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.

Comments

Post a Comment

Popular posts from this blog

Anti-Libertarian: re-post

The most pointed critique of social security and liberalism in general is the libertarian critique. The problem with libertarians, for a liberal, is that we have too much in common. We both believe in individual rights, tolerance of individual differences, and dislike government prescription of religion. The basic difference, it seems to me, is the different answers we give to Cain's (with thanks to the Captain - my original version had the corpse asking the question!) famous question: "Am I my brother's keeper?" That's not really my basic bitch against the libertarians though. My real complaint is the same as my complaint against most religion - its premise is a fraud. For those who can't stand to wait for the punchline, I believe that trying to implement libertarian principles leads to tyranny or social disintegration. Demonstrating that takes some historical (and pre-historical) context. For all but the last 15,000 or so of the 100,000 years the human spec...
Read more

Uneasy Lies The Head

Uneasy lies the head that wears a crown ........... Shakespeare Henry IV, Part II. So it is with us and our slightly distant primate cousins , so it seems. A 9-year study of wild baboons in Kenya by Princeton University and the Institute of Primate Research may turn conventional assumptions of alphas males upside down. The study found that alpha males have high testosterone levels, which allows them to dominate other baboons, get access to more food, and attract better mates. This is expected. Surprisingly, though, the alpha males also have high levels of stress hormone glucocorticoid, which scientists measured from their feces samples. In fact, the stress of alpha baboons was on par with low-ranking baboons. The convention wisdom is that access to food and females provides life security and thus less stress for dominant males. Conversely, weak males who are constantly threatened by starvation and physical violence from stronger males are thought to be more stressed. The st...
Read more

We Call it Soccer

The US played its best, and maybe only good game of World Cup, but lost thanks to brilliant goalkeeping by the Swedish keeper and the bizarre method soccer uses to settle ties when three US stars could not put the ball on frame from the 12 yard spot.  At the end it came down to a blocked shot that spun in by maybe a couple of centimeters. Well, that's football - too much like life.   Which brings me to a modest proposal.  Replace the thirty minute overtimes with as many 7-player 15 minute periods as needed to settle it.  Scoring should be much easier with fewer players.
Read more