  The different types of geometric, structural fields may be  represented from a modern mathematical point of view as cross  sections of appropriate fiber bundles over the manifold \(M\);  that is, the amorphous manifold \(M\) has associated with it  various geometric fields in terms of a mapping of a certain kind  (called a cross section) from the manifold \(M\) to the  corresponding bundle space over   \(M\).[63]  In particular, Einstein’s general theory of relativity postulates a  physical field, the metrical field, which, mathematically speaking,  may be characterized as a cross section of the bundle of  non-degenerate, second-order, symmetric, covariant tensors of Lorentz signature over \(M\). Weyl (1931a, 336) says of this world  structure: 