Wednesday, August 19th, 2009
I am reading David Foster Wallace’s Infinite Jest, and I need to complain. If you haven’t read it, and plan to, don’t worry, I won’t spoil it for you. If you hate nitpicking, on the other hand, maybe do worry a bit, because I will pick nits. Three of them.
Overall, the book is fabulous so far (page 100), and I love the combination of low brow comments with language so erudite it often borders on the pretentious. This is a great stylistic game to play, and it is enhanced by esoteric factoids, partly made up, partly accurate. But for it to work it needs to stay on the light side of the pretentiousness boundary, and the author needs to be in control of the pieces of knowledge he’s throwing around. Now lets pick some nits.
Nit the first. In a discussion of the philosophical aspects of tennis, Hal’s father is cited, obliquely, as telling people about how a tennis move affords n responses, and how there then are 2^n responses to that move, soon spiraling into “a Cantorian continuum of infinities”. Now, firstly, the correct formula for this is n^2. Wallace might have done this on purpose – somewhat suggestive is the fact that the date of Cantor’s diagonal argument is given in the endnote as 1905 (Einstein’s two seminal papers came out that year) instead of the actual 1891. This is probably a purposeful mixup put into the mouth of the fictitious narrator to highlight the distant past-ness of it all – but if so, I fail to see the point of giving the wrong formula. On top of that, however, talking about a continuum of infinities is not quite accurate. The number of replies approaches the number of elements in the continuum only for games with countably infinite many moves, and any transfinity beyond that (the actual family of infinities Cantor discovered and Wallace alludes to) is unreachable by any tennis match. Overall, the passage sounds like a bit of finitely hot air to me, unlikely to come out of the mouth of an MIT educated polymath with an actual interest in Cantor.
Nit the second. When we first meet the assassin Marathe on the mountainside, he watches his shadow wander out in the setting sun toward the city of Tucson and, as the sun gets low enough, eventually reach it across the plains. This can not happen. A circular object of 20 cm diameter (a human head, say), has the same angular size as the sun (about half a degree) at a distance of roughly 22 meters (or yards). At distances greater than that, the object can no longer fully block the sun and casts no total shadow, or umbra. Moreover, the darkest point of the penumbra actually cast rapidly loses contrast and definition. At 44 meters, the darkest point will have 75% of the luminance of the surround, at 88 it’s up to close to 94%. A shadow of a human or anything smaller, cast by the sun and reaching out visibly for kilometers, is a physical impossibility.
Nit the third. Again concerning shadows, in that same scene: when the sun finally sets, Marathe sees his shadow return to him up the incline. This would happen with a rising sun, not a setting, and of course he’d have to face west, not east. If the sun were a point, the shadow cast out by a sunset would retain definition across large distances and grow longer and longer until it hits the advancing terminator and fuses with it. It would not shorten back toward the object casting it.
Is it sloppy writing and editing? Or a deliberate ruse to tick off obsessive compulsive physicists like me? It doesn’t really matter, because the book is still great, and these are tiny complaints.
Later Addition: The term Bröckengespenst Wallace uses for his fictional shadow is a) inappropriate, since a Brockengespenst is actually a shadow cast into fog or clouds, and b) has false diacritical marks on the o. This German spelling SNÄFÜ is in tune however with his german character later on calling his students “mein kinder”, which sports the wrong numerus of the possessive. “Meine Kinder” would have been correct. I’m leaning toward the sloppy writing hypothesis.