A circle from a flat 2d manifold can be from a 3d sphere, cylinder, or other cross section. Our mental models don't extend well beyond 3, possibly 4, dimension

A circle from a flat 2d manifold can be from a 3d sphere, cylinder, or other cross section. Our mental models don't extend well beyond 3, possibly 4, dimensions, hence _all_ of our intuition starts to be doubtful after 3 dimensions.