Re: what relation do mathematical models have with reality?

From: Hal Finney <hal.domain.name.hidden>
Date: Fri, 22 Jul 2005 23:14:42 -0700 (PDT)

Colin Hales writes:
> The idea brings with it one unique aspect: none of the calculii we
> hold so dear, that are so wonderful to play with, so poweful in their
> predictive nature in certain contexts, are ever reified. None of them
> actually truly capture reality in any way. They only appear to in
> certain contexts. The only actual mathematics that captures the true
> nature of the universe is the universe itself as a calculus. It doesn't
> invalidate the maths we love. It just makes it merely a depiction in a
> certain context. Very useful but thats all.

You might like this quote from John Wheeler, in his textbook Gravitation written
with Charles Misner and Kip Thorne, which perhaps expresses a similar idea:

: Paper in white the floor of the room, and rule it off in one-foot
: squares. Down on one's hands and knees, write in the first square
: a set of equations conceived as able to govern the physics of the
: universe. Think more overnight. Next day put a better set of equations
: into square two. Invite one's most respected colleagues to contribute
: to other squares. At the end of these labors, one has worked oneself
: out into the door way. Stand up, look back on all those equations,
: some perhaps more hopeful than others, raise one's finger commandingly,
: and give the order `Fly!' Not one of those equations will put on wings,
: take off, or fly. Yet the universe 'flies'.

My current view is a little different, which is that all of the equations
"fly". Each one does come to life but each is in its own universe,
so we can't see the result. But they are all just as real as our own.
In fact one of the equations might even be our own universe but we can't
easily tell just by looking at it.

Hal Finney
Received on Sat Jul 23 2005 - 03:09:37 PDT