it can be, I think of a manifold (probably naively) as the mathematical abstraction that you end up with if you start from Euclidean space and fiddle with diffe

it can be, I think of a manifold (probably naively) as the mathematical abstraction that you end up with if you start from Euclidean space and fiddle with different features - e.g. if you're in a Euclidean space how do you get from one point to another - what are the minimum requirements? What if we want calculus to work what are the minimum requirements? If we're on a surface and we walk around is there any way to tell what shape that surface is?