Here under follows the transcription of the chapter Leonardo of Houston Stewart Chamberlain's Immanuel Kant, published by John Lane, The Bodley Head, 1914.

Leonardo da Vinci

LEONARDO DA VINCI
Painted by himself
Drawn and engraved by Charles Townley

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The original text in German: Immanuel Kant
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See also the reviews of this book:
Kant in the 20th century. Review in the London Times Literary Supplement, 1914
Kritische Urteile über Chamberlain's Kant. Collection of reviews in german, 1909
 
 

VOLUME I page
INTRODUCTORY 3
GOETHE 13
LEONARDO 101
DESCARTES 197
BRUNO 311




VOLUME II
PLATO 3
KANT 169
NOTES 415
INDEX 513

99

LEONARDO

CONCEPTION AND PERCEPTION

WITH AN EXCURSUS UPON PHYSICAL OPTICS
AND THE DOCTRINE OF COLOUR

Our soul is composed of harmony,
and harmony is never bred save
in moments when the proportions
of objects are seen or heard.
Leonardo.

100

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101


LEONARDO
THAT Seeing is a passive as well as an active function is a maxim as old as Aristotle. But the difference between passivity and activity in different men repeats itself in the degree and the more delicate qualities of both. It must be our business to bring into relief those personal peculiarities of Kant's way of Seeing which differentiate him from other Seers. It is with this object in view that we resort to comparison. We desire ourselves to observe and See the most important of the Seers, in the profound conviction that this will carry us further and to greater advantage than if we were to go into abstract theories about them, and hedge in their doctrines with finely pointed fences of definition.
    From our first comparison, — that with Goethe, — we have won a significant and lasting advantage. The intellectual individuality of Kant revealed itself in striking contrast to that of Goethe. In Kant we saw a peculiar quality of intuition developed to an absolutely astounding degree. We saw the power of appreciating mentally that which has been described: and that which is described is something which has been brought to our minds parcel-wise, or, to use the technical expression, analytically: for it is only by degrees that words can present a Whole, whereas the Eye first gives us a Whole, and only by degrees separates it into Parts. Moreover, in Kant we found an important development of that method of perception which is projected from within to without, geometrically in accordance with formula, humanly

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speaking creative, — namely the mathematical method. In Goethe, on the contrary, we found as a characteristic the insatiable hunger of the Eye, and in connection therewith the impulse to treat even matters of theory as something actually seen. In spite of this, inasmuch as the Doctrine of Metamorphosis had furnished us with a clear demonstration of the relationship between passivity and activity in Goethe's manner of Seeing, we recognised its harmony with Kant's mental vision and his analytical distinction between Experience and Idea.
    To-day I wish to carry this comparison with Goethe further, for it still contains a whole store of instruction. I hope to convince you that without the help of Kant we could hardly succeed in correctly grasping Goethe's view of nature, while at the same time no other man leads us so directly and patently to Kant, as does Goethe. This consideration, then, will give you a twofold advantage. Still, I wish to associate with these two men a third, — another great artist. I hit upon my choice without any reference to chronology; — simply with the intention of avoiding the ever-present danger of allowing our lazy thoughts to crystallise, and of contenting ourselves with some idle phrase about the antagonism between art and philosophy. Unfortunately no lesser man than Schopenhauer has given encouragement to so stark a fallacy: he is the most read of all philosophers, and in so far justly as he is by a long way the most readable; pity, that among his many perversities of thought, (I can find no other word for them,) there should be the asseveration that “Genius and a head for mathematics“ should be contradictions. 1 It is not possible here to enter upon a refutation of this detestable asseveration, to which, in the very first place, the whole phenomenon of Hellenism would have to fall a sacrifice: it would be easy and entertaining to carry out such a refutation with no other help than that of Schopenhauer's own writings:

