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

**Date:** Sun Mar 30 2008 - 23:10:39 MDT

**Next message:**Stathis Papaioannou: "Re: The GLUT and functionalism"**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: The GLUT and functionalism"**Reply:**Stuart Armstrong: "Re: The GLUT and functionalism"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Stuart writes

*> It seems differentiation is not the example to invoque [invoke] here.
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*>
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*> But the original idea can be adapted, as follows: let us define some
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*> other functional on the set of polynomials, via a GLUT, with
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*> maximalish Kolmogorov Complexity,
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It's this functional, I take it, that has maximalish KC. That is, the

image of the polynomial P is i(P), and to get from P to i(P) requires

an extremely non-obvious and highly complex functional "i". Right

so far?

*> subject to only one rule "R": it maps polynomials of the nth degree
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*> to polynomials of the (n-1)th degree.
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R is the original mapping whose analog back in the original problem

is the succession of causal states that characterize the consciousness

of some entity. In your earlier, now discarded, case, R happened to

be differentiation. Now R is some other Rule, which perhaps (I hope)

is by hypothesis closer to a causal description of what happens between

two succeeding states in a person.

*> We then hit the set S
*

where S, I take it, is i({P1, P2, P3, ... for possibly countably many

terms})? I apologize if I have misunderstood. Anyway, you are

hitting the entire set S with a hash function, which I assume has

the property that f( i{P1, P2, ...}) = f(i(P1), i(P2), ...), right?

Oh, oh. I think I've gone astray. Forget that. I now believe

that you mean for S to be the original set of polynomials.

*> with the usual hash function f, and have a new
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*> GLUT, called f(GLUT), of pretty much same complexity. The rule about
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*> polynomials is mapped to an equivalent rule f(R) on f(S),
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I'm sorry. But I have no conviction left that I have followed correctly.

Perhaps if you put me on the right track above, I can continue.

Thanks,

Lee

*> equivalent
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*> with an ordered partition of f(S). The complexity of f(R) depends on
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*> the details of S (in the best case, the rule is vacuous, in the worst
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*> case, it is as complicated a f(GLUT) itself). Generally, however, it
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*> will have much higher KC than R.
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*>
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*> So, schematically, R is an approximation of GLUT, while f(R) is an
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*> approximation of f(GLUT). However, generically, R will be much simpler
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*> than GLUT, and much simpler than f(R) is vis-a-vis f(GLUT).
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*>
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*> That is the mathematical statement of the original idea; there are
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*> equivalents when we replace the original GLUT with some object C that
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*> has less Kolmogorov Complexity. If we call C consciousness, and R is
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*> some simple, crude approximation of C, we can't expect that f(R) is a
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*> SIMPLE approximation of f(C). Hence my point for distinguishing between
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*> hash-function-equivalent setups.
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*>
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*> And ultimately, maybe, between consciousness and an equivalent GLUT.
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*>
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*>> > ...Many thanks. However, the red herring is still, in my view, a
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*>>
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*>> > distinction between a GLUT and a hash-equivalent GLUT.
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*>>
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*>>
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*>> I probably don't understand that. You did just get through pointing out
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*>> a vital difference between the GLUT in polynomial form, and a GLUT
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*>> in some hash function equivalent form. So what does the latter mean?
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*>
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*> Sorry, me bad and incompetent: "between a rule and a hash equivalent GLUT".
*

**Next message:**Stathis Papaioannou: "Re: The GLUT and functionalism"**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: The GLUT and functionalism"**Reply:**Stuart Armstrong: "Re: The GLUT and functionalism"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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