I’m the urban spaceman, baby; I’ve got speed.
I’ve got everything I need.
− Neil Innes, “I’m the Urban Spaceman” (Bonzo Dog Doo-Dah Band)
There’s an episode1 of a science-fiction television series in which space travelers land on a planet peopled by their own descendants. The descendants explain that the travelers will try to leave the planet and fail, accidentally stranding themselves several centuries in the past. Armed with this knowledge, the travelers can try to thwart their destiny; but are they willing to try if their successful escape would doom their descendants, leaving the travelers with the memory of descendants who, thanks to their escape, never were?
This is science fiction, but it’s also math. More specifically, it’s proof by contradiction. As Ben Blum-Smith recently wrote on Twitter: “Sufficiently long contradiction proofs *make me sad*! When you stick with the mathematical characters long enough, you start to get attached, and then they disappear, never to have existed in the first place.”
This will be an essay about things that seem to exist but which, when you study them deeply enough, turn out not to exist after all.