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.
As becoming is the foundation of the become, continuous living history that of fulfilled dead nature, the organic that of the mechanical, destiny that of causal law and the causally-settled, so too direction is the origin of extension. The secret of Life accomplishing itself which is touched upon by the word Time forms the foundation of that which, as accomplished, is understood by (or rather indicated to an inner feeling in us by) the word Space. Every extension that is actual has first been accomplished in and with an experience of depth, and what is primarily indicated by the word Time is just this process of extending, first sensuously (in the main, visually) and only later intellectually, into depth and distance, i.e., the step from the planar semi-impression to the macrocosmically ordered world-picture with its mysterious-manifest kinesis. We feel—and the feeling is what constitutes the state of all-round awareness in us—that we are in an extension that encircles us; and it is only necessary to follow out this original impression that we have of the worldly to see that in reality there is only one true “dimension” of space, which is direction from one’s self outwards into the distance, the “there” and the future, and that the abstract system of three dimensions is a mechanical representation and not a fact of life. By the depth-experience sensation is expanded into the world. We have seen already that the directedness that is in life wears the badge of irreversibility, and there is something of this same hall-mark of Time in our instinctive tendency to feel the depth that is in the world uni-directionally also—viz., from ourselves outwards, and never from the horizon inwards. The bodily mobility of man and beast is disposed in this sense. We move forward—towards the Future, nearing with every step not merely our aim but our old age—and we feel every backward look as a glance at something that is past, that has already become history.[[185]]
If we can describe the basic form of the understood, viz., causality, as destiny become rigid, we may similarly speak of spatial depth as a time become rigid. That which not only man but even the beast feels operative around him as destiny, he perceives by touching, looking, listening, scenting as movement, and under his intense scrutiny it stiffens and becomes causal. We feel that it is drawing towards spring and we feel in advance how the spring landscape expands around us; but we know that the earth as it moves in space revolves and that the duration of spring consists of ninety such revolutions of the earth, or days. Time gives birth to Space, but Space gives death to Time.
Had Kant been more precise, he would, instead of speaking of the “two forms of perception,” have called time the form of perception and space the form of the perceived, and then the connexion of the two would probably have revealed itself to him. The logician, mathematician, or scientist in his moments of intense thought, knows only the Become—which has been detached from the singular event by the very act of meditating upon it—and true systematic space—in which everything possesses the property of a mathematically-expressible “duration.” But it is just this that indicates to us how space is continuously “becoming.” While we gaze into the distance with our senses, it floats around us, but when we are startled, the alert eye sees a tense and rigid space. This space is; the principle of its existing at all is that it is, outside time and detached from it and from life. In it duration, a piece of perished time, resides as a known property of things. And, as we know ourselves too as being in this space, we know that we also have a duration and a limit, of which the moving finger of our clock ceaselessly warns us. But the rigid Space itself is transient too—at the first relaxation of our intellectual tension it vanishes from the many-coloured spread of our world-around—and so it is a sign and symbol of the most elemental and powerful symbol, of life itself.
