Stephen P. King (stephenk1@home.com)
Wed, 31 Mar 1999 20:58:25 -0500
Dear Ben,
Ben Goertzel wrote:
>
> > Could "entanglement entropy" be similar to "mutual entropy"?
>
> I don't think they are the same
>
> However, it is tempting to think of the "wholeness" of a system as having to do with
> the mutual entropy generated by placing the parts of the system together as a whole
>
> Mutual entropy is a special case of what I call "emergent pattern" -- the emergent
> pattern in a set {A,B} being roughly
>
> | Patterns({A,B}) - Patterns(A) - Patterns(B) |
>
> where | | is a norm operation on the space of patterns in question and Patterns(X)
> refers to the set of patterns in X
>
> Mutual entropy results from this definition if one restricts consideration
> to "Markovian patterns" in dynamical trajectories, i.e. to statistical analysis of
> transition probabilities between cells in state space.
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
> >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. ;)
>
> I have been through this process before, I note.
>
> I was involved in a FOUR YEAR LONG e-mail dialogue involving the radical physicist
> Tony Smith, the philosopher Kent Palmer and a Norwegian physics/math student
> Onar Aam (who now works with me at Intelligenesis). We made a lot of conceptual
> progress in a very abstract way, beginning from the shared intuition that
> octonionic algebra and Clifford algebras are essential to the structure of the
> universe. However, we didn't solve the crucial problems we set out to solve -- not yet,
> anyway; and the discussion sort of petered out a year ago, although we're all still good friends. I felt
> that Tony clung too tightly to all the details of his theory; and Onar and Kent didn't
> have the math background to really get into the nitty-gritty details
:)
> I don't mean to be negative in any way -- this kind of conversation is great fun, and if
> it never leads to anything but fun, it's worth more than most things in human life!!!!
>
> But if we really want to solve the puzzle of modern physics, we need to be resolute
> about not clinging too closely to our pet ideas -- taking what is best from
> them and paring away the inessentials, and moving always toward the essence.
Absolutely. This is a very important point! :)
> There are after all literally hundreds of radical physics theories out
> there, and probably at least 10-20% of them have a big element of truth to them. But they are
> all too complicated, and they lack the basic conceptual simplicity that to me has
> the "ring of truth" about it.
>
> Hitoshi's theory does have that "ring of truth" in its articulation of a
> very simple principles:
> wholes may have different laws than parts
>
> Tony Smith's theory also had that ring of truth to me, in the way that it derived ALL
> structures from the same finite algebra, the octonions. Space was an 8-dimensional
> discrete lattice, formed from integral octonions. At each corner of the lattice was
> an octonion element -- first generation particles are single octonions,
> then second generation particles are pairs and third generation particles are triples. (the fact
> that there are only 3 generations, and 2^3=8 is probably important). Particle interactions are
> explained by octonion multiplication.
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
> mechanism is used to explain gravity as a spin-2 field.... This loses the conceptual
> intuition of General Relativity, which feels wrong to me.
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
> have moved.
> He does have some papers at xxx.lanl.gov, but they don't describe the
> discrete physics framework that we worked out together.)
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
> algebra for parts, an algebra for wholes, and an algebraic mapping (homomorphism?) from the part
> algebra into the whole algebra.
> 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.
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
Kindest regards,
Stephen
This archive was generated by hypermail 2.0b3 on Sun Oct 17 1999 - 22:31:50 JST