RE: Renormalization

From: Niclas Thisell <niclas.domain.name.hidden>
Date: Wed, 5 Jan 2000 11:37:55 +0100

Marchal wrote in part
<snip>
> With a UTM using dynamical data structure, you
> don't even need to specify the needed precision. So the program using
> arbitrary great precision is the shorter program. You don't need busy-
> beaver for generating vastly huge outputs, the little
> counting algorithm
> does it as well, though more slowly but that is not relevant for the
> measure.

Perhaps I wrote faster than I could think yesterday. And I write pretty
slowly.

If we assume that the universe can be simulated by a set of difference
equations and sums that only involve '+', '-', '*' and '/', we can
indeed get away with using rational numbers with Lisp-type integers (or
unary lists or whatever). Of course, mathematical models of the universe
do tend to include some pi:s and stuff. But they can hopefully be baked
into fundamental constants or gotten rid of altogether by change of
units.

This part of the problem is then indeed shifted to simply specifying the
set of fundamental constants. They too must be specified, but they don't
really require an insane 'precision'. And if this really is the case,
and the lattice resolution is finite, we should expect fundamental
constants to be rational numbers, I guess (!?!).
But the question on lattice resolution remains; Will the difference
equations and sums be indistinguishable from differential equations and
integrals? If so, the 'rationality' of the fundamental constants may
vanish.

Best regards,
Niclas Thisell
Received on Wed Jan 05 2000 - 02:45:32 PST