FOM: Re: General intellectual interest/challenges

[Torkel Franzen]

   Harvey Friedman says:

   >What's at stake is: a defendable and appropriate
   >approach to intellectual life, open to everyone; or an indefensible and
   >inappropriate approach to intellectual life, open to only an inner circle.
   >Open insight for everybody to see, versus imbred technicalities and secret
   >backroom deals.

   A splendid manifesto, but hardly one that is supported by harping on
the supposed intellectual openness of talk about P=NP - or the
foundations of mathematics - as opposed to the deplorable backroom
mentality of number theory, or mainstream mathematics in general.

   Your conviction that P=NP is both interesting and easily understandable
to a general audience is most commendable, and no doubt conducive to
zeal and enthusiasm in your own presentations, but not altogether in touch
with reality. (That P=NP means "polynomial equals non-polynomial" is,
I might add, a view not infrequently expressed on the net by - American -
college students.)

   Consider Godel's work, which you yourself mentioned. There is
nothing in logic that has wider general appeal than the incompleteness
theorems.  Nevertheless these are perhaps more often misunderstood and
misapplied than not, and this not only by college students, but by
professional mathematicians, scientists, philosophers. As for Godel's
other work, it is simply unknown to a general audience, for all its
significance.  It is hardly to be expected that any other work in
logic will do better. In particular, reverse mathematics will most
likely seem not only supremely boring, but largely incomprehensible,
even to an audience of intelligent professionals.

   I quite agree that we should all, to the best of our ability (and
different kinds of abilities are needed in all fields) try to make our
activities open, understandable, potentially interesting to a general
audience. Dreaming up unrealistic prospects or indulging in strenuous
squabbling is not a good way of achieving this, however. Further, how
well we succeed, and how interested we are in this sort of thing,
isn't determined by what field we are working in, or what problems we
are working on, but by our general inclinations and abilities.