If you turn on a tap very gently and wait a few seconds for the flow to settle down, you can usually produce a regular series of drops of water, falling at equally spaced times in a regular rhythm. It would be hard to find anything more predictable than this. But if you slowly turn the tap to increase the flow, you can set it so that the sequence of drops falls in a very irregular manner, one that sounds random. It may take a little experimentation to succeed, and it helps if the tap turns smoothly. Don't turn it so far that the water falls in an unbroken stream; what you want is a medium-fast trickle. If you get it set just right, you can listen for many minutes without any obvious pattern becoming apparent.

In 1978, a bunch of iconoclastic young graduate students at the University of California at Santa Cruz formed the Dynamical Systems Collective. When they began thinking about this water-drop system, they realized that it's not as random as it appears to be. They recorded the dripping noises with a microphone and analyzed the sequence of intervals between each drop and the next. What they found was shortterm predictability. If I tell you the timing of three successive drops, then you can predict when the next drop will fall. For example, if the last three intervals between drops have been 0.63 seconds, 1.17 seconds, and 0.44 seconds, then you can be sure that the next drop will fall after a further 0.82 seconds. (These numbers are for illustrative purposes only.) In fact, if you know the timing of the first three drops exactly, then you can predict the entire future of the system.