Topic challenge: alien geometry

I propose an topic challenge.

Its often hard to tweak the mathematics of a world (for example, you can't really make 2+2=5 in a reasonable way), but one way you can is by tweaking the geometry. This can lead to many interesting implications, including chemical, biological, and even cultural implications.

Here are some examples of 3-manifolds for inspiration; (3-manifolds are similar to our world locally). (4-manifolds are also similar if you include time.)

Also, the use of quotient spaces helps too.

EDIT: It appears to be finished. If someone wants to propose another tag challenge, go ahead.

• Didn't we drop the topic challenges? ...And a search says yes and no. Commented Jan 23, 2018 at 13:17
• @Frostfyre we dropped periodic topic challenges, but if somebody wants to call for one from time to time, that seems fine to me. Commented Jan 23, 2018 at 13:49
• I don't think I had previously noticed that we have an alien-geometry tag. :-) Commented Jan 23, 2018 at 13:50
• @MonicaCellio Which is what the question I linked says. Commented Jan 23, 2018 at 13:52
• Of all the topic challenges to try to renew interest in the subject you pick alien-geometry? I don't even know what that means... Commented Jan 23, 2018 at 14:21
• @kingledion You could try one (although I'm not sure what the rules are if multiple people want to do topic challenges). Commented Jan 23, 2018 at 18:41
• @PyRulez I'm trying to do this one! I can't think of what to ask about alien geometry. Its so....alien... Commented Jan 23, 2018 at 18:53
• @kingledion Browsing over the other questions might help. One simple thing to do is to just "glue" things together. Or you can just ask a question about one of the worlds asked about in the other questions (for example, you could ask what political system would be best in the infinite flat world). Commented Jan 23, 2018 at 18:55
• What exactly is a topic challenge? Commented Jan 23, 2018 at 20:36
• @adaliabooks uhm, I guess it means your challenged to write posts with this tag? Commented Jan 23, 2018 at 20:37
• @PyRulez I thought that was probably it but wanted to check... thanks Commented Jan 23, 2018 at 20:44
• Dunno, there are so many variations of geometry already in our world that it may suffice to take a trip to math.stackexchange.com rather than inconvenience distant aliens. It may be easier worldbuilding on alien-[empirical science] tags than using purely abstract disciplines. Or, perhaps, asking about the physics of worlds where the only possible triangles are Penrose triangles, and the only possible bottles are Klein bottles...
– NofP
Commented Jan 25, 2018 at 16:40
• @NofP Even though many different geometries "exist" abstractly, the cultural implications of such geometries are only realized if a universe if based off them. Asking about world building of math.se would be off topic. Commented Jan 25, 2018 at 17:25
• @NofP, Ah, you may want to take a look at the tag wiki. alien-geometry means we replace Euclidean (ignoring general relativity) geometry of our universe with some other geometry (such as the projective plane or something), no more, no less. I suppose the term "alien-geometry" is slightly misleading, since these geometries where discovered by humans. (It was named that based on the TV Tropes article by the same name.) Commented Jan 25, 2018 at 17:39
• For what it's worth we stopped holding periodic topic challenges and when we did so we mentioned specifically that users are free to create their own when they choose to do so. Not sure you will get a ton of support/interest on alien geometry but stranger things have happened here :) Commented Jan 29, 2018 at 21:02