FOM: affectionate jokes, reply to Simpson
cxm7 at po.cwru.edu
Sun Mar 15 15:33:50 EST 1998
Reply to message from simpson at math.psu.edu of Sun, 15 Mar
Simpson quoted Friedman
> > I have said on the fom that categorical foundationalists have a
> > profound misunderstanding of f.o.m. I claim that this is worse than
> > Simpson.
>Yes indeed, that's "worse" (i.e. more pointed and provative) than
>anything I've said on the FOM list. But many mathematicians routinely
>say even worse things, e.g. when they refer to category theory as
Friedman has indeed been more "pointed and provocative"
than Simpson, and that's fine. No one is complaining about "pointed,
provocative" posts. Some people have complained about combative
ill-informed posts, and this reference to "abstract nonsense" is
Friedman brought the same term up in an earlier post, but
he noted that it is usually used jokingly by people who like
category theory. The story ought to be well known by now.
Norman Steenrod first hung this tag on category theory.
He had spent years trying to axiomatize homology, encouraged by
Solomon Lefschetz. Lefschetz had also backed the young topologist
Sammy Eilenberg, and encouraged Eilenberg's collaboration with the
algebraist Mac Lane explicating certain calculations in homology.
When Eilenberg and Mac Lane created category theory, Steenrod saw
he could use their way of emphasizing morphisms at least as
much as objects. He happily said this "abstract nonsense"
was the key to solving his problem.
The phrase was popularized by Lang's ALGEBRA, which
had an index entry under "abstract nonsense". The page numbers
sent you to various one line proofs such as "By abstract
nonsense, tensor products are unique up to isomorphism when
they exist". The joke got old and survives only vestigially in
the latest edition.
When you take an old affectionate joke to be a "worse"
condemnation, it shows a general lack of attention to the
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