Wednesday, September 15, 2010

Chaos Theory: Deep

The name "chaos theory" derives from systems that are apparently disordered, but may not actually be so.  It is, then, really about finding the underlying order in apparently random data.  The behavior of these systems is highly sensitive to initial conditions, popularly referred to as the "butterfly effect".  Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes in chaotic systems, rendering long-term prediction impossible.  (Rounding to three decimal places from six can produce astoundingly different predictions depending on the frequency of the calculation.)  This happens even though their future behavior is fully determined by their initial conditions, with no random elements involved.  This behavior is known as "chaos", as opposed to its study (chaos theory).  Chaotic behavior can be observed in many natural systems, such as the weather.  Explanation of such behavior may be sought through analysis of a chaotic mathematical model, although there are many other ways to study chaos theory - which has become an acknowledged area of science in its own right.  Some scientists currently believe that there are only three basic theories that underlie all of science: quantum theory, relativity, and chaos theory.  Stay tuned for more on chaos theory, but don't hold your breath.