For the involuntary and unqualified realization of depth, which dominates the consciousness with the force of an elemental event (simultaneously with the awakening of the inner life), marks the frontier between child and ... Man. The symbolic experience of depth is what is lacking in the child, who grasps at the moon and knows as yet no meaning in the outer world but, like the soul of primitive man, dawns in a dreamlike continuum of sensations (in traumhafter Verbundenheit mit allem Empfindungshaften hindämmert). Of course the child is not without experience of the extended, of a very simple kind, but there is no world-perception; distance is felt, but it does not yet speak to the soul. And with the soul’s awakening, direction, too, first reaches living expression—Classical expression in steady adherence to the near-present and exclusion of the distant and future; Faustian in direction-energy which has an eye only for the most distant horizons; Chinese, in free hither-and-thither wandering that nevertheless goes to the goal; Egyptian in resolute march down the path once entered. Thus the Destiny-idea manifests itself in every line of a life. With it alone do we become members of a particular Culture, whose members are connected by a common world-feeling and a common world-form derived from it. A deep identity unites the awakening of the soul, its birth into clear existence in the name of a Culture, with the sudden realization of distance and time, the birth of its outer world through the symbol of extension; and thenceforth this symbol is and remains the prime symbol of that life, imparting to it its specific style and the historical form in which it progressively actualizes its inward possibilities. From the specific directedness is derived the specific prime-symbol of extension, namely, for the Classical world-view the near, strictly limited, self-contained Body, for the Western infinitely wide and infinitely profound three-dimensional Space, for the Arabian the world as a Cavern. And therewith an old philosophical problem dissolves into nothing: this prime form of the world is innate in so far as it is an original possession of the soul of that Culture which is expressed by our life as a whole, and acquired in so far that every individual soul re-enacts for itself that creative act and unfolds in early childhood the symbol of depth to which its existence is predestined, as the emerging butterfly unfolds its wings. The first comprehension of depth is an act of birth—the spiritual complement of the bodily.[[186]] In it the Culture is born out of its mother-landscape, and the act is repeated by every one of its individual souls throughout its life-course. This is what Plato—connecting it with an early Hellenic belief—called anamnesis. The definiteness of the world-form, which for each dawning soul suddenly is, derives meaning from Becoming. Kant the systematic, however, with his conception of the form a priori, would approach the interpretation of this very riddle from a dead result instead of along a living way.
From now on, we shall consider the kind of extension as the prime symbol of a Culture. From it we are to deduce the entire form-language of its actuality, its physiognomy as contrasted with the physiognomy of every other Culture and still more with the almost entire lack of physiognomy in primitive man’s world-around. For now the interpretation of depth rises to acts, to formative expression in works, to the trans-forming of actuality, not now merely in order to subserve necessities of life (as in the case of the animals) but above all to create a picture out of extensional elements of all sorts (material, line, colour, tone, motion)—a picture, often, that re-emerges with power to charm after lost centuries in the world-picture of another Culture and tells new men of the way in which its authors understood the world.
But the prime symbol does not actualize itself; it is operative through the form-sense of every man, every community, age and epoch and dictates the style of every life-expression. It is inherent in the form of the state, the religious myths and cults, the ethical ideals, the forms of painting and music and poetry, the fundamental notions of each science—but it is not presented by these. Consequently, it is not presentable by words, for language and words are themselves derived symbols. Every individual symbol tells of it, but only to the inner feelings, not to the understanding. And when we say, as henceforth we shall say, that the prime-symbol of the Classical soul is the material and individual body, that of the Western pure infinite space, it must always be with the reservation that concepts cannot represent the inconceivable, and thus at the most a significative feeling may be evoked by the sound of words.
Infinite space is the ideal that the Western soul has always striven to find, and to see immediately actualized, in its world-around; and hence it is that the countless space-theories of the last centuries possess—over and above all ostensible “results”—a deep import as symptoms of a world-feeling. In how far does unlimited extension underlie all objective things? There is hardly a single problem that has been more earnestly pondered than this; it would almost seem as if every other world-question was dependent upon the one problem of the nature of space. And is it not in fact so—for us? And how, then, has it escaped notice that the whole Classical world never expended one word on it, and indeed did not even possess a word[[187]] by which the problem could be exactly outlined? Why had the great pre-Socratics nothing to say on it? Did they overlook in their world just that which appears to us the problem of all problems? Ought we not, in fact, to have seen long ago that the answer is in the very fact of their silence? How is it that according to our deepest feeling the “world” is nothing but that world-of-space which is the true offspring of our depth-experience, and whose grand emptiness is corroborated by the star-systems lost in it? Could a “world” of this sense have been made even comprehensible to a Classical thinker? In short, we suddenly discover that the “eternal problem” that Kant, in the name of humanity, tackled with a passion that itself is symbolic, is a purely Western problem that simply does not arise in the intellects of other Cultures.
