Interestingly, it's the same problem than to determine if live in a flat or curved space(-time). You can determine curvature by intrinsic means. I you go from n

Interestingly, it's the same problem than to determine if live in a flat or curved space(-time). You can determine curvature by intrinsic means. I you go from north pole to Ecuador painting your direction, turn 90º, advance a quarter of the equator, turn 90º still, and go home the Pole, your arrival direction is at still 90 degreess relative to your starting direction. the angles sum 270º! Instead of the 180 that should sum in flat Euclidean space. IIRC Gauss went to the mountains with ropes and instruments to verify things by himself, in a striking display of intelectual independence, defying any common sense of the time, and in fact he was shown right by the physics of last century. His shitty ropes just hadn't enough measuring accuracy.