The decline of the West

by Oswald Spengler

XV

It remains now to sketch the last stage of Western science. From our standpoint of to-day, the gently-sloping route of decline is clearly visible.

This too, the power of looking ahead to inevitable Destiny, is part of the historical capacity that is the peculiar endowment of the Faustian. The Classical died, as we shall die, but it died unknowing. It believed in an eternal Being and to the last it lived its days with frank satisfaction, each day spent as a gift of the gods. But we know our history. Before us there stands a last spiritual crisis that will involve all Europe and America. What its course will be, Late Hellenism tells us. The tyranny of the Reason—of which we are not conscious, for we are ourselves its apex—is in every Culture an epoch between man and old-man, and no more. Its most distinct expression is the cult of exact sciences, of dialectic, of demonstration, of causality. Of old the Ionic, and in our case the Baroque were its rising limb, and now the question is what form will the down-curve assume?

In this very century, I prophesy, the century of scientific-critical Alexandrianism, of the great harvests, of the final formulations, a new element of inwardness will arise to overthrow the will-to-victory of science. Exact science must presently fall upon its own keen sword. First, in the 18th Century, its methods were tried out, then, in the 19th, its powers, and now its historical rôle is critically reviewed. But from Skepsis there is a path to “second religiousness,” which is the sequel and not the preface of the Culture. Men dispense with proof, desire only to believe and not to dissect.

The individual renounces by laying aside books. The Culture renounces by ceasing to manifest itself in high scientific intellects. But science exists only in the living thought of great savant-generations, and books are nothing if they are not living and effective in men worthy of them. Scientific results are merely items of an intellectual tradition. It constitutes the death of a science that no one any longer regards it as an event, and an orgy of two centuries of exact scientific-ness brings satiety. Not the individual, the soul of the Culture itself has had enough, and it expresses this by putting into the field of the day ever smaller, narrower and more unfruitful investigators. The great century of the Classical science was the third, after the death of Aristotle; when Archimedes died and the Romans came, it was already almost at its end. Our great century has been the 19th. Savants of the calibre of Gauss and Humboldt and Helmholtz were already no more by 1900. In physics as in chemistry, in biology as in mathematics, the great masters are dead, and we are now experiencing the decrescendo of brilliant gleaners who arrange, collect and finish-off like the Alexandrian scholars of the Roman age. Everything that does not belong to the matter-of-fact side of life—to politics, technics or economics—exhibits the common symptom. After Lysippus no great sculptor, no artist as man-of-destiny, appears, and after the Impressionists no painter, and after Wagner no musician. The age of Cæsarism needed neither art nor philosophy. To Eratosthenes and Archimedes, true creators, succeed Posidonius and Pliny, collectors of taste, and finally Ptolemy and Galen, mere copyists. And, just as oil-painting and instrumental music ran through their possibilities in a few centuries, so also dynamics, which began to bud about 1600, is to-day in the grip of decay.

But before the curtain falls, there is one more task for the historical Faustian spirit, a task not yet specified, hitherto not even imagined as possible. There has still to be written a morphology of the exact sciences, which shall discover how all laws, concepts and theories inwardly hang together as forms and what they have meant as such in the life-course of the Faustian Culture. The re-treatment of theoretical physics, of chemistry, of mathematics as a sum of symbols—this will be the definitive conquest of the mechanical world-aspect by an intuitive, once more religious, world-outlook, a last master-effort of physiognomic to break down even systematic and to absorb it, as expression and symbol, into its own domain. One day we shall no longer ask, as the 19th Century asked, what are the valid laws underlying chemical affinity or diamagnetism—rather, we shall be amazed indeed that minds of the first order could ever have been completely preoccupied by questions such as these. We shall inquire whence came these forms that were prescribed for the Faustian spirit, why they had to come to our kind of humanity particularly and exclusively, and what deep meaning there is in the fact that the numbers that we have won became phenomenal in just this picture-like disguise. And, be it said, we have to-day hardly yet an inkling of how much in our reputedly objective values and experiences is only disguise, only image and expression.

The separate sciences—epistemology, physics, chemistry, mathematics, astronomy—are approaching one another with acceleration, converging towards a complete identity of results. The issue will be a fusion of the form-worlds, which will present on the one hand a system of numbers, functional in nature and reduced to a few ground-formulæ, and on the other a small group of theories, denominators to those numerators, which in the end will be seen to be myths of the springtime under modern veils, reducible therefore—and at once of necessity reduced—to picturable and physiognomically significant characters that are the fundamentals. This convergence has not yet been observed, for the reason that since Kant—indeed, since Leibniz—there has been no philosopher who commanded the problems of all the exact sciences.

Even a century ago, physics and chemistry were foreign to one another, but to-day they cannot be handled separately—witness spectrum analysis, radioactivity, radiation of heat. Fifty years ago the essence of chemistry could still be described almost without mathematics, and to-day the chemical elements are in course of volatilizing themselves into the mathematical constants of variable relation-complexes, and with the sense-comprehensibility of the elements goes the last trace of magnitude as the term is Classically and plastically understood. Physiology is becoming a chapter of organic chemistry and is making use of the methods of the Infinitesimal Calculus. The branch of the older physics—distinguished, according to the bodily senses concerned in each, as acoustics, optics and heat—have melted into a dynamic of matter and a dynamic of the æther, and these again can no longer keep their frontiers mathematically clear. The last discussions of epistemology are now uniting with those of higher analysis and theoretical physics to occupy an almost inaccessible domain, the domain to which, for example, the theory of Relativity belongs or ought to belong. The sign-language in which the emanation-theory of radioactivity expresses itself is completely de-sensualized.

Chemistry, once concerned with defining as sharply as possible the qualities of elements, such as valency, weight, affinity and reactivity, is setting to work to get rid of these sensible traits. The elements are held to differ in character according to their derivation from this or that compound. They are represented to be complexes of different units which indeed behave (“actually”) as units of a higher order and are not practically separable but show deep differences in point of radioactivity. Through the emanation of radiant energy degradation is always going on, so that we can speak of the lifetime of an element, in formal contradiction with the original concept of the element and the spirit of modern chemistry as created by Lavoisier. All these tendencies are bringing the ideas of chemistry very close to the theory of Entropy, with its suggestive opposition of causality and destiny, Nature and History. And they indicate the paths that our science is pursuing—on the one hand, towards the discovery that its logical and numerical results are identical with the structure of the reason itself, and, on the other, towards the revelation that the whole theory which clothes these numbers merely represents the symbolic expression of Faustian life.

And here, as our study draws to its conclusion, we must mention the truly Faustian theory of “aggregates,” one of the weightiest in all this form-world of our science. In sharpest antithesis to the older mathematic, it deals, not with singular quantities but with the aggregates constituted by all quantities [or objects] having this or that specified morphological similarity—for instance all square numbers or all differential equations of a given type. Such an aggregate it conceives as a new unit, a new number of higher order, and subjecting it to criteria of new and hitherto quite unsuspected kinds such as “potency,” “order,” “equivalence,” “countableness,” and devising laws and operative methods for it in respect of these criteria. Thus is being actualized a last extension of the function-theory.[^[528]] Little by little this absorbed the whole of our mathematic, and now it is dealing with variables by the principles of the Theory of Groups in respect of the character of the function and by those of the Theory of Aggregates in respect of the values of the variables. Mathematical philosophy is well aware that these ultimate meditations on the nature of number are fusing with those upon pure logic, and an algebra of logic is talked of. The study of geometrical axioms has become a chapter of epistemology.

The aim to which all this is striving, and which in particular every Nature-researcher feels in himself as an impulse, is the achievement of a pure numerical transcendence, the complete and inclusive conquest of the visibly apparent and its replacement by a language of imagery unintelligible to the layman and impossible of sensuous realization—but a language that the great Faustian symbol of Infinite space endows with the dignity of inward necessity. The deep scepticism of these final judgments links the soul anew to the forms of early Gothic religiousness. The inorganic, known and dissected world-around, the World as Nature and System, has deepened itself until it is a pure sphere of functional numbers. But, as we have seen, number is one of the most primary symbols in every Culture; and consequently the way to pure number is the return of the waking consciousness to its own secret, the revelation of its own formal necessity. The goal reached, the vast and ever more meaningless and threadbare fabric woven around natural science falls apart. It was, after all, nothing but the inner structure of the “Reason,” the grammar by which it believed it could overcome the Visible and extract therefrom the True. But what appears under the fabric is once again the earliest and deepest, the Myth, the immediate Becoming, Life itself. The less anthropomorphic science believes itself to be, the more anthropomorphic it is. One by one it gets rid of the separate human traits in the Nature-picture, only to find at the end that the supposed pure Nature which it holds in its hand is—humanity itself, pure and complete. Out of the Gothic soul grew up, till it overshadowed the religious world-picture, the spirit of the City, the alter ego of irreligious Nature-science. But now, in the sunset of the scientific epoch and the rise of victorious Skepsis, the clouds dissolve and the quiet landscape of the morning reappears in all distinctness.

The final issue to which the Faustian wisdom tends—though it is only in the highest moments that it has seen it—is the dissolution of all knowledge into a vast system of morphological relationships. Dynamics and Analysis are in respect of meaning, form-language and substance, identical with Romanesque ornament, Gothic cathedrals, Christian-German dogma and the dynastic state. One and the same world-feeling speaks in all of them. They were born with, and they aged with, the Faustian Culture, and they present that Culture in the world of day and space as a historical drama. The uniting of the several scientific aspects into one will bear all the marks of the great art of counterpoint. An infinitesimal music of the boundless world-space—that is the deep unresting longing of this soul, as the orderly statuesque and Euclidean Cosmos was the satisfaction of the Classical. That—formulated by a logical necessity of Faustian reason as a dynamic-imperative causality, then developed into a dictatorial, hard-working, world-transforming science—is the grand legacy of the Faustian soul to the souls of Cultures yet to be, a bequest of immensely transcendent forms that the heirs will possibly ignore. And then, weary after its striving, the Western science returns to its spiritual home.

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[1]. Kant’s error, an error of very wide bearing which has not even yet been overcome, was first of all in bringing the outer and inner Man into relation with the ideas of space and time by pure scheme, though the meanings of these are numerous and, above all, not unalterable; and secondly in allying arithmetic with the one and geometry with the other in an utterly mistaken way. It is not between arithmetic and geometry—we must here anticipate a little—but between chronological and mathematical number that there is fundamental opposition. Arithmetic and geometry are both spatial mathematics and in their higher regions they are no longer separable. Time-reckoning, of which the plain man is capable of a perfectly clear understanding through his senses, answers the question “When,” not “What” or “How Many.”

[2]. One cannot but be sensible how little depth and power of abstraction has been associated with the treatment of, say, the Renaissance or the Great Migrations, as compared with what is obviously required for the theory of functions and theoretical optics. Judged by the standards of the physicist and the mathematician, the historian becomes careless as soon as he has assembled and ordered his material and passes on to interpretation.

[3]. In the original, these fundamental antitheses are expressed simply by means of werden and sein. Exact renderings are therefore impossible in English.—Tr.

[4]. The attempts of the Greeks to frame something like a calendar or a chronology after the Egyptian fashion, besides being very belated indeed, were of extreme naïveté. The Olympiad reckoning is not an era in the sense of, say, the Christian chronology, and is, moreover, a late and purely literary expedient, without popular currency. The people, in fact, had no general need of a numeration wherewith to date the experiences of their grandfathers and great-grandfathers, though a few learned persons might be interested in the calendar question. We are not here concerned with the soundness or unsoundness of a calendar, but with its currency, with the question of whether men regulated their lives by it or not; but, incidentally, even the list of Olympian victors before 500 is quite as much of an invention as the lists of earlier Athenian archons or Roman consuls. Of the colonizations, we possess not one single authentic date (E. Meyer. Gesch. d. Alt. II, 442. Beloch. Griech. Gesch. I, 2, 219) “in Greece before the fifth century, no one ever thought of noting or reporting historical events.” (Beloch. I, 1, 125). We possess an inscription which sets forth a treaty between Elis and Heraea which “was to be valid for a hundred years from this year.” What “this year” was, is however not indicated. After a few years no one would have known how long the treaty had still to run. Evidently this was a point that no one had taken into account at the time—indeed, the very “men of the moment” who drew up the document, probably themselves soon forgot. Such was the childlike, fairy-story character of the Classical presentation of history that any ordered dating of the events of, say, the Trojan War (which occupies in their series the same position as the Crusades in ours) would have been felt as a sheer solecism.

