God has particular languages, and one of them is music and one of them is mathematics.
— David Foster Wallace, The Boston Globe, 2003
TO THE EXTENT THAT HE WAS AT HOME anywhere, David Foster Wallace was at home in the world of math. As an undergraduate, he studied modal logic; Everything and More, his book on infinity, explained Georg Cantor’s work on set theory to a general audience, and Infinite Jest includes a two-page footnote that uses the Mean Value Theorem to determine the distribution of megatonnage among players in a nuclear fallout game.
But Wallace didn’t just talk about math. He structured his work with it. In a 1996 Bookworm interview with Michael Silverblatt, Wallace explained that he modeled Infinite Jest after a Sierpinski Gasket, a type of fractal in which a triangle is infinitely subdivided into smaller triangles using the midpoint of its borders. Pressed by Silverblatt on why he chose such a formation, Wallace elaborated: “Its chaos is more on the surface; its bones are its beauty.”
Now, many people agree that Infinite Jest is a singular novel, sui generis, akin perhaps only to Moby-Dick in its originality, but the qualities that earn the book that praise — its grotesque hyperrealism, exuberant asides, and melding of academese and slang, its spikes and spurts of kindness and abjection — seem to have nothing to do with Wallace’s experimental use of fractals. Wallace’s genius lies in his guts, his encyclopedic imagination, his eyes and ears, but not, it appears, in his tricks with advanced math. And yet perhaps the fact that the casual reader remains oblivious to the Sierpinski Gasket is proof of its success. Traditional narrative structures — the Fichtean curve, Aristotle’s rising action — are designed to keep us engaged and organized, yet remain invisible; a well placed climax pops and hooks, even if we don’t notice its strategic placement. And as an organizing principle, the fractal has an intuitive logic: the best novels already have a fractionalized quality — each chapter, and indeed every paragraph and sentence, reproduce in miniature its central conflict and arc. Wallace’s comment to Silverblatt made me wonder if fractals, or some other mathematical pattern, might generate order from everyday experience without the ordinary contrivances of plot.
The more I thought about it, the more it seemed that a novel structured like a fractal would make cellular sense to a reader, even if she never consciously thought Ah, a fractal. Fractals occur so often in nature, in such a wide array of phenomenon, that it’s difficult to avoid the conclusion that the universe is, on some deep level, intricately patterned. Study snowflakes, mountains, coastlines, cauliflower, rivers, blood vessels, DNA, and ferns for long enough, and it is easy to believe that fractals are indeed one of God’s languages. To make a novel in the shape of a fractal, then, is to claim literature as another example of this unifying language.
Yet, is a fractal beautiful or true in the same way that a story can be beautiful or true? A story, a good one, surprises us. The interruption of expectation, the breaking of routine, is the engine of storytelling, whereas fractals, a...read more