On Feb 8, 2008 1:53 AM, Pat Hayes <phayes@xxxxxxx> wrote:
>
> At 2:05 PM +0100 2/7/08, Jakub Kotowski wrote:
> Rob Freeman napsal(a):
> > 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:
> >
> > "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)
> >
> The highly organized objects, they refer to, correspond exactly to the
> complete subgraphs I was talking about. In this sense perhaps yes - the
> chaotic are not empty sometimes in a precise sense :)
>
>
> Are you guys using 'chaotic' here in the technical sense from chaos theory,
> or in some looser sense? Because Ramsey Schmamsey, chaos-theory-type chaotic
> systems certainly do *exist*. (01)
I don't remember where we questioned the existence of chaotic systems,
Pat. If we did it was probably unintentional. I understood this
exchange with Jakub to be about the information content of chaotic
systems. (02)
Jakub and I were establishing a very precise sense for my gloss that
they were "not empty". (03)
Can you tell us anything about the information content of chaotic systems? (04)
> ...information theory is all about measuring
> information-bearing capacity. Its like a theory of the volume of buckets: it
> says nothing about what kind of liquid is actually in the bucket. So
> according to Kolmogoroff theory, a random sequence has maximum information
> (capacity). True: but the only information it can bear is information about
> itself. One gets a kind of informational rigidity, where the possible
> content is reduced to zero when the capacity is at a theoretical maximum. If
> I knew more about QED I might suggest an analogy with Bohr/Heisenberg
> complementarity, but I don't so I won't. (05)
This "informational rigidity" is interesting. Do you have any
references for it? Google gives 13 hits for it. I need better keywords
to find what you mean. (06)
Bohr/Heisenberg if I understand you correctly refers to our inability
to measure some qualities simultaneously. If that is true I also think
it is very relevant. By "informational rigidity" are you saying our
ability to describe all qualities of a system simultaneously (c.f.
momentum and position in a quantum system) is reduced to zero when its
information bearing capacity is at a maximum? (07)
-Rob (08)
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