Hi Rob, (01)
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."
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 :)
> I don't know how chaos is regarded in information theory.
I unfortunately do not have much background in information or chaos
theory but I am interested in it too. I googled a paper that may be of
interest to you because except chaos and information theory it also
refers to Kolmogorov's algorithmic complexity (algorithmic entropy).
However, they are more concerned with measuring information and entropy
of finite strings (with a possible application to data compression):
Deterministic Chaos and Information Theory (Mark R. Titchener, Werner
> I'm backing into all of this from the kinds of patterns we see when we
> try to learn classes from flat text.
What kind of patterns you mean?
> 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.
> If you have any theoretical perspectives they would be very welcome.
I unfortunately don't. Kolmogorov complexity reminds me only of neural
networks and complexity of their learning . (02)
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