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but one feels almost ashamed to enter the lists against this much too clever man when one hears him in an important passage cite Alfieri as having been unable to master the fourth proposition of Euclid, and again bringing forward some unnamed French mathematician who, on reading through Racine's Iphigénie, shrugged his shoulders, and asked, “Qu'est-ce que cela prouve?“ 2 If those are arguments then one might, with equal force, come to the conclusion that because a certain nineteenth-century poet at the age of forty, and in spite of living in the country, did not yet know that tadpoles turn into frogs, therefore no Poet is gifted with the power of observing nature. The mischief of such phrases, when they are presented with the seductive eloquence of a Schopenhauer, is that they are scattered far and wide, and establish themselves as dogmas, and so it comes to pass that to-day we find many men who because, like Alfieri, they are incapable of something, pose as men of genius, and who, not content with the fact that “the pride of the human intellect,“ as Kant calls mathematics, is none of theirs, plume themselves upon their impotence. Nay more, these mental waifs who cannot even grasp the simple problem of the equilateral triangle, look down from the height of their superiority on the most important men if only they show any aptitude for mathematics, and catalogue them as second-rate goods. But we need not dwell upon this, though it is difficult to prevent our wrath from blazing up over the impertinence of so fundamentally perverted a dogma. It is time for us to enter at once upon the heart of our subject. 3
    Schopenhauer's thesis affects genius in general. Sometimes, however, he propounds it in a narrower and therefore more plausible form: in this sense he writes, “Experience has proved that men of great genius in art have no aptitude for mathematics.“ That is an important limitation, for even in his eyes it is not the

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artist alone who can lay claim to genius: indeed, he is fond of quoting himself as an example, and certainly he had no artistic sense. Nevertheless this contention, which is to be found in the thirty-sixth paragraph of the first volume of his principal work, is so fundamentally false, that one asks oneself how Schopenhauer could have been blind enough to let it stand unaltered from the year 1818 to the day of his death. If we only think of German artists, the very first that comes to our thoughts is the man who was so specially admired even by Goethe, the great, the only, I had almost said the holy, Albrecht Dürer. He is one of those great “men of genius in art“ of whom one can say that they were the beginning and the end and the culminating point, all in one. Of course historically they spring from what has gone before, and they lead to what is to follow after, but that association hangs about their noble forms like a mantle. Like the goddess from the sea-foam, the individual rises out of the mass, something new, something incomparable, that never was before, and never can be again. At the sight of such men we are struck by Schopenhauer's fine saying, “Art is everywhere triumphant.“ Perfection it is that blazes out upon us out of all the feverish struggles of these artists, — Peace that smiles upon us, full of trust, and resting from the hurry of the eternal strife for something higher. And where labour and thought and prayer have wrought together as tireless journeymen, there at last reigns Harmony, divinely restful, incapable of failure. Among these giants is Dürer — and mark this. Not only had he an aptitude for mathematics, but that aptitude was something quite out of the common. Dürer is the author of the first textbook of applied geometry in the German language! Besides that, he devoted a whole work to the hopelessly dry, and only mathematically interesting, subject of Fortification; and his lectures on the proportion of the human figure are a little miracle

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of intricate geometrical descriptions. In his partiality for mathematics, in his sure eye for the study, and the weight that he lays upon it for the educational equipment of the artist — as he writes, “mensuration is the right foundation of all painting“ 4 — we have the special characteristic of this great artist. This one example is enough to prove that Schopenhauer's contention that the great artist has no aptitude for mathematics is an untenable generalisation from single instances. Further, you will easily understand that I must have it at heart to refute the insinuation that Kant belonged to the class of inferior minds lacking genius, because he had a talent for mathematics: far rather do we see that the possession of that talent gives us no right to infer a lack of artistic feeling.
    Now, at last, I call up the man whose radiant name I should be loath to cloud with polemics — Leonardo da Vinci. No greater painter ever lived; and this great painter was like Dürer, and even more than Dürer, a pre-eminent mathematician and mechanician. At the same time — as we see every day more clearly — a man of an all-embracing intellect, a Seer who penetrated all that his eye saw, a Discoverer so inexhaustible that the world has perhaps never seen his like, a deep, bold Thinker. Let us compare his method of Seeing with the methods of Goethe and Kant: that, I hope, will save us from all future danger of the crystallisations of the phrase-mongers.
    Like Goethe, this man is all Eye. He calls the Eye the Window of the soul, finestra dell' anima, 5 whose precious qualities he is never weary of praising; the Eye is signore de' sensi, “Lord of the senses,“ 6 the Eye is the Source of all Knowledge. Those who rely solely on the study of learned writings, instead of becoming acquainted with the works of Nature by means of their own Eyes, are only grandchildren not Sons of Nature, that one

