And there is something of this primitive expression of world-fear in the way in which all systematic philosophies use mere names as a last resort for getting rid of the Incomprehensible, the Almighty that is all too mighty for the intellect. We name something or other the “Absolute,” and we feel ourselves at once its superior. Philosophy, the love of Wisdom, is at the very bottom defence against the incomprehensible. What is named, comprehended, measured is ipso facto overpowered, made inert and taboo.[[107]] Once more, “knowledge is power.” Herein lies one root of the difference between the idealist’s and the realist’s attitude towards the Unapproachable; it is expressed by the two meanings of the German word Scheu—respect and abhorrence.[[108]] The idealist contemplates, the realist would subject, mechanize, render innocuous. Plato and Goethe accept the secret in humility, Aristotle and Kant would open it up and destroy it. The most deeply significant example of this realism is in its treatment of the Time problem. The dread mystery of Time, life itself, must be spellbound and, by the magic of comprehensibility, neutralized.
All that has been said about time in “scientific” philosophy, psychology and physics—the supposed answer to a question that had better never have been asked, namely what is time?—touches, not at any point the secret itself, but only a spatially-formed representative phantom. The livingness and directedness and fated course of real Time is replaced by a figure which, be it never so intimately absorbed, is only a line, measurable, divisible, reversible, and not a portrait of that which is incapable of being portrayed; by a “time” that can be mathematically expressed in such forms as √t, t², -t, from which the assumption of a time of zero magnitude or of negative times is, to say the least, not excluded.[[109]] Obviously this is something quite outside the domain of Life, Destiny, and living historical Time; it is a purely conceptual time-system that is remote even from the sensuous life. One has only to substitute, in any philosophical or physical treatise that one pleases, this word “Destiny” for the word “time” and one will instantly see how understanding loses its way when language has emancipated it from sensation, and how impossible the group “time and space” is. What is not experienced and felt, what is merely thought, necessarily takes a spatial form, and this explains why no systematic philosopher has been able to make anything out of the mystery-clouded, far-echoing sound symbols “Past” and “Future.” In Kant’s utterances concerning time they do not even occur, and in fact one cannot see any relation which could connect them with what is said there. But only this spatial form enables time and space to be brought into functional interdependence as magnitudes of the same order, as four-dimensional vector analysis[[110]] conspicuously shows. As early as 1813 Lagrange frankly described mechanics as a four-dimensional geometry, and even Newton’s cautious conception of “tempus absolutum sive duratio” is not exempt from this intellectually inevitable transformation of the living into mere extension. In the older philosophy I have found one, and only one, profound and reverent presentation of Time; it is in Augustine—“If no one questions me, I know: if I would explain to a questioner, I know not.”[[111]]
When philosophers of the present-day West “hedge”—as they all do—by saying that things are in time as in space and that “outside” them nothing is “conceivable,” they are merely putting another kind of space (Räumlichkeit) beside the ordinary one, just as one might, if one chose, call hope and electricity the two forces of the universe. It ought not, surely, to have escaped Kant when he spoke of the “two forms” of perception, that whereas it is easy enough to come to a scientific understanding about space (though not to “explain” it, in the ordinary sense of the word, for that is beyond human powers), treatment of time on the same lines breaks down utterly. The reader of the “Critique of Pure Reason” and the “Prolegomena” will observe that Kant gives a well-considered proof for the connexion of space and geometry but carefully avoids doing the same for time and arithmetic. There he did not go beyond enunciation, and constant reassertion of analogy between the two conceptions lured him over a gap that would have been fatal to his system. Vis-à-vis the Where and the How, the When forms a world of its own as distinct as is metaphysics from physics. Space, object, number, notion, causality are so intimately akin that it is impossible—as countless mistaken systems prove—to treat the one independently of the other. Mechanics is a copy of the logic of its day and vice versa. The picture of thought as psychology builds it up and the picture of the space-world as contemporary physics describes it are reflections of one another. Conceptions and things, reasons and causes, conclusions and processes coincide so nicely, as received by the consciousness, that the abstract thinker himself has again and again succumbed to the temptation of setting forth the thought-“process” graphically and schematically—witness Aristotle’s and Kant’s tabulated categories. “Where there is no scheme, there is no philosophy” is the objection of principle—unacknowledged though it may be—that all professional philosophers have against the “intuitives,” to whom inwardly they feel themselves far superior. That is why Kant crossly describes the Platonic style of thinking “as the art of spending good words in babble” (die Kunst, wortreich zu schwatzen), and why even to-day the lecture-room philosopher has not a word to say about Goethe’s philosophy. Every logical operation is capable of being drawn, every system a geometrical method of handling thoughts. And therefore Time either finds no place in the system at all, or is made its victim.
