[urinotherapist]

If two people are in parallel, they will make two parallel circles. If two people aimed at a singe point, they are not in parallel.

Space-time is 4d array: array of framebuffers. You can stretch your mathematical model all day long, but you knowledge must be mapped to reality somehow. In model we have space-time, while in real world we have "physical vaccum" ("something nothing" or "phaccuum", for short). I prefer to name that thing "ether", because I like that word.

[AdamH12113]

> If two people are in parallel, they will make two parallel circles. If two people aimed at a singe point, they are not in parallel.

In spherical geometry, the equivalent of a straight line is a great circle. There are no parallel great circles. That's why I used the phrase "initially parallel" -- at the starting point, both people's paths are at a 90-degree angle to the great circle connecting their locations.

I didn't want to get into "locally flat" vs. "globally curved" in something that started as an ELI5 thread.

[urinotherapist]

> In spherical geometry, the equivalent of a straight line is a great circle.

Yes, of course. If we substitute parallel lines with straight lines in spherical geometry and mix 2D and 3D spaces, then our mental model will be nonsensical but cute.

We found no evidence of fourth dimension in the real world, so we cannot map this cute mathemagical model to reality.