[FOM] The irrelevance of Friedman's polemics and results
hendrik@topoi.pooq.com
hendrik at topoi.pooq.com
Mon Feb 6 13:03:57 EST 2006
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
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