RE: pots and kettles

RE: pots and kettles

[Marta Bunge]

Dear Paul,


>I suggest that he and Marta Bunga should go for a long walk to calm down.

First of all, my name is Marta Bunge (not Bunga), in case you never saw it
written. Secondly, I do not understand why Eduardo and I are put together in
this, when we wrote independently to the categolries list -- is it because
we are both Argentinians? (The Malvinas-Falklands war is over and both of
our governments profitted from it; no need to keep the antagonism open.)
Thirdly, I cannot go for a long walk in this weather (very cold in Montreal,
in case you did not know), although your advice is probably good (my doctors
would agree with you). Finally, I think that it is you who needs to take it
easy. I hope that from now on this discussion will be civilized and about
ideas, not people -- or else I will be really sorry that I started it!

Best wishes,
Marta

Re: pots and kettles

[jim stasheff]

"generalised abstract nonsense"
I'm pretty sure it was current while I was a grad student at princeton
1956-58

it wasn't necessarily perjorative

category theory certainly applies marvelously to knot theory

but Yetter should wade in on that aspect

jim



Paul Taylor wrote:
>
> I wonder when the phrases "generalised abstract nonsense" and "empty set
> theory" came into circulation?   I seem to remember hearing them when I was
> an undergraduate.
>

pots and kettles

[Paul Taylor]

I wonder what Eduardo Dubuc means by "the Benabou-Taylor confrontation".
Could he possibly be referring to the Christmas flame-war to which Eduardo
was himself a major contributor, but which I attempted to settle with him
privately and amicably?

I suggest that he and Marta Bunga should go for a long walk to calm down.

I'm not pointing any fingers at Eduardo or Marta, but those who were active
in category theory in the 1960s and 70s would be well advised to think twice
before accusing those who came later of bringing category theory into disrepute.

I wonder when the phrases "generalised abstract nonsense" and "empty set
theory" came into circulation?   I seem to remember hearing them when I was
an undergraduate.

I wonder which generation it was that got prestigeous jobs in mathematics
departments at a time when (at least in Britain) they were being given away
in corn flakes packets?   Which generation is it that struggles to get jobs
in computer science departments?  Which subject was it, according to the
participants of a parallel conference in Vancouver in 2004, whose followers
were "easily recognisable because they're all so old"?

Which generation was it that alienated other mathematicians by making
outrageous claims about the foundations of mathematics that it never
backed up with theorems?   Which generation actually got its hands dirty
and proved the theorems that relate category theory to other foundational
disciplines?

I have no idea what John Baez's standing is amongst physicists. Therefore
Marta is quite correct in warning me that it would be foolish for me to
base public claims of the value of category theory on its applications
to physics.   John is nevertheless very welcome in our community, in my
humble opinion, BECAUSE he brings in new ideas from physics, BECAUSE
he exports some of our ideas in return, and because he is good at
presenting ideas of either kind.

Also, I don't need to be specific about them to say that the applications
to physics, computation, topology, geometry, analysis, ... are the reasons
why I consider that category theory is a Good Thing.   In my experience,
category theory as a tool usually points me in the right direction, whereas
set theory usually points me in the wrong one.  (To give credit where
it is due, Jamie Gabbay's work on alpha-equivalence is a counterexample.)

Category theory has been successful on many many occasions - starting in
algebraic topology - in removing the clutter of ad hoc definitions that
have no conceptual anchor.   For example, I was once told that "a matrix
is an array of numbers".   I am currently looking into Interval Analysis,
in which all of the textbooks begin with a chapter of miscellaneous notation
based on defining an interval as a pair [a,b] or as the subset of classical
real numbers that lie between them - "analysis with double vision", as
I call it.   (To give credit again where it is due, the "Interval Newton"
algorithm is a genuine insight into solving equations - it does not just
do what you might imagine it does.)

So I urge Marta, Eduardo and everybody else to stop trying to "police"
category theory, and instead celebrate its achievements in many areas of
mathematics.

Paul Taylor
www.cs.man.ac.uk/~pt - new web pages and new stuff.