This is the refutation of that widely-spread misunderstanding which connects time with arithmetic and space with geometry by superficial analogies, an error to which Kant ought never to have succumbed—though it is hardly surprising that Schopenhauer, with his incapacity for understanding mathematics, did so. Because the living act of numbering is somehow or other related to time, number and time are constantly confused. But numbering is not number, any more than drawing is a drawing. Numbering and drawing are a becoming, numbers and figures are things become. Kant and the rest have in mind now the living act (numbering) and now the result thereof (the relations of the finished figure); but the one belongs to the domain of Life and Time, the other to that of Extension and Causality. That I calculate is the business of organic, what I calculate the business of inorganic, logic. Mathematics as a whole—in common language, arithmetic and geometry—answers the How? and the What?—that is, the problem of the Natural order of things. In opposition to this problem stands that of the When? of things, the specifically historical problem of destiny, future and past; and all these things are comprised in the word Chronology, which simple mankind understands fully and unequivocally.
Between arithmetic and geometry there is no opposition.[[112]] Every kind of number, as has been sufficiently shown in an earlier chapter, belongs entirely to the realm of the extended and the become, whether as a Euclidean magnitude or as an analytical function; and to which heading should we have to assign the cyclometric[[113]] functions, the Binomial Theorem, the Riemann surfaces, the Theory of Groups? Kant’s scheme was refuted by Euler and d’Alembert before he even set it up, and only the unfamiliarity of his successors with the mathematics of their time—what a contrast to Descartes, Pascal and Leibniz, who evolved the mathematics of their time from the depths of their own philosophy!—made it possible for mathematical notions of a relation between time and arithmetic to be passed on like an heirloom, almost uncriticized.
But between Becoming and any part whatsoever of mathematics there is not the slightest contact. Newton indeed was profoundly convinced (and he was no mean philosopher) that in the principles of his Calculus of Fluxions[[114]] he had grasped the problem of Becoming, and therefore of Time—in a far subtler form, by the way, than Kant’s. But even Newton’s view could not be upheld, even though it may find advocates to this day. Since Weierstrass proved that continuous functions exist which either cannot be differentiated at all or are capable only of partial differentiation, this most deep-searching of all efforts to close with the Time-problem mathematically has been abandoned.
III
Time is a counter-conception (Gegenbegriff) to Space, arising out of Space, just as the notion (as distinct from the fact) of Life arises only in opposition to thought, and the notion (as distinct from the fact) of birth and generation only in opposition to death.[[115]] This is implicit in the very essence of all awareness. Just as any sense-impression is only remarked when it detaches itself from another, so any kind of understanding that is genuine critical activity[[116]] is only made possible through the setting-up of a new concept as anti-pole to one already present, or through the divorce (if we may call it so) of a pair of inwardly-polar concepts which as long as they are mere constituents, possess no actuality.[[117]] It has long been presumed—and rightly, beyond a doubt—that all root-words, whether they express things or properties, have come into being by pairs; but even later, even to-day, the connotation that every new word receives is a reflection of some other. And so, guided by language, the understanding, incapable of fitting a sure inward subjective certainty of Destiny into its form-world, created “time” out of space as its opposite. But for this we should possess neither the word nor its connotation. And so far is this process of word-formation carried that the particular style of extension possessed by the Classical world led to a specifically Classical notion of time, differing from the time-notions of India, China and the West exactly as Classical space differs from the space of these Cultures.[[118]]
For this reason, the notion of an art-form—which again is a “counter-concept”—has only arisen when men became aware that their art-creations had a connotation (Gehalt) at all, that is, when the expression-language of the art, along with its effects, had ceased to be something perfectly natural and taken-for-granted, as it still was in the time of the Pyramid-Builders, in that of the Mycenæan strongholds and in that of the early Gothic cathedrals. Men become suddenly aware of the existence of “works,” and then for the first time the understanding eye is able to distinguish a causal side and a destiny side in every living art.
In every work that displays the whole man and the whole meaning of the existence, fear and longing lie close together, but they are and they remain different. To the fear, to the Causal, belongs the whole “taboo” side of art—its stock of motives, developed in strict schools and long craft-training, carefully protected and piously transmitted; all of it that is comprehensible, learnable, numerical; all the logic of colour, line, structure, order, which constitutes the mother-tongue of every worthy artist and every great epoch. But the other side, opposed to the “taboo” as the directed is to the extended and as the development-destiny within a form-language to its syllogisms, comes out in genius (namely, in that which is wholly personal to the individual artists, their imaginative powers, creative passion, depth and richness, as against all mere mastery of form) and, beyond even genius, in that superabundance of creativeness in the race which conditions the rise and fall of whole arts. This is the “totem” side, and owing to it—notwithstanding all the æsthetics ever penned—there is no timeless and solely-true way of art, but only a history of art, marked like everything that lives with the sign of irreversibility.[[119]]