From: Stuart Armstrong (email@example.com)
Date: Mon Mar 31 2008 - 07:59:16 MDT
We got on this point after a long tortuous route: so let's simplify!
S = a finite set of polynomials.
G = a GLUT on S.
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.
f = a hash function from S (to f(S))
f(G) = the GLUT on f(S) equivalent to G on S.
f(R) = the rule on f(S) equivalent to R on S.
Main point: G has very high KC (as does f(G)), R has low KC, but f(R)
has high KC.
Theorem (which will be left as as excercise to the reader - i.e. I
haven't caluclated it, but it seems obvious):
KC(f(R)) / KC(f(G)) can be made arbitrarily higher than KC(R) / KC(G) .
Corrolary: 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 consiousness, (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.
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