FOM: Steve's barber; Lou on Faltings' theorem

[Stephen G Simpson]

Steve's barber:

John Baldwin writes:
 > So maybe this is too low a level for `general intellectual interest'.
 > Although I thought Steve mentioned his barber.

I mentioned barbers in the course of arguing against the view that
Faltings' theorem (stated as a theorem about rational points on
curves) is automatically of general intellectual interest.  Part of
the argument is as follows:

  You could certainly explain the interest of curves to your barber
  (in terms of curly hair, baseball pitches, off-ramps, etc) and you
  would probably even be able to explain the interest of rational
  numbers to your barber (in terms of percentages, the income tax,
  cutting up a pizza, etc.).  But I think you might have a much more
  difficult time explaining the interest of rational points on curves
  and Faltings' theorem to your barber.  Of course I wouldn't rule out
  the possibility; if you do manage to find a way to explain the
  interest of rational points on curves to your barber, more power to
  you.

However, all this talk about barbers is merely a crude surrogate for
the very serious and important foundational issues that we are
discussing.  Harvey has explained this surrogate relationship very
well.  The need for crude surrogates arises from the sad fact that
many people, even many scientists, are congenitally incapable of
appreciating the foundational point of view, because they can't grasp
the meaning of key statements of the form "X is more basic than Y with
respect to the hierarchy of concepts", or even "X is of general
intellectual interest".  Such people just don't get it; the
foundational perspective makes no sense to them.  Perhaps the only way
to communicate with these people at some level about foundational
issues is to replace "X is more basic than Y" by crude surrogates such
as "barbers are interested in X but are not interested in Y".  They
still won't really get the point, but at least there is some sort of
basis for discussion.

Lou on Faltings:

I'm very happy with the way our exchange about Faltings' theorem has
progressed.  At first I thought it was leading nowhere, but now we are
getting to some serious issues.  It's exciting that Lou has promised
to explicate the general intellectual interest of Faltings' and other
famous theorems of number theory.  I'm looking forward to Lou's
posting after he has looked up the necessary references and done the
necessary research.  This may turn out to be an example of how pure
mathematics can profit from the foundational perspective.

-- Steve