**From:** Lee Corbin (*lcorbin@rawbw.com*)

**Date:** Tue Apr 01 2008 - 23:26:35 MDT

**Next message:**Lee Corbin: "Memory Addition and The Clock/Torture Experiment"**Previous message:**Lee Corbin: "Re: The GLUT and functionalism"**In reply to:**Stuart Armstrong: "Re: The GLUT and functionalism"**Next in thread:**Stuart Armstrong: "Re: Mathematical Model of GLUTs and Lookups"**Reply:**Stuart Armstrong: "Re: Mathematical Model of GLUTs and Lookups"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Stuart writes

*> We got on this point after a long tortuous route: so let's simplify!
*

*>
*

*> S = a finite set of polynomials.
*

I pretty much have to visualize everything, and probably don't

have your mathematical talent, so thanks for your patience :-)

Here I see (off to the left, actually) a finite set of polynomials

in mathematical platonia (Diagram 1)

*> G = a GLUT on S.
*

Here I see a giant lookup table whose entries actually are

elements of S. But I am maybe guessing at what "on S"

means. Anyway, I visualize this GLUT being at the center

of a whiteboard. (Diagram 2).

*> R = a rule that says that any polynomial of n-th degree will be
*

*> mapped, under G, to a polynomial of (n-1)-th degree.
*

Now I would have thought that this rule existed between

elements of S: a mathematical-platonic rule analogous to

the rule that exists under the name differentiation, but

vastly more complex (I presume). But you say that R

connects n-th degree polynomials *in G* (that is, as

table entries of the GLUT) to particular other polynomials

also in G. Well, I suppose that it amounts to the same

thing. Okay. [ But it sounds a bit odd to refer to G as

a mapping, unless it was (incorrectly) taken to be a

mapping from platonia (Diagram 1) to the GLUT

(Diagram 2), where G(P) is the particular table entry

containing P. <end incorrect interpretation> ]

*> f = a hash function from S (to f(S))
*

Back to Diagram 1 in my mental imagery. Right "underneath"

every polynomial in S written in a differently colored marker

is f(S), a string of apparent gibberish output by f.

*> f(G) = the GLUT on f(S) equivalent to G on S.
*

We may have here Diagram 3, (which I visualize as being

at the extreme right of a whiteboard) and which is very

analogous to Diagram 2 (the GLUT, as you say, "on S").

Here too is a GLUT, but its entries are f(P) for each P in S.

*> f(R) = the rule on f(S) equivalent to R on S.
*

Yes, I think I'm getting it. Just as R was a rule (see Diagram 2)

that connected polynomial entries in the first GLUT, e.g.

GLUTentry(P2) = R(GLUTentry(P1)), we now have in

Diagram 3

GLUT2entry( f(P2) ) = f(R)( GLUT2entry( f(P1) ) )

where I may visualize P1 and P2 as being in S, f(P1) and f(P2)

being their "shadows" still in Diagram 1, and the two GLUT2

entries being connected by the new rule f(R) in Diagram 3.

*> Main point: G has very high KC (as does f(G)),
*

I don't know what that means. (Ah, but see below.)

Perhaps you mean the rule R that functionally connects

two elements of G = GLUT1 has high KC? I think I

know what the KC of a rule or a function would be.

If so, that does seem a bit odd, since where I thought you

were going was to have here an analogy between consecutive

states of a conscious entity. But these latter are causally

connected, hence, I believe have a low KC rule (e.g. Conway's

Life has quite a low KC rule connecting a generation to a

subsequent generation).

*> R has low KC, but f(R) has high KC.
*

Oh, all right---that seems to make perfect sense. But I

guess I still don't know what "G has very high KC" means.

*> Theorem (which will be left as as exercise to the reader - i.e. I
*

*> haven't calculated it, but it seems obvious):
*

*>
*

*> KC(f(R)) / KC(f(G)) can be made arbitrarily higher than KC(R) / KC(G) .
*

Lost here. I understand KC(R), but still don't grok KC(G),

likewise I understand KC(f(R)) but not KC(f(G)).

I'll reply to the remainder here when I've understood better my

problems with the above.

It all does continue to sound quite promising, though.

Lee

*> Corollary: We can decrease the KC of G to some extent, and still get
*

*> the inequality above. We want to do this, because we don't want G to
*

*> be a full GLUT but something more "understandable".
*

*>
*

*> Inspiration: If we imagine that G is the rules of consciousness, and R
*

*> is some much simpler property of consciousness (say: it learns form
*

*> experience), then R is only much simpler than G in our current
*

*> description of the universe; in hash equivalent settings, R does not
*

*> qualify as being "much simpler".
*

*>
*

*> Philosophical consequence: different hash equivalent ways of looking
*

*> at problems are not equivalent. Since we essentially cannot deal with
*

*> hash functions in any computable way, the different ways things are
*

*> set up are very important.
*

*>
*

*> Punch line: Let E be an explanation of consciousness, (an explanation
*

*> in the sense we are used to). Let F be a GLUT, hash equivalent to E.
*

*> Then though E and F are hash equivalent, they are not equivalent,
*

*> especially from our point of view.
*

*>
*

*> Hope this helps! I don't know if it's all that useful, though.
*

**Next message:**Lee Corbin: "Memory Addition and The Clock/Torture Experiment"**Previous message:**Lee Corbin: "Re: The GLUT and functionalism"**In reply to:**Stuart Armstrong: "Re: The GLUT and functionalism"**Next in thread:**Stuart Armstrong: "Re: Mathematical Model of GLUTs and Lookups"**Reply:**Stuart Armstrong: "Re: Mathematical Model of GLUTs and Lookups"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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