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teacher of all teachers. All Arts, all Sciences, all Thought, are according to Leonardo “daughters of the Eye,“ and so it is that the painter is nipote à Dio, “the grandson of God.“ The Eye of this remarkable man is nevertheless, like Goethe's, far from being an exclusively artistic organ, — it has also the power of penetrating the universe. A brilliant light radiates from his Eye — for it is the special characteristic of the Eye of such men that it not only takes up light as others do, but also sends out rays of light illuminating the darkness, glowing through the impenetrable until it becomes transparent. A ray of light radiates, I say, from Leonardo's Eye so brilliantly, that even the most prosaic historians must admit that in him the intuitive power of divination of this organ verges upon the fabulous. Leonardo anticipated our whole modern natural science, — that is to say so far as this was possible, relying upon the Eye alone and without the help of the higher mathematics, — which were not then known, — of the new instruments, and of the mass of observations which had to be mastered by whole generations. For example, this man who died in 1519, who had been brought up in the strict belief of the Church in a flat earth laid between Heaven and Hell, knew the principles of the Cosmic system as Copernicus developed them thirty years later. How he gained this knowledge, and in what connection it came to him, we know not. For his observations, up to the present time far from being all deciphered and published, are for the most part aphoristic, often forming an unsolvable tangle of the most various thoughts, jotted down in the midst of, or under, or across his sketches, or on the backs of his sheets of drawings — thoughts often occurring to him in the midst of his painting, which he evidently seizes in a hurry, in order to use them elsewhere. Sometimes he writes expressly, “This is how I must deal with the matter in my work,“ or something of the same sort: or they are

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clear and neat preparations for books which he seems never to have written, and it is only from the outline that we can make a guess at the direction of his thought. So in Leonardo's writings we find no astronomical system. Yet on one sheet, under a number of mathematical calculations, we find written in unusually large letters, il sole non si muove, “the sun does not move.“ Not another word. Here we have clearly a sudden inspiration. But Leonardo is no visionary: his was throughout a positive intellect, never weary of seeking the certezza delle scientie by the strictly empirical and mathematical road. Sperientia è commune madre di tutte le scientie e arti. “Experience is the common mother of all the arts and sciences,“ — and nissuna humana investigatione si po dimandare vera scientia, s'essa non passa per le matematiche dimostrationi, “no human investigation can lay claim to being true science, unless it can stand the test of mathematical demonstration.“ Experiment, therefore, and calculation must be brought into court as tests of the correctness of any assumed fact. In the same way on other sheets we find a succession of investigations and deductions all circling round this central idea of a stationary sun and an earth which is in motion. Take, for instance, the important recognition come la terra non è nel mezzo del cerchio del sole, ne nel mezzo del mondo, 7 “that the earth is not in the centre of the sun's orbit, nor in the centre of the universe.“ In this connection we over and over again find the remark that the sun is greater than the earth, together with the assertion that there are many stars that are many times bigger than the star which is the earth. Molte stelle vi sono che son moltissime volte maggiore che la stella che è la terra. 8 The recognition of the fact that the dark earth reflects light leads him to the further assumption that the light of the planets is also reflected light, and that our earth seen from the moon would have

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exactly the same appearance as that which the moon gives us. 9 From this recognition there was but one step to the affirmation that the earth must be nearly spherical in shape and revolve round its axis. Certainly, so far as I know, we possess no written proof that Leonardo in any of his abrupt sentences ever gave expression to the further fundamental thought of the heliocentric system; but a great portion of his work is as yet unpublished, and this idea of motion follows so necessarily from the tenets which I have cited, that we are compelled to accept the belief that it was known to him. If now we turn our attention from the movements of the constellations to the hidden inner movements of the body, we find that Leonardo with the help of a like magical power of vision suspected, and even had a clear idea of, the circulation of the blood. This has been denied on the ground that in one passage Leonardo compared the movements of the blood with the ebb and flow of the tide. But the objection breaks down, because the notes which we possess of Leonardo's thoughts date from the most various periods of his life, and nothing can blot out the words which we have in his own hand, in black and white, concerning il continuo corso che fa il sangue per le sue vene, “the continuous course of the blood racing through its veins,“ and over and above this that the blood which flows back to the heart, il sangue che torna indirieto, differs from that which, when the blood is driven out, closes the valves of the heart, che riserra le porte del core. 10 These words suffice to prove a deep insight into the mechanism of the circulation, which at that time was unsuspected and not discovered until a century later: for Leonardo knows that the blood “runs an uninterrupted course through the veins,“ he knows that it proceeds from the heart, and finds its way back to the heart, and he makes a distinction between the venous blood and the arterial blood. And here we must bear in mind that the most important

