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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. It is a mathematical toolkit that allows us to extract beautifully ordered structures from a sea of chaos - a window into the complex workings of such diverse natural systems as the beating of the human heart and the trajectories of asteroids. Keeping an eye on the asteroids is difficult but worthwhile, since such chaotic effects may one day fling an unwelcome surprise our way. 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. Chaos (n): the inherent unpredictability in the behaviour of a complex natural system. It was the first chaotic system to be discovered, long before there was a Chaos Theory.

Chaos Theory is a delicious contradiction - a science of predicting the behaviour of "inherently unpredictable" systems. At the centre of Chaos Theory is the fascinating idea that order and chaos are not always diametrically opposed. Explainer: what is Chaos Theory? 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. The best we can do for three bodies is to predict their movements moment by moment, and feed those predictions back into our equations … When necessary for balls to be restored or cleaned, the referee will restore disturbed balls to their original positions to the best of his ability. Straight pool is a ‘call-pocket’ game, which means that before shooting, players must say which ball will go in which pocket. A snooker maximum 147 took Ronnie O'Sullivan a little over five minutes to compile at The Crucible two years ago and he had to pocket 36 balls. Surprisingly, 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.

Lorenz had found the seeds of chaos. The answers can be found in three common features shared by most chaotic systems. One fascinating aspect of mathematical billiards is that it gives us a geometrical method to determine the least common multiple and the greatest common divisor of two natural numbers. Handheld gimbals, motorized gimbals, and gimbal heads are common in the industry, helping reduce camera shake and achieving smooth gimbal shots. Cushions: The cushions on carom tables are designed for maximum accuracy and minimal rebound, as precision is crucial for carom shots. Without gimbals, we couldn't navigate or travel in space with any precision. Because the astronauts were in a set of gimbals, they could reorient themselves in different directions, just as they could in space. He created a mathematical model which, when supplied with a set of numbers representing the current weather, could predict the weather a few minutes in advance. The starting weather conditions had been virtually identical. 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.

What at first glance appears to be random behaviour is completely deterministic - it only seems random because imperceptible changes are making all the difference. On the other hand, this stability is somewhat of an inconvenience to fighter pilots who prefer their aircraft to make rapid changes with minimal effort. Commercial aircraft are aerodynamically stable, so that a small turbulent nudge (possibly butterfly-related) won’t push the plane out of a level flightpath. Modern fighter jets achieve great manoeuvrability by virtue of being aerodynamically unstable - the slightest nudge is enough to drastically alter their flightpath. Welcome to one of the most marvellous fields of modern mathematics. One problem with gimbal systems is the gimbal lock. Pin tumbler lock picking consists of raising the cuts on each pin stack to the shear line, one by one, until the plug turns freely. To determine which pin stacks have these pins, gently push up each "set" pin. I usually find that the very top of the plug, directly in front of the pins, to be a good place to apply torque, but you have to be careful that the tool doesn't touch the front-most pin.

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