  Riemann assumed the validity of the Pythagorean metric only in the  infinitely small. Riemannian geometry is essentially a geometry of  infinitely near points and conforms to the requirement that all laws  are to be formulated as field laws. Field laws are  close-action-laws which relate the field magnitudes only to  infinitesimally neighbouring points in   space.[35]  The value of some field magnitude at each point depends only on the  values of other field magnitudes in the infinitesimal neighbourhoods  of the corresponding points. The field magnitudes consist of partial  derivatives of position functions at some point, and this requires  the knowledge of the behavior of the position functions only with  respect to the neighbourhood of that point. To construct a field law, only the behavior of the world in the infinitesimally small is   required.[36] 