What then was it that Classical man, whose insight into his own world-around was certainly not less piercing than ours, regarded as the prime problem of all being? It was the problem of ἀρχή, the material origin and foundation of all sensuously-perceptible things. If we grasp this we shall get close to the significance of the fact—not the fact of space, but the fact that made it a necessity of destiny for the space-problem to become the problem of the Western, and only the Western, soul.[[188]] This very spatiality (Räumlichkeit) that is the truest and sublimest element in the aspect of our universe, that absorbs into itself and begets out of itself the substantiality of all things, Classical humanity (which knows no word for, and therefore has no idea of, space) with one accord cuts out as the nonent, τὸ μὴ ὄν, that which is not. The pathos of this denial can scarcely be exaggerated. The whole passion of the Classical soul is in this act of excluding by symbolic negation that which it would not feel as actual, that in which its own existence could not be expressed. A world of other colour suddenly confronts us here. The Classical statue in its splendid bodiliness—all structure and expressive surfaces and no incorporeal arrière-pensée whatsoever—contains without remainder all that Actuality is for the Classical eye. The material, the optically definite, the comprehensible, the immediately present—this list exhausts the characteristics of this kind of extension. The Classical universe, the Cosmos or well-ordered aggregate of all near and completely viewable things, is concluded by the corporeal vault of heaven. More there is not. The need that is in us to think of “space” as being behind as well as before this shell was wholly absent from the Classical world-feeling. The Stoics went so far as to treat even properties and relations of things as “bodies.” For Chrysippus, the Divine Pneuma is a “body,” for Democritus seeing consists in our being penetrated by material particles of the things seen. The State is a body which is made up of all the bodies of its citizens, the law knows only corporeal persons and material things. And the feeling finds its last and noblest expression in the stone body of the Classical temple. The windowless interior is carefully concealed by the array of columns; but outside there is not one truly straight line to be found. Every flight of steps has a slight sweep outward, every step relatively to the next. The pediment, the roof-ridge, the sides are all curved. Every column has a slight swell and none stand truly vertical or truly equidistant from one another. But swell and inclination and distance vary from the corners to the centres of the sides in a carefully toned-off ratio, and so the whole corpus is given a something that swings mysterious about a centre. The curvatures are so fine that to a certain extent they are invisible to the eye and only to be “sensed.” But it is just by these means that direction in depth is eliminated. While the Gothic style soars, the Ionic swings. The interior of the cathedral pulls up with primeval force, but the temple is laid down in majestic rest. All this is equally true as relating to the Faustian and Apollinian Deity, and likewise of the fundamental ideas of the respective physics. To the principles of position, material and form we have opposed those of straining movement, force and mass, and we have defined the last-named as a constant ratio between force and acceleration, nay, finally volatilized both in the purely spatial elements of capacity and intensity. It was an obligatory consequence also of this way of conceiving actuality that the instrumental music of the great 18th-Century masters should emerge as a master-art—for it is the only one of the arts whose form-world is inwardly related to the contemplative vision of pure space. In it, as opposed to the statues of Classical temple and forum, we have bodiless realms of tone, tone-intervals, tone-seas. The orchestra swells, breaks, and ebbs, it depicts distances, lights, shadows, storms, driving clouds, lightning flashes, colours etherealized and transcendent—think of the instrumentation of Gluck and Beethoven. “Contemporary,” in our sense, with the Canon of Polycletus, the treatise in which the great sculptor laid down the strict rules of human body-build which remained authoritative till beyond Lysippus, we find the strict canon (completed by Stamitz about 1740) of the sonata-movement of four elements which begins to relax in late-Beethoven quartets and symphonies and, finally, in the lonely, utterly infinitesimal tone-world of the “Tristan” music, frees itself from all earthly comprehensibleness. This prime feeling of a loosing, Erlösung, solution, of the Soul in the Infinite, of a liberation from all material heaviness which the highest moments of our music always awaken, sets free also the energy of depth that is in the Faustian soul: whereas the effect of the Classical art-work is to bind and to bound, and the body-feeling secures, brings back the eye from distance to a Near and Still that is saturated with beauty.