When we consider Poincaré’s arguments, there is very little to be said against them. Nevertheless, the physicist must concentrate his attention on the space with which he can cope, with the one that can be explored by physical methods. This attitude defended by Einstein (which was also the attitude of Gauss and Riemann) leads us to the space whose geometry is defined by the paths of light rays, by the laws of nature when expressed in their simplest form, and again by the numerical results of measurement obtained with material rods maintained under constant conditions of pressure and temperature. It is with this space that we shall be concerned. [Pg 188] But before proceeding, let us make it quite plain that according to the present view the office of our rods is to reveal the pre-existing structure of space much as a thermometer reveals the pre-existing differences of temperature throughout the house. On no account, therefore, may it be claimed that the rods are assumed to create space any more so than the thermometer creates temperature or the weather glass creates the weather. The rods permit us to explore space because they adjust themselves or mould themselves to its structure, or metrical field. The origin of this structure is still very mysterious. For Riemann it was created by matter; but by matter he did not mean the matter of our rod: he meant the total aggregate matter of the entire universe. Einstein’s cylindrical universe confirms Riemann’s views. At all events, regardless of the mysterious problem of the ultimate origin of the metrical field, regardless of whether this structure of space exist per se as a characteristic of physical space or whether it be generated by the masses of the cosmos, in either case it pre-exists to our local exploration with rods, whose masses are far too insignificant to modify it to any perceptible degree. Also let us recall that when we discuss space, we must specify it by referring it to a frame of reference, in particular to a Galilean frame (one in which no forces of inertia are experienced). We then proceed to consider the laws of disposition of our congruent bodies in this frame, and the nature of the geometrical results obtained will define the geometry of space. As we know, Euclidean geometry is the outcome (at least to a first approximation).