Beyond Infinity

[I was saving this post for a later time, but Jonathan's recent post about dumb & smart postmodernism makes it somehow timely.]

Georg Cantor, it is said, showed that there are numbers greater than infinity. Specifically, he proved that there are more real numbers than natural numbers, though there are of course infinitely many of both. I have my doubts. Following Wittgenstein, I'm more inclined to think that Cantor invented a game to play with numbers than that he discovered a fact about them. Today, that makes me a crank, I'm told. (On some days, I also don't think pi is a number—a view I apparently share with the late Buckminster Fuller, who was strange enough, but perhaps a little too famous, to be called a crank.) Fortunately, for the purposes of this post I can assume that Cantor was right, at least for the sake of argument.

So, suppose it is true that there are numbers greater than infinity. Let's agree that this does not affect the truths of arithmetic. Though there may be more real numbers than natural ones, two plus two is still four. Now, suppose a movement among math teachers arose to teach Cantor's theory to students at an early age. After all, the theory is true, and it tells us something interesting, perhaps even fundamental, about what numbers are. Up to a certain point we could allow it. But now suppose, further, that after a few years of this heady pedagogy (grounded in Cantor's altogether true theory about numbers, remember), we find that while some of the students are holding forth impressively about the many "orders of infinity" a substantial number of them are regularly making basic errors of arithmetic. On closer investigation, we find that they don't know their multiplication tables and don't master long division. They "get through" by using their pocket calculators whenever they can. Ask them about infinities and imaginary numbers, they'll come up with an answer. But part of you is beginning to suspect they're just bullshitting you. These are students who can't confidently add 1017 to 479, you remind yourself. What can they possibly know of infinity?

This, unfortunately, is what I think has happened in writing instruction. Impressed by sophisticated theories of authorship, language and discourse, we have neglected the basic skill of describing a fact. We ask students to write after both "the death of the author" and the "elision of the subject", which is to say after Barthes and after Foucault, but we don't teach them how to write down what they know, how to say what they think. We have abandoned assertion and rejected mastery; we have allowed the students to "perform" for us rather than be their "authentic" selves. We have become as tolerant of their "patchwriting" (which we don't call out as plagiarism) as a math teacher who does not ban the use of calculators for assignments. Something has to change.