Book Review: Everything And More

Everything and More: A Compact History of Infinity
David Foster Wallace
Mathematics

DISCLAIMER: David Foster Wallace graduated from Amherst College a year before me. As far as I know, our paths never crossed.

It's hard to assess Everything and More. It's probably too consciously literary for most mathematicians, and it's certainly too mathematical for most humanists. David Foster Wallace set out to write a book about advanced mathematics that would be reasonably accurate, stylishly written, and demanding of no more than high-school math. It's no surprise that he didn't fully succeed; the wonder is that he succeeded at all.

The book starts zippily enough. If you're not actually math-phobic, you can probably get through the first 100-150 pages pretty easily, particularly if you're willing to skim some bits (which I was not, but never mind). By the time we get to EMERGENCY GLOSSARY II, that's not really an option. If you want to profit from this book, you won't need to do differential equations, but you will need slow down and seriously think through some stuff.

If you're willing to do that, your reward will be a not-totally-rigorous-but-mathematically-informed understanding of some deep concepts, such as:

• Why some infinities are larger than other infinities
• Zeno's Paradoxes
• What set theory really is, and what it's good for, and why it matters
• Some mathematical proofs that are both brilliant and quite simple

So that's half the challenge. The other half is that Wallace is absolutely writing to impress. Which is not necessarily a bad thing. I much prefer his literary pyrotechnics to the turgid Academic-ese that often clogs the arteries of intellectually-challenging books. On the other hand, Wallace's consciously literary register--I'm tempted to say "postmodern", except that I'm never sure that "postmodern" means anything--is equally disconcerting if you're expecting the straight, pellucid prose of (say) John Allen Paulos, or even the New Yorkerly eloquence of a John McPhee. Everything and More brims with interpolations, with irony, and with a certain self-aware hipness. You Have Been Warned.

To bracket the target audience, then, I'll give two comparisons. 

• Subject-matter-wise, there's a pretty good overlap with Douglas Hofstadter's classic Gödel, Escher, Bach. Some of the same actors, and some of the same math concepts, pop up in each.
• Stylistically, it pairs well with Neal Stephenson, most particularly his excellent philosophical geek-heroic science fiction adventure (yes, really) Anathem. By no coincidence, Stephenson provides the introduction to the 2010 edition of the present opus.

E&M (to be a little Wallaceish about it) is their love child. If and only if you can read that sentence and think "Hmm ... what a great idea!", this book is for you.