Re: [ontolog-forum] Axiomatic ontology

[Pat Hayes <phayes@xxxxxxx>]

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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