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. (01)
That's good. I agree strongly with that analysis. (02)
I would still like to isolate _what_ it is about these theories which
is good. It's not the reals themselves. What is it? (03)
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. (04)
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. Why are they separately being related to AI?
(Personally I think it is in the complexity of combinations of
elements.) (05)
> 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... (06)
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.) (07)
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. (08)
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. (09)
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. (010)
-Rob (011)
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