Equally backward was the geographical science of the Classical world as compared with that of the Egyptians and the Babylonians. E. Meyer (Gesch. d. Alt. II, 102) shows how the Greeks’ knowledge of the form of Africa degenerated from Herodotus (who followed Persian authorities) to Aristotle. The same is true of the Romans as the heirs of the Carthaginians; they first repeated the information of their alien forerunners and then slowly forgot it.

[5]. Contrast with this the fact, symbolically of the highest importance and unparalleled[unparalleled] in art-history, that the Hellenes, though they had before their eyes the works of the Mycenæan Age and their land was only too rich in stone, deliberately reverted to wood; hence the absence of architectural remains of the period 1200-600. The Egyptian plant-column was from the outset of stone, whereas the Doric column was wooden, a clear indication of the intense antipathy of the Classical soul towards duration.

[6]. Is there any Hellenic city that ever carried out one single comprehensive work that tells of care for future generations? The road and water systems which research has assigned to the Mycenæan—i.e., the pre-Classical—age fell into disrepair and oblivion from the birth of the Classical peoples—that is, from the Homeric period. It is a remarkably curious fact, proved beyond doubt by the lack of epigraphic remains, that the Classical alphabet did not come into use till after 900, and even then only to a limited extent and for the most pressing economic needs. Whereas in the Egyptian, the Babylonian, the Mexican and the Chinese Cultures the formation of a script begins in the very twilight of dawn, whereas the Germans made themselves a Runic alphabet and presently developed that respect for writing as such which led to the successive refinements of ornamental calligraphy, the Classical primitives were entirely ignorant of the numerous alphabets that were current in the South and the East. We possess numerous inscriptions of Hittite Asia Minor and of Crete, but not one of Homeric Greece. (See Vol. II, pp. 180 et seq.)

[7]. From Homer to the tragedies of Seneca, a full thousand years, the same handful of myth-figures (Thyestes, Clytæmnestra, Heracles and the like) appear time after time without alteration, whereas in the poetry of the West, Faustian Man figures, first as Parzeval or Tristan, then (modified always into harmony with the epoch) as Hamlet, Don Quixote, Don Juan, and eventually Faust or Werther, and now as the hero of the modern world-city romance, but is always presented in the atmosphere and under the conditions of a particular century.

[8]. It was about 1000 A.D. and therefore contemporaneously with the beginning of the Romanesque style and the Crusades—the first symptoms of a new Soul—that Abbot Gerbert (Pope Sylvester II), the friend of the Emperor Otto III, invented the mechanism of the chiming wheel-clock. In Germany too, the first tower-clocks made their appearance, about 1200, and the pocket watch somewhat later. Observe the significant association of time measurement with the edifices of religion.

[9]. Newton’s choice of the name “fluxions” for his calculus was meant to imply a standpoint towards certain metaphysical notions as to the nature of time. In Greek mathematics time figures not at all.

[10]. Here the historian is gravely influenced by preconceptions derived from geography, which assumes a Continent of Europe, and feels himself compelled to draw an ideal frontier corresponding to the physical frontier between “Europe” and “Asia.” The word “Europe” ought to be struck out of history. There is historically no “European” type, and it is sheer delusion to speak of the Hellenes as “European Antiquity” (were Homer and Heraclitus and Pythagoras, then, Asiatics?) and to enlarge upon their “mission” as such. These phrases express no realities but merely a sketchy interpretation of the map. It is thanks to this word “Europe” alone, and the complex of ideas resulting from it, that our historical consciousness has come to link Russia with the West in an utterly baseless unity—a mere abstraction derived from the reading of books—that has led to immense real consequences. In the shape of Peter the Great, this word has falsified the historical tendencies of a primitive human mass for two centuries, whereas the Russian instinct has very truly and fundamentally divided “Europe” from “Mother Russia” with the hostility that we can see embodied in Tolstoi, Aksakov or Dostoyevski. “East” and “West” are notions that contain real history, whereas “Europe” is an empty sound. Everything great that the Classical world created, it created in pure denial of the existence of any continental barrier between Rome and Cyprus, Byzantium and Alexandria. Everything that we imply by the term European Culture came into existence between the Vistula and the Adriatic and the Guadalquivir and, even if we were to agree that Greece, the Greece of Pericles, lay in Europe, the Greece of to-day certainly does not.

[11]. See Vol. II, pp. 31, 175.

[12]. Windelband, Gesch. d. Phil. (1903), pp. 275 ff.

[13]. In the New Testament the polar idea tends to appear in the dialectics of the Apostle Paul, while the periodic is represented by the Apocalypse.

[14]. As we can see from the expression, at once desperate and ridiculous, “newest time” (neueste Zeit).

[15]. K. Burdach, Reformation, Renaissance, Humanismus, 1918, pp. 48 et seq. (English readers may be referred to the article Joachim of Floris by Professor Alphandery in the Encyclopædia Britannica, XI ed., Tr.)

[16]. The expression “antique”—meant of course in the dualistic sense—is found as early as the Isagoge of Porphyry (c. 300 A.D.).

[17]. “Mankind? It is an abstraction. There are, always have been, and always will be, men and only men.” (Goethe to Luden.)

[18]. “Middle Ages” connotes the history of the space-time region in which Latin was the language of the Church and the learned. The mighty course of Eastern Christianity, which, long before Boniface, spread over Turkestan into China and through Sabæa into Abyssinia, was entirely excluded from this “world-history.”

[19]. See Vol. II, p. 362, foot-note. To the true Russian the basic proposition of Darwinism is as devoid of meaning as that of Copernicus is to a true Arab.

[20]. This is conclusively proved by the selection that determined survival, which was governed not by mere chance but very definitely by a deliberate tendency. The Atticism of the Augustan Age, tired, sterile, pedantic, back-looking, conceived the hall-mark “classical” and allowed only a very small group of Greek works up to Plato to bear it. The rest, including the whole wealth of Hellenistic literature, was rejected and has been almost entirely lost. It is this pedagogue’s anthology that has survived (almost in its entirety) and so fixed the imaginary picture of “Classical Antiquity” alike for the Renaissance Florentine and for Winckelmann, Hölderlin, and even Nietzsche.

[In this English translation, it should be mentioned, the word “Classical” has almost universally been employed to translate the German antike, as, in the translator’s judgment, no literal equivalent of the German word would convey the specific meaning attached to antike throughout the work, “antique,” “ancient” and the like words having for us a much more general connotation.—Tr.]

[21]. As will be seen later, the words zivilisierte and Zivilisation possess in this work a special meaning.—Tr.

[22]. English not possessing the adjective-forming freedom of German, we are compelled to coin a word for the rendering of grossstädtisch, an adjective not only frequent but of emphatic significance in the author’s argument.—Tr.

[23]. See Vol. II, pp. 117 et seq.

[24]. One cannot fail to notice this in the development of Strindberg and especially in that of Ibsen, who was never quite at home in the civilized atmosphere of his problems. The motives of “Brand” and “Rosmersholm” are a wonderful mixture of innate provincialism and a theoretically-acquired megalopolitan outlook. Nora is the very type of the provincial derailed by reading.

[25]. Who forbade the cult of the town’s hero Adrastos and the reading of the Homeric poems, with the object of cutting the Doric nobility from its spiritual roots (c. 560 B.C.).

[26]. A profound word which obtains its significance as soon as the barbarian becomes a culture-man and loses it again as soon as the civilization-man takes up the motto “Ubi bene, ibi patria.”

[27]. Hence it was that the first to succumb to Christianity were the Romans who could not afford to be Stoics. See Vol. II, pp. 607 et seq.

[28]. In Rome and Byzantium, lodging-houses of six to ten stories (with street-widths of ten feet at most!) were built without any sort of official supervision, and frequently collapsed with all their inmates. A great part of the cives Romani, for whom panem et circenses constituted all existence, possessed no more than a high-priced sleeping-berth in one of the swarming ant-hills called insulæ. (Pohlmann, Aus Altertum und Gegenwart, 1911, pp. 199 ff.)

[29]. See Vol. II, 577.

[30]. German gymnastics, from the intensely provincial and natural forms imparted to it by Jahn, has since 1813 been carried by a very rapid development into the sport category. The difference between a Berlin athletic ground on a big day and a Roman circus was even by 1914 very slight.

[31]. See Vol. II, 529.

[32]. The conquest of Gaul by Cæsar was frankly a colonial, i.e., a one-sided, war; and the fact that it is the highest achievement in the later military history of Rome only shows that the well of real achievement was rapidly drying up.

[33]. The modern Germans are a conspicuous example of a people that has become expansive without knowing it or willing it. They were already in that state while they still believed themselves to be the people of Goethe. Even Bismarck, the founder of the new age, never had the slightest idea of it, and believed himself to have reached the conclusion of a political process (cf. Vol. II, 529).

[34]. This is probably the meaning of Napoleon’s significant words to Goethe: “What have we to-day to do with destiny? Policy is destiny.”

[35]. Corresponding to the 300-50 B.C. phase of the Classical world.

[36]. Which in the end gave its name to the Empire (Tsin = China).

[37]. See Vol. II, 521-539.

[38]. See Vol. II, 373 ff.

[39]. The work referred to is embodied in Vol. II (pp. 521 et seq., 562 et seq., 631 et seq.).

[40]. The philosophy of this book I owe to the philosophy of Goethe, which is practically unknown to-day, and also (but in a far less degree) to that of Nietzsche. The position of Goethe in West-European metaphysics is still not understood in the least; when philosophy is being discussed he is not even named. For unfortunately he did not set down his doctrines in a rigid system, and so the systematic philosophy has overlooked him. Nevertheless he was a philosopher. His place vis-à-vis Kant is the same as that of Plato—who similarly eludes the would-be-systematizer—vis-à-vis Aristotle. Plato and Goethe stand for the philosophy of Becoming, Aristotle and Kant the philosophy of Being. Here we have intuition opposed to analysis. Something that it is practically impossible to convey by the methods of reason is found in individual sayings and poems of Goethe, e.g., in the Orphische Urworte, and stanzas like “Wenn im Unendlichen” and “Sagt es Niemand,” which must be regarded as the expression of a perfectly definite metaphysical doctrine. I would not have one single word changed in this: "The Godhead is effective in the living and not in the dead, in the becoming and the changing, not in the become and the set-fast; and therefore, similarly, the reason (Vernunft) is concerned only to strive towards the divine through the becoming and the living, and the understanding (Verstand) only to make use of the become and the set-fast" (to Eckermann). This sentence comprises my entire philosophy.

[41]. At the end of the volume.

[42]. Weltanschauung im wörtlichen Sinne; Anschauung der Welt.

[43]. The case of mankind in the historyless state is discussed in Vol. II, pp. 58 et seq.

[44]. With, moreover, a “biological horizon.” See Vol. II, p. 34.

[45]. See Vol. II, pp. 327 et seq.

[46]. Also “thinking in money.” See Vol. II, pp. 603 et seq.

[47]. Dynasties I-VIII, or, effectively, I-VI. The Pyramid period coincides with Dynasties IV-VI. Cheops, Chephren and Mycerinus belong to the IV dynasty, under which also great water-control works were carried out between Abydos and the Fayum.—Tr.

[48]. As also those of law and of money. See Vol. II, pp. 68 et seq., pp. 616 et seq.

[49]. Poincaré in his Science et Méthode (Ch. III), searchingly analyses the “becoming” of one of his own mathematical discoveries. Each decisive stage in it bears “les mêmes caractères de brièveté, de soudaineté[soudaineté] et de certitude absolue” and in most cases this “certitude” was such that he merely registered the discovery and put off its working-out to any convenient season.—Tr.

[50]. One may be permitted to add that according to legend, both Hippasus who took to himself public credit for the discovery of a sphere of twelve pentagons, viz., the regular dodecahedron (regarded by the Pythagoreans as the quintessence—or æther—of a world of real tetrahedrons, octahedrons, icosahedrons and cubes), and Archytas the eighth successor of the Founder are reputed to have been drowned at sea. The pentagon from which this dodecahedron is derived, itself involves incommensurable numbers. The “pentagram” was the recognition badge of Pythagoreans and the ἄλογον (incommensurable) their special secret. It would be noted, too, that Pythagoreanism was popular till its initiates were found to be dealing in these alarming and subversive doctrines, and then they were suppressed and lynched—a persecution which suggests more than one deep analogy with certain heresy-suppressions of Western history. The English student may be referred to G. J. Allman, Greek Geometry from Thales to Euclid (Cambridge, 1889), and to his articles “Pythagoras,” “Philolaus” and “Archytas” in the Ency. Brit., XI Edition.—Tr.

