Chapter IX

of G. H. Lewes’s _Life of Goethe_—a work that, taken all in all, is one of the wisest biographies ever written. In reading his critique of Goethe’s theory, of course, it has to be borne in mind that he wrote before the modern development of the electro-magnetic theory, which has substituted a merely mathematical existence for the Newtonian physical existence of colour-rays as such in white light. Now, this physical existence was just what, in substance, Goethe denied. What he affirmed, in the simpler language of his day, was that white light was something simple and colourless that becomes coloured through diminutions or modifications imposed upon it by “darkness.” The modern physicist, using a subtler hypothesis than Newton’s and a more refined “balance” than that which Lewes reproaches Goethe for “flinging away,” has found in white light, not the Newtonian mixture of colour-rays, but a surge of irregular wave-trains which are only regularized into colour-vibrations through being acted upon by analysers of one sort and another, from prisms to particulate matter. This necessity of a counter-agent for the production of colour seems—to a critical outsider at any rate—very like the necessity of an efficient negative principle or “opaque” that Goethe’s intuitive interpretation of his experiments led him to postulate. It is this that is the heart of the theory, and not the “simplicity” of light _per se_.

So much it seems desirable to add to the text and the reference, in order to expand the author’s statement that “both were right.” For Lewes, with all his sympathetic penetration of the man and real appreciation of his scientific achievement, feels obliged to regard his methods and his theory as such as “erroneous.” And it is perhaps not out of place in this book to adduce an instance of the peculiar nature and power of intuitive vision (which entirely escapes direct description) in which Vision frankly challenges Reason on its own ground, meets with refutation (or contempt) from the Reason of its day, and yet may come to be upheld in its specific rightness (its rightness as vision, that is, apart from its technical enunciation by the seer) by the Reason of a later day.—_Tr._

Footnote 178:

See p. 123.

Footnote 179:

See page 123.

Footnote 180:

The word _dimension_ ought only to be used in the singular. It means extension but not extensions. The idea of the three directions is an out-and-out abstraction and is not contained in the immediate extension-feeling of the body (the “soul”). Direction as such, the direction-essence, gives rise to the mysterious _animal_ sense of right and left and also the _vegetable_ characteristic of below-to- above, earth to heaven. The latter is a fact felt dream-wise, the former a truth of waking existence to be learned and therefore capable of being transmuted. Both find expression in architecture, to wit, in the symmetry of the plan and the energy of the elevation, and it is only because of this that we specially distinguish in the “architecture” of the space around us the angle of 90° in preference, for example, to that of 60°. Had not this been so, the conventional number of our “dimensions” would have been quite different.

Footnote 181:

The want of perspective in children’s drawings is emphatically not perceptible to the children themselves.

Footnote 182:

His idea that the _a priori_-ness of space was proved by and through the unconditional validity of simple geometrical facts rests, as we have already remarked, on the all-too-popular notion that mathematics are either geometry or arithmetic. Now, even in Kant’s time the mathematic of the West had got far beyond this naïve scheme, which was a mere imitation of the Classical. Modern geometry bases itself not on space but on multiply-infinite number-manifolds—amongst which the three-dimensional is simply the undistinguished special case—and within these groups investigates functional formations with reference to their structure; that is, there is no longer any contact or even possibility of contact between any possible kind of sense-perception and mathematical facts in the domain of such extensions as these, and yet the demonstrability of the latter is in no wise impaired thereby. Mathematics, then, are independent of the perceived, and the question now is, how much of this famous demonstrability of the forms of perception is left when the artificiality of juxtaposing both in a supposedly single process of experience has been recognized.

Footnote 183:

It is true that a geometrical theorem may be proved, or rather demonstrated, by means of a drawing. But the theorem is differently constituted in every kind of geometry, and that being so, the drawing ceases to be a _proof_ of anything whatever.

Footnote 184:

So much so that Gauss said nothing about his discovery until almost the end of his life for tear of “the clamour of the Bœotians.”

Footnote 185:

The distinction of right and left (see p. 169) is only conceivable as the outcome of this directedness in the dispositions of the body. “In front” has no meaning whatever for the body of a plant.

