October 10, 2009

Mystical Maths

In Moe's this morning I buy a copy of Alain Badiou's "Number and Numbers", and present it to the clerk, a guy who's sold books to me here for years.

Him: "Ah, Badiou! Man of the moment!"
Me: "But I bet you thought you'd never sell any copies of this book…".
Him: "It's Berkeley. Someone's going to buy a copy eventually…"
Me: "Yeah, that someone's me, I guess. I just love reading stuff like this to see what happens when philosophers try to take on math; it's nearly always some sort of semi-mystical train wreck."
Him: "Ha! A friend of mine used to read Badiou — and Deleuze and Derrida and all those guys — a lot, but he was always high, and he never stopped giggling and chuckling his way through it all. Made me kinda wonder what was in those books."
Me: "Yeah. Treating it as a species of entertainment is probably the best way to cope."

I'm hopeful of a little bit more than entertainment, though: there's evidence in a quick flip through the book that Badiou's not just interested in waving his hands ostentatiously in front of the usual mathematically-ignorant philosophy types. We shall see….

Later, in the supermarket, with some typically overheated Dylan song supplying a smooth soundtrack, the (huge) woman behind the deli counter has a (huge) black and white badge on her chest that says "God is good — all the time!". Somewhere out there, God's rolling in his grave.

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February 11, 2009

Superprime

I think I've always thought of Euclid's proof of the infinitude of primes as one of those magically-clear and simple things you can understand immediately you come across it but that seems to have come out of absolutely nowhere (Cantor's diagonal works for me in the same way as well). It's sometimes hard not to write about maths in mystical terms that get really boring to anyone not a nerd like me, but it's like seeing your first Rothko or Pollock in the flesh, that delicious mixture of recognition and where the hell did that come from?

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May 28, 2008

On A Generalization Of The Second Theorem Of Bourbaki

In Moe's I pick up a small paperback, "The Artist And The Mathematician: The Story of Nicolas Bourbaki, the Genius Mathematician Who Never Existed" by Amir D. Aczel (Thunder's Mouth Press, NY). The world's crying out for a good Bourbaki biography, but this ain't it, unfortunately. It's a confused, repetitive, portentous, and rather plodding attempt to … well, what, exactly? And that's the problem, I think: it's trying to be a bunch of things, and doesn't really do any of them well.

It rather half-heartedly tries to play on the suspense of Bourbaki's identity, but the Bourbaki in-joke won't be any sort of mystery to maths insiders, or anyone who's read the jacket blurb, so that vein can't be mined for much. It's also a weird Grothendieck booster — but that falls flat, too, if only because most non-maths types won't understand why Grothendieck might deserve the adulation (especially since this will almost certainly be the first time they've ever heard of him), but more importantly because Aczel just lets that part of the story trail off, without actually explaining G's importance (he was important, to be sure, but he's the sort of guy — like Tesla, in a different field — who attracts True Believers). He seems to think it's self-evident; but without a good maths or maths history background, it's not clear at all.

In fact, the one thing it might have done to pull the whole thing together would have been to help explain the maths and the maths background, but the book seems to assume either (or both) that the reader can't or won't understand the maths, or that they already know it. It's a strange omission, for sure: a history of a mathematical identity (in several different usages of that term) that doesn't explain the maths at all.

The book's also a claim that Bourbaki was either a spark of Structuralism or sparked Structuralism, something that I hadn't heard claimed before and that struck me as potentially interesting. But as with so much of this book, that trail just sort of petered out after a lot of suggestive but inconclusive tidbits. I'd guess Bourbaki was very weakly both a spark of Structuralism and sparked Structuralism (there's a lot of vague metaphorical stuff in common if you don't spend too much time looking at the details), but it seems a real stretch to make him one of the great Structuralist prime movers.

And the book claims that Bourbaki almost single-handedly founded modern maths, which strikes me as ludicrous: Bourbaki was an interesting sidetrack or sideline at best, and, like the book's many claims, really went nowhere in a sea of words. I don't know any mathematicians who spend much time reading Bourbaki (I personally find him more unreadable than most maths writers, and given the field, that's really saying something), and few think of Bourbaki's rigid and scholastic attempts to reground mathematics as having led anywhere much at all.

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March 15, 2008

Cantor Rulez!!! (A Philospher Writes…)

Why Cantor matters (and Wittgenstein's just an interesting historical oddity): "Writing decades after Cantor's death, Wittgenstein lamented that mathematics is 'ridden through and through with the pernicious idioms of [Cantor's] set theory,' which he dismissed as 'utter nonsense' that is 'laughable' and 'wrong'." (from Wikipedia's entry on Cantor).

From the Olympian heights of philosophy, mathematics must seem so grubby, and, well, useful, but to this reader, it's hard to get past Cantor's transfinite numbers for examples of abstract beauty and the stringent clarity of the purely counter-intuitive. I think the first time I read about — and understood — the various comparative transfinite cardinalities of the integers, the rationals, the reals, etc., (and, crucially, the associated proofs) was when I realised I could do mathematics in ways I can't do arithmetic (don't ask me to add things up). To a young Woy Woy boy struggling with high school in the foreign reaches of Canberra, this was a revelation.

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