"Moorad Alexanian" wrote:
> One cannot make long range prediction in system that are very sensitive to
> initial conditions. In addition, randomness would make forward or backward
> prediction even less possible.
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.
> I think that is just more jargon and less science. That is the difficulty with
> a theory that is just words and can never attain the rigor of a true science.
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.
-- George A. Andrews Jr. Physics/Applied Science College of William & Mary P.O. Box 8795 Williamsburg, VA 23187-8795
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