Re: [ontolog-forum] What words mean

[Pat Hayes <phayes@xxxxxxx>]

At 6:49 PM +0800 2/11/08, Rob Freeman wrote:

> On Feb 11, 2008 1:05 PM, John F. Sowa
> <sowa@xxxxxxxxxxx> wrote:
> >
> > RF> I don't think the term "continuous mathematical
> methods"
> >  > captures what is interesting about holograms at
> all.
> >
> > I certainly agree.  The point, however, is that
> holograms,
> > catastrophe theory, and many related methods go beyond the
> > Boolean algebra to continuous methods that have not been
> > widely explored in AI and computational linguistics.
> >
> > In general, there are many such methods that depend on
> > continuous fields.  For the purposes we have been
> discussing,
> > these methods are extremely powerful.  As the article by
> > Lenore Blum points out, they have the potential to
> > revolutionize how we do AI.  Holograms and catastrophe
> > theory are two examples, but there are others.
>
> That's good. I agree strongly with that analysis.
>
> I would still like to isolate _what_ it is about these theories
> which
> is good. It's not the reals themselves. What is it?

The reals are simply a way to quantify continuous variations which admit of arbitrarily small changes, and functions on them which can be differentiated, so it is meaningful to speak of rates of change. The basic "_what_" is probably continuity and differentiability. These fields all study phenomena which arise only in such continuous/differentiable domains.

> BTW I can't find where Blum mentions AI.
> On my quick read he seemed to
> be attempting a reformulation of computational theory based on
> numerical analysis. Possibly powerful, as you say, but I didn't
> see
> where he related it to AI.

If it is relevant to computation in any fundamental way then it is probably relevant to AI, since AI is entirely concerned with computations.

> Any references for the possible relevance
> of all this (catastrophe
> theory, chaos, many-body systems, and now holograms) to AI,
> interests
> me greatly. I don't care whether it is presented in terms of reals
> or
> computational theory.

You should, as you will get very different perspectives on the topics. AFAIK, there is no such thing as a discrete catastrophe theory, for example. But more fundamentally, your list is a list of *theories*, so of course it matters how they are phrased.

> Why are they separately being related to
> AI?
> (Personally I think it is in the complexity of combinations of
> elements.)
>
> > RF> In the "Axiomatic ontology" thread you accused
> me of the
> >  > "misuse" of words. Since "misuse"
> (to my mind) implies definitive
> >  > use, I would like to invite you to present your theory
> of
> >  > definitive word meaning.
> >
> > I'm sorry that I used the word 'misuse'.  In principle, I
> agree
> > with Humpty Dumpty's theory that the speaker is the master.
> > Therefore, it is impossible for anyone to misuse any word.
> >
> > On the other hand, it is helpful to adopt some conventions to
> > avoid misunderstandings...
>
> I agree technical terms have their applications. More commonly as
> a
> convenience among peers who broadly agree. But I reserve the right
> to
> use words more generally if I feel it will communicate my meaning
> more
> effectively (or if no such community of broadly agreeing peers yet
> exists.)

But in all these cases, such a community does exist, and indeed has co-opted the English word (chaos, catastrophe, continuous, random, compute) to its own purposes, or invented an entirely new word (hologram) with a precise meaning. In either case, to ignore such usage in a technical forum such as this, and especially when referring to the technical usage itself, is almost certain to cause misunderstanding.

> In particular we are talking here about a
> number of fields which are
> not traditionally thought to be related, but which separately have
> been related to cognition, and which have separately chosen to use
> words which are related in common parlance, even if their formal
> elaboration varies greatly.
>
> If one says structure appears to be probabilistic. Another
> that
> learnable structure is contradictory.
> Another that demonstrable
> structure is incomplete. Another that the most compact structure
> is
> random. Another that structure is governed by symmetries. Another
> that
> fundamental structure is uncertain. These all have narrow
> technical
> definitions. But I think it is fair to point out that the
> unconscious
> motivations in their choice of words may reveal patterns of which
> we
> are not yet formally aware.

In this context, 'formal' refers to word usage. The intuitions and concepts underlying these various theories are not 'formal', however. If there are underlying patterns uniting such various topics, they will be found by understanding these intuitions and relating them, not by making vague analogies based on word usage. You use words in the above so casually that you do not even state the ideas properly. For example, Kolmogoroff theory does not say that 'the most compact structure is random'. It refers to having the most information in a very precise sense. In fact, AFAIK, none of these theories refer to 'structure' as though it was something that can be measured. I have no idea where you derive such statements as "learnable structure is contradictory" (what does it mean, and which theory suggests it?) or "demonstrable structure is incomplete" (what does that mean, and how do you derive it? What senses of 'demonstrable' and 'incomplete' are you using?) Do you get "structure appears to be probabilistic" from quantum theory? If so, you have this slightly wrong: the 'reality' hypothesized by QT is actually an action field which yields a probability when squared. So it is the square root of a probability. Good luck getting your head around that one (I can't!)

BTW, technical usage should not be described as 'narrow'. Technical usage tends to be 'wide' in the sense that it conveys a lot more information than casual usage, which is great for chatting but not so good for doing science or engineering with.

Pat

> But we are talking communication, and if a particular word causes
> a
> problem it is easy to back away and try to describe the underlying
> phenomenon, which I always recommend when these disputes arise,
> which
> they do with yawn gaping
> regularity.
> -Rob
>  
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