In class there was a little bit of discussion regarding whether Everything and More even needed to include all the technical math terms, symbols, and proofs. Since DFW seems to be trying to illuminate the historical/aesthetic aspect of infinity, why not just stick to descriptive writing, right? For most of the people in class, it seemed that the math became a big headache. Some math majors felt that the technical aspect of the book came off as reductive and serous. For most of the humanities people, the math jargon was either ignored or dismissed as way too abstruse. I’m going to submit, however, that the technical breakdowns are necessary for Wallace to communicate the beauty and profundity he sees in the history of infinity.
(Note: whether Wallace conveys this effectively isn’t what this post is addressing. I’m just saying if this is what the book is going for, technical explanations are necessary)
A key component of the aforementioned communication is our ability to appreciate the subject Wallace is dealing with. Wallace needs to show us not just why, but how, to appreciate Cantor’s discovery. Since appreciation, I think, derives from experience, we need to some how experience the buildup toward infinity.
Analogy: We appreciate Michael Jordan’s jump shot because we know how difficult it is to make a basket over a defender. We appreciate Wallace’s essays because we know how hard it is to write well, and we’ve read lots of mediocre writing. In the case of Everything in More, we need to experience the abstractness and difficulty in thinking about infinity to truly appreciate the astounding discoveries of Cantor and company (another subject of our appreciation is the historical context: mathemeticians being dismissed as heretics, their battle against the beliefs of time, etc., but that’s for another post).
Hence Wallace’s opens the book by saying that “abstractions ha[ve] all kinds of problems and headaches built in, we all know” (11). He’s already starting to get us to think about this stuff in a broad sense. When we actually get to specifics like derivatives, integrals, and number lines, we accordingly need more specific explanations. It’s arguable that broad definitions could get the job done, e.g., to just say that an integral is the “area bound by a curve” – and Wallace does this in the emergency glossary (p. 109) – but it doesn’t do much in communicating serious meaning, I think.
If one actually sits down and fights through one of these proofs, however, one might actually gain deeper apprecation for the ingenious mind behind it. For most non-math people, these concepts are not easy – that’s the point. If we can feel the difficulty of these abstract ideas, we can begin to form some sense of the sheer brilliance of Cantor, Dedekind, et al. It’s more than paying lip-service to their genius because they’ve been exalted by history; it’s more like feeling it. To know, empirically, that they have done something incredible. And as far as I can tell, beauty and profundity always manifest as feelings.