and the orbit of Earth display non-chaotic behaviour; the spherical pendulum displays chaotic behaviour. The pathway on which the pendulum bob and Earth eventually settles is called an attractor. The attractor for the simple pendulum is a point: the final resting position of the bob. The attractor for Earth is an ellipse.
The bob of the spherical pendulum moves about erratically but nevertheless remains in a bounded region of space. The region of space traced out by such motions is called a strange attractor. The tiniest inaccuracy in measuring the position and speed of the chaotically moving bob quickly leads to huge errors in predicting its path.
In each of these three examples, the motion of the particle is specified by simple and precise laws. In the first two cases, the particle moves regularly and predictably; in the case of the spherical pendulum, the particle behaves as if it were moving randomly.
A non-chaotic system is predictable into the long-term future; a chaotic system is not. The ease of predictability is determined by sensitivity to initial conditions. Take the case of the simple pendulum. You can calculate the position of the bob at any time in the future by accurately noting its position now, then carrying out simple calculations. If you make an error in determining its current position, your prediction will also be off, and your initial error will accumulate linearly with time.
ON THE other hand, when dealing with chaotic behaviour, any initial error made in determining the position of the particle grows exponentially with time. This means the error quickly grows so large as to swamp the calculation.
The only way to ensure accuracy of longer-term prediction in a chaotic system is to have an infinitely accurate measurement of the current position, which is, of course, impossible in practice.
Weather is an example of a natural chaotic system. Meteorologists can forecast tomorrow's weather with reasonable accuracy. But as we move day-by-day into the future, the accuracy of the predictions sharply declines. No meteorologist can do better than guess at the weather 14 days from now. Local weather is confined to a strange attractor characteristic of that region, of course. So we know summer temperatures in Ireland never exceed certain values, winter temperatures never drop below certain values, we will not experience monsoons and so on.
Many strange attractors are fractals. Fractals are shapes that look the same no matter how you magnify or demagnify them. These irregular geometrical shapes, which repeat themselves endlessly on smaller and smaller scales, were first described by the mathematician Benoit Mandelbrot, in 1975. Fractal shapes are very common in nature: coastlines, trees, mountains, the cardiovascular system, forked lightning, cauliflowers - each floret resembles the whole - and so on.
Science is founded on the assumption that the physical world is ordered. The laws of physics express this order most powerfully. We see these laws in operation all around us: the rhythm of night and day, the pattern of planetary motion, the effects of gravity, the ticking of a clock.
These are all non-chaotic systems, but the world also contains a wide range of chaotic systems: weather, ecosystems, dripping taps, turbulent flow in rivers and so on. These chaotic systems have extremely limited predictability.
Even if one were devote the entire capacity of the universe to computing the behaviour of one chaotic system, it would rapidly exhaust itself. In other words, the universe is unable to compute the exact future behaviour of even a small part of itself.
This is a profound conclusion. It means the future of the universe is in some sense open: the future is not rigidly fixed, and each new day really does offer new opportunities.
William Reville is a senior lecturer in biochemistry and director of microscopy at UCC