**Previous message:**John W Burgeson: "Web site"**In reply to:**Moorad Alexanian: "RE: Random thoughts" **Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

Hi Moorad;

"Moorad Alexanian" wrote:

*> One cannot make long range prediction in system that are very sensitive to
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*> initial conditions. In addition, randomness would make forward or backward
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*> prediction even less possible.
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I think we need to be careful here. One can make long range predictions for

chaotic systems in a very certain sense. Once the existence of a strange

attractor is known, the system will remain and evolve on the attractor--by

definition of an attractor: i.e. the system is bounded by the limits associated

with the attractor. It is a matter of coarseness or graininess in the phase space

that is the origin of the unpredictable nature of chaotic systems. In fact, one

can even control the evolution of noisy chaotic systems with more noise or other

chaotic sources. There are echoes of quantum uncertainty here. For the phase

space of a chaotic system is defined as--and therefore partitioned--by dx . dp

(space times momentum). As long as you don't look too close in a chaotic system,

because of strict determinism, you can make predictions . This is similar to

quantum systems where, e.g., energy levels are precisely known but the

Heisenburg uncertainty principle limits what can be known further -- if one wants

to know -- simultaneously -- known about life times.

*>
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*> I think that is just more jargon and less science. That is the difficulty with
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*> a theory that is just words and can never attain the rigor of a true science.
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*>
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*> Moorad
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*>
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*>
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Moorad, such dismissal is very naive. Mathematical biology is very much a true

science and the founding of evolution upon complexity theory, which has its

origins in chaos, is providing humans great insight into nature: this is by

definition, true science.

Sincerely;

George A.

-- George A. Andrews Jr. Physics/Applied Science College of William & Mary P.O. Box 8795 Williamsburg, VA 23187-8795

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