This paper investigates the effects of geometrical factors characterizing the shape of a river basin on the features of its hydrologic response. In particular, we wonder if by measuring the hydrologic response (i.e., gauging) the salient geomorphic features of the basin can be recovered. We argue that the basic structure of the channel network tends, in ideal conditions, to yield some universal characters of the width function W(x) defining the relative proportion of a contributing area at a distance x from the outlet. W(x) exhibits low-frequency features, which are geometry-dominated, and high-frequency features determined by recurrent aggregation patterns. It is suggested that given the shape of the basin one can indeed forecast in a rational manner the main characters of the hydrologic response which are imprinted in reproducible width functions. However, the inverse problem (i.e., the determination of the shape from the measure of the hydrologic response) is less solidly defined because of the possible loss of irretrievable information induced by the dynamics of runoff processes. Therefore the question posed in the title cannot be solved in general, although many elements for a general theory are seemingly established.