01.29.04 - 5:18 p.m.
I got my wisdom teeth removed today. I was looking forward to being put under, since I've never done that before. When they stuck the needle in my vein I concentrated intently. Nothing... nothing... and then next thing I know I'm opening my eyes and two hours have gone by. There was no intermediate stage at all; you go from alert to unconscious in seconds. I guess I was hoping it would be more like when you're falling asleep but not quite asleep yet and you have these bizarre stream-of-consciousness dreams.
My mouth's all numb but other than that, feeling pretty good. They gave me percoset, which (according to erowid) is stronger than vicodin. Ideally I won't be needing it, because what's the fun of painkillers if you need them?
I've been meaning to write something here about my recent obsession with math. It's unclear what's brought on this sudden mania, but here's a partial list of books I've been reading (with various degrees of comprehension):
The Honor's Class - Hilbert's Problems and Their Solvers
Prime Obsession - Bernard Riemann and the Greatest Unsolved Problem in Mathematics
Algebraic Number Theory and Fermat's Last Theorem
More Mathematical People
e: The Story of a Number
Who Got Einstein's Office?
Differential Topology: First Steps
Everything and More: A Compact History of Infinity
The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time
There's an interesting article in some back issue of The Believer where the author discusses how often mountaineering/rock climbing metaphors are used to describe math problems. He claims that this stems from the fact that math problems and mountains are both prototypical challenges, where a challenge needs to meet some or all of the following criteria:
The danger part is the only dicey comparison, but "in popular accounts, math is about as hazardous to the mind as a solo ascent of K2 is to the body. [The books and play] A Beautiful Mind and Proof both feature deranged mathematicians as main characters; in the movie Pi and the novel Presumed Innocent, the crazy mathematicians are explicitly made so by their mathematical frustrations." In Everything and More, David Foster Wallace comments aptly on this: "The Math Melodrama's own allegorical template appears to be more classically Tragic, its hero a kind of Prometheus-Icarus figure whose high-altitude genius is also hubris and Fatal Flaw. If this sounds a bit grandiose, well, it is; but it's also a fair description of the way Math Melodramas characterize the project of pure math-- as nothing less than the mortal quest for Divine Truth."
- The challenge is difficult
- The challenge is dangerous
- It is unambiguous whether you've succeeded in the challenge
- Personal virtues help you succeed in the challenge
- The challenge is undertaken for its own sake
Of all the books I've been reading, Algebraic Number Theory is the toughest and most purely mathematical. It's a textbook, basically, but to really dive into it you have to have an understanding of abstract algebra (groups, rings, fields, modules), which is turning out to be a hard thing to teach myself. Modern math is so unbelievably abstract. Numbers don't really have a lot to do with abstract algebra; they're just a particular case of this much broader class of objects that obey certain properties. My dim intuition is no help here, nor is recourse to memorization of definitions. I struggle on because like poetry, these formulas are a compact distillation of deep and beautiful ideas. Unlike poetry, the formulas are grounded in rigor and logic. I think for that reason I prefer them. If free verse is like "playing tennis without the net", then poetry in general is like that with respect to mathematics. I like the constraints imposed by math; the creativity that blossoms within those constraints appeals to me more than the lesser constraints of meter and rhyme. n-dimensional space, different sizes of infinity, undecidable problems... there are more things in this philosophy than are dreamt of in heaven and earth.
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