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Can the flapping of a single butterfly's wing result in a cyclone in a month's time? Most of us would say what nonsense, but in theory the answer, as discovered by Edward Lorenz in 1960, is YES! |
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At this time, Lorenz was using a series of twelve mathematical equations to try accurately to model weather patterns. Experimenting with data collected from weather stations, he ran a series of computer programs to test his model. Occasionally he would repeat an experiment. On one such occasion, instead of re-entering all the data he truncated the number .506127 to .506 and ran his program using this approximate value. To his amazement the new results were totally different. A very small change in his input data could result in a major change to his predictions. In addition, these changes appeared to be random in nature. Puzzled by these findings Lorenz simplified his original model to one involving only three equations. The reduced system still exhibited sensitivity to input data, but now he could view the results in 3 dimensional space. Prior to Lorenz's experiments, mathematicians and physicists had observed two kinds of systems. There are those which settle into a steady state (a fixed point), just as the temperature of a cup of coffee tends to room temperature, and those which repeat their behaviour after a specified time period, such as the motion of the earth around the sun. But Lorenz's solutions were much more complicated, never repeating themselves nor settling to a single point; they filled out a strange fractal-like set in 3 dimensions similar to a double spiral and were very sensitive to small changes in the starting values. Lorenz's discovery shocked the scientific world. Chaotic systems soon began to be recognised in all branches of science. As mathematicians started to unravel its mysteries, science reeled before the implications of an uncertain world intricately bound up with chance. The human heartbeat is chaotic, the stock market, the solar system and of course the weather. In fact the more we learn about chaos the more closely it seems to be bound up with nature. Fractal structures seem to be everywhere we look: in ferns, cauliflowers, the coral reef, kidneys… Rather than turn its back on chaos, nature appears to use it and science is beginning to do the same. Recently mathematicians
have shown that you can control chaos. For instance here in the Mathematics
and Physics Departments at The University of Queensland theoretical
and experimental work with lasers shows that the rich structure inherent
in chaos can be harnessed to expand the capabilities of lasers. Perhaps
in the future single systems, which are capable of multi-tasking, such
as the brain, will be modelled by chaotic systems. We still have a lot
to learn about how nature uses chaos, but perhaps unpredictable behaviour
is not undesirable. As Henry Adams For more see: |
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