Tuesday, January 1, 2013

Chaos


By Julie Rahm

           Chaos theory is the study of nonlinear dynamics in which seemingly random events are actually predictable from simple deterministic equations. Chaos means a state of disorder. However, in chaos theory, the term is defined more precisely. Although there is no universally accepted scientific definition of chaos, a commonly used definition says that for a system to be classified as chaotic, it must be sensitive to initial conditions, it must be topologically mixing, and its periodic orbits must be dense. Got all that?
An early pioneer of chaos theory was Edward Lorenz. In 1961, Lorenz was using a simple digital computer for his weather simulations. Lorenz’s computer worked with 6-digit precision, but the variables, when printed, were rounded off to a 3-digit number. This difference is tiny and should have had practically no effect. However, Lorenz discovered that small changes in initial conditions produced large changes in the long-term outcome. Lorenz's discovery showed that detailed atmospheric modeling cannot make long-term weather predictions. Lorenz went on to publish his famous 1972 paper, “Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?” In short, weather is usually predictable only about a week ahead. Sorry Skip Waters. Weather is a chaotic system.
          Next is topologic mixing. In informal terms, a system is chaotic if exactly where you start has a huge impact on where you'll end up. And, no matter how close together two points are, no matter how long their trajectories are close together, at any time, they can suddenly go in completely different directions. And, no matter how far apart two points are, no matter how long their trajectories stay far apart, eventually, they'll wind up in almost the same place. All of this is a complicated way of saying that in a chaotic system, you don’t know what the heck is going to happen! No matter how long the system's behavior appears to be perfectly stable and predictable, there's absolutely no guarantee that the behavior is actually in a periodic orbit. It could, at any time, diverge into something totally unpredictable. There's a reason that chaotic systems are an analysis nightmare. The most miniscule errors in any aspect of anything will produce drastic divergence.
         Lastly, in chaos, there must be dense periodic orbits. In a dynamical system, an orbit is just a set of points through the phase space of the system. It may never repeat. But, it’s an orbit. For example, if a log floats down a river, the path that it takes is an orbit. But it obviously can’t repeat – the log isn’t going to go back up to the beginning of the river. An orbit that repeats is called a periodic orbit.  Make sense?
       So, this week, my point is that your life is not a chaotic system. It may seem chaotic. But, it doesn’t meet the three requirements. You can fix the turmoil. To quiet the chaos in your life contact me through my website http://www.AmericasMindsetMechanic.com.   

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