Mort Luby Jr., the grandson of Dave Luby, decided the sport of billiards needed its own magazine, and debuted the first issue of Billiards Digest 65 years after the premier of Bowlers Journal. Surprisingly, the solar system is a chaotic system too - with a prediction horizon of a hundred million years. 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. Now we want to predict where the balls go, and we’ll say that the prediction fails when a ball leaves a collision 90 degrees from where we predicted - it’s obvious that after that point we can’t usefully predict anything. The billiard balls, formerly made of ivory or Belgian clay, are now usually plastic; they each measure from about 21/4 to 23/8 inches (5.7 to 6 cm) in diameter, the larger balls being used in carom billiards. At the centre of Chaos Theory is the fascinating idea that order and chaos are not always diametrically opposed. Chaos Theory is a delicious contradiction - a science of predicting the behaviour of "inherently unpredictable" systems. In 1887, the French mathematician Henri Poincaré showed that while Newton’s theory of gravity could perfectly predict how two planetary bodies would orbit under their mutual attraction, adding a third body to the mix rendered the equations unsolvable.

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. There are three ways of scoring: (1) the losing hazard, or loser, is a stroke in which the striker’s cue ball is pocketed after contact with another ball; (2) the winning hazard, or pot, is a stroke in which a ball other than the striker’s cue ball is pocketed after contact with another ball; (3) the cannon, or carom, is a scoring sequence in which the striker’s cue ball contacts the two other balls successively or simultaneously. However, the editors are always interested in amateur tournament reports from around the world, so feel free to send in results, descriptions and a contact source. We don’t know one thing: there are some people standing around the table, and we don’t know where they are, so we don’t know what their gravitational fields look like. Each red ball when pocketed remains in the pocket, while the colours when pocketed, as long as any reds remain on the table, are placed on their respective spots.

The other principal games are played on tables that have six pockets, one at each corner and one in each of the long sides; these games include English billiards, played with three balls; snooker, played with 21 balls and a cue ball; and pocket billiards, or pool, played with 15 balls and a cue ball. The small end of the cue, with which the ball is struck, is fitted with a plastic, fibre, or ivory reinforcement to which is cemented a leather cue tip. The game is played with three balls, two white and one red, with one of the white balls having a small red dot, or spot, to distinguish it. During play, when a player cannot hit the ball that the rules require him to hit (because of obstruction by another ball or balls), he is said to be snookered and loses his turn; this situation gives the game its name.

One of the white balls (plain or spot) serves as the cue ball for each player, the red ball and other white ball serving as his object balls. In play, the object is to stroke the cue ball so that it hits the two object balls in succession, scoring a carom, or billiard, which counts one point. It may be inferred that it developed from a variety of games in which propelling a ball was a main feature. All billiards games require the basic equipment of a table, cue sticks, and balls. The game of English billiards is played on a relatively large table, usually 6 feet 1.5 inches by 12 feet (1.9 by 3.7 m); it is played with three balls as in carom-a plain white, a white with a spot, and a red. Pro Billiards is a sports game about billiards. Snooker is played on the same table and with the same size balls used for English billiards. The first case is billiards, and we’ll consider a completely idealised billiard table: completely smooth, flat and rigid, completely round balls with completely known properties (so how elastic they are etc), and the same for the cushions.

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