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Posted by Claude Kordo on February 11, 1998 at 20:29:01:
In Reply to: Chaos Theory posted by Micaela Callahan on January 10, 1998 at 11:11:14:
Ms. Callahan:
You've certainly chosen a fun topic for your paper. Could you let me know what level cl your writing this for? Considering the actually infinite scope of your subject, you've got a lot of room to work in.
The problem, as you undoubtably know, is one of Determinism versus Chaos. Determinism states that if the precise initial conditions of a system are known, all succeeding states can be determined from those conditions.
Laplace, with the inception of Newtonian mechanics, became excited enough about predictability (and probability) to remark that "we
ought then to regard the present state of the universe as the effect of its preceding state, and as the cause of its succeeding state. "
That was wonderfully insightful, until Poincare pointed out a flaw if dealing with something on as vast a scale as the universe. While Laplace was mathematically correct, precise measurements regarding intial conditions in the universe are impossible to make. And thus, in the words of Poincare, "Determinism is a fantasy due to Laplace."
However, it gets much worse and far more interesting. According to Chaos Theory, the outcomes of games of chance display the very pattern of unpredictably random behavior observed in many newtonian systems.
Why don't you write your paper using as an illustration of this puzzle a game of dice (craps) played for an infinite duration.
You'll have to know a bit of probability theory, but actual research may help you there. You could utilize a small or large infinity, but as Bernoulli has proven, chances eventually favor the probable, which has then become the predictable. From the point of view of Chaos Theory, this is a paradox.
Also, I would advise you not to confuse predictability with probability at quantum levels,
as your tenured professor may take great umbrage with such superhuman armchair musings.. From the above paragraph, you may have deduced that this hypothetical game of craps is a "game within a game."
As you can see, there's more to chaos than meets the eye.
Cordially,
Claude Kordo (irekorzz@aol.com)
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