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
said "Chaos often breeds life, when order breeds habit."
For more see:
http://www.exploratorium.edu/complexity/java/lorenz.html
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