From: Mike Dougherty (msd001@gmail.com)
Date: Mon Jan 05 2009 - 21:35:35 MST
On Mon, Jan 5, 2009 at 10:20 PM, Peter de Blanc <peter@spaceandgames.com> wrote:
> My objection is to the statement "If X simulates Y, then K(X) > K(Y)."
> There's no such theorem. For example, you could write a program which
> simulates every possible program. This program would have some fixed
> complexity K, but since it simulates every program, it will simulate some
> with complexity >K.
re: "You could write a program which simulates every possible program"
No I can't. I am mostly certain that you can't either.
We have devised some means to categorically deal with situations that
are beyond countability. "Infinity" is a simple label for a concept
that can be described but not quantitatively expressed. A program
which simulates every program is the same kind of impossible as a
number that contains every other number. K(magical handwaving) is not
infinite and not zero; it's simply not meaningful.
Upon reconsideration of your original request to cease with
'pseudomathmatics' - I will concede that K(a0) > K(a1) isn't something
you can 'math' on a Wal-Mart calculator. You can probably also agree
that the rigorous proof required to assert the calculus of K as a
measure of complexity exceeds the available bandwidth (and interest)
of an email discussion - especially since (with few possible
exceptions) everyone reading this list has internet access to research
the key concepts.
I agree with Vladimir Nesov's point earlier: the definition of
"simulate" as I believe Matt is using it would require that the larger
machine have exactly a bit-for-bit representation of the smaller
machine contained within it. If we define simulation more loosely as
in "weather simulation" where there are rules built from observation
that model future behavior - then it is possible to contrive a
scenario where we might discuss a smaller machine modelling a larger
machine within some tolerance of lossy compression or other divination
of state. After all, our limited intelligences believe we have a
model of the universe in which we live - which might forever be
Incomplete.
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