Philosophic Noodling (was Re: Internet Health)
Levi Pearson
levipearson at gmail.com
Wed Oct 6 11:06:38 MDT 2010
On Wed, Oct 6, 2010 at 8:48 AM, Paul Seamons <paul at seamons.com> wrote:
> While I find the discussion about what is "real" intriguing, after some
> time I finally give up and laugh and remember what little I understand
> of Godel's Incompleteness theorem, essentially that a comprehensive
> definition of a system can't be gathered while constrained to the that
> same system. I eventually end up at your conclusion that even though I
> can't explain everything perfectly, my accepted definitions of them are
> useful and meaningful to me. I don't know how time operates
> fundamentally, but I can measure it consistently and reliably; and it is
> useful enough to me to know that from my frame of reference time passes
> by far too quickly, and sometimes not fast enough.
Godel's Incompleteness theorems are very interesting and have some
pretty deep implications in the field of mathematics, but some people
give them a bit more philosophical weight than they actually deserve.
What they actually do is prove that a certain kind of formal system
(one that is recursively enumerable, or from which all the theorems in
it can be mechanically generated from its axioms) cannot prove all
statements expressible in the system that describe true facts about
the natural numbers. The second theorem shows that a theorem that is
capable of proving true facts about the natural numbers cannot also
prove its own consistency (i.e., that it does not enumerate both a
statement and its inverse).
There still can be systems that are both consistent and complete so
long as they do not meet the criteria for Godel's theorems. They can
still include the natural numbers so long as they aren't expressive
enough to define the natural numbers or develop their basic
properties. There are complete and consistent formulations of
Euclidian geometry that don't fall under Godel's theorems, for
example.
Anyway, there are things besides the limits of formal systems that
prevent us from peering too deeply into the fabric of the universe, so
we may have to be content with dealing with approximations, models,
and speculations without ever being able to prove that any one model
has an absolute correspondence to the very basic physical properties
of the universe.
> And to return to a slightly more on topic and flame-able subject,
> spending too much time worrying about the reality or dimensionality of
> time is akin to using a graphics only screen saver that consumes 80% CPU
> (it is nice to look at and pass the time but wastes a lot of energy not
> getting anything done).
Sure, but the screen saver *does* prevent the burn-in of the phosphors
on your CRT monitor! Actually, although modern displays don't have a
"burn-in" problem, Plasma and OLED displays with their individual
light-emitting elements do have an issue with uneven wear, so if you
use either of those display technologies you should be aware that
static images could cause image ghosting problems over time, though
not in precisely the same way as CRT burn-in.
--Levi
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