[51]. Horace’s words (Odes I xi): “Tu ne quæsieris, scire nefas, quem mihi quem tibi finem di dederint, Leuconoë, nec Babylonios temptaris numeros ... carpe diem, quam minimum credula postero.”—Tr.

[52]. See Vol. II, pp. 11 et seq.

[53]. In the only writing of his that survives, indeed, Aristarchus maintains the geocentric view; it may be presumed therefore that it was only temporarily that he let himself be captivated by a hypothesis of the Chaldaean learning.

[54]. Giordano Bruno (born 1548, burned for heresy 1600). His whole life might be expressed as a crusade on behalf of God and the Copernican universe against a degenerated orthodoxy and an Aristotelian world-idea long coagulated in death.—Tr.

[55]. F. Strunz, Gesch. d. Naturwiss. im Mittelalter (1910), p. 90.

[56]. In the “Psammites,” or “Arenarius,” Archimedes framed a numerical notation which was to be capable of expressing the number of grains of sand in a sphere of the size of our universe.—Tr.

[57]. This, for which the ground had been prepared by Eudoxus, was employed for calculating the volume of pyramids and cones: “the means whereby the Greeks were able to evade the forbidden notion of infinity” (Heiberg, Naturwiss. u. Math. i. Klass. Alter. [1912], p. 27).

[58]. Dr. Anster’s translation.—Tr.

[59]. See Vol. II, Chapter III.

[60]. Oresme was, equally, prelate, church reformer, scholar, scientist and economist—the very type of the philosopher-leader.—Tr.

[61]. Oresme in his Latitudines Formarum used ordinate and abscissa, not indeed to specify numerically, but certainly to describe, change, i.e., fundamentally, to express functions.—Tr.

[62]. Alexandria ceased to be a world-city in the second century A.D. and became a collection of houses left over from the Classical civilization which harboured a primitive population of quite different spiritual constitution. See Vol. II, pp. 122 et seq.

[63]. Born 1601, died 1665. See Ency. Brit., XI Ed., article Fermat, and references therein.—Tr.

[64]. Similarly, coinage and double-entry book-keeping play analogous parts in the money-thinking of the Classical and the Western Cultures respectively. See Vol. II, pp. 610 et seq.

[65]. The same may be said in the matter of Roman Law (see Vol. II, pp. 96 et seq.) and of coinage (see Vol. II, pp. 616 et seq.).

[66]. That is, “it is impossible to part a cube into two cubes, a biquadrate into two biquadrates, and generally any power above the square into two powers having the same exponent.” Fermat claimed to possess a proof of the proposition, but this has not been preserved, and no general proof has hitherto been obtained.—Tr.

[67]. Thus Bishop Berkeley’s Discourse addressed to an infidel mathematician (1735) shrewdly asked whether the mathematician were in a position to criticize the divine for proceeding on the basis of faith.—Tr.

[68]. From the savage conjuror with his naming-magic to the modern scientist who subjects things by attaching technical labels to them, the form has in no wise changed. See Vol. II, pp. 116 et seq., 322 et seq.

[69]. See Vol. II, pp. 137 et seq.

[70]. A beginning is now being made with the application of non-Euclidean geometries to astronomy. The hypothesis of curved space, closed but without limits, filled by the system of fixed stars on a radius of about 470,000,000 earth-distances, would lead to the hypothesis of a counter-image of the sun which to us appears as a star of medium brilliancy. (See translator’s footnote, p. 332.)

[71]. That only one parallel to a given straight line is possible through a given point—a proposition that is incapable of proof.

[72]. It is impossible to say, with certainty, how much of the Indian mathematics that we possess is old, i.e., before Buddha.

[73]. The technical difference (in German usage) between Grenz and Grenzwert is in most cases ignored in this translation as it is only the underlying conception of “number” common to both that concerns us. Grenz is the “limit” strictly speaking, i.e., the number a to which the terms a₁₁, a₂₂, a₃ ... of a particular series approximate more and more closely, till nearer to a than any assignable number whatever. The Grenzwert of a function, on the other hand, is the “limit” of the value which the function takes for a given value a of the variable x. These methods of reasoning and their derivatives enable solutions to be obtained for series such as (1⁄m¹,) (1⁄m²,) (1⁄m³,) ... (1⁄m^x) or functions such as

x(2x - 1)

y = —————

(x + 2)(x - 3)

where x is infinite or indefinite.—Tr.

[74]. “Function, rightly understood, is existence considered as an activity” (Goethe). Cf. Vol. II, p. 618, for functional money.

[75]. Built for August II, in 1711, as barbican or fore-building for a projected palace.—Tr.

[76]. From the standpoint of the theory of “aggregates” (or “sets of points”), a well-ordered set of points, irrespective of the dimension figure, is called a corpus; and thus an aggregate of n - 1 dimensions is considered, relatively to one of n dimensions, as a surface. Thus the limit (wall, edge) of an “aggregate” represents an aggregate of lower “potentiality.”

[77]. See p. [55], also Vol. II, pp. 25 et seq.

[78]. “Anti-historical,” the expression which we apply to a decidedly systematic valuation, is to be carefully distinguished from “ahistorical.” The beginning of the IV Book (53) of Schopenhauer’s Welt als Wille und Vorstellung affords a good illustration of the man who thinks anti-historically, that is, deliberately for theoretical reasons suppresses and rejects the historical in himself—something that is actually there. The ahistoric Greek nature, on the contrary, neither possesses nor understands it.

[79]. “There are prime phenomena which in their godlike simplicity we must not disturb or infringe.”

[80]. The date of Napoleon’s defeat, and the liberation of Germany, on the field of Leipzig.—Tr.

[81]. See Vol. II, pp. 25 et seq., 327 et seq.

[82].

“All we see before us passing

Sign and symbol is alone.”

From the final stanza of Faust II (Anster’s translation).—Tr.

[83]. This phrase, derived by analogy from the centre of gravity of mechanics, is offered as a translation of “mithin in einim Zeitpunkte ger nicht zusammengefasst werden können.”—Tr.

[84]. Cf. Vol. II, p. 33 et seq.

[85]. Not the dissecting morphology of the Darwinian’s pragmatic zoology with its hunt for causal connexions, but the seeing and overseeing morphology of Goethe.

[86]. See Vol. II, pp. 41 et seq.

[87]. See Vol. II, pp. 227 et seq.

[88]. See Vol. II, pp. 116 et seq. What constitutes the downfall is not, e.g., the catastrophe of the Great Migrations, which like the annihilation of the Maya Culture by the Spaniards (see Vol. II, p. 51 et seq.) was a coincidence without any deep necessity, but the inward undoing that began from the time of Hadrian, as in China from the Eastern Han dynasty (25-220).

[89]. St. Bernward was Bishop of Hildesheim from 993 to 1022, and himself architect and metal-worker. Three other churches besides the cathedral survive in the city from his time or that of his immediate successors, and Hildesheim of all North German cities is richest in monuments of the Romanesque.—Tr.

[90]. By “Saxony,” a German historian means not the present-day state of Saxony (which was a small and comparatively late accretion), but the whole region of the Weser and the lower Elbe, with Westphalia and Holstein.—Tr.

[91]. Vases from the cemetery adjoining the Dipylon Gate of Athens, the most representative relics that we possess of the Doric or primitive age of the Hellenic Culture (about 900 to 600 B.C.).—Tr.

[92]. See Vol. II, pp. 381 et seq.

[93]. In English the word “cast” will evidently satisfy the sense better on occasion. The word “stil” will therefore not necessarily be always rendered “style.”—Tr.

[94]. See Vol. II, pp. 109 et seq.

[95]. See Vol. II, pp. 36 et seq.

[96]. I will only mention here the distances apart of the three Punic Wars, and the series—likewise comprehensible only as rhythmic—Spanish Succession War, Silesian wars, Napoleonic Wars, Bismarck’s wars, and the World War (cf. Vol. II, p. 488). Connected with this is the spiritual relation of grandfather and grandson, a relation which produces in the mind of primitive peoples the conviction that the soul of the grandfather returns in the grandson, and has originated the widespread custom of giving the grandson the grandfather’s name, which by its mystic spell binds his soul afresh to the corporeal world.

[97]. The word is used in the sense in which biology employs it, viz., to describe the process by which the embryo traverses all the phases which its species has undergone.—Tr.

[98]. The first draft of Faust I, discovered only comparatively recently.—Tr.

[99]. See Ency. Brit., XIth Ed., articles Owen, Sir Richard; Morphology and Zoology (p. 1029).—Tr.

[100]. It is not superfluous to add that there is nothing of the causal kind in these pure phenomena of “Living Nature.” Materialism, in order to get a system for the pedestrian reasoner, has had to adulterate the picture of them with fitness-causes. But Goethe—who anticipated just about as much of Darwinism as there will be left of it in fifty years from Darwin—absolutely excluded the causality-principle. And the very fact that the Darwinians quite failed to notice its absence is a clear indication that Goethe’s “Living Nature” belongs to actual life, "cause"-less and "aim"-less; for the idea of the prime-phenomenon does not involve causal assumptions of any sort unless it has been misunderstood in advance in a mechanistic sense.

[101]. Reigned 246-210 B.C. He styled himself “first universal emperor” and intended a position for himself and his successors akin to that of “Divus” in Rome. For a brief account of his energetic and comprehensive work see Ency. Brit., XI Ed., article China, p. 194.—Tr.

[102]. The sensuous life and the intellectual life too are Time; it is only sensuous experience and intellectual experience, the “world,” that is spatial nature. (As to the nearer affinity of the Feminine to Time, see Vol. II, pp. 403 et seq.)

[103]. The expression “space of time” (Zeitraum) which is common to many languages, is evidence of our inability to represent direction otherwise than by extension.

[104]. I.e., the translated Bible.—Tr.

[105]. See Vol. II, pp. 19 et seq.

[106]. See p. [80] of this volume, and Vol. II, pp. 166, 328.

[107]. See Vol. II, p. 137.

[108]. The nearest English equivalent is perhaps the word “fear.” “Fearful” would correspond exactly but for the fact that in the second sense the word is objective instead of subjective. The word “shy” itself bears the second meaning in such trivial words as gun-shy, work-shy.—Tr.

[109]. The Relativity theory, a working hypothesis which is on the way to overthrowing Newton’s mechanics—which means at bottom his view of the problem of motion—admits cases in which the words “earlier” and “later” may be inverted. The mathematical foundation of this theory by Minkowski uses imaginary time units for measurement.

[110]. The dimensions are x, y, z (in respect of space) and t (in respect of time), and all four appear to be regarded as perfectly equivalent in transformations. [The English reader may be referred to A. Einstein, “Theory of Relativity,” Ch. XI and appendices I, II.—Tr.]

[111]. Si nemo ex me quaerat, scio; si quaerenti explicari velim, nescio. (Conf. XI, 14.)

[112]. Save in elementary mathematics. (It may be remarked that most philosophers since Schopenhauer have approached these questions[questions] with the prepossessions of elementary mathematics.)

[113]. The “inverse circular functions” of English text-books.—Tr.

[114]. The Newtonian form of the differential calculus was distinct from the Leibnizian, which is now in general use. Without going into unnecessary detail, the characteristic of Newton’s method was that it was meant not for the calculation of quadratures and tangents (which had occupied his predecessors), nor as an organ of functional theory as such (as the differential calculus became much later), but quite definitely as a method of dealing with rate of change in pure mechanics, with the “flowing” or “fluxion” of a dependent variable under the influence of a variable which for Newton was the “fluent,” and which we call the argument of a function.—Tr.

[115]. See Vol. II, pp. 13, 19.

[116]. See Vol. II, p. 16.

[117]. The original reads: “(So ist jede Art von Verstehen ... nur dadurch möglich ...) dass ein Begriffspaar von innerem Gegensatz gewissermassen durch Auseinandertreten erst Wirklichkeit erhält.”—Tr.

[118]. At this point the German text repeats the paragraph which in this edition begins at “But inquiry” (p. 121) and ends at the close of section I (p. 121).—Tr.

[119]. See Vol. II, pp. 137, 159.

[120]. Here the author presumably means history in the ordinary acceptation of the word.—Tr.

[121]. Œd. Rex., 642. κακῶς εἴληφα τοὐμὸν σῶμα σὺν[κακῶς εἴληφα τοὐμὸν σῶμα σὺν] τέχνῃ κακῇ. (Cf. Rudolf Hirsch, Die Person (1914), p. 9.)

