  An \(n\)-dimensional manifold \(M\), which is an affinely  connected manifold, Weyl (1918b) interprets physically as an  \(n\)-dimensional world (spacetime) filled with a gravitational  field. Weyl says, “…the affine connection appears in  physics as the gravitational field…” Since  there exists at each spacetime point a geodesic coordinate system in  which the components \(\Gamma^{i}_{jk}\) of the symmetric linear  connection vanish, the gravitational field can be made to vanish at  each point of the manifold. 