Möbius Polar Coordinate System Based on Entangled Pull Back of Contradictory Oneself and Its Topos

In this paper, the emergence of the contradiction oneself of object u is not only attributed to a mechanism that opposite transmission between the function x(t) that carrying the location information of u and its returned back x⁻¹ (t⁻¹) and is meeting at a contradiction point, but also is conversed into the questions: "How long time will be taken for the function x(t) transports from own position to v with the velocity $\dot{x}\left(t\right)$, and return back?" It is shown that not only a pair of dual categories and their presheaft and topos can be induced by x(t) and x⁻¹ (t⁻¹), but also a Möbius Entangled Polar Coordinate System can be established by an entangled pull back and a dual of mirror manifolds. In this way, a framework that runs through Philosophy, Information, Mathematics, Physic, Logic to Neural Network can be constructed too. (paper)