“A cold sweat streamed from his forehead and his shoulders jerked spasmodically. ‘Beyond life there are’ — his face grew ashen with terror — ‘things that I cannot distinguish. They move slowly through angles. They have no bodies, and they move slowly through outrageous angles.’

Did I do my homework? No. Did I animate how movement on a hyperbolic plane results in rotation? Yes. (I hope, I did my best)

In response to http://greeks-bearing-tentacles.tumblr.com/post/25586534079/bastion-spoilers-at-the-ending-its-revealed-that I know I haven't played Bastion, but I am fond of nonEuclidean geometry, being silly, and overthinking things. I drew a diagram! (apologies for quality- I had to rush it) So what happens is there are two 'seams' in what we would conventionally consider threespace, which work normally if you are going 'up' (opposite gravity) but lead to a different place than you cam from if you go back 'down'. Light passing through the top seam skips over the islands entirely, goes to the planet, and is relected back up, so the islands are still lit. When Kid falls, he hits the lower seam, finding himself back above the islands. The issues with this are that: (a) looking up, you would see the bottom of the islands, not the sun or sky, and (b) shadows would go the wrong directions. If you start doing strange things involving speed of light you might be able to get around those, but I'm not sure I know enough physics.