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works of Leonardo in this connection, as in others, are up to the present unpublished. They lie idle in the dust of libraries.
    I have chosen these two examples, the astronomical and the physiological, out of the great mass of material. Leonardo seems to have interested himself in every branch of science, and everywhere, through the mere penetrating power of his sight, coupled with the sagacity of his judgment, he appears to have forestalled science — often by centuries. Think only of his right appreciation of the significance of petrifactions and of the geological strata at a time when people used to explain the one as the playful products of a vis plastica, while for the other at best the Deluge was made responsible! But to my regret I can give no more time to this captivating subject. If you want more particulars I must refer you to the books upon Leonardo. 11 I must be content if, by quoting typical instances, I have made you familiar with the wonderful quality and astounding penetration of this power of perception. Words are insufficient, what we need is facts — and these facts patent to every man, even to the unlearned, point to an intellect whose kinship with that of Goethe is at once striking: the same ever-open Eye, never satiated, the Eye of the warder Lynceus (as he called it in my first lecture), surveying the whole world, and uninterruptedly entertaining the monarch imprisoned in the Tower with new pictures: at the same time it is an Eye which creates. Yet we are struck by two important differences. Leonardo sees more exactly than Goethe, his Eye is sharper, and he can do what Goethe never could: he can reproduce what he has seen so that it becomes something seen by others: he is a painter, and for that reason still further removed from Kant than Goethe. But just as the outer sense is more refined in Leonardo than in Goethe, so it is too in the case of that inner schematic power of perception, which Goethe hardly

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possessed, but which in Kant was conspicuously developed. In this respect the relationship is reversed: Leonardo is nearer to Kant than Goethe was; in mechanics, indeed, he is as richly gifted with genius as he is in Art. Take up the six beautiful volumes into which Ravaisson-Mollien has divided all Leonardo's manuscripts in the Bibliothèque de l'Institut, in facsimile and deciphered, and you will see that nine-tenths of these notes refer to mathematics and mechanics. Leonardo never ceased to calculate. His mind was busy with the squaring of the circle, and with groping attempts at infinitesimal calculation; from the flight of birds to the observation of a waterfall, in every direction the interest in mathematics and mechanics forces itself upon him side by side with that of the painter. In one place he speaks of mechanics as “a Paradise,“ and says of it, “the science of machinery or mechanics is the noblest of all the sciences“ — La scientia strumentale over machinale è nobilissima. On the sheet which contains perhaps the very first sketch for the Last Supper, we find immediately under the subject a geometrical problem drawn and solved in ciphers, and another sheet which contains studies for the Apostles and a pathetic sketch for the Christ, shows under these figures a plan for a piece of machinery with explanatory notes. So if Leonardo and Goethe are two men in whom, in contradistinction to Kant, the Eye is the organ of life, still two very different intellects must be looking out from this finestra dell' anima, two very different modes of activity, to quote Aristotle, and therefore at the same time two very different systems of philosophy. Starting from the outward and visible signs we shall reach the very core of the question if we pay attention to one thing, — that Goethe wished to paint and could not, whilst Leonardo presents such a culminating point of pictorial genius, that few can reach his level, none surpass him.

