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Re: [ontolog-forum] Axiomatic ontology

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Thu, 7 Feb 2008 11:53:21 -0600
Message-id: <p06230901c3d0dbe78cc2@[]>
At 2:05 PM +0100 2/7/08, Jakub Kotowski wrote:
Hi Rob,

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*.

> 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):

Yes, quite. Remember that 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.


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