[122]. Œd. Col., 355. μαντεῖα ... ἃ[ἃ] τοῦδ’ ἐχρήσθη σώματος.

[123]. Choëphoræ, 710. ἐπὶ ναυάρχῳ σώματι ... τῷ βασιλείῳ.

[124]. Phidias, and through him his patron Pericles, were attacked for alleged introduction of portraits upon the shield of Athene Parthenos. In Western religious art, on the contrary, portraiture was, as everyone knows, a habitual practice. Every Madonna, for instance, is more or less of a portrait.

With this may be compared again the growing resistance of Byzantine art, as it matured, to portraiture in sacred surroundings, evidenced for instance in the history of the nimbus or halo—which was removed from the insignia of the Prince to become the badge of the Saint—in the legend of the miraculous effacement of Justinian’s pompous inscription on Hagia Sophia, and in the banishment of the human patron from the celestial part of the church to the earthly.—Tr.

[125]. Who was criticized as “no god-maker but a man-maker” and as one who spoilt the beauty of his work by aiming at likeness.

Cresilas, the sculptor from whom the only existing portrait of Pericles is derived, was a little earlier; in him, however, the “ideal” was still the supreme aim.—Tr.

[126]. The writers immediately succeeding Aristophanes.—Tr.

[127]. See Vol. II, pp. 360 et seq.

[128]. Diels, Antike Technik (1920), p. 159.

[129]. About 400 B.C. savants began to construct crude sun-dials in Africa and Ionia, and from Plato’s time still more primitive clepsydræ came into use; but in both forms, the Greek clock was a mere imitation of the far superior models of the older East, and it had not the slightest connexion with the Greek life-feeling. See Diels, op. cit., pp. 160 et seq.

[130]. Horace’s monumentum ære perennius (Odes III, 30) may seem to conflict with this: but let the reader reconsider the whole of that ode in the light of the present argument, and turn also to Leuconoe and her “Babylonian” impieties (Odes I, 11) inter alia, and he will probably agree that so far as Horace is concerned, the argument is supported rather than impugned.—Tr.

[131]. Ordered, for us, by the Christian chronology and the ancient-mediæval-modern scheme. It was on those foundations that, from early Gothic times, the images of religion and of art have been built up in which a large part of Western humanity continues to live. To predicate the same of Plato or Phidias is quite impossible, whereas the Renaissance artists could and did project a classical past, which indeed they permitted to dominate their judgments completely.

[132]. See pp. 9. et seq.

[133]. The Indian history of our books is a Western reconstruction from texts and monuments. See the chapter on epigraphy in the “Indian Gazetteer,” Vol. II.—Tr.

[134]. See Vol. II, pp. 482, 521 et seq.

[135]. There is one famous episode in Greek history that may be thought to contradict this—the race against time of the galley sent to Mitylene to countermand the order of massacre (Thucydides, III, 49). But we observe that Thucydides gives twenty times the space to the debates at Athens that he gives to the drama of the galley-rowers pulling night and day to save life. And we are told that it was the Mitylenean ambassadors who spared no expense to make it worth the rowers’ while to win, whereupon “there arose such a zeal of rowing that....” The final comment is, strictly construing Thucydides’s own words: “Such was the magnitude of the danger that Mitylene passed by” (παρὰ τοσοῦτον μὲν ἡ[τοσοῦτον μὲν ἡ] Μυτιλήνη ἦλθε κινδύνου), a phrase which recalls forcibly what has just been said regarding the “situation-drama.”—Tr.

[136]. Besides the clock, the bell itself is a Western “symbol.” The passing-bell tolled for St. Hilda of Whitby in 680, and a century before that time bells had come into general use in Gaul both for monasteries and for parish churches. On the contrary, it was not till 865 that Constantinople possessed bells, and these were presented in that year by Venice. The presence of a belfry in a Byzantine church is accounted a proof of “Western influence”: the East used and still largely uses mere gongs and rattles for religious purposes. (British Museum “Handbook of Early Christian Antiquities)”.[Antiquities)”.]—Tr.

[137]. May we be permitted to guess that the Babylonian sun-dial and the Egyptian water-clock came into being “simultaneously,” that is, on the threshold of the third millennium before Christ? The history of clocks is inwardly inseparable from that of the calendar; it is therefore to be assumed that the Chinese and the Mexican Cultures also, with their deep sense of history, very early devised and used methods of time-measurement.

(The Mexican Culture developed the most intricate of all known systems of indicating year and day. See British Museum “Handbook of May on Antiquities.”[Antiquities.”]—Tr.)

[138]. Let the reader try to imagine what a Greek would feel when suddenly made acquainted with this custom of ours.

[139]. The Chinese ancestor-worship honoured genealogical order with strict ceremonies. And whereas here ancestor-worship by degrees came to be the centre of all piety, in the Classical world it was driven entirely into the background by the cults of present gods; in Roman times it hardly existed at all.

(Note the elaborate precautions taken in the Athenian “Anthesteria” to keep the anonymous mass of ghosts at bay. This feast was anything but an All Souls’ Day of re-communion with the departed spirits.—Tr.)

[140]. With obvious reference to the resurrection of the flesh (ἐκ νεκρῶν). But the meaning of the term “resurrection” has undergone, from about 1000 A.D., a profound—though hardly noticed—change. More and more it has tended to become identified with “immortality.” But in the resurrection from the dead, the implication is that time begins again to repeat in space, whereas in “immortality” it is time that overcomes space.

[141]. For English readers, the most conspicuous case of historic doubt is the Shakespeare-Bacon matter. But even here, it is only the work of Shakespeare that is in question, not his existence and personality, for which we have perfectly definite evidence.—Tr.

[142]. Originally a philosophical and scientific lecture-temple founded in honour of Aristotle, and later the great University of Alexandria, bore the title Μουσεῖον. Both Aristotle and the University amassed collections but they were collections of (a) books, (b) natural history specimens, living or taken from life. In the West, the collection of memorials of the past as such dates from the earliest days of the Renaissance.—Tr.

[143]. The connotation of “care” is almost the same as that of “Sorge,” but the German word includes also a certain specific, ad hoc apprehension, that in English is expressed by “concern” or “fear.”—Tr.

[144]. The Lingayats are one of the chief sects of the Saivas (that is, of the branch of Hinduism which devotes itself to Shiva) and Paewati worshippers belong to another branch, having the generic name of Saktas, who worship the “active female principle” in the persons of Shiva’s consorts, of whom Paewati is one. Vaishnavism—the Vishnu branch of Indian religion—also contains an erotic element in that form which conceives Vishnu as Krishna. But in Krishna worship the erotic is rather less precise and more amorous in character.

See “Imperial Gazetteer of India,” Vol. I, pp. 421 et seq., and Ency. Brit., XI Edition, article Hinduism.—Tr.

[145]. British Museum.—Tr.

[146]. Dresden.—Tr.

[147]. See Vol. II, p. 316.

[148]. In connexion with this very important link in the Author’s argument, attention may be drawn to a famous wall-painting of very early date in the Catacomb of St. Priscilla. In this, Mary is definitely and unmistakably the Stillende Mutter. But she is, equally unmistakably, different in soul and style from her “Early-Christian-Byzantine” successor the Theotokos. Now, it is well known that the art of the catacombs, at any rate in its beginnings, is simply the art of contemporary Rome, and that this “Roman” art had its home in Alexandria. See Woermann’s Geschichte der Kunst, III, 14-15, and British Museum “Guide to Early Christian Art,” 72-74, 86. Woermann speaks of this Madonna as the prototype of our grave, tenderly-solicitous Mother-Madonnas. Dr. Spengler would probably prefer to regard her as the last Isis. In any case it is significant that the symbol disappears: in the very same catacomb is a Theotokos of perhaps a century later date.—Tr.

[149]. Vol. II, pp. 403 et seq.

[150]. See, further, the last two sections of Vol. II (Der Staat and Wirtschaftsleben).—Tr.

[151]. Sesenheim is the home of Friederike, and a student’s holiday took him thither: Weimar, of course, is the centre from which all the activity of his long life was to radiate.—Tr.

[152]. Vermeintlich. The allusion is presumably to the fact that Copernicus, adhering to the hypothesis of circular orbits, was obliged to retain some elements of Ptolemy’s geocentric machinery of epicycles, so that Copernicus’s sun was not placed at the true centre of any planetary orbit.—Tr.

[153]. Sprüche in Reimen.

[154]. See Vol. II, pp. 294 et seq., 359 et seq.

[155]. The path from Calvin to Darwin is easily seen in English philosophy.

[156]. This is one of the eternal points of dispute in Western art-theory. The Classical, ahistorical, Euclidean soul has no “evolution”; the Western, on the contrary, extends itself in evolving like the convergent function that it is. The one is, the other becomes. And thus all Classical tragedy assumes the constancy of the personality, and all Western its variability, which essentially constitutes a “character” in our sense, viz., a picture of being that consists in continuous qualitative movement and an endless wealth of relationships. In Sophocles the grand gesture ennobles the suffering, in Shakespeare the grand idea (Gesinnung) ennobles the doing. As our æsthetic took its examples from both Cultures, it was bound to go wrong in the very enunciation of its problem.

[157]. “The older one becomes, the more one is persuaded that His Sacred Majesty Chance does three-quarters of the work of this miserable Universe.” (Frederick the Great to Voltaire.) So, necessarily, must the genuine rationalist conceive it.

[158]. See Vol. II, pp. 20 et seq.

[159]. The incident which is said to have precipitated the French war on Algiers (1827).—Tr.

[160]. Act. II, Scene VII.—Tr.

[161]. In the general upheaval of 1848 a German national parliament was assembled at Frankfurt, of a strongly democratic colour, and it chose Frederick William IV of Prussia as hereditary emperor. Frederick William, however, refused to “pick up a crown out of the gutter.” For the history of this momentous episode, the English reader may be referred to the Cambridge Modern History or to the article Germany (History) in the Ency. Brit., XI Edition.—Tr.

[162]. It is the fact that a whole group of these Cultures is available for our study that makes possible the “comparative” method used in the present work. See Vol. II, pp. 42 et seq.

[163]. Derived from μείρομαι, to receive as one’s portion, to have allotted to one, or, colloquially, to “come in for” or “step into.”—Tr.

[164]. The expedition of the Ten Thousand into Persia is no exception. The Ten Thousand indeed formed an ambulatory Polis, and its adventures are truly Classical. It was confronted with a series of “situations.”—Tr.

[165]. Helios is only a poetical figure; he had neither temples nor cult. Even less was Selene a moon-goddess.

[166]. The original is somewhat obscure. It reads: "Welche Form die Wahrscheinlichkeit für sich hat, ist bereits eine Frage des historischen—und also des tragischen—Stils."—Tr.

[167]. The words of Canning at the beginning of the XIXth century may be recalled. “South America free! and if possible English!” The expansion idea has never been expressed in greater purity than this.

[168]. The Western Culture of maturity was through-and-through a French outgrowth of the Spanish, beginning with Louis XIV. But even by Louis XVI’s time the English park had defeated the French, sensibility had ousted wit, London costume and manners had overcome Versailles, and Hogarth, Chippendale and Wedgwood had prevailed over Watteau, Boulle and Sèvres.

[169]. The allusion is to the voyage of Linois’s small squadron to Pondichéry in 1803, its confrontation by another small British squadron there, and the counter-order which led Linois to retire to Mauritius.—Tr.

[170]. Hardenberg’s reorganization of Prussia was thoroughly[thoroughly] English in spirit, and as such incurred the severe censure of the old Prussian Von der Marwitz. Scharnhorst’s army reforms too, as a breakaway from the professional army system of the eighteenth-century cabinet-wars, are a sort of “return to nature” in the Rousseau-Revolutionary sense.

[171]. Where in 295 B.C. the Romans decisively defeated the last great Samnite effort to resist their hegemony over Italy.—Tr.

[172]. Which, inasmuch as it has been detached from time, is able to employ mathematical symbols. These rigid figures signify for us a destiny of yore. But their meaning is other than mathematical. Past is not a cause, nor Fate a formula, and to anyone who handles them, as the historical materialist handles them, mathematically, the past event as such, as an actuality that has lived once and only once, is invisible.

[173]. That is, not merely conclusions of peaces or deathdays of persons, but the Renaissance style, the Polis, the Mexican Culture and so forth—are dates or data, facts that have been, even when we possess no representation of them.