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    Goethe's lack of capability in the plastic arts would be less striking if we did not see him from childhood so passionately striving to attain mastery in this very direction. We know that as a student in Leipzig he painted more than he read. It was Oeser's studio, not the lecture-rooms of the juristic Faculty, that he haunted. And with what touching industry did he carry on this struggle for the impossible!
Doch unvermögend Streben, Nachgelalle,
Bracht' oft den Stift, den Pinsel bracht's zu Falle;
Auf neues Wagnis endlich blieb doch nur
Vom besten Wollen halb und halbe Spur.
In the end Goethe himself was bound to confess, “I was lacking in the true plastic power,“ and he adds the precious words of irony against himself, “my attempts at representing nature were more like distant suspicions of given forms, and my figures resembled the light vaporous beings in Dante's Purgatorio, shadowless themselves, and terror-stricken at the shadows of real bodies.“ What this defect meant Goethe accurately realised; for in a conversation with Eckermann he quotes with praise words of our Leonardo, — “If your son lacks the sense to make what he draws stand out in relief by powerful shadowing, so that one might grasp it in one's hand, then he has no talent.“ And do you know why Goethe had no talent for drawing? Why his copies were mere “distant suspicions of given forms“? Because he was deficient in the sense of Geometry. Because we men are so built that we are incapable of accurately grasping any form which nature presents to us, unless, consciously or unconsciously, we have held before it by way of comparison the complex network of possible forms which is innate in us, and have in this way assimilated that which is outside all rule, incalculable, and which has never existed, by contrasting it with that which is regular, calculated and for ever unalterable. This happens

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without our thinking of it during every second of our life: we are incessantly schematising. Later on you will learn from Kant to what degree our whole intellectual being is under the domination of Scheme. “This schematising of our understanding, when we are face to face with phenomena,“ he writes, “is an art hidden in the depths of the human soul.“ For the images which we receive from without, that is to say the complex of the impressions of our senses, cannot be grasped directly, but our intellect — the “activity“ of Aristotle — must first, as Kant says in a happy figure of speech, have impressed its monogram upon them. “It is only by means of the Scheme that images and conception can be brought into union.“ You see that from without to within there is an intermediary action similar to that which takes place from within to without. Our ideas, as you will remember from the metamorphosis, were only able to reach the Eye by borrowing a symbol, e.g. the leaf, from the world of the senses: but this world of the senses — so runs the new creed — can penetrate the thinking consciousness in no other way than by the intermediary of schemes of the understanding; and these schemes coincide with the perceptions with no more exactitude than the symbols coincided with the ideas. It is not my intention at this moment to weary you with metaphysical disquisitions; on the contrary, I wanted only to call your attention to the fact that the plastic artist shows us this secret domination of the “hidden art“ of schematisation in bright daylight, and so smooths the way for the understanding of one of the most difficult passages of Kant's Critique of the Doctrine of Perception. For the great painter, consciously and in the sight of all men, puts into concrete form that which in others exists in the unconscious “depths of the soul.“
    That is why Dürer wrote those words which perhaps may have struck you as strange a little while ago — “The

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art of mensuration is the true foundation of all painting,“ and the same order of thought gives rise to what he writes on the next page: “The outer (practical) work must be the indication of the inner understanding.“ And in order that you may realise how powerfully the geometrical and schematic principle is developed in so pre-eminent a modeller, and how busily it is at work, I would beg you to take up another work of Dürer's, “the four Books of human proportion,“ — not in a modern abbreviated edition, but in the original small folio of 1528, with all the charts and tables, as they left the master's hands. You will be astounded at the world of numbers and geometrical figures in which Dürer lived; they are enough to make you giddy. Indeed, every complication can be solved by figures, yielding of its own accord without any involving of the imagination: but one can hardly grasp how any man should have been able to carry in his head, as something visible, such complicated geometrical figures, as Dürer was obviously able to do. In the two first books the many charts of figures and the painful precision of the measurements will strike you as imposing. But now look at the third book! Here Dürer teaches us how we may at will change the fixed proportions; for instance, he takes a woman of average proportions that he has already shown us, and makes her first long and thin, then short and monstrously fat; or else he changes one part of the body, leaving the other parts as they were, etc., and all this he does without ever departing from the established foundations of geometrical schemes, and with the help of instruments which he calls “the perverter,“ “the falsifier,“ etc. The fourth book is almost more interesting: it shows “how you may distort the previously described images,“ and yet it is no simple doctrine of perspective in our sense of the word, but rather what mathematicians call the geometry of position, bound up with that of projection. You need