Footnote 186:

It may not be out of place here to refer to the enormous importance attached in savage society to initiation-rites at adolescence.—_Tr._

Footnote 187:

Either in Greek or in Latin, τόπος (= _locus_) means spot, locality, and also social position; χώρα (= _spatium_) means space-between, distance, rank, and also ground and soil (e.g., τὰ ἐκ τῆς χώρας, produce); τὸ κένον (_vacuum_) means quite unequivocally a hollow body, and the stress is emphatically on the envelope. The literature of the Roman Imperial Age, which attempted to render the _Magian_ world- feeling through Classical words, was reduced to such clumsy versions as ὁρατὸς τόπος (sensible world) or _spatium inane_ (“endless space,” but also “wide surface”—the root of the word “spatium” means to swell or grow fat). In the true Classical literature, the idea not being there, there was no necessity for a word to describe it.

Footnote 188:

It has not hitherto been seen that this fact is implicit in Euclid’s famous parallel axiom (“through a point only one parallel to a straight line is possible”).

This was the only one of the Classical theorems which remained unproved, and as we know now, it is incapable of proof. But it was just that which made it into a dogma (as opposed to any experience) _and therefore the metaphysical centre_ and main girder of that geometrical system. Everything else, axiom or postulate, is merely introductory or corollary to this. This one proposition is necessary and universally-valid for the Classical intellect, _and yet not deducible_. What does this signify?

It signifies that the statement is a _symbol_ of the first rank. It contains the structure of Classical corporeality. It is just this proposition, theoretically the weakest link in the Classical geometry (objections began to be raised to it as early as Hellenistic times), that reveals its soul, and it was just this proposition, self-evident within the limits of routine experience, that the Faustian number- thinking, derived from incorporeal spatial distances, fastened upon as the centre of doubt. It is one of the deepest symbols of _our_ being that we have opposed to the Euclidean geometry not one but _several_ other geometries all of which for us are equally true and self- consistent. The specific tendency of the anti-Euclidean group of geometries—in which there may be no parallel or two parallels or several parallels to a line through a point—lies in the fact that by their very plurality the corporeal sense of extension, which Euclid _canonized_ by his principle, is entirely got rid of; for what they reject is that which all corporeal postulates but all spatial denies. The question of which of the three Non-Euclidean geometries is the “correct” one (i.e., that which underlies actuality)—although Gauss himself gave it earnest consideration—is in respect of world-feeling entirely Classical and therefore it should not have been asked by a thinker of our sphere. Indeed it prevents us from seeing the true and deep meaning implicit in the plurality of these geometries. The specifically Western symbol resides not in the reality of one or of another, but in the true plurality of _equally possible_ geometries. It is the _group_ of space-structures—in the abundance of which the classical system is a mere particular case—that has dissolved the last residuum of the corporeal into the pure space-feeling.

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V

Each of the great Cultures, then, has arrived at a secret language of world-feeling that is only fully comprehensible by him whose soul belongs to that Culture. We must not deceive ourselves. Perhaps we can read a little way into the Classical soul, because its form-language is almost the exact inversion of the Western; how far we have succeeded or can ever succeed is a question which necessarily forms the starting- point of all criticism of the Renaissance, and it is a very difficult one. But when we are told that probably (it is at best a doubtful venture to meditate upon so alien an expression of Being) the Indians conceived numbers which according to our ideas possessed neither value nor magnitude nor relativity, and which only became positive and negative, great or small units in virtue of position, we have to admit that it is impossible for us exactly to re-experience what spiritually underlies this kind of number. For us, 3 is always _something_, be it positive or negative; for the Greeks it was unconditionally a positive magnitude, +3; but for the Indian it indicates a possibility without existence, to which the word “something” is _not yet_ applicable, outside both existence and non-existence which are _properties_ to be introduced into it. +3, -3, ⅓, are thus emanating actualities of subordinate rank which reside in the mysterious substance (3) in some way that is entirely hidden from us. It takes a Brahmanic soul to perceive these numbers as self-evident, as ideal emblems of a self- complete world-form; to us they are as unintelligible as is the Brahman Nirvana, for which, as lying beyond life _and_ death, sleep _and_ waking, passion, compassion _and_ dispassion and yet somehow actual, words entirely fail us. Only this spirituality could originate the grand conception of _nothingness as a true number, zero_, and even then this zero is the Indian zero for which existent and non-existent are equally external designations.[189]

Arabian thinkers of the ripest period—and they included minds of the very first order like Alfarabi and Alkabi—in controverting the ontology of Aristotle, _proved_ that the body as such did not necessarily assume space for existence, and deduced the essence of this space—the _Arabian_ kind of extension, that is—from the characteristic of “one’s being in a position.”

