Chaos...

The Complex Adaptive Systems seminar was today and--in the spirit of interdisciplinarity--today was a presentation by a mathematical modeler on chaos and complexity.  I think I had just enough math to get what he talked about, but--unlike most other presentations so far--today was really quiet on the question side of things.

For anyone who doesn't know, the idea of chaos isn't one of randomness (stochasticity), it's essentially one where you can predict an outcome with the probability of a specific outcome being greater closer to the origin and the probability of a general outcome (or distribution) being greater farther from the origin.  In other words, the closer to home you look at, say, a route taken bicycling, the more predictable you'll find the exact path the bike takes.  However, over time, you lose that ability but pick up the ability to predict a general group of paths usually taken.

It's interesting in an esoteric sort of way.  Ironically, my introduction to chaos as an idea came with discussions of mathematics in field artillery.  My first adult "job" was as a field artillery weather observer and--as part of the initial training--we were introduced to the artillery round-off rule that used the oddness or evenness of a the terminal digit to determine which direction to round an otherwise terminal 5.  This somewhat stochastic method was intended to avoid a directional tendency in the the rounding of the myriad of mathematical calculations required when artillery was targeted.  Because of the number of calculations, the number of times numbers are rounded, and the potential hazard of an incorrectly placed artillery round (typically, more than one), the concept was to try to make any error more uniformly distributed around the actual values being estimated.

(I think this connection between math and large things dropping out of the blue and going boom! is one reason I take mathematics a little more seriously than many of my friends.)

My second interaction with the idea was courtesy of Michael Crighton and--yes--Jeff Goldblum's voice creeps into the shadowy periphery of my mind every time I hear the word "chaos".  Given I read the book prior to the movie, I did get the more detailed if still fiction-driven conceptual explanation...

...but--as one of my oldest son's favorite movies as a kid was Jurassic Park--I can not begin to count the number of times I've seen the scene with the water off the hand explanation of initial conditions influencing outcomes.

Got to love popular culture.