Re: Computational irreducibility and the simulability of worlds

From: Eric Hawthorne <egh.domain.name.hidden>
Date: Sat, 17 Apr 2004 09:26:41 -0700

Hal Finney wrote:

> How about Tegmark's idea that all mathematical structures exist, and we're
>
>living in one of them? Or does that require an elderly mathematician,
>a piece of parchment, an ink quill, and some scribbled lines on paper in
>order for us to be here?
>
>It seems to me that mathematics exists without the mathematician.
>And since computer science is a branch of mathematics, programs and
>program runs exist as well without computers.
>
>
Ok, but real computers are "math with motion". You have to have the
program counter touring
around through the memory in order to make a narrative sense of anything
"happening".

Mathematics, being composed of our symbols, is an abstract
"re-presentation". I think what Tegmark
must be saying is that "something" exists which is amenable to
description by all self-consistent
mathematical theories (logical sentence sets) , and by no inconsistent
theories. To me, this is just
equivalent to saying that "all possible configurations of differences
exist" and that any SAS that
represents its environment accurately (e.g. via abstract mathematics) is
constrained, by its own
being part of the information structure, to only perceive
self-consistent configurations of differences
as existing. Self-consistency of mathematical theory, as it translates
from the representation level
to the represented level, just means that things "perceived" can only be
one way at a time, and that's
the kind of thing that a consistent mathematical theory describes.
Received on Sat Apr 17 2004 - 12:45:17 PDT