THE WHATIS.COM WORD-OF-THE-DAY
August 7, 2001
chaos theory
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TODAY'S WORD: chaos theory
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In a scientific context, the word chaos has a slightly different
meaning than it does in its general usage as a state of confusion,
lacking any order. Chaos, with reference to chaos theory, refers to
an apparent lack of order in a system that nevertheless obeys
particular laws or rules; this understanding of chaos is synonymous
with dynamical instability, a condition discovered by the physicist
Henri Poincare in the early 20th century that refers to an inherent
lack of predictability in some physical systems. The two main
components of chaos theory are the ideas that systems - no matter how
complex the may be - rely upon an underlying order, and that very
simple or small systems and events can cause very complex behaviors
or events. This latter idea is known as sensitive dependence on
initial conditions, a circumstance discovered by Edward Lorenz (who
is generally credited as the first experimenter in the area of chaos)
in the early 1960s.
Lorenz, a meteorologist, was running computerized equations to
theoretically model and predict weather conditions. Having run a
particular sequence, he decided to replicate it. Lorenz reentered the
number from his printout, taken half-way through the sequence, and
left it to run. What he found upon his return was, contrary to his
expectations, these results were radically different from his first
outcomes. Lorenz had, in fact, entered not precisely the same number,
.506127, the rounded figure of .506. According to all scientific
expectations at that time, the resulting sequence should have
differed only very slightly from the original trial, because
measurement to three decimal places was considered to be fairly
precise. Because the two figures were considered to be almost the
same, the results should have likewise been similar. Since repeated
experimentation proved otherwise, Lorenz concluded that the slightest
difference in initial conditions - beyond human ability to measure -
made prediction of past or future outcomes impossible, an idea that
violated the basic conventions of physics. As the famed physicist
Richard Feynman pointed out, "Physicists like to think that all you
have to do is say, these are the conditions, now what happens next?"
Newtonian laws of physics are completely deterministic: they assume
that, at least theoretically, precise measurements are possible, and
that more precise measurement of any condition will yield more
precise predictions about past or future conditions. The assumption
was that - in theory, at least - it was possible to make nearly
perfect predictions about the behavior of any physical system if
measurements could be made precise enough, and that the more accurate
the initial measurements were, the more precise would be the
resulting predictions. Poincare discovered that in some astronomical
systems (generally consisting of three or more interacting bodies),
even very tiny errors in initial measurements would yield enormous
unpredictability, far out of proportion with what would be expected
mathematically. Two or more identical sets of initial condition
measurements - which according to Newtonian physics would yield
identical results - in fact, most often led to vastly different
outcomes. Poincare proved mathematically that, even if the initial
measurements could be made a million times more precise, that the
uncertainty of prediction for outcomes did not shrink along with the
inaccuracy of measurement, but remained huge. Unless initial
measurements could be absolutely defined - an impossibility -
predictability for complex - chaotic - systems performed scarcely
better than if the predictions had been randomly selected from
possible outcomes.
The butterfly effect, first described by Lorenz at the December 1972
meeting of the American Association for the Advancement of Science in
Washington, D.C., vividly illustrates the essential idea of chaos
theory. In a 1963 paper for the New York Academy of Sciences, Lorenz
had quoted an unnamed meteorologist's assertion that, if chaos theory
were true, a single flap of a single seagull's wings would be enough
to change the course of all future weather systems on the earth. By
the time of the 1972 meeting, he had examined and refined that idea
for his talk, "Predictability: Does the Flap of a Butterfly's Wings
in Brazil set off a Tornado in Texas?" The example of such a small
system as a butterfly being responsible for creating such a large and
distant system as a tornado in Texas illustrates the impossibility of
making predictions for complex systems; despite the fact that these
are determined by underlying conditions, precisely what those
conditions are can never be sufficiently articulated to allow
long-range predictions.
Although chaos is often thought to refer to randomness and lack of
order, it is more accurate to think of it as an apparent randomness
that results from complex systems and interactions among systems.
According to James Gleick, author of Chaos : Making a New Science,
chaos theory is "a revolution not of technology, like the laser
revolution or the computer revolution, but a revolution of ideas.
This revolution began with a set of ideas having to do with disorder
in nature: from turbulence in fluids, to the erratic flows of
epidemics, to the arrhythmic writhing of a human heart in the moments
before death. It has continued with an even broader set of ideas that
might be better classified under the rubric of complexity."
RELATED TERMS:
fractal
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fractal image examples
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S E L E C T E D L I N K S
[1] James Gleick's book can be ordered at Amazon.com.
http://www.amazon.com/exec/obidos/ASIN/0140092501/qid%3D995824138/sr%3D1-3/ref%3Dsc%5Fb%5F3/104-5956351-1340758
[2] ThinkQuest provides more information about chaos theory.
http://www.thinkquest.org/library/lib/site_sum_outside.html?tname=3120&url=3120/
[3] At the University of Texas, Matthew Trump has written a primer on
chaos theory.
http://order.ph.utexas.edu/chaos/
[4] The California Institute of Technology provides a demonstration
of the butterfly effect.
http://www.cmp.caltech.edu/~mcc/chaos_new/Lorenz.html
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