The Decline of the West| Project Gutenberg

175. The formation of hypotheses in Chemistry is much more thoughtless, owing to the less close relation of that science to mathematics. A house of cards such as is presented to us in the researches of the moment on atom-structure (see, for example, M. Born, Der Aufbau der Materie, 1920) would be impossible in the near neighbourhood of the electro-magnetic theory of light, whose authors never for a moment lost sight of the frontier between mathematical vision and its representation by a picture, or of the fact that this was only a picture.

176. There is no difference essentially between these representations and the switchboard wiring-diagram.

177. Goethe’s theory of colour openly controverted Newton’s theory of light. A long account of the controversy will be found in 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.

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.

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

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.

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.

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.”

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.

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.

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.

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.

189. This zero, which probably contains a suggestion of the Indian idea of extension—of that spatiality of the world that is treated in the Upanishads and is entirely alien to our space-consciousness—was of course wholly absent in the Classical. By way of the Arabian mathematics (which completely transformed its meaning) it reached the West, where it was only introduced in 1554 by Stipel, with its sense, moreover, again fundamentally changed, for it became the mean of +1 and -1 as a cut in a linear continuum, i.e., it was assimilated to the Western number-world in a wholly un-Indian sense of relation.

190. The word Höhlengefühl is Leo Frobenius’s (Paideuma, p. 92). (The Early-Christian Church of the Nativity at Bethlehem [A.D. 327] is built over a natural cave.—Tr.)

191. Strzygowski’s Ursprung der Christlichen Kirchenkunst (1920), p. 80.

192. See Vol. II, p. 101 et seq.

193. See Vol. II, pp. 345 et seq.

194. Müller-Decker, Die Etrusker (1877), II, pp. 128 et seq. Wissowa, Religion und Kultus der Römer (1912), p. 527. The oldest plan of Roma Quadrata was a “templum” whose limits had nothing to do with the building-up of the city but were connected with sacral rules, as the significance of this precinct (the “Pomœrium”) in later times shows. A “templum,” too, was the Roman camp whose rectangular outline is visible to-day in many a Roman-founded town; it was the consecrated area within which the army felt itself under the protection of its gods, and originally had nothing whatever to do with fortification, which is a product of Hellenistic times. (It may be added that Roman camps retained their rigidity of outline even where obvious “military considerations” of ground, etc., must have suggested its modification.—Tr.) Most Roman stone-temples ("ædes") were not “templa” at all. On the other hand, the early Greek τέμενος of Homeric times must have had a similar significance.

195. The student may consult the articles “Church History,” “Monasticism,” “Eucharist” and other articles therein referred to in the Encyclopædia Britannica, XI Edition.—Tr.

196. English readers may remember that Cobbett (“Rural Rides,” passim) was so impressed with the spaciousness of English country churches as to formulate a theory that mediæval England must have been more populous than modern England is.—Tr.

197. Cf. my introduction to Ernst Droem’s Gesänge, p. ix.

198. The oldest and most mystical of the poems of the “Elder Edda.”—Tr.

199. See Vol. II, p. 358 et seq.

200. See Vol. II, pp. 241 et seq.

201. See Vol. II, p. 354.

202. This refers to the diaphonic chant of Church music in the eleventh and twelfth centuries. The form of this chant is supposed to have been an accompaniment of the “plain chant” by voices moving parallel to it at a fourth, fifth, or octave.—Tr.

203. Hölscher, Grabdenkmal des Königs Chephren; Borchardt, Grabdenkmal des Sahurê; Curtius, Die Antike Kunst, p. 45.

204. See Vol. II, p. 342; Borchardt, Re-Heiligtum des Newoserri; Ed. Mayer, Geschichte des Altertums, I, 251.

205. “Relief en creux”; compare H. Schäfer, Von ägyptischer Kunst (1919), I, p. 41.

