Wo makes several good points about my imaginative resistance paper. It will take me a while to respond to all of them, but I just want to respond to one point for now. Wo suggests that my impossible time travel stories are not really impossible, they are just taking place in branching time. This is a good objection. I have to say more than I’ve said to show these really are impossible stories that don’t generate imaginative resistance.

One point is that the Restaurant at the end of the Universe wasn’t just supposed to be an impossible time travel story. It was supposed to be a story that was internally incoherent. I have my doubts that one could watch the end of the universe even once. Wouldn’t you be seeing it after it happened, which is after the universe ended?

I don’t have a full story here, but I think that even without the time travel component (you know, the going back and seeing it again from the same spot without running into yourself) there’s an impossibility here. And I think the impossibility arises from combinatorialism run amok. We can imagine a certain event, say the end of the universe. We can imagine ourselves watching a different event, say a lunar eclipse. So we can imagine watching the end of the universe, by substituting the first event in place of the lunar eclipse. And voila, impossibility in imagination!

Here’s another try at an impossible story that doesn’t generate imaginative resistance. At least, there’s no alethic puzzle. It’s pretty clearly true in the story that quadragons exist. You’ll have to read it to find out what a quadragon is, but suffice to say, it’s impossible.

The story is long, so I put it in the expanded section. I also don’t want to claim any virtues for the quality of the writing. If I ever use it I’ll try hamming it up a bit more because it’s meant to be a parody of cartoon superhero stories. (Whether this kind of parody is cheating, a point that Wo alludes to at the end of his post, is hard to say. I should try writing the story straight.)

Like Villains in the Movies

McBain turned the radio on and Luthor’s voice appeared.

–So that settles it, out next mission will be to blow up Yankee Stadium when the first pitch is thrown this afternoon.

–Is that a recording, I asked. They must have been stopped somehow – Yankee Stadium is still standing. But no one’s stopped Luthor before.

–No, grasshopper, said McBain, it’s live. I bugged their meeting room.

–You bugged their meeting room! How? It’s the most secure building on the planet.

–Just slipped under the door, said McBain.

–You just slipped a bug under the door. Wouldn’t that have been fairly obvious?

–No I slipped the bug inside Luthor’s desk. I slipped under the door to get in there. You see, my new invention, the Enflattenor, has the ability to make me perfectly flat, and still capable of movement and regular bodily functioning.

–If you’re flat, wouldn’t all your blood spill everywhere, I asked, puzzled by McBain’s latest flight of genius.

–I worried about that problem, but eventually I saw a way to solve it. I learned from this book, he said as he picked up a copy of David Lewis’s Papers in Metaphysics and Epistemology, that the only important relations between objects are spatio-temporal. So I thought, if I can just map all the points in a solid object onto a plane without changing the distances between any two of them, the object should be fully functional while flat. The geometry was quite hard, but it turns out this can be done.

–No it can’t, I insisted. It’s impossible. Some three-dimensional arrangements can’t be mapped onto a plane. Look, here’s a proof, I said reaching for a notepad.

–Very well, it’s impossible. Then let this be one of the six impossible things we do before breakfast, grinned McBain, pulling out a small tetrahedron.

–Before breakfast, I spluttered, it’s, it’s,… And I didn’t know what time it was, so I had to check my watch. Nearly game time I saw.

–Well, before breakfast tomorrow, said McBain, pulling a ray gun out of his other pocket.

He zapped the tetrahedron with the ray gun and it turned flat. And, though I couldn’t really believe this, each of its four vertices, for they clearly were still vertices, were the same distance from each other.

–It’s a quadragon, said McBain as I stood awestruck. At first I thought it was playing with something like curvature in space, but it turns out it is fully flat. It is even, get this, flatter than the space-time in which it is contained. Even I couldn’t figure out how that happened.

–It’s amazing, I said. I started to imagine what my favourite geometric artists could have done had they known about the quadragon. I tried to imagine St Paul’s with a quadragonal altar, or a Kandinsky painting with quadragons thrown into the geometric mix. I must have looked rather hazy when thinking about these possibilities, because McBain’s next statement startled me.

–Come on, we have to stop Luthor before he blows up Yankee Stadium.

–But we can’t stop them, they’re the greatest criminals in world history. And, remembering what time it was, we’ll never make it to Yankee Stadium in time in this traffic.

–You obviously haven’t seen my new experimental hyper-car, said McBain, glowing with pride. And he hit the remote control to raise the garage door.