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Lorenz, Edward (Norton) - CHAOS

chaotic motion systems unpredictable


Electrocardiograph showing fibrillation in human heart ventricles. Long thought to be fully chaotic, in 1998 it was shown in dogs that there is some pattern and order in the electrical activity at the surface of the affected heart.

In the traditional world of Newtonian physics, dynamical systems are described by equations which allow the future motion of an object to be predicted with great certainty. For example, the movement of the planets can be reliably computed years ahead to within a fraction of a second. For centuries it was assumed that the dynamics of all systems were inherently calculable, even if some are so complicated as to be beyond our practical computational ability.

Contrary to intuition, however, there are many natural systems whose motion turns out to be inherently chaotic. The first example of such a system to be recognized as such was the weather, or rather equations used to model it. These never settle into a steady state, but constantly vary in an aperiodic, apparently random manner showed that they also exhibit an extreme dependency on their initial conditions, a factor that makes long-range weather forecasting effectively impossible.

Many other phenomena in all branches of science have since been recognized to be chaotic. Examples are the motion of a simple dynamo, which can undergo unpredictable reversals and which may model the erratic reversals of the Earth’s magnetic field throughout geological history. In biology, cardiac arrhythmias and erratic nerve impulses are chaotic, and in astronomy, once the showpiece of Newtonian physics, the motion of some objects is now known to be chaotic, such as the moon Hyperion, which orbits Saturn in an unpredictable tumbling motion. Turbulence is a classic example, as are wildlife populations, which undergo unpredictable cycles.

Chaos has been defined as the irregular, unpredictable behaviour of deterministic, nonlinear dynamical systems. As such, fractals are highly visual examples of chaotic systems, where apparently simple shapes are seen, upon closer inspection, to reveal an infinity of detail on progressively finer scales.

[ lo rens] (1917– ) US meteorologist.

After serving as a meteorologist in the US Army Air Corps during the Second World War, Lorenz was one of the first to develop numerical models of the atmosphere and to use computers for weather forecasting. He demonstrated the inherent impossibility of long-range forecasting, and helped found the study of chaos.

Lorenz observed that minute differences in the initial conditions of his numerical models of the atmosphere could, after a relatively short time, lead to radically different outcomes. He realized that the differential equations used to describe atmospheric behaviour, while deterministic, were also highly dependent on initial conditions and that this limited the usefulness of practical weather forecasts to about a week. This phenomenon has become known as the butterfly effect, from the idea that the small air movement caused by a butterfly flapping its wings in one part of the globe could in theory result in a storm weeks later thousands of miles away.

He went on to investigate other examples of chaotic behaviour, establishing in 1963 that even very simple deterministic systems can show chaotic behaviour. One of his examples was the motion of a waterwheel, which, as he demonstrated, becomes unpredictable and prone to random reversals in direction when the rate of water flow exceeds a threshold value. In order to illustrate the chaotic dynamics of such systems, Lorenz devised the Lorenz attractor, a three-dimensional curve in which the location of a point represents the motion of a dynamical system in phase space. The curve shows how the motion of the system oscillates aperiodically between the two directions and never settles into a steady state.

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