206. See Vol. II, pp. 350 et seq.

207. O. Fischer, Chinesische Landmalerei (1921), p. 24. What makes Chinese—as also Indian—art so difficult a study for us is the fact that all works of the early periods (namely, those of the Hwangho region from 1300 to 800 B.C. and of pre-Buddhist India) have vanished without a trace. But that which we now call “Chinese art” corresponds, say, to the art of Egypt from the Twentieth Dynasty onward, and the great schools of painting find their parallel in the sculpture schools of the Saïte and Ptolemaic periods, in which an antiquarian preciosity takes the place of the living inward development that is no longer there. Thus from the examples of Egypt we are able to tell how far it is permissible to argue backwards to conclusions about the art of Chóu and Vedic times.

208. C. Glaser, Die Kunst Ostasiens (1920), p. 181.

209. Glaser, op. cit., p. 43.

210. See Vol. II, pp. 135 et seq.

211. The monologue-art of very lonely natures is also in reality a conversation with self in the second person. But it is only in the intellectuality of the megalopolitan stages that the impulse to express is overcome by the impulse to communicate (see Vol. II, p. 135) which gives rise to that tendencious art that seeks to instruct or convert or prove views of a politico-social or moral character, and provokes the antagonistic formula of “Art for Art’s sake”—which is itself rather a view than a discipline, though it does at least serve to recall the primitive significance of artistic expression.

212. See Vol. II, pp. 138 et seq., and Worringer, Abstraktion und Einführung, pp. 66 et seq.

213. Imitation, being life, is past in the very moment of accomplishment. The curtain falls, and it passes either into oblivion or, if the product is a durable artifact, into art-history. Of the songs and dances of old Cultures nothing remains, of their pictures and poems little. And even this little contains, substantially, only the ornamental side of the original imitation. Of a grand drama there remains only the text, not the image and the sound; of a poem only the words, not the recital; and of all their music the notes at most, not the tone-colours of the instruments. The essential is irrevocably gone, and every “reproduction” is in reality something new and different.

214. For the workshop of Thothmes at Tell-el-Amarna, see Mitteilungen der Deutschen Orient-Gesellschaft, No. 52, pp. 28 et seq.

215. K. Burdach, Deutsche Renaissance, p. 11. The pictorial art of the Gothic period also has its strict typism and symbolism.

216. E. Norden, Antike Kunst-prosa, pp. 8 et seq.

217. See Vol. II, p. 323.

218. The translation is so far a paraphrase here that it is desirable to reproduce the German original: “Alles Schöne vergeht mit dem Lebenspulsschlag (dessen) der es aus dem kosmischen Takt heraus als solches empfindet.”

219. Hence the ornamental character of script.

221. See Vol. II, p. 104.

222. E.g., the Slavonic round-villages and Teutonic street-villages east of the Elbe. Similarly, conclusions can be drawn as to many of the events of the Homeric age from the distribution of round and rectangular buildings in ancient Italy.

223. See Vol. II, p. 109.

225. See Vol. II, pp. 142 et seq.

228. The same applies to the architecture of Thinite Egypt and to the Seleucid-Persian sun and fire temples of the pre-Christian area.

229. The combination of scrolls and “Greek keys” with the Dragon or other emblem of storm-power.—Tr.

230. Dvorák, Idealismus und Naturalismus in der got. Skulptur u. Malerei (Hist. Zeitschrift, 1918, pp. 44 et seq.).

231. And, finally, ornament in the highest sense includes script, and with it, the Book, which is the true associate of the cult-building, and as an art-work always appears and disappears with it. (See Vol. II, pp. 182. et seq., pp. 298 et seq.) In writing, it is understanding as distinct from intuition that attains to form: it is not essences that those signs symbolize but notions abstracted therefrom by words, and as for the speech-habituated human intellect rigid space is the presented objective, the writing of a Culture is (after its stone-building) the purest of all expressions of its prime-symbol. It is quite impossible to understand the history of Arabesque if we leave the innumerable Arabian scripts out of consideration, and it is no less impossible to separate Egyptian and Chinese style-history from the history of the corresponding writing-signs and their arrangement and application.

