Tuesday, December 11, 2007

Attractive Fixed Points

Math Man specializes in the mathematics of dynamical systems, in chaos theory. I dabble in chaos too, just in its embodied form, rather than the theoretical. Chaotic systems are not random, though they might appear to be. Given a particular set of starting conditions (two sons, one cat, teaching two classes, a spouse on leave), the unfolding of the system is completely determined (a December calendar that requires 5 colors to keep track of everyone's obligations).

Not every system ultimately leads to chaos (where every possible state is eventually experienced), some eventually arrive at an equilibrium state - called an attractive fixed point. I think I'm approaching a fixed point tomorrow, though I'm not finding it all that attractive personally! All obligations (musicals, concerts, dinners, rehearsals, auditions) are being sucked in to the 6 hours between 3 pm and 9 pm on December 13th. Some fixed points have basins around them, where the conditions all lead to the same end point (exhaustion?). Others find a new fixed point to hone in on with a subtle change in conditions. So what will the potential ice storm do to my spiral?


The spirals above are three related species in a damped oscillating chemical reaction.

The Jesuits hold that you can find God in all things, presumably even chaos. I note that ergodic is another term for chaotic. QED, or perhaps I should say AMDG?

3 comments:

  1. *Sympathetic laughter*

    Holding you in the Light.

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  2. Chaos drives the universe, whether the larger, infinite one, or the microscopic ones of our lives.

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  3. I'm not sure I understood all this but I enjoyed it anyway. Good luck surviving tomorrow. You'll have reason to rejoice on Pink Sunday when it's over anyway.

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