Re: Pi in space

From: Eray Ozkural exa (examachine_at_gmail.com)
Date: 12/06/04 

Date: 5 Dec 2004 16:07:19 -0800

israel@math.ubc.ca (Robert Israel) wrote in message news:<covlk6$m2h$1@nntp.itservices.ubc.ca>...
> In article <320e992a.0412050031.7b70c67@posting.google.com>,
> Eray Ozkural exa <examachine@gmail.com> wrote:
>
> >The concept of Pi, however, should not be regarded transcendental or
> >anything like that since it is represented perfectly with a small
> >program. True, it is an idealization, but what is transcendental? In
> >my opinion, nothing transcends physical reality, and if Pi is part of
> >physical models, it is for a good reason: physics is mostly about
> >ideal models that work in ideal conditions, etc.
>
> I think you need to look up the definition of transcendental number.
> You seem to be confusing it with some philosophical notion.

Thanks for the suggestion Robert, but I don't see how he talks about
the concept of a transcendental number. AFAICT, the notion of a
transcendental number is not relative to a give geometry, or the true
geometry of our universe. Pi is a transcendental number, according to
the definition of a transcendental number in mathematics. I do think
his question ought to be philosophical. Why should he talk about
relativity then? What difference is there between any continuous
metric and a Riemann tensor regarding the fact that Pi is a
transcendental number?

Maybe, I think, his friend's intention was to give a better definition
of what it means for a number to be transcendental than the ordinary
usage. He might want to pick another term, though, or highlight the
difference than the ordinary usage carefully. Otherwise, we become
confused in argumentation. I thought so, and said that this
philosophical sense is probably irrelevant to a computable real like
Pi which captures a general geometric fact in a compact form!

Regards, 

--
Eray Ozkural