Hi Jakub, (01)
On Feb 6, 2008 8:19 PM, Jakub Kotowski <jakubkotowski@xxxxxxx> wrote:
> Rob Freeman napsal(a):
> > P.S. Thanks for the reference to Ramsey, Jakub. I understand this to
> > be a proof chaotic systems are not empty. Do you know of any work
> > which looks at the amount of information which can be coded in a
> > chaotic system as opposed to a classical system?
> >
> I do not understand what you mean by saying that chaotic systems are not
> empty. (02)
I probably used the words "not empty" because I had just read Ramsey's
Theorem stated in terms of systems with objects "within" them in this
definition I found on the Web: (03)
"No matter how jumbled and chaotic you try to arrange certain objects,
you will find yourself creating a very highly organized and structured
object within it."
(http://www.math.uchicago.edu/~mileti/museum/ramsey.html) (04)
> And regarding the work about infomation coding in chaotic systems -
> isn't that what information theory is about? Entropy implies how much
> information which "system" carries. (05)
I don't know how chaos is regarded in information theory. (06)
I'm backing into all of this from the kinds of patterns we see when we
try to learn classes from flat text. From this point of view a link
between chaos theory and Kolmogorov complexity makes sense, but I
don't know how it is seen in either field. (07)
If you have any theoretical perspectives they would be very welcome. (08)
-Rob (09)
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