Gauss appears to have been the first to undertake space explorations of this sort, when he conducted experiments on light rays transmitted from one mountain top to another. But his observations were too crude and executed over too small an area to detect any trace of non-Euclideanism. Lobatchewski suggested astronomical observations conducted on the course of rays of starlight through interstellar space. For instance, if two light rays emitted from a very distant star and striking the earth at two different points of its orbit appeared to manifest converging directions, we should know that space was Riemannian. If the two rays appeared to diverge from a common point, space would be Lobatchewskian; and, finally, if for very distant stars these two directions appeared identical, space would be truly Euclidean. Yet the most refined astronomical measurements of stellar parallaxes failed to reveal the slightest trace of non-Euclideanism. Hence it was assumed that if any trace of non-Euclideanism was present in real space it was without doubt exceedingly slight, so that for all practical purposes the geometry of space might be regarded as Euclidean. Such were the results obtained by a physical exploration of space. From all this we see that the physicist, basing his exploration of space on empirical methods, is perfectly justified in stating that its geometry can be determined, that a true definition of congruence can be arrived at, and that the equality of two lengths and of two spatial configurations has a definite significance in nature. And yet, when we submit all these various examples to a critical analysis, we cannot help but see that this determination of the geometry of space is essentially physical and is, therefore, contingent on the behaviour of material objects and of rays of light. Had the behaviour of material bodies when displaced been regulated by other physical laws, had rays of light followed different courses, the geometry we should have attributed to space might have been entirely different. And we may well wonder what the behaviour of physical objects should have to do with the geometry of space. We shall return to this aspect of the problem later. Also, it has sometimes been argued that our recognition of shape and size must possess a much deeper significance and cannot be attributed merely to the laws of behaviour of material objects and of rays of light. For instance, it is pointed out that even a child who knows nothing of measurement judges, on simple visual inspection, that a coin (when viewed from a perpendicular direction) is round and an egg oval. He does not feel it necessary to verify this fact by applying a ruler. However, regardless of what opinions we may eventually defend on the subject of a geometry intrinsic to physical space, it can scarcely be held that this last argument of the critic proves his point in the slightest degree.