But this does not prove that as against Aristotle and Kant they were in error or that their thinking was muddled (as we so readily say of what our own brains cannot take in). It shows that the Arabian spirit possessed other world-categories than our own. They could have rebutted Kant, or Kant them, with the same subtlety of proof—and both disputants would have remained convinced of the correctness of their respective standpoints.

When we talk of space to-day, we are all thinking more or less in the same style, just as we are all using the same languages and word-signs, whether we are considering mathematical space or physical space or the space of painting or that of actuality, although all philosophizing that insists (as it must) upon putting an _identity_ of understanding in the place of such kinship of significance-feeling must remain somewhat questionable. But no Hellene or Egyptian or Chinaman could re-experience any part of those feelings of ours, and no artwork or thought-system could possibly convey to him unequivocally what “space” means for us. Again, the prime conceptions originated in the quite differently constituted soul of the Greek, like ἀρχή, ὕλη, μορφἠ, comprise the whole content of his world. But this world is differently constituted from ours. It is, for us, alien and remote. We may take these words of Greek and translate them by words of our own like “origin,” “matter” and “form,” but it is mere imitation, a feeble effort to penetrate into a world of feeling in which the finest and deepest elements, in spite of all we can do, remain dumb; it is as though one tried to set the Parthenon sculptures for a string quartet, or cast Voltaire’s God in bronze. The master-traits of thought, life and world-consciousness are as manifold and different as the features of individual men; in those respects as in others there are distinctions of “races” and “peoples,” and men are as unconscious of these distinctions as they are ignorant of whether “red” and “yellow” do or do not mean the same for others as for themselves. It is particularly the common symbolic of language that nourishes the illusion of a homogeneous constitution of human inner-life and an identical world-form; in this respect the great thinkers of one and another Culture resemble the colour-blind in that each is unaware of his own condition and smiles at the errors of the rest.

And now I draw the conclusions. There is a plurality of prime symbols. It is the depth-experience through which the world becomes, through which perception _extends itself_ to world. Its signification is for the soul to which it belongs and only for that soul, and it is different in waking and dreaming, acceptance and scrutiny, as between young and old, townsmen and peasant, man and woman. It actualizes for every high Culture the possibility of form upon which that Culture’s existence rests and it does so of deep necessity. All fundamentals words like our mass, substance, material, thing, body, extension (and multitudes of words of the like order in other culture-tongues) are emblems, obligatory and determined by destiny, that out of the infinite abundance of world-possibilities evoke in the name of the individual Culture those possibilities that alone are significant and therefore necessary for it. None of them is exactly transferable just as it is into the experiential living and knowing of another Culture. And none of these prime words ever recurs. The _choice of prime symbol_ in the moment of the Culture- soul’s awakening into self-consciousness on its own soil—a moment that for one who can read world-history thus contains something catastrophic— decides all.

Culture, as the soul’s total expression “become” and perceptible in gestures and works, as its mortal transient body, obnoxious to law, number and causality:

As the historical drama, a picture in the whole picture of world- history:

As the sum of grand emblems of life, feeling and understanding:

—this is the language through which alone a soul can tell of what it undergoes.

The macrocosm, too, is a property of the individual soul; we can never know how it stands with the soul of another. That which is implied by “infinite space,” the space that “passeth all understanding,” which is the creative interpretation of depth-experience proper and peculiar to us men of the West—the kind of extension that is nothingness to the Greeks, the Universe to us—dyes our world in a colour that the Classical, the Indian and the Egyptian souls had not on their palettes. One soul listens to the world-experience in A flat major, another in F minor; one apprehends it in the Euclidean spirit, another in the contrapuntal, a third in the Magian spirit. From the purest analytical Space and from Nirvana to the most somatic reality of Athens, there is a series of prime symbols each of which is capable of forming a complete world out of itself. And, as the idea of the Babylonian or that of the Indian world was remote, strange and elusive for the men of the five or six Cultures that followed, so also the Western world will be incomprehensible to the men of Cultures yet unborn.

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## CHAPTER VI MAKROKOSMOS

II

APOLLINIAN, FAUSTIAN AND MAGIAN SOUL

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