233. Certainly the Greeks at the time when they advanced from the Antæ to the Peripteros were under the mighty influence of the Egyptian series-columns—it was at this time that their sculpture in the round, indisputably following Egyptian models, freed itself from the relief manner which still clings to the Apollo figures. But this does not alter the fact that the motive of the Classical column and the Classical application of the rank-principle were wholly and peculiarly Classical.

234. The surface of the space-volume itself, not that of the stone. Dvorák, Hist. Ztschr., 1918, pp. 17 et seq.

235. Dehio, Gesch. der deutschen Kunst, I, p. 16.

236. For descriptions and illustrations of types of Doming and Vaulting, see the article Vault in Ency. Brit., XI Ed.—Tr.

237. “Mosque of Omar.”—Tr.

238. H. Schäfer, Von Aegyptischer Kunst, I, pp. 15 et seq.

(The bulls are shown in Fig. 18 in the article Egypt in the Encyclopædia Britannica, XI Edition, Vol. IX, pp. 65-66.—Tr.)

239. Frankl, Baukunst des Mittelalters (1918), pp. 16 et seq.

240. See Vol. II, pp. 361 et seq. The lack of any vertical tendency in the Russian life-feeling is perceptible also in the saga-figure of Ilya Murometz (see Vol. II, p. 231). The Russian has not the smallest relation with a Father-God. His ethos is not a filial but purely a fraternal love, radiating in all directions along the human plane. Christ, even, is conceived as a Brother. The Faustian, wholly vertical, tendency to strive up to fulfilment is to the real Russian an incomprehensible pretension. The same absence of all vertical tendency is observable in Russian ideas of the state and property.

241. The cemetery church of Kishi has 22.

242. J. Grabar, “History of Russian Art” (Russian, 1911), I-III. Eliasberg, Russ. Baukunst (1922), Introduction.

243. The disposition of Egyptian and that of Western history are so clear as to admit of comparison being carried right down into the details, and it would be well worth the expert’s while to carry out such an investigation. The Fourth Dynasty, that of the strict Pyramid style, B.C. 2930-2750 (Cheops, Chephren), corresponds to the Romanesque (980-1100), the Fifth Dynasty (2750-2625, Sahu-rê) to the early Gothic (1100-1230), and the Sixth Dynasty, prime of the archaic portraiture (2625-2475, Phiops I and II), to the mature Gothic of 1230-1400.

244. That which differentiates the Japanese harakiri from this suicide is its intensely purposeful and (so to put it) active and demonstrative character.—Tr.

245. See Vol. II, p. 626.

246. Koldewey-Puchstein, Die griech. Tempel in Unter-Italien und Sizilien, I, p. 228.

247. See Vol. II, Chapter III.

248. See Vol. II, pp. 240 et seq.

249. Stilfragen, Grundlage zu einer Geschichte der Ornamentik (1893). Spatrömische Kunstindustrie (1901).

250. Amida (1910). Die bildende Kunst des Ostens (1916), Altai-Iran (1917). Die Baukunst der Armenier und Europa (1918).

251. These contradictions of detail are not greater, after all, than those between Doric, Attic and Etruscan art, and certainly less than those which existed about 1450 between Florentine Renaissance, North French, Spanish and East-German (brick) Gothic.

252. See Vol. II, pp. 304 et seq.

253. For a brief description of the components of a Mithræum, the student may be referred to the Encyclopædia Britannica, XI Edition, art. Mithras (Section II).—Tr.

254. The oldest Christian designs in the Empire of Axum undoubtedly agree with the pagan work of the Sabæans.

255. See Vol. II, pp. 143 et seq.

256. See Vol. II, pp. 316 et seq.

257. Kohl & Watzinger, Antike Synagogen in Galilãa (1916). The Baal-shrines in Palmyra, Baalbek and many other localities are basilicas: some of them are older than Christianity and many of them were later taken over into Christian use.

258. Frauberger, Die Akropolis von Baalbek, plate 22. (See Ency. Brit., XI Edition, art. “Baalbek,” for plan, etc.—Tr.)

259. Diez, Die Kunst der islamischen Völker, pp. 8 et seq. In old Sabæan temples the altar-court (mahdar) is in front of the oracle chapel (makanat).