[174]. See Vol. II, pp. 403 et seq., 589 et seq.

[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.

[178]. See p. [123].

[179]. See page [123].

[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.

[220]. See p. [188].

[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.

[224]. See p. [167].

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

[226]. See p. [128].

[227]. See p. [62].

[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.

[232]. See p. [173].

[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.

[274]. Our pedantic method has given us an art-history that excludes music-history; and while the one has become a normal element of higher education, the other has remained an affair solely for the expert. It is just as though one tried to write a history of Greece without taking Sparta into account. The result is a theory of “Art” that is a pious fraud.

[275]. This sentence is not in the original. It has been inserted, and the following sentence modified, for the sake of clarity.—Tr.

[276]. See Vol. II, p. 110. The aspect of the streets of Old Egypt may have been very similar to this, if we can draw conclusions from tesseræ discovered in Cnossus (see H. Bossert, Alt Kreta (1921), T. 14). And the Pylon is an undoubted and genuine façade. (Such tesseræ, bearing pictures of windowed houses, are illustrated in Art. “Ægean Civilization,” Ency. Brit., XI Edition, Vol. I, p. 251, plate IV, fig. 1.—Tr.).

[277]. Ghiberti has not outgrown the Gothic, nor has even Donatello; and already in Michelangelo the feeling is Baroque, i.e., musical.

[278]. The struggle to fix the problem is visible in the series of “Apollo-figures.” See Déonna, Les Apollons archaïques (1909).

[279]. Woermann, Geschichte der Kunst, I (1915), p. 236. The first tendency is seen in the Samian Hera of Cheramues and the persistent turning of columns into caryatids; the second in the Delian figure dedicated to Artemis by Nicandra, with its relation to the oldest metope-technique.

[280]. Miletus was in a particular relation with Egypt through Naucratis.—Tr.

[281]. Most of the works are pediment-groups or metopes. But even the Apollo-figures and the “Maidens” of the Acropolis could not have stood free.

[282]. V. Salis, Kunst der Griechen (1919), pp. 47, 98 et seq.

[283]. The decisive preference of the white stone is itself significant of the opposition of Renaissance to Classical feeling.

[284]. All Greek scales are capable of reduction to “tetrachords” or four-note scales of which the form E—note—note—A is typical. In the diatonic the unspecified inner notes are F, G; in the chromatic they are F, F sharp; and in the enharmonic they are E half-sharp, F. Thus, the chromatic and enharmonic scales do not provide additional notes as the modern chromatic does, but simply displace the inner members of the scale downwards, altering the proportionate distances between the same given total. In Faustian music, on the contrary, the meaning of “enharmonic” is simply relational. It is applied to a change, say from A flat to G sharp. The difference between these two is not a quarter-tone but a “very small” interval (theory and practice do not even agree as to which note is the higher, and in tempered instruments with standardized scales the physical difference is eliminated altogether). While a note is being sounded, even without any physical change in it, its harmonic co-ordinates (i.e., substantially, the key of the harmony) may alter, so that henceforth the note, from A flat, has become G sharp.—Tr.

[285]. In the same way the whole of Russian music appears to us infinitely mournful, but real Russians assure us that it is not at all so for themselves.

[286]. See articles under these headings in Grove’s “Dictionary of Music.”—Tr.

[287]. See Vol. II, p. 238.

[288]. In Baroque music the word “imitation” means something quite different from this, viz., the exact repetition of a motive in a new colouring (starting from a different note of the scale).

[289]. For all that survives performance is the notes, and these speak only to one who still knows and can manage the tone and technique of the expression-means appropriate to them.

[290]. See articles Fauxbourdon, Discant and Gimel in Grove’s “Dictionary of Music.”—Tr.

[291]. Note that Oresme was a contemporary of Machault and Philippe de Vitry, in whose generation the rules and prohibitions of strict counterpoint were definitively established.

[292]. See p. [19] and Vol. II, p. 357.

[293]. Even the first great troubadour, Guilhem of Poitiers, though a reigning sovereign, made it his ambition to be regarded as a “professional,” as we should say.—Tr.

[294]. See also Vol. II, p. 365.

[295]. See p. [74].

[296]. A movement in sonata form consists essentially of (a) First Subject; (b) Second Subject (in an allied key); (c) Working-out, or free development of the themes grouped under (a) and (b); and (d) Recapitulation, in which the two subjects are repeated in the key of the tonic.

The English usage is to consider (a) and (b) with the bridge or modulation connecting them, together as the “Exposition,” and the form is consequently designated “three-part.”—Tr.

[297]. Einstein, Gesch. der Musik, p. 67.

[298]. Coysevox lived 1640-1720. Much of the embellishment and statuary of Versailles is his work.—Tr.

[299]. See Vol. II, pp. 357 et seq., 365 et seq.

[300]. It was not merely national-Italian (for that Italian Gothic was also): it was purely Florentine, and even within Florence the ideal of one class of society. That which is called Renaissance in the Trecento has its centre in Provence and particularly in the papal court at Avignon, and is nothing whatever but the southern type of chivalry, that which prevailed in Spain and Upper Italy and was so strongly influenced by the Moorish polite society of Spain and Sicily.

[301]. Renaissance ornament is merely embellishment and self-conscious "art"-inventiveness. It is only with the frank and outspoken Baroque that we return to the necessities of high symbolism.

[302]. Jacob Burckhardt, Die Cultur der Renaissance in Italien. (An English translation was published in 1878.—Tr.)

[303]. Inclusive of Paris itself. Even as late as the fifteenth century Flemish was as much spoken there as French, and the architectural appearance of the city in its oldest parts connects it with Bruges and Ghent and not with Troyes and Poitiers.

[304]. A. Schmarsow, Gotik in der Renaissance (1921); B. Haendke, Der niederl. Einfluss auf die Malerei Toskana-Umbriens (Monatshefte für Kunstwissensch. 1912).

[305]. The colossal statue of Bartolommeo Colleone at Venice.—Tr.

[306]. Svoboda, Römische und Romanische Paläste (1919); Rostowzew, Pompeianische Landschaften und Römische Villen (Röm. mitt., 1904).

[307]. Environs of Rome. They date from the late 17th and the mid-18th centuries respectively; the gardens of the V. Ludovisi were laid out by Le Nôtre.—Tr.

[308]. That is, the expression for the sum of a convergent series beyond any specified term.—Tr.

[309]. See Vol. II, pp. 117 et seq.

[310]. In Classical painting, light and shadow were first consistently employed by Zeuxis, but only for the shading of the thing itself, for the purpose of freeing the modelling of the body painted from the restriction of the relief-manner, i.e., without any reference to the relation of shadows to the time of day. But even with the earliest of the Netherlanders light and shade are already colour-tones and affected by atmosphere.

[311]. The brilliant polish of the stone in Egyptian art has a deep symbolic significance of much the same kind. Its effect is to dematerialize the statue by causing the eye to glide along its exterior. Hellas on the contrary manifests, by its progress from “Poros” stone, through Naxian, to the translucent Parian and Pentelic marbles, how determined it is that the look shall sink right into the material essence of the body.

[312]. See Vol. II, pp. 314 et seq.

[313]. The life and teaching of St. Francis were, morally and æsthetically alike, the centres of inspiration for Cimabue, Giotto and the Italian Gothic generally.—Tr.

[314]. Der nordische im Grenzenlose schweifende Pantheismus.

[315]. On the following page is a translation of this chorus.—Tr.

Raphael. The Sun outsings the brother-spheres

in olden rivalry of song,

and thunder-girt pursues the years

the preordainèd path along.

’Tis from his face the angels gain

their strength; but scan it no one may.

Thought is outranged and Works remain

sublime as on Creation-Day.

Gabriel. And, swift beyond description, flies

the circling scene of land and sea,

in alternance of Paradise

with dark and awful Mystery.

The ocean swings, the billows sway,

back from the cliff the waves are hurled.

But cliff and waves alike obey

the mightier movement of the World.

Michael. And storms arise and swell and ebb

o’er sea and mountain, lake and field,

in wild contention weave a web

of forces purposed though concealed.

The lightning is thy flaming sword,

the thunder veils thee on thy way,

yet ever spare thy envoys, Lord,

the gentle changing of thy day.

The Three. ’Tis from thy face the angels gain

their strength, but scan it no one may.

Beyond all thought thy Works remain

sublime as on Creation-Day.

[316]. His portrait of Frau Gedon, all steeped in brown, is the last Old-Master portrait of the West; it is painted entirely in the style of the past.

[317]. The strings in the Orchestra represent, as a class, the colours of the distance. The bluish green of Watteau is found already in the Neapolitan bel canto of about 1700, in Couperin, in Mozart and Haydn; and the brown of the Dutch in Corelli, Handel and Beethoven. The woodwind, too, calls up illumined distances. Yellow and red, on the other hand, the colours of nearness, the popular colours, are associated with the brass timbre, the effect of which is corporeal often to the point of vulgarity. The tone of an old fiddle is entirely bodiless. It is worth remarking that the Greek music, insignificent as it is, underwent an evolution from the Dorian lyre to the Ionian flute (aulos and syrinx) and that even in the time of Pericles strict Dorians blamed this as an enervating and lowering tendency.

(The horn is an exception, and is always treated as an exception, to the brass generally. Its place is with the woodwind, and its colours are those of the distance.—Tr.)

[318]. The use of gold in this way, viz., to add brilliancy to bodies standing freely in the open, has nothing in common with its employment in Magian art to provide glittering backgrounds for figures seen in dim interiors.

[319]. The Chinese also attach enormous importance to the patinas of their old bronzes, which, owing to the different alloys used and the strong chemical characters of the soil, are of infinite variety and natural intricacy. They too, in later phases, have come to the production of artificial patina.—Tr.

[320]. Pausanias, it should be observed, was neither by date nor by origin a Greek.—Tr.

[321]. “In places, as you stand on it, the great towered and embattled enceinte produces an illusion: it looks as if it were still equipped and defended. One vivid challenge at any rate it flings down before you; it compels you to make up your mind on the matter of restoration. For myself, I have no hesitation; I prefer in every case the ruined, however ruined, to the reconstructed however splendid.... After that, I am free to say that the restoration of Carcassonne is a splendid achievement.” (Henry James, “A Little Tour in France,” xxiii.) Yet if ever there was a reconstruction carried out with piety and scholarship as well as skill, it was Viollet-le-Duc’s reconstruction of these old town-walls.—Tr.

[322]. Home, an English philosopher of the 18th Century, declared in a lecture on English parks that Gothic ruins represented the triumph of time over power, Classical ruins that of barbarism over taste. It was that age that first discovered the beauty of the ruin-studded Rhine, which was thenceforward the historic river of the Germans.

[323]. English readers will very likely think of the case of Shaw’s “Back to Methuselah,” with its extreme contrast of the cheaply-satirical present-day scene and the noble and tragic scenes of far past and far future.—Tr.

[324]. One need only contrast the Greek artist with Rubens and Rabelais.

[325]. Of whom one of his mistresses remarked that he “smelt like a carcass” (qu’il puait comme une charogne). Note also how the musician generally has a reputation for uncleanliness.

[326]. From the solemn canon of Polycletus to the elegance of Lysippus the same process of lightening is going on in the body-build as that which brought the column from the Doric to the Corinthian order. The Euclidean feeling was beginning to relax.

[327]. See p. [19].—Tr.

[328]. In other countries, e.g., old Egypt and Japan (to anticipate a particularly foolish and shallow assertion), the sight of naked men was a far more ordinary and commonplace thing than it was in Athens, but the Japanese art-lover feels emphasized nudity as ridiculous and vulgar. The act is depicted (as for that matter it is in the “Adam and Eve” of Bamberg Cathedral), but merely as an object without any significance of potential whatsoever.

[329]. Kluge, Deutsche Sprachgesch. (1920), pp. 202 et seq.

[330]. A. Conze, Die Attischen Grabreliefs (1893 etc.).

[331]. Louvre. Replicas of the pair in the Vict. and Alb. Museum, London.—Tr.

[332]. Olympia—the only unquestioned original that we have from the “great age.” References would be superfluous, for few, if any, Classical works are better or more widely known.—Tr.

[333]. Of the several copies that have survived, all imperfectly preserved, that in the Palazzo Massimi is accounted the best. The restoration which, once seen, convinces, is Professor Furtwängler’s (shown in Ency. Brit., XI Ed., article Greek Art, fig. 68).—Tr.

[334]. A cast of this is in the British Museum (illustrated in the Museum Guide to Egypt. Antiq., pl. XXI).—Tr.

