[FOM] The irrelevance of Friedman's polemics and results

[hendrik@topoi.pooq.com]

On Fri, Feb 03, 2006 at 12:58:40AM +0200, Eray Ozkural wrote:
> On 2/2/06, hendrik at topoi.pooq.com <hendrik at topoi.pooq.com> wrote:
> > Practicing physicist seem to act as if every set of real numbers is
> > measurable, for example.
> 
> I believe this is an interesting point. So why do physicists think
> of R as an adequate model for "real" space geometry
> at all? Is it just an accident of history or do they seriously believe
> that unmeasurable things exist?

It is, I believe, an accident of history.  Back few hundred years ago, 
mathematics and physics pretty well agreed on the nature of real 
numbers.  But I the physicist has no need for unmeasurable things or 
the axiom of choice, a direction mathematicians seem to have chosen.
Physicists would be better served by the alternative axiom that bounded 
sets of real numbers are measurable.  But the physicists are generally 
not concerned with such esoterica.  When I confront one with such an 
unmeasurable function, he smiles at my attempt at humour or says 
condescendingly that that isn't the kind of function that occurs in 
physics.  The R of mathematicians doesn't quite fit the needs of 
physicists,  but the physicists are not concerned with such esoterica.  
They might be better served with a different R,  but the mathematicians' 
R is servicable enough.  It's easier, when a physicist is being 
pedantically rigorous, to sprinkle the adjective "measurable" 
liberally in his paper than to explain he are using a completely 
different conception of real numbers.

As I have said before, the upward path of theories of ever ascending
strength is not unique.  While it may be important for some FOMers for
it to be so, the resulting escalator does not necessarily serve 
applications well.

Or are the theoretical physicists to be denied the status of "core 
mathematicians"?

-- hendrik boom