260. Wulff, Altchristliche und byzantinische Kunst, p. 227.

261. Pliny records that this region was rich in temples. It is probable that the type of the transept-basilica—i.e., with the entrance in one of the long sides—which is found in Hauran and is distinctly marked in the tranverse direction of the altar space of St. Paul Without at Rome, is derived from a South Arabian archetype. (For the Hauran type of church see Ency. Brit., XI Ed., Vol. II, p. 390; and for St. Paul Without, Vol. III, p. 474.—Tr.

262. Neither technically nor in point of space-feeling has this piece of purely interior architecture any connexion whatever with Etruscan round-buildings. (Altmann, Die ital. Rundbauten, 1906.) With the cupolas of Hadrian’s Villa at Tibur (Tivoli), on the contrary, its affinity is evident.

263. Probably synagogues of domical type reached these regions, and also Morocco, long before Islam, through the missionary enterprise of Mesopotamian Judaism (see Vol. II, p. 253), which was closely allied in matters of taste to Persia. The Judaism of the Pseudomorphosis, on the contrary, built basilicas; its Roman catacombs show that artistically it was entirely on a par with Western Christianity. Of the two, it is the Judæo-Persian style coming from Spain that has become the pattern for the synagogues of the West—a point that has hitherto entirely escaped the notice of art-research.

264. Generally called the “Basilica of Constantine.”—Tr.

265. The Grail legend contains, besides old Celtic, well-marked Arabian elements; but where Wolfram von Eschenbach goes beyond his model Chrestien de Troyes, his Parzival is entirely Faustian. (See articles Grail and Perceval, Ency. Brit., XI Ed.)Ed.)—Tr.

266. The relation of column and arch spiritually corresponds to that of wall and cupola, and the interposition of the drum between the rectangle and the dome occurs “simultaneously” with that of the impost between the column and the arch.

267. A. Riegl, Stilfragen (1893), pp. 248 et seq., 272 et seq.

268. The Ghassanid Kingdom flourished in the extreme North-west of Arabia during the sixth century of our reckoning. Its people were essentially Arab, and probably came from the south; and an outlying cousinry inhabited Medina in the time of the Prophet.—Tr.

269. Dehio, Gesch. der deutschen Kunst, I, pp. 16 et seq.

270. Wulff, Altchristl.-byzant. Kunst, pp. 153 et seq.

271. See Vol. II, p. 315, Geffcken, Der Ausgang des griech-röm. Heidentums (1920), p. 113.

272. Die bildenden Künste. The expression is a standard one in German, but unfamiliar in English. Ordinarily, however, “die bildenden Künste” (shaping arts, arts of form) are contrasted with “die redenden Künste” (speaking arts)—music, as giving utterance rather than spatial form to things, being counted among the latter.—Tr.

273. As soon as the word, which is a transmission-agent of the understanding, comes to be used as the expression-agent of an art, the waking consciousness ceases to express or to take in a thing integrally. Not to mention the read word of higher Cultures—the medium of literature proper—even the spoken word, when used in any artificial sense, separates hearing from understanding, for the ordinary meaning of the word also takes a hand in the process and, as this art grows in power, the wordless arts themselves arrive at expression-methods in which the motives are joined to word-meanings. Thus arises the Allegory, or motive that signifies a word, as in Baroque sculpture after Bernini. So, too, painting very often develops into a sort of painting-writing, as in Byzantium after the second Nicene Council (787) which took from the artist his freedom of choice and arrangement. This also is what distinguishes the arias of Gluck, in which the melody grew up out of the meaning of the libretto, from those of Alessandro Scarlatti, in which the texts are in themselves of no significance and mostly serve to carry the voices. The high-Gothic counterpoint of the 13th Century is entirely free from any connexion with words: it is a pure architecture of human voices in which several texts, Latin and vernacular, sacred and secular, were sung together.