  From the physical point of view, Weyl emphasized the roles of light  propagation and free (fall) motion in revealing the conformal-causal  and the projective structures respectively. However, from the  mathematical point of view, Weyl did not use these two structures  directly in order to derive from them and their compatibility  relation, the metric field. Rather, Weyl regarded the metric and  affine structures as fundamental and showed that the conformal and  the projective structures respectively arise from those structures by mathematical abstraction. 