It may be instructive to consider this illustration in greater detail. In the first place, we must realise that all we are in a position to appreciate when merely viewing an object, is its image on our retina. Indeed, were we to interpose a microscope or a deforming lens between object and eye, the object would suffer no change; but its image cast on our retina would, of course, be modified. As a result, our judgment [Pg 51] of its shape and size would vary. Hence, when we decide unhesitatingly that the coin is round, the only inference to be drawn is that the coin’s image on the retina is judged by the brain (or the mind, or whatever we decide to call it) to be circular. We do not wish to intrude on the ground of the eye-specialist or physiologist, who is better equipped than we are to proceed farther in this analysis, but we may point out that the problem which we are now considering is of an entirely different nature from the one whence we started. There we were considering whether shape in empty space was absolute; here we are considering whether an image cast on our retina should impress itself upon our recognition with any definite shape. The difference amounts to just this: In mathematical space, and even in physical space, absolute measurement seemed to elude us, since in view of the continuity of space it appeared impossible to proceed with an enumeration of points. But in the case of the retina, its surface is no longer homogeneous; it possesses a heterogeneous structure like all tissues, probably a discrete one forming a pattern. In all such cases a definite metrics suggests itself naturally, just as on a net, in the absence of a ruler, we would compare lengths instinctively by counting the holes separating our points. Whether or not, in the case of the retina, our appreciation of the coin’s roundness comes from some unconscious counting process is a problem for the specialist to decide; but at all events, when we consider that the retina and the eye are Euclidean bodies just like our rulers, the concordance between our computations of shape and size, as determined by rods, and our direct visual appreciation of shape does not appear to present much of a mystery. But there is still a further point to be considered. Were we to have a direct intuition of congruence and of absolute shape or length, our measurements with rods would have to be adjusted so as to conform to this intuition. The introduction of rods would thus be contemplated merely as an adjunct, in order to obtain greater definiteness. But it so happens that such is not the case. Our intuitive visual appreciations yield results which differ from results obtained with rods, not merely accidentally as a result of the imperfection of human observation, but systematically.