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Re: [ontolog-forum] Axiomatic ontology

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Fri, 8 Feb 2008 00:21:17 -0600
Message-id: <p06230902c3d19f7ef5d1@[192.168.1.2]>
At 9:38 AM +0800 2/8/08, Rob Freeman wrote:
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*.

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.

Maybe I wasn't following the conversation properly. Forgive me if I interrupted inappropriately.


Jakub and I were establishing a very precise sense for my gloss that
they were "not empty".

Can you tell us anything about the information content of chaotic systems?

Nope :-)

> ...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.

This "informational rigidity" is interesting. Do you have any
references for it?

No, I made up the term to express an idea that I only have a vague, tentative and intuitive grasp of.
Google gives 13 hits for it. I need better keywords
to find what you mean.

I take it to be obvious that a random sequence cannot encode information about anything other than itself. Right? The key word here is "about". Information - actual information - is always information about something. Information theory does not address this idea: it only measures quantity and capacity of information.

Bohr/Heisenberg if I understand you correctly refers to our inability
to measure some qualities simultaneously.

Well, not just ability: the two values really don't exist to be measured. But yes, that was the idea.

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?

Simpler than that. The 'aboutness' requires some lost informational capacity. I have no idea why, or even whether this makes sense. I probably shouldn't have raised the matter: it was only a very suggestive and intuitive analogy. I can't defend or elaborate it any better at present.

Thanks for your interest.

Pat


-Rob
 
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