[sdiy] slightly ot: Chua circuit and chaos
Stromeko at compuserve.de
Tue Feb 11 20:19:09 CET 2003
On Monday 10 February 2003 12:31, Czech Martin wrote:
> I'm just reading a book a second time, just to make sure I
> understand. The statement of this book is shocking:
> there is no real chaos in physics, it is only the models
> that can act chaotic. This topic was covered before,
> even by the "inventor" of numerical chaos, Lorentz.
That statement is profoundly wrong if it indeed appears in such
generality. It is of course the case that modeling assumptions and
nonlinearities introduced by discretization and finite range that are
inherent to numerical simulations can lead to models that exhibit
behaviour that does notoccur in reality. Note that this does apply
generally, not just to chaotic behaviour. It is also true that with
each new theory there's a bunch of folks running around telling that it
either invalidates everything that was know before or that it explains
everything or both. You don't have to wait for long for the rebuttals
and some of them invariably throw out the baby with the bathwater.
The complete term for the type of chaos we're presumably talking about
is incidentally deterministic chaos, which means (I'm simplifying) that
the models are completely predictable, but any long-term output is not.
So in a sense it is exactly the other way around: the models are not
chaotic, but the system still is.
> I think the autor (Mr. Wehr) has done a good job
> showing how parasites take up a new fashion of science
> and draw more then speculative statements out of it.
That always happens. Look a few years back for instance to read the
most outrageous claims about how everything but fuzzy logic and neural
networks is obsolete.
> He also shows what huge methodical questions come up
> if physics takes place in the computer and not
> in the lab any more. Questions like:
> can we trust computer simulations, if different operation systems
> and hardware bring very different results for the same problem?
> Are real numbers a correct model for physicl quantities?
That are all valid questions that any competent modeler will have to
answer, but this does not apply to the claim that chaos does not exist
Specifically, take a look at what is known as Chua's circuit. I've had
the fortune to hear a guest lecture by Leon Chua on the topic and he
did not make any undue claims about it, btw. The significance of Chua's
circuit is that for a while it was believed that only inherently
nonlinear systems would exhibit chaos - this circuit proved that
conjecture wrong: it is piecewise linear. That made it possible to
prove mathematically that the chaos it produces is not some artifact of
residual nonlinearities, but it is also exhibited by the ideal circuit.
In fact, the determinism is strong enough that one is able to produce
two different circuits producing the same output (in a sense). Looking
at the signal with various statistical tools you'd conclude that the
output is noise, but if you take the twin circuit you can completely
correlate the signal (this idea was once publicized as a means to
"encrypt" electronic signals).
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