David Foster Wallace on 3
Another David Foster Wallace interview, this time on his book about infinity.
I enjoyed the discussion of whether 3 is physically real, starting around 44:00:
DFW: But by real, you mean mathematically real or physically real?
Interviewer: Physically real.
DFW: But are numbers physically real?
Interviewer: I had thought that they were, in some way...
DFW: So you're a bit of a Platonist then.
...
DFW: We're brainwashed into being Platonists in elementary school, because it's the easiest way to think about [numbers]...
Nobody wants to tell a fourth-grader the metaphysics of the integer 3. So we got this idea that 3 is this thing, and that we're manipulating things. But in fact that's the first step of the math abstraction process. We're not manipulating things.
We're manipulating certain symbols that stand absolutely generally for, I guess, the set of all triples in the world.
That's the thing to me that's really interesting about the book... that these are not things.
And a bit later on:
DFW: The stuff that we lie in bed at night, that seems to have nothing to do with our lives that just drives us crazy, is – when you think about it – the really, really, really basic stuff.
What are numbers? What exactly are these three dimensions we're sitting in?
It's embarrassing to talk about out loud... because it does just sound like pot-smoking "oh, oh, oh." But in some sense, this is what mathematicians – and back in the Greek, philosophers, because there was no difference – this is what they [do].