[335]. In the Bargello, Florence. Replica in Vict. and Alb. Museum, London.—Tr.

[336]. The “Apollo with the lyre” at Munich was admired by Winckelmann and his time as a Muse. Till quite recently a head of Athene (a copy of Praxiteles) at Bologna passed as that of a general. Such errors would be entirely impossible in dealing with a physiognomic art, e.g., Baroque.

[337]. In his portrait of Frau Gedon, already alluded to, p. 252.

[338]. See p. [136] and also Vol. II, p. 354.

[339]. The so-called “Three Fates” in the British Museum.—Tr.

[340]. The Orphic springtime contemplates the Gods and does not see them. See Vol. II, p. 345.

[341]. There was indeed a beginning of this in the aristocratic epic of Homer—so nearly akin to the courtly narrative art of Boccaccio. But throughout the Classical age strictly religious people felt it as a profanation; the worship that shines through the Homeric poems is quite without idolatry, and a further proof is the anger of thinkers who, like Heraclitus and Plato, were in close touch with the temple tradition. It will occur to the student that the unrestricted handling of even the highest divinities in this very late art is not unlike the theatrical Catholicism of Rossini and Liszt, which is already foreshadowed in Corelli and Händel and had, earlier even, almost led to the condemnation of Church music in 1564.

(The event alluded to in the last line is the dispute in and after the Council of Trent as to the nature and conduct of Church music. If Wagner’s suggestion that Pope Marcellus II tried to exclude it altogether is exaggerated, it is certain at least that the complaints were deep and powerful, and that the Council found it necessary to forbid “unworthy music in the house of God” and to bring the subject under the disciplinary control of the Bishops.—Tr.)

[342]. Harmodius and Aristogiton. At Naples. Illustrated in Ency. Brit. XI ed., article Greek Art, fig. 50. Cast in British Museum.—Tr.

[343]. The famous statue now in the Lateran Museum, Rome.—Tr.

[344]. See foot-note, p. 130. An antique copy is in the British Museum.—Tr.

[345]. In the Vatican Museum.—Tr.

[346]. Even the landscape of the Baroque develops from composed backgrounds to portraits of definite localities, representations of the soul of these localities which are thus endowed with faces.

[347]. It could be said of Hellenistic portrait art that it followed exactly the opposite course.

[348]. British Museum.—Tr.

[349]. Pinakothek, Munich.—Tr.

[350]. Art Gallery, Vienna.—Tr.

[351]. Nothing more clearly displays the decadence of Western art since the middle of the 19th century than its absurd rendering of acts by masses; the deeper meaning of act-study and the importance of the motive have been entirely forgotten.

[352]. By that test Rubens, and, among moderns, especially Feuerbach and Böcklin, lose, while Goya, Daumier, and, in Germany, Oldach, Wasmann, Rayski[Wasmann, Rayski] and many another almost forgotten artist of the earlier 19th Century, gain. And Marées passes to the rank of the very greatest.

[353]. Tombs of the Scaligers, Verona.—Tr.

[354]. National Gallery, London.—Tr.

[355]. Museo Nazionale, Florence.—Tr.

[356]. It is the same “noble simplicity and quiet greatness”—to speak in the language of the German Classicists—that produces such an impression of the antique in the Romanesque of Hildesheim, Gernrode, Paulinzella and Hersfeld. The ruined cloisters of Paulinzella, in fact, have much of what Brunellesco so many centuries later strove to obtain in his palace-courts. But the basic feeling that underlies these creations is not something which we got from the Classical, but something that we projected on to our own notion of Classical being. And our own notion of peace is one of an infinite peace. We feel the “Rest in God” to be an expanse of quietude. All Florentine work, in so far as sureness does not turn into the Gothic challenge of Verrocchio, is characterized by this feeling, with which Attic σωφροσύνη has nothing whatever in common.

[357]. It has never been sufficiently noticed that the few sculptors who came after Michelangelo had no more than a mere workaday relation with marble. But we see at once that it is so when we think of the deeply intimate relation of great musicians to their favourite instruments. The story of Tartini’s violin, which shattered itself to pieces on the death of the master—and there are a hundred such stories—is the Faustian counterpart of the Pygmalion legend. Consider, too, E. T. A. Hoffmann’s “Johannes Kreisler the Kapellmeister”; he is a figure worthy to stand by the side of Faust, Werther and Don Juan. To see his symbolic significance and the inward necessity of him, we have only to compare him with the theatrical painter-characters in the works of contemporary Romanticists, who are not in any relation whatever with the idea of Painting. As the fate of 19th-Century art-romances shows—a painter cannot be made to stand for the destiny of Faustian art.

(E. T. A. Hoffmann, the strange many-sided genius who was at once musician, caricaturist, novelist, critic, wit, able public official and winebibber, at one time in his career wrote in the character of “Johannes Kreisler.” See his Fantasiestücke in Callots Manier and Der Kater Murr, also Thomas Carlyle’s “Miscellanies” and the biographical sketches of Hoffmann in Grove’s Dictionary of Music and the Ency. Brit.—Tr.)

[358]. Although gunpowder is much older than the Baroque, its application in real earnest to long-ranging fire-arms was only accomplished during the 16th Century. It cannot be said that there was any technical reason why 100 years should have elapsed between the first use of powder in European warfare and the first effective soldier’s fire-arm. No careful student of this period of military history can fail to be struck with this fact—the significance of which, not being technical, must be cultural. Much the same could be said of printing, which, so far as concerns technical factors, might just as well have been invented in the 10th as in the 15th Century.—Tr.

[359]. Uffizi, Florence.—Tr.

[360]. Sistine Chapel, Rome.—Tr.

[361]. “Doctor Marianus.”—Tr.

[362]. Vatican.—Tr.

[363]. In Renaissance work the finished product is often quite depressingly complete. The absence of “infinity” is palpable. No secrets, no discoveries.

[364]. Hence the impossibility of achieving a genuinely religious painting on plein-air principles. The world-feeling that underlies it is so thoroughly[thoroughly] irreligious, so worthless for any but a “religion of reason” so-called, that every one of its efforts in that direction, even with the noblest intentions (Uhde, Puvis de Chavannes), strikes us as hollow and false. One instant of plein-air treatment suffices to secularize the interior of a church and degrade it into a showroom.

[365]. State Museum, Berlin.—Tr.

[366]. I.e., the “giants” of the great frieze, who were in fact Galatians playing the part. This Gigantomachia, a programme-work like the Ring, represented a situation, as the Ring represented characters, under mythological labels.—Tr.

[367]. See Vol. II, pp. 138 et seq.

[368]. See pp. 197 et seq.

[369]. See pp. 55 et seq.

[370]. See p. [126].

[371]. Primitive languages afford no foundations for abstract ordered thought. But at the beginning of every Culture an inner change takes place in the language that makes it adequate for carrying the highest symbolic tasks of the ensuing cultural development. Thus it was simultaneously with the Romanesque style that English and German arose out of the Teutonic languages of the Frankish period, and French, Italian and Spanish out of the “lingua rustica” of the old Roman provinces—languages of identical metaphysical content though so dissimilar in origin.

[372]. See p. [262].

[373]. See p. [172].

[374]. That is, discussion of the doctrines of the Eleatic school regarding unity and plurality, the Ent and Nonent, focussed themselves, in Zeno, down to the famous paradoxes concerning the nature of motion (such as “Achilles and the Tortoise”) which within the Greek discipline were unanswerable. Their general effect was to show that motion depended upon the existence of an indefinitely great plurality, that is, of infinitely small subdivisions as well as infinitely great quantities, and, the denial of this plurality being the essential feature of the Eleatic philosophy, its application to motion was bound to produce “paradoxes.”

The enunciations, with a brief but close critique, will be found in the Ency. Brit., XI ed., Article Zeno of Elea. Here it suffices to draw attention to the difficulties that are caused by the absence (or unwelcome presence) of time and direction elements, not only in the treatment of plurality itself (which is conceived of indifferently as an augmentation or as a subdivision of the finite magnitude) but especially in the conclusion of the “arrow” paradox and in the very obscure enunciation of Paradox 8.—Tr.

[375]. See Vol. II, pp. 296 et seq.

[376]. De Boer, Gesch. d. Philos. im Islam (1901), pp. 93, 108.

[377]. A detailed summary will be found in Ency. Brit., XI ed., article Kabbalah, by Dr. Ginsburg and Dr. Cook.—Tr.

[378]. See Windelband, Gesch.[Gesch.] d. neueren Philosophie (1919), I, 208; also Hinnebert, Kultur der Gegenwart, I, V (1913), p. 484.

[379]. See Ency. Brit., XI ed., article Cartesianism (V, 421).—Tr.

[380]. See Vol. II, p. 296.

[381]. When, therefore, in the present work also, precedence is consistently given to Time, Direction and Destiny over Space and Causality, this must not be supposed to be the result of reasoned proofs. It is the outcome of (quite unconscious) tendencies of life-feeling—the only mode of origin of philosophic ideas.

[382]. See p. [201].

[383]. See Vol. II, p. 363.

[384]. In the German, “Vor allem aber sein eignes Ich.” (But in Luther’s Bible, characteristically, “Auch dazu sein eigen Leben.”)—Tr.

[385]. Barnasha. The underlying idea is not the filial relation, but an impersonal coming-up in the field of mankind.

[386]. ἐθέλω and βούλομαι imply, to have the intention, or wish, or inclination (βουλή means counsel, council, plan, and ἐθέλω has no equivalent noun). Voluntas is not a psychological concept but, like potestas and virtus, a thoroughly Roman and matter-of-fact designation for a practical, visible and outward asset—substantially, the mass of an individual’s being. In like case, we use the word energy. The “will” of Napoleon is something very different from the energy of Napoleon, being, as it were, lift in contrast to weight. We must not confuse the outward-directed intelligence, which distinguishes the Romans as civilized men from the Greeks as cultured men, with “will” as understood here. Cæsar is not a man of will in the Napoleonic sense. The idioms of Roman law, which represent the root-feeling of the Roman soul far better than those of poetry, are significant in this regard. Intention in the legal sense is animus (animus occidendi); the wish, directed to some criminal end, is dolus as distinct from the unintended wrongdoing (culpa). Voluntas is nowhere used as a technical term.

[387]. The Chinese soul “wanders” in its world. This is the meaning of the East-Asiatic perspective, which places the vanishing point in the middle of the picture instead of in the depth as we do. The function of perspective is to subject things to the “I,” which in ordering comprehends them; and it is a further indication that “will”—the claim to command the world—is absent from the Classical make-up that its painting denies the perspective background. In Chinese perspective as in Chinese technique (see Vol. II, p. 627), directional energy is wanting, and it would not be illegitimate to call East-Asiatic perspective, in contrast with the powerful thrust into depth of our landscape-painting, a perspective of “Tao”; for the world-feeling indicated by that word is unmistakably the operative element in the picture.

[388]. Obviously, atheism is no exception to this. When a Materialist or Darwinian speaks of a “Nature” that orders everything, that effects selections, that produces and destroys anything, he differs only to the extent of one word from the 18th-Century Deist. The world-feeling has undergone no change.

[389]. Lines 525-534:

ΧΟ. τούτων ἄρα Ζεύς ἐστιν ἀσθενέστερος;

ΠΡ. οὔκουν ἂν ἐκφύγοι[ἂν ἐκφύγοι] γε τὴν πεπρωμένην, etc.—Tr.

[390]. Iliad, XXII, 208-215.—Tr.

[391]. The great part played by learned Jesuits in the development of theoretical physics must not be overlooked. Father Boscovich, with his system of atomic forces (1759), made the first serious advance beyond Newton. The idea of the equivalence of God and pure space is even more evident in Jesuit work than it is in that of the Jansenists of Port Royal with whom Descartes and Pascal were associated.

(Boscovich’s atomic theory is discussed by James Clerk Maxwell in Ency. Brit., XI ed., XVIII, 655—a reference that, for more general reasons, no student of the Faustian-as-scientist should fail to follow up.—Tr.)

[392]. Luther placed practical activity (the day’s demands, as Goethe said) at the very centre of morale, and that is one of the main reasons why it was to the deeper natures that Protestantism appealed most cogently. Works of piety devoid of directional energy (in the sense that we give the words here) fell at once from the high esteem in which they had been sustained (as the Renaissance was sustained) by a relic of Southern feeling. On ethical grounds monasticism thenceforth falls into ever-increasing disrepute. In the Gothic Age entry into the cloister, the renunciation of care, deed and will, had been an act of the loftiest ethical character—the highest sacrifice that it was possible to imagine, that of life. But in the Baroque even Roman Catholics no longer felt thus about it. And the institutions, no longer of renunciation but merely of inactive comfort, went down before the spirit of the Enlightenment.

