SQ

Re: Conceptual Mathematics: A First Introduction to Categories (Paperback)
by F. William Lawvere (Author), Stephen Hoel Schanuel (Author)

Even genius has its limitations.
Stupidity is not thus constrained.

Unfortunately, I keep demonstrating the second half of the couplet. For some time I have owed Arun a response on his question, but have delayed out of feelings of guilt:

Did you get much beyond Brouwer's theorems?

A funny thing happened when I tried to do Exercise 1 in the Brouwer's theorem chapter. I hit a pole in my stupidity quotient. I am convinced that it is pretty easy, but every time I thought about it, my brain found a good reason to be somewhere else. So for a couple of months I just stopped.

I finally decided to just go on, and have worked about the next dozen or so exercises in Article III, but that's as far as I've gotten.

It is a very good book, but I'm unable to take any of the ideas and apply meaningfully to anything outside the book, and so am feeling a bit frustrated. Probably need to think a lot more and with more patience

I haven't found any real application either, but I have toyed with a couple of ideas. You might recall that Malcolm Gladwell, in his New Yorker article on IQs, mentioned that the KhoiSan, when asked to group objects, always picked functional relationships (knife cuts potato) rather than taxonomic (knife is like spoon). I think that that is analogous to the Category theoretic notion of emphasizing maps rather than sets.

Even a bit further out is the notion of relating forgetful functors to mutations in evolution. It may be silly, but I find it fun.

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