G'day all.
Quoting "Richard A. O'Keefe" <[EMAIL PROTECTED]>:
(5) Precisely because it seeks generality, category theory seems
difficult to "concrete thinkers". And books on category theory
tend to be extremely fast-paced, so ideas which are not in themselves
particularly esoteric (which may in fact be eminently practical)
tend to be presented in a way which people trying to study by
themselves have trouble with. So people can be scared off by
what _ought_ to be a big help to them.
I agree, but I don't think it needs to be this way.
Books on category theory tend to be written for mathematicians or
computer scientists who already grok the things that need generalising,
even understand in a general sense how they're similar, and really just
need to learn the language to express what they already know.
In one respect, this makes sense (you learn the concrete, then you learn
how to abstract away the details), but it also raises the barrier to the
point where in learning mathematics, you're really learning history.
Mathematics isn't immune from this, of course. Many scientists in
disparate fields have complained that textbooks for their fields are
really history books in disguise, and the material is more confused and
tedious than it needs to be as a result.
Example complaints:
http://insti.physics.sunysb.edu/~siegel/history.html
http://jchemed.chem.wisc.edu/journal/issues/1998/jul/abs817.html
Cheers,
Andrew Bromage
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