[393]. προσῶπον meant in the older Greek “visage,” and later, in Athens, “mask.” As late as Aristotle the word is not yet in use for person. “Persona,” originally also a theatre-mask, came to have a juristic application, and in Roman Imperial times the pregnant Roman sense of this word affected the Greek προσῶπον also. See R. Hirzel, Die Person (1914), pp. 40 et seq.

[394]. See pp. 127 et seq.

[395]. W. Creizenach, Gesch. d. neueren Dramas (1918), II, 346 et seq.

[396]. See p. [265].

[397]. We too have our anecdote, but it is of our own type and diametrically opposed to the Classical. It is the “short story” (Novelle)—the story of Cervantes, Kleist, Hoffmann and Storm—and we admire it in proportion as we are made to feel that its motive is possible only this once, at this time and with these people, whereas the mythic type of anecdote, the Fable, is judged by precisely opposite criteria.

[398]. See pp. 143 et seq.

[399]. The Fates of the Greeks are represented as spinning, measuring out and cutting the thread of a man’s destiny, but not as weaving it into the web of his life. It is a mere dimension.—Tr.

[400]. See p. [129].

[401]. The evolution of meaning in the Classical words pathos and passico corresponds with this. The second was formed from the first only in the Imperial period, and carried its original sense in the “Passion” of Christ. It was in the early Gothic times, and particularly in the language of the Franciscan “Zealots” and the disciples of Joachim of Floris, that its meaning underwent the decisive reversal. Expressing thenceforward a condition of profound excitement which strained to discharge itself, it became finally a generic name for all spiritual dynamic; in this sense of strong will and directional energy it was brought into German as Leidenschaft by Zesen in 1647.

[402]. The Eleusinian mysteries contained no secrets at all. Everyone knew what went on. But upon the believers they exercised a strange and overpowering effect, and the “betrayal” consisted in profaning them by imitating their holy forms outside the temple-precinct. See, further, A. Dieterich, Kleine Schriften (1911), pp. 414 et seq.

[403]. See Vol. II, pp. 345 et seq.

[404]. The dancers were goats, Silenus as leader of the dance wore a horsetail, but Aristophanes’s “Birds,” “Frogs” and “Wasps” suggest that there were still other animal disguises.

[405]. See pp. 283 et seq.

[406]. As the student of cultural history to-day is not necessarily familiar with technical Greek, it may be helpful to reproduce from Cornish’s edition of Smith’s “Greek and Roman Antiquities,” s.v. “Tragoedia,” the following paragraph, as clear as it is succinct:

“Tragedy is described by Aristotle (Poet., VI, 2) as effecting by means of pity and terror that purgation [of the soul] (κάθαρσις) which belongs to [is proper for] such feelings.”... Tragedy excites pity and terror by presenting to the mind things which are truly pitiable and terrible. When pity and terror are moved, as tragedy moves them, by a worthy cause, then the mind experiences that sense of relief which comes from finding an outlet for a natural energy. And thus the impressions made by Tragedy leave behind them in the spectator a temperate and harmonious state of the soul. Similarly Aristotle speaks of the enthusiastic worshippers of Dionysus as obtaining a κάθαρσις, a healthful relief, by the “lyric utterance of their sacred frenzy.”—Tr.

[407]. The evolution of ideals of stage-presentation in the minds of Æschylus, Sophocles and Euripides successively is perhaps comparable with that of sculptural style which we see in the pediments of Ægina, of Olympia and of the Parthenon.

[408]. It must be repeated that the Hellenistic shadow-painting of Zeuxis and Apollodorus is a modelling of the individual body for the purpose of producing the plastic effect on the eye. There was no idea of rendering space by means of light and shade. The body is “shaded” but it casts no shadow.

(Contrast with this Dante’s exact and careful specification of the time-of-day in every episode of the Purgatorio and the Paradiso, sublimely imaginative as these poems are.—Tr.)

[409]. The great mass of Socialists would cease to be Socialists if they could understand the Socialism of the nine or ten men who to-day grasp it with the full historical consequences that it involves.

[410]. See p. [239] et seq.

[411]. See p. [68].

[412]. See Vol. II, p. 363, note.

[413]. As we increase the powers of the telescope we find that the number of newly appearing stars falls off rapidly towards the edges of the field.

[414]. The thrill of big figures is a feeling peculiar to Western mankind. In the Civilization of to-day this significant passion for gigantic sums, for indefinitely big and indefinitely minute measurements, for “records” and statistics, is playing a conspicuous part.

(Our very notation of number is ceasing to rest on sense-standards. Science has carried number, as ordinarily written, so high and so low that it now uses a movable base for its numerical statements. For example, a number in astronomy is written, not as 3,450,000,000 but as 3.45 × 10⁹, one relating to ordinary experience as 3.45 (i.e., 3.45 × 10⁰) and one in electromagnetic theory, not as 0.00000345 but as 3.45 × 10^-6. Under this system the conceptual unit may be as large or as small, compared with the unit of daily experience, as the region of thought in which the calculation is taking place requires. And different conceptual worlds can be connected as to number [say, a number of kilometres brought into an order of thought that deals with millimetres] by simply changing the ten-power.—Tr.)

[415]. In stellar calculations even the mean radius of the earth’s orbit (1.493 × 10¹³ cm.) hardly suffices as unit, as the distance of a star of one second parallax is already 206,265 such units away from us; star-distances are reckoned therefore either in light-years or in terms of the unit distance of a star of this standard parallax.—Tr.

[416]. As early as the second millennium before Christ they worked from Iceland and the North Sea past Finisterre to the Canaries and West Africa. An echo of these voyagings lingers in the Atlantis-saga of the Greeks. The realm of Tartessus (at the mouth of the Guadalquivir) appears to have been a centre of these movements (see Leo Frobenius, Das unbekannte Afrika, p. 139). Some sort of relation, too, there must have been between them and the movements of the “sea peoples,” Viking swarms which after long land-wanderings from North to South built themselves ships again on the Black Sea or the Ægean and burst out against Egypt from the time of Rameses II (1292-1225). The Egyptian reliefs show their ship-types to have been quite different from the native and the Phœnician; but they may well have been similar to those that Cæsar found afterwards among the Veneti of Brittany. A later example of such outbursts is afforded by the Varyags or Varangians in Russia and at Constantinople. No doubt more light will shortly be thrown on the courses of these movement-streams.

[417]. Here there is no need to postulate firearms (as distinct from gunpowder used in fireworks) in the Chinese Culture. The archery of the Chinese and Japanese was such as only the British 14th-century archery could match in the Western and nothing in the Classical.

It should be noted also that it was in our 14th Century that—quite independently of gunpowder[gunpowder]—archery and the construction of siege-engines reached their zenith in the West. The “English” bow had long been used by the Welsh, but it was left to Edward I and Edward III to make it the tactical weapon par excellence.—Tr.

[418]. See Vol. II, pp. 626 et seq.

[419]. Half as long again as Nelson’s Victory and about the same length as the last wooden steam three-deckers (e.g., Duke of Wellington) of the mid-19th Century.—Tr.

[420]. See Vol. II, pp. 207 et seq., and Chapter IV B.

[421]. See Vol. II, p. 80.

[422]. I.e., adherents of the various syncretic cults. Sec Vol. II, pp. 212 et seq.

[423]. This applies even more forcibly to the other “long-range” episode, that of the Ten Thousand (Xenophon, Anabasis I).—Tr.

[424]. In this place it is exclusively with the conscious, religio-philosophical morale—the morale which can be known and taught and followed—that we are concerned, and not with the racial rhythm of Life, the habit, Sitte, ἦθος, that is unconsciously present. The morale with which we are dealing turns upon intellectual concepts of Virtue and Vice, good and bad; the other, upon ideals in the blood such as honour, loyalty, bravery, the feeling that attributes nobility and vulgarity. See Vol. II, 421 et seq.

[425]. The original is here expanded a little for the sake of clarity.—Tr.

[426]. After what has been said above regarding the absence of pregnant words for “will” and “space” in the Classical tongues, the reader will not be surprised to hear that neither Greek nor Latin affords exact equivalents for these words action and activity.

[427]. See Vol. II, pp. 293 et seq.

[428]. “He who hath ears to hear, let him hear”—there is no claim to power in these words. But the Western Church never conceived its mission thus. The “Glad Tidings” of Jesus, like those of Zoroaster, of Mani, of Mahomet, of the Neo-Platonists and of all the cognate Magian religions were mystic benefits displayed but in nowise imposed. Youthful Christianity, when it had flowed into the Western world, merely imitated the missionarism of the later Stoa, itself by that time thoroughly Magian. Paul may be thought of as urgent; the itinerant preachers of the Stoa were certainly so, as we know from our authorities. But commanding they were not. To illustrate by a somewhat farfetched parallel—in direct contrast to the physicians of the Magian stamp who merely proclaimed the virtues of their mysterious arcana, the medical men of the West seek to obtain for their knowledge the force of civil law, as for instance in the matter of vaccination or the inspection of pork for trichina.

[429]. For the Buddhist Four Truths see Ency. Brit., XI ed., Vol. IV, p. 742. English translation of Kant’s Kritik der praktischen Vernunft by T. K. Abbott.—Tr.

[430]. See p. [201].

[431]. See p. [205] and [222] et seq.

[432]. See Vol. II, p. 334.

[433]. The philosophy and dogma of charity and almsgiving—a subject that English research seems generally to have ignored—is dealt with at length in Dr. C. S. Loch’s article Charity and Charities, Ency. Brit., XI ed.—Tr.

[434]. Not only as local sovereigns enforcing order, like the good Bishop Wazo of Liége who fought down his castled robber-barons one by one in the middle of the 11th Century, but even as high commanders for the Emperor in distant Italy. The battle of Tusculum in 1167 was won by the Archbishops of Köln and Mainz. English history, too, contains the figures of warlike prelates—not only leaders of national movements like Stephen Langton but strong-handed administrators and fighters. The great Scots invasion of 1346 was met and defeated by the Archbishop of York. The Bishops of Durham were for centuries “palatines”; we find one of them serving on pay in the King’s army in France, 1348. The line of these warlike Bishops in our history extends from Odo the brother of William the Conqueror to Scrope, archbishop and rebel in Henry IV’s time.—Tr.

[435]. A paraphrase of the opening of “John Tanner’s Revolutionist’s Handbook,” Ch. V.—Tr.

[436]. See Vol. II, pp. 116 et seq.

[437]. Rousseau’s Contrat Social is paralleled by exactly equivalent productions of Aristotle’s time.

[438]. The first on the atheistical system of Sankhya, the second (through Socrates) on the Sophists, the third on English sensualism.

[439]. See Vol. II, pp. 441 et seq.

[440]. It was many centuries later that the Buddhist ethic of life gave rise to a religion for simple peasantry, and it was only enabled to do so by reaching back to the long-stiffened theology of Brahmanism and, further back still, to very ancient popular cults. See Vol. II, pp. 378, 285.

[441]. The articles Buddha and Buddhism in the Ency. Brit., XI ed., by T. W. Rhys Davids, may be studied in this connexion.—Tr.

[442]. See “The Questions of King Milinda,” ed. Rhys Davids.—Tr.

[443]. Of course, each Culture naturally has its own kind of materialism, conditioned in every detail by its general world-feeling.

[444]. To begin with, it would be necessary to specify what Christianity was being compared with it—that of the Fathers or that of the Crusades. For these are two different religions in the same clothing of dogma and cult. The same want of psychological flair is evident in the parallel that is so fashionable to-day between Socialism and early Christianity.

[445]. The term must not be confused with anti-religious.

[446]. Note the striking similarity of many Roman portrait-busts to the matter-of-fact modern heads of the American style, and also (though this is not so distinct) to many of the portrait-heads of the Egyptian New Empire.

[447]. See Vol. II, pp. 122 et seq.

[448]. The original is here very obscure; it reads: “... es ist der ‘Gebildete,’ jener Anhänger eines Kultus des geistigen Mittelmasses und der Offentlichkeit als Kultstätte.”—Tr.

[449]. See P. Wendland, Die hellenist.-röm. Kultur (1912), pp. 75 et seq.

[450]. See Vol. II, pp. 318 et seq.

