Comments have helped me hopefully sumarize the question better: Is there a type of geometry under which center connects to periphery?
Edit: Based on mr_e_man's comment below, I now believe what I'm looking for may be a sort of higher-dimensional analogue for a mobius strip. Does such a thing exist?
Original Question:
I am not trained in mathematics so my language is imprecise. My apologies. Please keep your answers as free of high-level terminology as possible.
Under what conditions could you (theoretically) reach the centre of a 2-sphere by traveling away from it? In other words, imagine you are a magical housefly not bound to three-dimensional space or by the rules which apply to most people's ordinary everyday conceptions of geometry. You are sitting on the exterior surface of a 2-sphere. After a while, you lift off and fly as far as you can away from it some artibrary direction, only to find yourself at some distant point within the 2-sphere, at its center.
Intutively I feel this would be possible in four dimensions. Am I right? Or am I talking about some kind of non-euclidean geometry--or both--or neither?