On this year’s Strange Spaces course, which came to an end last week, we were able to show off a visualization of 2-dimensional hyperbolic space thanks to the indie game HyperRogue. Below the fold is a video of someone wandering around on HyperRogue’s space, which students who followed the course might recognise as a Poincare disk.

Although it at first appears to be a flat disk, or perhaps a sphere seen from the top, if you look more closely you’ll see the distortions of lines and angles go “the wrong way” for either of these possibilities. This is a space with constant negative curvature: something we have to omagine and represent indirectly because we can’t create such a thing in our own 3D space.

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We’ve found a few games you can play on paper using the polygonal presentations of surfaces we looked at in Session 1 (the easiest and most obvious is noughts and crosses), but those aren’t terribly exciting. What we are excited about is forthcoming game Miegakure, which promises to allow us to navigate four spatial dimensions (and, of course, use a fifth time dimension to do it). Here’s a video explaining the idea behind it:

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Miegakure hasn’t been released yet but hopefully we’ll get to run Strange Spaces next year and use it to add some intuition to this hard-to-visualize subject.

Incidentally, we’ve also been enjoying Monument Valley lately, but that has more to do with perspective illusions and projective geometry — a subject of one of our other courses, for which we hope to have an online coursebook available later in the spring:

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