but we can also put the game on a torus. again, the ship doesn't know it's on a torus. it just knows it's blasting asteroids out of its way. for us to play the game really well, we just have to reorient our thinking a little to be part of its global topology and not be tricked by its local topology. but are there other universes for our game to play itself on besides a sphere and a torus? and if there are, what might those be like? well, this is what can happen if you're not an expert in topology sometimes. so i'm very happy to be here with greg leibon, a mathematician at dartmouth college. >> thank you, dan. >> our poor topologist, it turns out he was on a torus, but in fact he could have been on many other kinds of surfaces, right? >> that's right. when you go to classify or think about what are the possibilities of surfaces, there are two major kinds, especially in terms of what you need to get used to to think about them. >> so there's a first distinction: there are orientable surfaces and there are nonorientable surfaces. >> that's right. and it's nice to think --