From: Stuart Armstrong (dragondreaming@googlemail.com)
Date: Thu Mar 27 2008 - 07:59:40 MDT
> I don't quite understand, or perhaps it's merely that I don't agree.
Your comment showed you didn't understand the point. However,
rereading the point, I realised the point was utterly wrong, which
kind of undermines my feelings of smug superiority :-) It seems
differentiation is not the example to invoque 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, subject to only one rule "R": it
maps polynomials of the nth degree to polynomials of the (n-1)th
degree.
We then hit the set S 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), 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 distingushing 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".
Stuart
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