Suppose now that the parallaxes of the very distant stars turned out to be negative: would Euclidean geometry and Euclidean space have to be abandoned? As Poincaré points out, this would by no means be necessary or even advisable. It is true that if we assumed, as is the custom, that rays of starlight follow geodesics through space, negative parallaxes would imply a trace of Riemannianism in space; but the primary point to decide is, “How do we know that rays of light follow geodesics?” Obviously this is capable neither of proof nor of disproof. An empirical proof that such a contention was correct or incorrect would be possible only were we to know beforehand how the geodesics of space were situated, for then we could determine by observation whether rays of light followed them or not. But how could we establish the way the geodesics lie unless we were already apprised of this geometry which we now proposed to determine? Obviously, our procedure would be circular. Can we at least assume that rays of light must inevitably follow geodesics? Would any other assumption be impossible? Certainly not. A denial of the assumption would modify our understanding of optical phenomena; but what if it did? We could always get out of the difficulty by varying the laws of optical transmission, and still retain Euclidean geometry. In other words, the geometry the [Pg 55] physicist credits to space is contingent on his acceptance of a number of physical laws; and by varying these laws in an appropriate way he could still account for observed facts and credit corresponding types of geometry to space. Since all these various systems of physical laws would account for the facts of experience, how can we ever hope to decide which one of these systems corresponds to reality? And under the circumstances, what use is there in discussing the real geometry of space? All we can discuss is expediency. In other words, Poincaré, by divorcing space from its material content, geometry from physics, places space and its geometry beyond the control of experiment; so that there is really nothing left for the physicist to argue about.