[carb]

As cool as that would be, most experiments still believe the curvature of space to be flat, which means if you travel endlessly in one direction relative to a starting point, you will never return to that starting point.

https://en.m.wikipedia.org/wiki/Shape_of_the_universe

[ben_w]

Not returning to your start means not connected, rather than not flat. Pac Man and Asteroids are flat but connected, a helix is curved everywhere but not connected.

[carb]

That's true but when talking about space being flat vs having a curve, 2D and 3D visualizations are just to help explain the concept.

All current evidence points to the shape of space and the universe being relatively "boring" in that it behaves roughly like people would expect unless in the presence of a strong gravitational field.

[debugnik]

From your own link:

> Although it is usually assumed in the literature that a flat or negatively curved universe is infinite, this need not be the case if the topology is not the trivial one. For example, a multiply connected space may be flat and finite, as illustrated by the three-torus.

[sillysaurusx]

Exactly. Which leads straight to the contradiction when saying that the universe was only 10cm in diameter at a certain early time. If there’s no end, how does it have a diameter?

[SAI_Peregrinus]

The portion of the universe we can observe was 10cm in diameter. If there's more it's outside our light cone and we can never reach it or be affected by it, so it may as well not exist. The observable universe seems to be fininte, but seems to act like a finite portion of an infinite universe.

[kuchenbecker]

The apple explanation is wrong and needs to be qualified with "observable". Your understanding is correct.