[451]. See Vol. II, pp. 269 et seq.

[452]. Compare my Preussentum und Sozialismus, pp. 22 et seq.

[453]. See Vol. II, pp. 324 et seq., 368 et seq.

[454]. See Vol. II, p. 345. It is possible that the peculiar style of Heraclitus, who came of a priestly family of the temple of Ephesus, is an example of the form in which the old Orphic wisdom was orally transmitted.

[455]. See Vol. II, p. 307.

[456]. Here we are considering only the scholastic side. The mystic side, from which Pythagoras and Leibniz were not very far, reached its culminations in Plato and Goethe, and in our own case it has been extended beyond Goethe by the Romantics, Hegel and Nietzsche, whereas Scholasticism exhausted itself with Kant—and Aristotle—and degenerated thereafter into a routine-profession.

[457]. Zeno the Stoic, not to be confused with Zeno of Elea, whose mathematical fineness has already been alluded to.—Tr.

[458]. Neue Paralipomena, § 656.

[459]. Even the modern idea that unconscious and impulsive acts of life are completely efficient, while intellect can only bungle, is to be found in Schopenhauer (Vol. II, cap. 30).

[460]. In the chapter “Zur Metaphysik der Geschlechtsliebe” (II, 44) the idea of natural selection for the preservation of the genus is anticipated in full.

[461]. See Vol. II, pp. 36 et seq.

[462]. This began to appear in 1867. But the preliminary work Zur Kritik der politischen Ökonomie came out in the same year as Darwin’s masterpiece.

[463]. Vol. II, p. 625. See, for example, Leonard, Relativitäts-Prinzip, Aether, Gravitation (1920), pp. 20 et seq.

[464]. See Vol. II, pp. 369 et seq., 624 et seq.

[465]. See p. [57].

[466]. E.g., in Boltzmann’s formulation of the Second Law of Thermodynamics: “the logarithm of the probability of a state is proportional to the entropy of that state.” Every word in this contains an entire scientific concept, capable only of being sensed and not described.

[467]. See Vol. II, p. 369.

[468]. See Vol. II, pp. 382 et seq.

[469]. E. Wiedermann, Die Naturwissensch. bei den Arabern (1890). F. Struntz, Gesch. d. Naturwissensch. im Mittelalter (1910), p. 58.

[470]. An order of encyclopædists and philosophers; see Ency. Brit., XI ed., Vol. II, p. 278a.—Tr.

[471]. M. P. E. Berthelot, Die Chemie im Altertum u. Mittelalter (1909), pp. 64 et seq. (The reference is evidently to a German version; Berthelot published several works on the subject, viz., Les origines de l’Alchémie [1885]; Introduction à l’étude de la chimie des anciens et du moyen âge [1889]; Collection des anciens alchimistes grecs [1887, translations of texts]; La chimie au moyen âge [1893].—Tr.

[472]. For the metals, “mercury” is the principle of substantial character (lustre, tensility, fusibility), “sulphur” that of the attributive generation (e.g., combustion, transmutation). See Struntz, Gesch. d. Naturwissensch. im Mittelalter (1910), pp. 73 et seq.

(It seems desirable to supplement this a little for the non-technical reader, by stating, however roughly and generally, the principle and process of transmutation as the alchemist saw them. All metals consist of mercury and sulphur. Remove “materiality” from common mercury (or from the mercury-content of the metal under treatment) by depriving it (or the metal) of “earthness,” “liquidness” and “airiness” (i.e., volatility) and we have a prime, substantial (though not material) and stable thing. Similarly, remove materiality from sulphur (or the sulphur-content of the metal treated) and it becomes an elixir, efficient for generating attributes. Then, the prime matter and the elixir react upon one another so that the product on reassuming materiality is a different metal, or rather a “metallicity” endowed with different characters and attributes. The production of one metal from another thus depends merely on the modalities of working processes.—Tr.)

[473]. See Vol. II, pp. 370, 627.

[474]. See Vol. II, pp. 314 et seq.

[475]. See the article under this heading, and also that under Alchemy, Ency. Brit., XI ed.—Tr.

[476]. During the Gothic age, in spite of the Spanish Dominican Arnold of Villanova (d. 1311), chemistry had had no sort of creative importance in comparison with the mathematical-physical research of that age.

[477]. For even Helmholtz had sought to account for the phenomena of electrolysis by the assumption of an atomic structure of electricity.

[478]. Which in their physical aspect are individual centres of force, without parts or extension or figure. (For their metaphysical aspect, see Ency. Brit., XI edition. Article Leibniz, especially pp. 387-8.—Tr.)

[479]. M. Born, Aufbau der Materie (1920), p. 27.

(So many books and papers—strict, semi-popular and frankly popular—have been published in the last few years that references may seem superfluous, the more so as the formulation of this central theory of present-day physics. The article Matter by Rutherford in the Ency. Brit., XIIth edition (1922), and Bertrand Russell, The A.B.C. of Atoms, are perhaps the clearest elementary accounts that are possible, having regard to the scientist’s necessary reservations of judgment.—Tr.

[480]. See p. [231].

[481]. See p. [172].

[482]. See p. [121] and Vol. II, pp. 11 et seq.

[483]. See p. [169].

[484]. See p. [166] and Vol. II, p. 18.

[485]. See p. [152].

[486]. See p. 116 et seq., pp. 151 et seq.

[487]. See Vol. II, pp. 369 et seq.

[488]. J. Goldziher, Die islam. und jüd. Philosophie (“Kultur der Gegenwart,” I, V, 1913), pp. 306 et seq.

[489]. See Vol. II, pp. 27 et seq., 427 et seq.

[490]. And it may be asserted that the downright faith that Haeckel, for example, pins to the names atom, matter, energy, is not essentially different from the fetishism of Neanderthal Man.

[491]. See p. [126].

[492]. Compare Vol. II, pp. 38 et seq.

[493]. See Vol. II, p. 305.

[494]. See Vol. II, pp. 343 et seq., and p. 346.

[495]. E. Mogk, Germ. Mythol., Grundr. d. Germ. Philos., III (1900), p. 340.

[496]. See Vol. II, p. 241 et seq., 306 et seq.

[497]. See p. [268].

[498]. The pantheistic idea of Pan, familiar in European poetry, is a conception of later Classical ages, acquired in principle from Egypt.—Tr.

[499]. Few passages in the Acts of the Apostles have obtained a stronger hold on our imagination than Paul’s meeting with the altar of “the Unknown God” at Phalerum (Acts XVII, 23). And yet we have perfectly definite evidence, later than Paul’s time, of the plurality of the gods to whom this altar was dedicated. Pausanias in his guide-book (I, 24) says: “here there are ... altars of the gods styled Unknowns, of heroes, etc.” (βωμοί δε θεῶν τε ὀνομαζομένων Ἀγνώστων καὶ ἡρῴων ... κ.τ.λ.). Such, however, is the force of our fixed idea that even Sir J. G. Frazer, in his “Pausanias and Other Studies,” speaks of “The Altar to the Unknown God which St. Paul, and Pausanias after him, saw.” More, he follows this up with a description of a dialogue “attributed to Lucian” (2nd Cent. A.D.) in which the Unknown God of Athens figures in a Christian discussion; but this dialogue (the Philopatris) is almost universally regarded as a much later work, dating at earliest from Julian’s time (mid-4th Cent.) and probably from that of Nicephorus Phocas (10th Cent.).—Tr.

[500]. Wissowa, Religion und Kultus der Römer (1912), p. 38.

[501]. See Ency. Brit., XI ed., article Great Mother of the Gods.—Tr.

[502]. In Egypt Ptolemy Philadelphus was the first to introduce a ruler-cult. The reverence that had been paid to the Pharaohs was of quite other significance.

[503]. See Vol. II, pp. 241 et seq.

[504]. Significantly enough, the formula of the oath sworn by this stone was not “per Jovis lapidem” but “per Jovem lapidem.”—Tr.

[505]. The Erechtheum, similarly, was a group of cult-sites, each refraining from interference with the others.—Tr.

[506]. Juppiter Dolichenus was a local deity of Doliche in Commagene, whose worship was spread over all parts of the Empire by soldiers recruited from that region; the tablet dedicated to him which is in the British Museum was found, for example, near Frankfurt-on-Main.

Sol Invictus is the Roman official form of Mithras. Troop-movements and trade spread his worship, like that of Juppiter Dolichenus, over the Empire.—Tr.

[507]. To whom the inhabitants of “Roman” Carthage managed to attach even Dido.—Tr.

[508]. Wissowa, Kult. und. Relig. d. Römer (1912), pp. 98 et seq.

[509]. Wissowa, Relig. u. Kult. der Römer (1912), p. 355.

[510]. The symbolic importance of the Title, and its relation to the concept and idea of the Person, cannot here be dealt with. It must suffice to draw attention to the fact that the Classical is the only Culture in which the Title is unknown. It would have been in contradiction with the strictly somatic character of their names. Apart from personal and family names, only the technical names of offices actually exercised were in use. “Augustus” became at once a personal name, “Cæsar” very soon a designation of office. The advance of the Magian feeling can be seen in the way in which courtesy-expressions of the Late-Roman bureaucracy, like “Vir clarissimus,” became permanent titles of honour which could be conferred and cancelled. In just the same way, the names of old and foreign deities became titles of the recognized Godhead; e.g., Saviour and Healer (Asklepios) and Good Shepherd (Orpheus) are titles of Christ. In the Classical, on the contrary, we find the secondary names of Roman deities evolving into independent and separate gods.

[511]. Diagoras, who was condemned to death by the Athenians for his “godless” writings, left behind him deeply pious dithyrambs. Read, too, Hebbel’s diaries and his letters to Elise. He “did not believe in God,” but he prayed.

[512]. See Vol. II, p. 376.

[513]. See Vol. II, p. 244.

[514]. Livy XL, 29.—Tr.

[515]. In the famous conclusion of his “Optics” (1706) which made a powerful impression and became the starting-point of quite new enunciations of theological problems, Newton limits the domain of mechanical causes as against the Divine First Cause, whose perception-organ is necessarily infinite space itself.

[516]. As has been shown already, the dynamic structure of our thought was manifested first of all when Western languages changed “feci” to “ego habeo factum,” and thereafter we have increasingly emphasized the dynamic in the phrases with which we fix our phenomena. We say, for instance, that industry “finds outlets for itself” and that Rationalism “has come into power.” No Classical language allows of such expressions. No Greek would have spoken of Stoicism, but only of the Stoics. There is an essential difference, too, between the imagery of Classical and that of Western poetry in this respect.

[517]. The law of the equivalence of heat and work.—Tr.

[518]. See p. [307].

[519]. Original: “Keine dem abendländischen Geist natürliche Art der Deutung mechanischer Tatsachen, welche die Begriffe Gestalt und Substanz (allenfalls Raum und Masse) statt Raum, Zeit, Masse, und Kraft zugrunde liegt.”

[520]. See foot-note, p. 314.—Tr.

[521]. See p. [355].

[522]. See Vol. II, p. 618.

[523]. See M. Planck, Entstehung und bisherige Entwicklung der Quantentheorie (1920), pp. 17-25.

[524]. Which in many cases have led to the supposition that the “actual existence” of atoms has now at last been proved—a singular throw-back to the materialism of the preceding generation.

[525]. This sentence follows the original word for word and phrase for phrase. Its significance depends wholly on the precise meaning to be attached to such words as “dead,” “free,” “latent,” and to attempt any sharper formulation of the processes in English would require not only the definition of these (or other) basic terms but also extended description of what they imply.

The Second Law of Thermodynamics is something which is absorbed by, rather than specified for, the student. Elsewhere in this English edition, indications have been frequently given to enable the ordinary student to follow up matters referred to more allusively in the text. But in this difficult domain such minor aids would be worthless. All that is possible is to recommend such students to make a very careful study of some plain statement of the subject like Professor Soddy’s “Matter and Energy” (especially chapters 4 and 5) and to follow this up—to the extent that his mathematical knowledge permits—in the articles Energy, Energetics and Thermodynamics in the Ency. Brit., XI ed.—Tr.

[526]. See foot-note, p. 157.

[527]. The application of the idea of “lifetime” to elements has in fact produced the conception of “half-transformation times” [such as 3.85 days for Radium Emanation.—Tr.].

[528]. The text of this paragraph has been slightly condensed, as in such a field as this of philosophical mathematics partial indications would serve no useful purpose. The mathematical reader may refer to the articles Function, Number, and Groups in the Ency. Brit., XI ed.—Tr.