From: Lee Corbin (lcorbin@rawbw.com)
Date: Sun Mar 30 2008 - 23:10:39 MDT
Stuart writes
> It seems differentiation is not the example to invoque [invoke] here.
>
> But the original idea can be adapted, as follows: let us define some
> other functional on the set of polynomials, via a GLUT, with
> maximalish Kolmogorov Complexity,
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
> to polynomials of the (n-1)th degree.
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
> GLUT, called f(GLUT), of pretty much same complexity. The rule about
> polynomials is mapped to an equivalent rule f(R) on f(S),
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
> with an ordered partition of f(S). The complexity of f(R) depends on
> the details of S (in the best case, the rule is vacuous, in the worst
> case, it is as complicated a f(GLUT) itself). Generally, however, it
> will have much higher KC than R.
>
> So, schematically, R is an approximation of GLUT, while f(R) is an
> approximation of f(GLUT). However, generically, R will be much simpler
> than GLUT, and much simpler than f(R) is vis-a-vis f(GLUT).
>
> That is the mathematical statement of the original idea; there are
> equivalents when we replace the original GLUT with some object C that
> has less Kolmogorov Complexity. If we call C consciousness, and R is
> some simple, crude approximation of C, we can't expect that f(R) is a
> SIMPLE approximation of f(C). Hence my point for distinguishing between
> hash-function-equivalent setups.
>
> And ultimately, maybe, between consciousness and an equivalent GLUT.
>
>> > ...Many thanks. However, the red herring is still, in my view, a
>>
>> > distinction between a GLUT and a hash-equivalent GLUT.
>>
>>
>> I probably don't understand that. You did just get through pointing out
>> a vital difference between the GLUT in polynomial form, and a GLUT
>> in some hash function equivalent form. So what does the latter mean?
>
> Sorry, me bad and incompetent: "between a rule and a hash equivalent GLUT".
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