FOM: Canonical non-computable number?

[Kanovei]

> Date: Fri, 7 Sep 2001 17:31:24 -0400 (EDT)
> From: William Calhoun <wcalhoun at planetx.bloomu.edu>
  
> I think the definition of "canonical" needs to be considered.  To think
> this through, I'm going to consider an analogous question:  What is a
> canonical irrational number? 

This does not seem to be a meaningful question 
(neither does a version for non-algebraic numbers). 
Indeed, the word *canonical* is used in mathematics mostly as 
*canonical form of such-and-such equation* etc, 
meaning that any equation (or other object considered) can be 
transformed to a canonical equation so that something essential 
is preserved. 

An assertion like "$\pi$ (or sqrt(2)) is a canonical irrational" 
just cannot be thought of this way. 
The simplest known, perhaps, but not canonical. 

> Finally, why is pi a canonical irrational?  It is canonical in the sense
> that it is a constant that naturally appears everywhere 

If we really have in mind extraterrestrials, *everywhere* is too a 
strong description, because in spaces with very different geometry 
(in vicinity of a black hole, for instance) 
\pi may naturally appear only as one of dosens funny constants 
in depths of advanced papers.  

V.Kanovei

PS. I add a note of condolence to FOM colleagues in NYC and Washington