Ben Goertzel (ben@goertzel.org)
Wed, 31 Mar 1999 12:30:03 -0500
> 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.
> 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.
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.
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 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 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.
Ben
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