ABSTRACT
The sort of curvature that can exist independently of an embedding space is known as 'intrinsic'. The diameter of the equatorial circle in flat two-dimensional space does not exist in the curved space that we are currently considering. Viewing motion as a process unfolding in spacetime does not require or involve the abandonment of the classical conception of space as a three-dimensional Euclidean structure. In 1733, an Italian Jesuit, Girolamo Saccheri, tried to prove the parallel postulate by assuming it to be false, and deducing an absurdity from this assumption and the other four postulates. The topological properties of an object are insensitive to continuous transformations. Spatial geometry is just one aspect of a physical theory, and the complexity that comes with non-Euclidean geometries can be more than compensated for by simplifications elsewhere.
