FOM: Rota's United Front versus f.o.m.

[Stephen G Simpson]

In my FOM posting of 13 Oct 1998 00:32:15, I reported on the first 15
chapters of Gian-Carlo Rota's book `Indiscrete Thoughts'.  I now want
to finish the task by reporting on the rest of the book, chapters 16
through 21.

Chapters 16 and 17 are an attempt to popularize Heidegger's ideas on
identity.  They left me cold, so I won't comment on them.  

Chapters 18 through 21 are, as I said in my earlier posting, "a
grab-bag of gossip, book reviews, advice for young mathematicians,
etc."  Of these chapters I also said:

 > There is reason to believe that they will disgust me, because some
 > of Rota's ideas and practices regarding evaluation of mathematical
 > writing and research are known to be cynical in the extreme.

I can now report that, as I feared, Rota's views did disgust me
considerably.  I am referring specifically to Rota's cynical idea that
it's always wrong for mathematicians to criticize each other.  Rota
expounds this in an avuncular essay entitled `Ten Rules for the
Survival of a Mathematics Department'.  Among the ten rules are:

  1. Never wash your dirty linen in public.
  3. Never compare fields.
  8. View the mathematical community as a United Front.

Rota is saying that there is to be no explicit evaluation of the
relative merits of various research directions in the mathematical
sciences; no debunking of exaggerated claims; no criticism of
unethical practices; no attempt to expose secret deals.  In short, NO
STANDARDS.  See no evil, hear no evil, speak no evil -- those are the
Rota rules.  And the rules apply doubly in the presence of
non-mathematicians.  In other words, NO GENERAL INTELLECTUAL
STANDARDS.  Mathematics is to be a Closed Shop (another trade union
term) run by secret committees meeting in smoke-filled back rooms.

I'm sorry Gian-Carlo, but as a man of the Enlightenment I find this
repulsive.  

I believe in standards.  See my FOM postings of 13 Aug 1998 15:23:45
and 14 Aug 1998 13:42:53 on "the need for standards".  

I believe in general intellectual standards and the unity of human
knowledge.  See my FOM postings of 13 Jan 1998 13:29:45 and others on
"the unity of human knowledge" and "general intellectual interest".

In addition, I want to point out that the Rota rules would, if
followed, have an especially devastating effect on f.o.m. within
mathematics departments.  This is because of the peculiar logical
relationship between f.o.m. and core mathematics.  Because of this
logical relationship combined with a general trend toward
compartmentalization, the typical second-rate core mathematician's
attitude toward logic and f.o.m. is one of ignorance, prejudice, fear,
and hostility.  Contrast this with the great prestige enjoyed by
mathematical logic and f.o.m. vis a vis other fields such as computer
science, information science, and philosophy.  Even while mathematical
logic is being undercut and denigrated by core mathematicians, it
looks much, much better to outsiders.  From this I conclude that, if
general intellectual standards were to be excluded from the
mathematics community, then f.o.m. would die a slow death at the hands
of bigoted core mathematicians.  This would be just one bad
consequence of the Rota rules, were we to obey them.

Let me end this message on a lighter note by saying that Gian-Carlo
Rota was one of my revered teachers at MIT, and I still consider him a
good friend and colleague.  Ten days ago he and I sat next to each
other at a banquet in honor of George Andrews, and we had a nice talk
about the "United Front".  I made some of the points above.
Gian-Carlo responded by saying that he is only "telling it like it
is", i.e. presenting things as they are rather than theorizing about
how they ought to be.  Is that "as" in the sense of "Fundierung"?  

A typical Rota-ism: "Cynicism is that which we don't like to hear."
Without attempting to refute that bromide, I'll simply ask the FOM
list: Which is it going to be?  The Rota rules, or f.o.m. and high
standards?  You decide.

-- Steve

P.S. I'm arranging for a copy of my new book `Subsystems of Second
Order Arithmetic' to be sent to Rota's journal `Advances in
Mathematics' for review.  This could get interesting!

Name: Stephen G. Simpson
Position: Professor of Mathematics
Institution: Penn State University
Research interest: foundations of mathematics
More information: www.math.psu.edu/simpson/