**Stephen P. King** (*stephenk1@home.com*)

*Wed, 31 Mar 1999 20:58:25 -0500*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 84] Re: [time 82] discrete models, QM vs. GR"**Previous message:**Ben Goertzel: "[time 82] discrete models, QM vs. GR"

Dear Ben,

Ben Goertzel wrote:

*>
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*> > Could "entanglement entropy" be similar to "mutual entropy"?
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*>
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*> I don't think they are the same
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*>
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*> However, it is tempting to think of the "wholeness" of a system as having to do with
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*> the mutual entropy generated by placing the parts of the system together as a whole
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*>
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*> Mutual entropy is a special case of what I call "emergent pattern" -- the emergent
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*> pattern in a set {A,B} being roughly
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*>
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*> | Patterns({A,B}) - Patterns(A) - Patterns(B) |
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*>
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*> where | | is a norm operation on the space of patterns in question and Patterns(X)
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*> refers to the set of patterns in X
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*>
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*> Mutual entropy results from this definition if one restricts consideration
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*> to "Markovian patterns" in dynamical trajectories, i.e. to statistical analysis of
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*> transition probabilities between cells in state space.
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Is this "Makovian patterns" related to the infamous Markov Chains? How

do we explain memories and/or histories? I apologize for being

difficult. :) I think we should look at Kosko's subsethood theorem, it

covers this, I think! :) Is the norm considered an invariant over all

possible patterns or over some finite subset?

*> > To put in my 2 cents :), we hope that a discussion with a wide variety
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*> >of people with differing backgrounds and specializations but with the
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*> >common goal of a good model of quantum gravity will accomplish more that
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*> >individuals working independently. ;)
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*>
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*> I have been through this process before, I note.
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*>
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*> I was involved in a FOUR YEAR LONG e-mail dialogue involving the radical physicist
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*> Tony Smith, the philosopher Kent Palmer and a Norwegian physics/math student
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*> Onar Aam (who now works with me at Intelligenesis). We made a lot of conceptual
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*> progress in a very abstract way, beginning from the shared intuition that
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*> octonionic algebra and Clifford algebras are essential to the structure of the
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*> universe. However, we didn't solve the crucial problems we set out to solve -- not yet,
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*> anyway; and the discussion sort of petered out a year ago, although we're all still good friends. I felt
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*> that Tony clung too tightly to all the details of his theory; and Onar and Kent didn't
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*> have the math background to really get into the nitty-gritty details
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:)

*> I don't mean to be negative in any way -- this kind of conversation is great fun, and if
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*> it never leads to anything but fun, it's worth more than most things in human life!!!!
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*>
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*> But if we really want to solve the puzzle of modern physics, we need to be resolute
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*> about not clinging too closely to our pet ideas -- taking what is best from
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*> them and paring away the inessentials, and moving always toward the essence.
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Absolutely. This is a very important point! :)

*> There are after all literally hundreds of radical physics theories out
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*> there, and probably at least 10-20% of them have a big element of truth to them. But they are
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*> all too complicated, and they lack the basic conceptual simplicity that to me has
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*> the "ring of truth" about it.
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*>
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*> Hitoshi's theory does have that "ring of truth" in its articulation of a
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*> very simple principles:
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*> wholes may have different laws than parts
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*>
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*> Tony Smith's theory also had that ring of truth to me, in the way that it derived ALL
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*> structures from the same finite algebra, the octonions. Space was an 8-dimensional
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*> discrete lattice, formed from integral octonions. At each corner of the lattice was
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*> an octonion element -- first generation particles are single octonions,
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*> then second generation particles are pairs and third generation particles are triples. (the fact
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*> that there are only 3 generations, and 2^3=8 is probably important). Particle interactions are
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*> explained by octonion multiplication.
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I have found Tony et al's discussions very interesting. I wonder if

they would be interesting in joining us? :) I think that there is

something to the octonions/Clifford algebras. I have two local friends

working on that angle. :)

*> Gravity is explained in a way that I don't like -- the MacDowell-Mansouri
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*> mechanism is used to explain gravity as a spin-2 field.... This loses the conceptual
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*> intuition of General Relativity, which feels wrong to me.
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I agree. How is a "localized" particle to be equivalent to an entire

space-time, of course I am using the idea that the spin-2 field had a

particle analogue. The main problem that I have always had with a

particle model of QG is that it trivializes the role of the observer to

the point that no novelty at all is possible. It is a mistake to assume

that an "absolute space-time" has any more existence than Newton's space

and time. The ordering of events in a spacetime can not be assumed to

exist ab initio, or in other words, the "history of the world is not

fixed". This is evident from the prohibition of a crisp Cauchy

hypersurface by the Uncertainty principle. This is also why I stress the

computer science guy's Pratt and Wegner... :)

*> (I was going to point you to the URL for Tony's website, but it seems to
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*> have moved.
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*> He does have some papers at xxx.lanl.gov, but they don't describe the
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*> discrete physics framework that we worked out together.)
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I still remember my first encounter with Tony Smith, back when he was a

student of David Finkelstein; David introduced me and invited me to

participate in their physics meeting on the subject of Quantum arrows,

David's pet project. I still have the packet that Tony gave me. I like

him, but it seems hard to get him to think "differently" ... :)

I found this:

http://www.innerx.net/personal/tsmith/TShome.html

I wonder that he is doing now?

*> I would like to express the whole/part distinction algebraically. An
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*> algebra for parts, an algebra for wholes, and an algebraic mapping (homomorphism?) from the part
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*> algebra into the whole algebra.
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*> This is very tricky; the standard model is described nicely by clifford algebras and lie algebras, but > general relativity's algebras are different. I haven't studied this kind of math in many years so I am a > bit rusty here.
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We are all busy studying! I am working on a post describing Kosko's

ideas and their implications with regard to whole-part relations. I am

dyslexic so my math SUCKS, I depend on you guys to correct me. :)

*> Ben
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Kindest regards,

Stephen

**Next message:**Stephen P. King: "[time 84] Re: [time 82] discrete models, QM vs. GR"**Previous message:**Ben Goertzel: "[time 82] discrete models, QM vs. GR"

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