Subject: categories: ridiculously abstract

From: Peter Freyd <[email-masked]>
Date: Tue, 28 Nov 2000 14:20:14 -0500 (EST)

If you take a look at 

     http://slate.msn.com/diary/00-11-27/diary.asp?iMsg=1

  you will find (in a column by Jim Holt) that "Category theory is a
  ridiculously abstract framework that takes all the meaning out of
  mathematics." At the end of the column is an invitation to make
  comments. (Please don't!) Only one such comment seems to be about
  category theory and it's this beauty:

Subject: category theory
From: John Rooney
Date: 28 Nov 2000 09:49
                                  
Category theory was not so bad when the Poles invented it. It was sort
of like reinventing the parts of speech or the distinction between
accident and substance. Later it was like subject and predicate, noun
and verb. The Dutch logicians have made it quite obscure. Here's to
better understanding of category theory and a less defeatist attitude.

  (This almost makes sense if you substitute "categorial grammar" for
  "category theory". But if you do that you then have to turn Jim
  Lambek into a Pole.)

  Here's the full Holt column. I'm certain that any attempt to counter
  the statement about category theory -- given the mood of the piece
  -- can only fail.

DIARY: Infiltrating the Mathematicians' Lair.

Jim Holt is a member of the Mathematical Sciences Research Institute
at the University of California, Berkeley, and a columnist for Lingua
Franca. His book on the history of the infinitesimal, Worlds Within
Worlds, will be published next fall.
                         
Posted: Monday, Nov. 27, 2000, at 4:00 p.m.  PT

Being at MSRI is a bit like going to heaven without all the bother and
expense of dying. I don't mean the sort of heaven where you wear
ermine and eat foie gras to the sound of trumpets. I mean the sort
where you spend your days languidly communing with beautiful,
timeless, abstract ideas: Platonic heaven.

MSRI stands for the Mathematical Sciences Research Institute. It is
the premier think tank in the world for pure mathematics. Even its
location is heavenly: It is housed in a Corbusian glass-and-wood
structure perched atop the loftiest of the hills above the University
of California at Berkeley, just below the ionosphere. From my office
window, I gaze down upon the skyscrapers of San Francisco, the isle of
Alcatraz, the Golden Gate Bridge, the Pacific Ocean. In a few minutes
I will leave my office, traverse some pristine white hallways, and
join a hundred of the most eminent mathematicians from around the
world in a commodious lecture room. Today's topic for contemplation:
the linear p-adic group, the p-adic Galois group, and the p-affine
Schur algebra.

But wait. I am not a mathematician (although I have sometimes
pretended to be one on NPR). I am a "trivial being," to use Paul
Erdos' term for those who are not among the mathematical elect. So
what am I doing in this Platonic heaven? I am here as a journalist in
residence. My mandate is to convey a little of the flavor of what goes
on in these ethereal precincts to my fellow trivial beings back in the
material world. I also cannot help thinking of myself as an
anthropologist, living among an alien tribe and observing their often
strange folkways. I must be careful not to give them measles.

How can I blend into this august tribe? As a longtime mathematical
dilettante, I sometimes understand a little of what they are saying. I
also do a good bit of faking. Luckily I have come up with a set of
all-purpose trick questions that have kept my ignorance from being
exposed in many a treacherous conversation. For example:

"Can that result be restated in terms of category theory?" (Category
theory is a ridiculously abstract framework that takes all the meaning
out of mathematics.)

"Isn't the constant in that equation suspiciously close to the square
root of pi divided by e cubed?"

"Wasn't your theorem prefigured in the work of Euler?" (Leonhard
Euler, who lived in the 18th century, was the most prolific
mathematician in history; nearly everything is prefigured in his
work.)

"But can you prove that lemma for the case of n=3?"

By the shrewd use of such feints, I, a trivial being, have been able
to chat as an apparent peer with many of my colleagues at MSRI. Above
all, I am careful not to let conversations about things like p-adic
Galois groups go on for too long. When skating over thin ice, speed is
your ally.