Reality is as reality is. Difference equations and pi are part of our
language, and I'm not sure whether it is interesting to speculate how
completely we are able to describe reality. I think Bruno's post below sums
up a broad and important point, namely that the 'mapping' of an infinite
sequence of integers onto reality is something that we do. There is no
objective mapping.

> -----Original Message-----
> From: Niclas Thisell [SMTP:[EMAIL PROTECTED]]
> Sent: Wednesday, January 05, 2000 10:38 AM
> To:   'Marchal'; [EMAIL PROTECTED]
> Subject:      RE: Renormalization
> 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 

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