III
Kant believed that he had decided the great question of whether this a priori element was pre-existent or obtained by experience, by his celebrated formula that Space is the form of perception which underlies all world impressions. But the “world” of the careless child and the dreamer undeniably possess this form in an insecure and hesitant way,[[181]] and it is only the tense, practical, technical treatment of the world-around—imposed on the free-moving being which, unlike the lilies of the fields, must care for its life—that lets sensuous self-extension stiffen into rational tridimensionality. And it is only the city-man of matured Cultures that really lives in this glaring wakefulness, and only for his thought that there is a Space wholly divorced from sensuous life, “absolute,” dead and alien to Time; and it exists not as a form of the intuitively-perceived but as a form of the rationally-comprehended. There is no manner of doubt that the “space” which Kant saw all around him with such unconditional certainty when he was thinking out his theory, did not exist in anything like so rigorous a form for his Carolingian ancestors. Kant’s greatness consists in his having created the idea of a "form a priori," but not in the application that he gave it. We have already seen that Time is not a “form of perception” nor for that matter a form at all—forms exist only in the extended—and that there is no possibility of defining it except as a counter-concept to Space. But there is the further question—does this word “space” exactly cover the formal content of the intuitively-perceived? And beyond all this there is the plain fact that the “form of perception” alters with distance. Every distant mountain range is “perceived” as a scenic plane. No one will pretend that he sees the moon as a body; for the eye it is a pure plane and it is only by the aid of the telescope—i.e. when the distance is artificially reduced—that it progressively obtains a spatial form. Obviously, then, the “form of perception” is a function of distance. Moreover, when we reflect upon anything, we do not exactly remember the impressions that we received at the time, but “represent to ourselves” the picture of a space abstracted from them. But this representation may and does deceive us regarding the living actuality. Kant let himself be misled; he should certainly not have permitted himself to distinguish between forms of perception and forms of ratiocination, for his notion of Space in principle embraced both.[[182]]
Just as Kant marred the Time-problem by bringing it into relation with an essentially misunderstood arithmetic and—on that basis—dealing with a phantom sort of time that lacks the life-quality of direction and is therefore a mere spatial scheme, so also he marred the Space-problem by relating it to a common-place geometry.
It befell that a few years after the completion of Kant’s main work Gauss discovered the first of the Non-Euclidean geometries. These, irreproachably demonstrated as regards their own internal validity, enable it to be proved that there are several strictly mathematical kinds of three-dimensional extension, all of which are a priori certain, and none of which can be singled out to rank as the genuine “form of perception.”
It was a grave, and in a contemporary of Euler and Lagrange an unpardonable, error to postulate that the Classical school-geometry (for it was that which Kant always had in mind) was to be found reproduced in the forms of Nature around us. In moments of attentive observation at very short range, and in cases in which the relations considered are sufficiently small, the living impressions and the rules of customary geometry are certainly in approximate agreement. But the exact conformity asserted by philosophy can be demonstrated neither by the eye nor by measuring-instruments. Both these must always stop short at a certain limit of accuracy which is very far indeed below that which would be necessary, say, for determining which of the Non-Euclidean geometries is the geometry of “empirical” Space.[[183]] On the large scales and for great distances, where the experience of depth completely dominates the perception-picture (for example, looking on a broad landscape as against a drawing) the form of perception is in fundamental contradiction with mathematics. A glance down any avenue shows us that parallels meet at the horizon. Western perspective and the otherwise quite different perspective of Chinese painting are both alike based on this fact, and the connexion of these perspectives with the root-problems of their respective mathematics is unmistakable.
Experiential Depth, in the infinite variety of its modes, eludes every sort of numerical definition. The whole of lyric poetry and music, the entire painting of Egypt, China and the West by hypothesis deny any strictly mathematical structure in space as felt and seen, and it is only because all modern philosophers have been destitute of the smallest understanding of painting that they have failed to note the contradiction. The “horizon” in and by which every visual image gradually passes into a definitive plane, is incapable of any mathematical treatment. Every stroke of a landscape painter’s brush refutes the assertions of conventional epistemology.
As mathematical magnitudes abstract from life, the “three dimensions” have no natural limits. But when this proposition becomes entangled with the surface-and-depth of experienced impression, the original epistemological error leads to another, viz., that apprehended extension is also without limits, although in fact our vision only comprises the illuminated portion of space and stops at the light-limit of the particular moment, which may be the star-heavens or merely the bright atmosphere. The “visual” world is the totality of light-resistances, since vision depends on the presence of radiated or reflected light. The Greeks took their stand on this and stayed there. It is the Western world-feeling that has produced the idea of a limitless universe of space—a space of infinite star-systems and distances that far transcends all optical possibilities—and this was a creation of the inner vision, incapable of all actualization through the eye, and, even as an idea, alien to and unachievable by the men of a differently-disposed Culture.