History of science month continues with David Foster Wallace’s Everything and More: A Compact History of Infinity . Initially, I was a bit wary of this book — a math book written by a lit’ry post-modern, hip feller like Wallace has all the makings of bad pop science. You know the signs: the over-simplifications, the hyping of dubious fringe stuff, the emphasis of biography at the expense of subject matter.
Surprisingly (or not; I don’t really know much about Wallace), these pitfalls are largely avoided. Wallace writes as someone who gives a damn about math, is irritated by shallow and off-the-point A Beautiful Mind-esque portraits of mathematicians, and really wants to get across the essential issues and elegant theorems of mathematical infinity. He’s working with some handicaps, of course, most notably that the audience he’s writing to is going to a) have wildly different levels of mathematical background (the book putatively requires nothing more than high-school pre-calculus), which b) are almost always rather less than they need to be to really understand the technical bits he needs to talk about.
Pleasantly, Wallace is rather open in his pedagogical approach; he remarks frankly about the explanatory trade-offs he’s making, he admits when he’s lying to children, he tries to stuff in as much footnotical clarification and expansion as he can without totally disrupting the main text, and when it’s required, he’s not afraid to roll up his sleeves and slog through a thicket of equations.
I’m unsure as to how successful he is, though. I’m basically his ideal reader — with four or five semesters of college math, I’m well-educated enough to understand most of the background he needs me to understand, but not so well-educated that I’m bored by his low-level explanation of the subject. Despite this, I still got bogged down at the end, when he got to Cantor and the math got more technical. I read through it, and understood it on some superficial level, but I didn’t actually get it in the way that perhaps I should have gotten it.
Then again, I’m a bit of a lazy reader, when I’m reading for un-work-related pleasure, so I didn’t work my way through the proofs in detail until they clicked, which may be my fault as much as Wallace’s. Still, I suspect my reading style is going to be the one that most readers bring; a more studious approach is only going to be widely found where grades are involved, and often not even then.
Despite that problem, though, I did find the book fascinating up until it got to Cantor — the actual historical bits were great. Wallace traces the concept of infinity, the problems it presents, and the uses it enables, from the Greeks through the Middle Ages, to the development of calculus, and from there to the 19th century. If you’ve got a decent calculus background, almost all of it will be entirely comprehensible and lucid; and because infinity is such a narrowly-focused (yet broadly applicable) topic, Everything and More doesn’t feel like Yet Another Survey Text, either.
Its distinctness is only enhanced by Wallace’s narrative voice, which I find myself deeply fond of. He writes very much like Neal Stephenson (to the point where I have to work to remind myself that they’re not actually the same person — or are they? (No.)), which is a good thing, particularly when dealing with such a potentially-dry topic as mathematics; Thomas and Finney should take lessons.
I generally like to end my entries with a vague sort of read-it-or-not recommendation, but Everything and More is idiosyncratically different enough that I couldn’t possibly make any broad recommendation. I suppose I could address all my readers individually (Chad: I think you’d like it; Kate: I doubt it; Bruce: I think you already read it; Novak: give it a whirl; Trent: probably not; Nathan: fuck if I know), but there’s a chance that I have more than the half-dozen readers I could address one-by-one, so that option isn’t especially practical. So I’ll say generically, if you think you might like it, you probably would; if you know you wouldn’t, you certainly wouldn’t. There.