Subject: categories: Re: cracks and pots

From: dusko <[email-masked]>
Date: Thu, 16 Mar 2006 04:05:46 -0800

On Mar 15, 2006, at 5:35 AM, RFC Walters wrote:

> The category theory community seems happy to accept uncritically, and
> give centre-stage to, any interest shown by an external field. In this
> context one should certainly look the gift horse in the mouth.

i think this is a very nice metaphor. but i am not sure that being
critical about science is as easy as looking in horses mouth. already
hilbert was largely wrong when he tried to prescribe a shape of a
science. and nowadays it is a much harder task. everyone sees just a
very small fragment. research advances by evolution, not by
intelligent design.

the division between pure and applied mathematics is not as simple as
it used to be. 20 years ago, if you wanted to work on something that
would never ever degrade into applications, then algebraic geometry
probably seemed like a good bet. nowadays, at each moment, millions
of transactions on the internet are secured using elliptic and
hyperelliptic curves; the structure of their picard groups is
discussed in standardisation bodies. if a bank protects its customers
from phishing by identity-based keys, they are using weil or tate
pairing...

so the purest math has become the most applied; the most spiritual
the most concrete. the other way around, these applications put a
babylonian library on everyone's desk. what was picard group again?
google for it. biology research is based on large public databases.
physics is documented (driven?) by blogs. even category theory is
discussed online.

so i think it is great that people get nasty, or personal about
category theory. the landscape of babylon: "the dog barks while the
caravan goes by."

just my 2p,
-- dusko