Comment by bmacho

> Mathematician, not physicist, but it seems reasonable to me that you could encode a sufficiently constrained 3D space on a 2D boundary. And if you have such an encoding, it also doesn't seem insane that some things might be more easily modeled on the 2D boundary than the 3D space.

Yes, you are missing the point entirely. Merely saying "you could encode a sufficiently constrained 3D space on a 2D boundary" as you correctly noticed, would be meaningless.

The observation is that the 3D space has properties that are weird in 3D but natural in its 2D representation.

> does it matter which is "real"?

No.

Also if you have different representations of something and your job/goal is to think and gain instinct then you should keep in mind all the representations, they very likely will be useful. (An observed property of mathematics is that if a mathematician pours 40 hours per week of work in an area for years in a topic other mathematicians haven't exhausted yet, she will find something there.)