Although in mathematical space the two distances would be equal or unequal according to our measuring conventions, in practical life we have unwittingly posited our measuring convention by walking. Our successive steps henceforth define in our estimation congruent distances; and under the circumstances distances become measurable in terms of these steps. But these steps are themselves controlled by our human frame; hence all we have done has been to measure space in terms of our legs. That measurement originated in this way is indicated clearly by such words as foot and cubit, or again by the definition of a yard as expressed by the distance between the tip of a certain king’s nose and the extremities of his fingers. And it is because our human limbs manifest the same type of congruence as the material bodies around us that this type of measurement once again imposes itself so strongly upon us. Indeed, measurements as computed with human limbs appear to be instinctive and are exemplified in children who, having grown, are surprised to find the rooms and buildings they have not seen for some years, appear considerably smaller. Instinctively, the child is measuring size in terms of his own height. Thus, in whatever way we examine the matter, there appears to be nothing mysterious in our natural belief in the absoluteness of shape and size or in a definite geometry pertaining to space. None of the examples mentioned thus far entitle us to maintain that physical space manifests a definite metrics and that congruence is other than conventional. If we consider the problem in its present state, we see that it is the physical behaviour of material bodies and light rays which is in the final analysis responsible for our natural belief in absolute shape. But this realisation brings with it the assurance that space itself has eluded us entirely in our discussions. Such was indeed Poincaré’s stand. He maintained that though for purposes of convenience it [Pg 53] was only natural for us to measure space as we do, yet if needs be we could disregard the behaviour of material bodies entirely, adopt non-Euclidean standards of measurement, and proceed as before. In spite of this change we could construct exactly the same engineering works, in fact rewrite the whole of physics. Needless to say, everything would be extremely complex, all our known laws would be disfigured, and hypotheses ad hoc would have to be introduced. But when all is said and done, the task would be theoretically possible; so that if we disregard the criteria of convenience and simplicity, there is nothing to choose between the various types of measurements, any more than between the metric system and the British units.