Adarain
It has been stated repeatedly that the cognitive realm is geometrically flat. Like, flat earth flat. However, it is mathematically impossible to turn a sphere (such as the surface of a planet) into a flat plane without cuts or overlaps [by the Borsuk-Ulam theorem]. So my question is simply… how does the cosmere resolve these issues? Are there places on every planet where if you walk across a line in the physical realm, you’d now be in a completely different spot in the cognitive realm? Or perhaps places where two points of the physical realm collide in the cognitive realm?
Peter Ahlstrom
Good question. And I don’t have an answer. I’ve always like Dymaxion maps, and those have big gaps. I would be fine with Shadesmar being non-Euclidean.
Adarain
Thanks for the answer! If I may ask for clarification, when you say non-Euclidean do you mean going back on the whole "Shadesmar is flat" thing (since Euclidean just means flat), or do you mean it having a structure like e.g. the mentioned Dymaxion map (or perhaps even wilder things like planets being entirely disconnected)?
Peter Ahlstrom
I mean something like when you get to where the edge of a segment on a Dymaxion map would be, you step across seamlessly into the next section even though there should be a huge gap.
Accomplished_Debt932
I had always envisioned the cognitive realm as a Möbius strip. Flat, one sided, infinite, and ultimately a (sort of) loop. Is that accurate?
Peter Ahlstrom
I don’t know if it’s a loop at all.