Cycle (Chakraview)

Ball (Chakraview)

Cycle or what is usually named \(n\)-Ball or \(n\)-Sphere (think of circle in 2-Dimension) is the Identity with respect to uniform metric in \((n+1)\) dimensions. Since it is Identity, it is compact. Covering it completely with a single Chart homeomorphic to \(\mathbb{R}^n\) (which is non-compact) is not possible. The best that a chart can cover the Sphere is everything except one point of the Sphere (called the Pole). This is done explicitly by the Stereographic Projection which connects each point on the sphere to its projection ( send it along the straight line from the pole as the centre) on the Euclidean Plane \(\mathbb{R}^n\). This leaves the point on the Pole itself without any image. Thus, to get out of a Chakraview, it suffices to find the one point (pole) which is not covered by any given chart. The worst case is when the pole of one chart is diametrically opposite to the pole of the next chart. The path to come out of such a chakraview is to find the first pole and then alternate to the diametrically opposite point. That is, North pole followed by South Pole followed by North pole and so on. Even if we are not Abhimanyu, the very process of getting born in this world indirectly teaches us to reach out from the one pole of the sphere (Identity is the womb) which is not covered.