Stephen P. King (stephenk1@home.com)
Wed, 31 Mar 1999 11:57:15 -0500
Dear Ben & Matti,
Ben Goertzel wrote:
>
> Hi,
>
> >In TGD the entropy associated with density matrix of subsystem is in
> >key role: strong form of Negentropy Maximization Principle states
> >that in a given quantum state quantum jump is performed by the subsystem
> >for which the negentropy gain is maximum in quantum jump reducing
> >entanglement entropy to zero. The 'physical' interpretation is following:
> >entanglement is measure for attentiveness not yet involving consciousness.
> >Entanglement entropy measures, not the information content of
> >conscious experience, but how 'catchy' the potential conscious
> >experience is. The most catchy consciouss experience is experience.
> >Mass media people would certainly agree with this!
>
> I don't know what "entanglement entropy" is, sorry. What is the formula
> for this? -- in the discrete case (to keep things simple)
Could "entanglement entropy" be similar to "mutual entropy"? I can
think of the "catchyness" of an idea (or to use Richard Dawkin's term
meme) as an example is interesting. Could we consider there to be a
"susceptibility" to a bit of information that is the complement of the
"catchyness"? Could we quantitate this in terms of the configurations
that interactive local systems (LSs) have "in common". I think of this
as how individuals have similar ideas and can thus understand each other
based upon these similar bits of information. We can think of bits as
either particular configurations of matter, as in the case of ink on
paper, or using information theory, as the bit string that maximally
describes the computation that defines the bit.
> >The problem is to find also a measure for the information content
> >of conscious experience and there are quite explicit ideas also about
> >this. The modification of Roy Frieden's ideas to TGD context lead to
> >the idea that the number of degenerate absolute minima of Kahler action
> >going through given 3-surface X^3 (there are several of them by classical
> >nondeterminism) is entropy type measure for the cognitive resources of
> >3-surface.
>
> I don't understand this. How do we get from this mathematical measure
> to "cognitive resources"??
Matti, I am still stumbling over what "Kahler action" is. :( Can you
think of me as the "man from Mars" and explain it to me in baby steps?
:)
> The relation between your very interesting TGD theory and Hitoshi's very
> interesting global/local theory is not at all clear to me.
To put in my 2 cents :), we hope that a discussion with a wide variety
of people with differing backgrounds and specializations but with the
common goal of a good model of quantum gravity will accomplish more that
individuals working independently. ;)
> Evidently you all think there is some kind of conceptual correspondence between
> them in spite of the different mathematical vocabularies.
>
> Maybe it would be useful for you two to articulate what you think the
> points of commonality and points of difference between the two approaches are. If you have been
> over this ground before in other forums please excuse me for being so presumptuous!
I think we are in the process of doing just that. :)
> I think that if we arrive at a sufficiently abstract and foundational
> perspective we will be able
> to see exactly where the two approaches coincide, and then where they
> diverge in the process
> of making additional mathematical assumptions to turn philosophy into science.
>
> Matti, does your theory fit into the general framework of
>
> -- one set of laws for parts
> -- one set of laws for wholes
> -- a bridging principle explaining how whole-laws and part-laws interrelate
>
> ??
If I could interject, Are either of you familiar with Bart Kosko's
work? He has a formalism that proposes to "bridge" the whole-part
interrelationship. It is the concept of "fuzzy subsethood" See: Neural
Networks and Fuzzy Systems, Prentice-Hall, 1991 (ISBN 0-13-611435-0). I
hope to elaborate on his ideas in the near future. :)
> This seems to be the philosophical structure of Hitoshi's theory...
> If your theory could somehow be cast into this form this would give us a
> way to proceed in producing a "conceptual diff" of the two theories...
>
> As I said before, I think that getting the ideas right is the key here and
> that mathematical tricks are not going to be the answer. There are too many mathematical
> tricks out there, the mathematical universe is full of elegance, but our universe only
> implements a limited assortment of the really nice things in the mathematical universe...
>
> ben
I think of mathematics as the result of humanity's effort to make sense
of the world that we share. We can work out grand schemes in our
attempts to "explain everything" and only succeed in making what to
others appears to be strange and cryptic markings in the sand. It is the
ideas, not the linguistic, math or English, representations that are
important. I find that the fact that "our universe only implements a
limited assortment of the really nice things in the mathematical
universe" is an example of how Local Systems can only implement (within
their finite configurations) a finite subset of the Universe, which
Hitoshi and I consider to be, in itself, Infinite, the Totality of
Existence.
Onward to the Unknown,
Stephen
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