# An illustrative explanation of manifolds

“[…] To find global information, the being would have the walk around both surfaces and be very careful to check angles and distances. If the being were nearsighted and could not check distances and angles, then its examination of the local vicinity, or neighborhood, would fail to detect any local distortions due to the curvature of the surface. It might then conclude that the surrounding space was Euclidean, or flat, in nature. This is what we mean when we say that a differential manifold looks locally like $\boldsymbol{R}^p$.