Though the dance of the planets has a lengthy prediction horizon, the effects of chaos cannot be ignored, for the intricate interplay of gravitation tugs among the planets has a large influence on the trajectories of the asteroids. Keeping an eye on the asteroids is difficult but worthwhile, since such chaotic effects may one day fling an unwelcome surprise our way. One of the oldest references to billiards is in Shakespeare’s play, Antony and Cleopatra, from 1674. But the game is actually older than that, dating back to the 1300s. Let’s learn about the history of billiards now. Once there it clings to its attractor as it is buffeted to and fro in a literal sea of chaos, and quickly moves back to the surface if temporarily thrown above or dumped below the waves. If released above the water it will fall, and if released underwater it will float. It also allows us to accurately predict how the system will respond if it is jolted off its attractor. Surprisingly, what is billiards the solar system is a chaotic system too - with a prediction horizon of a hundred million years. Some 50 years ago it was 18 hours. Comfortingly, it takes a large change in the flight controls to effect a large change in the plane’s motion.

Consequently, they are equipped with on-board computers which constantly and delicately adjust the flight surfaces to cancel out the unwanted butterfly effects, leaving the pilot free to exploit his own. No matter how consistent you are with the first shot (the break), the smallest of differences in the speed and angle with which you strike the white ball will cause the pack of billiards to scatter in wildly different directions every time. If you strike the other player’s cue ball and then pocket your cue ball, this "in-off" is worth 2 points. What happens if when you hit the billiard ball, it passes through one of the focus points of the elliptical table? The billiard table consists of a flat playing surface with six pockets. No matter where it starts, the ball will immediately move in a very predictable way towards its attractor - the ocean surface. Imagine taking a ping-pong ball far out into the ocean and letting it go.

In mathematical billiards the ball bounces around according to the same rules as in ordinary billiards, but it has no mass, which means there is no friction. Professional billiards tables are often larger than pool tables. In stroke contests (e.g. golf) a certain number of strokes are subtracted from or added to the scores, according to the strength of the players. Nine-Ball is a fast-paced game where players must pocket the balls in numerical order. Straight pool, also known as 14.1 continuous, is a game where players must pocket a set number of balls to reach a predetermined score. Finally, let’s talk about pool balls. Here a poet can talk poetry as much as he wants, but at the same time he hears something besides poetry. Although the computer’s new predictions started out the same as before, the two sets of predictions soon began diverging drastically. In the interests of saving time he decided not to start from scratch; instead he took the computer’s prediction from halfway through the first run and used that as the starting point. In the case of the weather, the prediction horizon is nowadays about one week (thanks to ever-improving measuring instruments and models).

The rate at which these tiny differences stack up provides each chaotic system with a prediction horizon - a length of time beyond which we can no longer accurately forecast its behaviour. Mathematicians use the concept of a "phase space" to describe the possible behaviours of a system geometrically. The modern house, although it had a well-designed south elevation, in which effective use had been made of mullioned oriel windows corbelled out from the first floor, was less successful inside-if the architect's intention had been to give the impression of age and dignity. In cricket you either hit a ball as hard as you like or you merely stop; that at any rate is the case when you first go in, and when you are nervous. The millions of cells that make up your heart are constantly contracting and relaxing separately as part of an intricate chaotic system with complicated attractors.