**Ben Goertzel** (*ben@goertzel.org*)

*Wed, 31 Mar 1999 12:30:03 -0500*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Ben Goertzel: "[time 82] discrete models, QM vs. GR"**Previous message:**Stephen P. King: "[time 80] Re: [time 77] Spacetime &consciousness"**Next in thread:**Matti Pitkanen: "[time 108] Re: [time 81] Entropy, wholeness, dialogue, algebras"

*> 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

**Next message:**Ben Goertzel: "[time 82] discrete models, QM vs. GR"**Previous message:**Stephen P. King: "[time 80] Re: [time 77] Spacetime &consciousness"**Next in thread:**Matti Pitkanen: "[time 108] Re: [time 81] Entropy, wholeness, dialogue, algebras"

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