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. IV The outcome, then, of Gauss’s discovery, which _completely_ altered the course of modern mathematics,[184] was the statement that there are severally equally valid structures of three-dimensional extension. That it should even be asked which of them corresponds to actual perception shows that the problem was not in the least comprehended. Mathematics, whether or not it employs visible images and representations as working conveniences, concerns itself with systems that are entirely emancipated from life, time and distance, with form-worlds of pure numbers whose validity—not _fact-foundation_—is timeless and like everything else that is “known” is known by causal logic and not experienced. With this, the difference between the living intuition-way and the mathematical form-language became manifest and the secret of _spatial becoming_ opened out.