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only look at the figures on page Y4, Z, and those that follow, in order to arrive at the understanding of what Dürer expects of the art-disciple.
    Leonardo's brain was organised in like fashion. To be sure he was not so self-tormenting — for instance, look at his doctrine of perspective, how bright it seems by the side of Dürer's, — yet always and everywhere he paid respect to the mathematical relations, always bringing calculation into play, always displaying the geometrical Scheme between the Eye and the Object. One hundred
QuincunxQuincunx
and fifty years ago, Charles Bonnet, the Genevan botanist, introduced the so-called doctrine of Phyllotaxy, that is to say, the exact observation of the relative position of the leaves on the stalk.
    To the most widely spread form of this relative position he gave the name of Quincunx: in this the sixth leaf after the stalk has been twice encircled invariably stands immediately above the first; accordingly every cycle of leaves consists of five leaves. This discovery was the result of years of study by an experienced professed botanist. But two hundred and fifty years earlier Leonardo's artist-eye had observed the Quincunx, and

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Leonardo - Sketch of treehad drawn it with the most painful care, and that too in his Book on Painting. 12 You see with what mathematical precision the painter observed! and not only with precision but also with schematisation, for as a matter of fact this 2/5 position is only approximatively existent. But in order that you may also see the geometrician at work, I have copied here a little sketch out of Ravaisson-Mollien — (M.S. M. f. 78 overleaf). To this Leonardo has added the note “all twigs possess lines which work towards the central point of the tree.“ In order to understand him you must naturally only take into consideration the youngest twigs, and you must realise how this so-called central point year by year moves upwards, quickly at first, then slowly. Even so there is great boldness in such a schematisation. On other pages you will see how Leonardo was at pains to apply to the human head a similar law of relationship to the line of circumference. His comparative studies of various human heads, including monstrous deformities, are so well known that I need do no more than allude to them. *
    This cursory outline may suffice to show you what special qualities must be at work in a man who is capable of reproducing that which he has seen. Where these qualities are lacking there can be no painter, because there is no organ for the correct assimilation of form, and every attempt yields nothing but “distant suspicions.“ Of such men who are willing but incapable, Leonardo says, Multi sono gli uomini chi anno desiderio e amore al disegno ma non disposizione — “many are the men who

    * Leonardo drew a circle, by the help of which he fixed every point of the human head in a Scheme — nose, chin, ears, eyes, etc.

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have the wish to draw and who take delight in it, but who have not the capability“ — the disposizione lies in the aptitude for schematising. Naturally the geometrical quality by itself is not enough: yet it must not be wanting. The man who keeps the scheme steadily before his Eye, notes every deviation in the form, whereas on the other hand a Goethe, as we have seen, was rather inclined to underestimate points of difference, and in everything to see the points of union. “I was born in the school of identity,“ is his confession, but that is no school of painting. On the other hand, it is certainly interesting to discover that the thinker with closed eyes, whose stupendous schematic power of representation thought out the theory of the Heavens, showed in this respect a true intellectual relationship with a Dürer and a Leonardo. However much the science of mathematics may on one side root itself in logic, and signify in many of its adepts a purely abstract logical exercise of the intellect, — still the living water that gives nourishment to the tree is the power of the Eye, and so it may happen that a Kant may in certain respects stand in closer relationship to Leonardo than Goethe. In order to keep up the association of ideas in what I have to say, I shall return to this subject later, but I shall beg you once for all not to forget that the power of schematisation is a true formative power.
    In the meantime we must still linger awhile over the comparison between Leonardo and Goethe. I wish to show you how far-reaching is the difference that we have here observed in the Eye at work. For this purpose Leonardo's judgments on the essence of Art will be of service to us. According to him the senses are the true agents in real art, and the man who, like the poet, excites the conceptions of the senses by descriptions alone, makes use of a subordinate and indirect species of Art. Leonardo exclaims proudly, se'l pittore vol vedere bellezze

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che lo innamorino egli n'è signore di generarle. That the poet is equally master of producing beauty that shall be capable of exciting his love, that Leonardo denies. For il senso piu nobile is the Eye, and next to this noblest sense follows the Ear, la musica si deve chiamare sorella minore della pittura, whereas the artist in words is only indirectly and not really an artist, because he can only produce forms by roundabout ways, and by steering clear of the impressions of the senses: e per questo il poeta resta, inquanto alla figurazione delle cose corporee, molto indietro al pittore, e delle cose invisibili rimane indietro al musico, “the Poet in the representation of bodily things remains far behind the painter, and in that of invisible things, behind the musician.“ But the strongest objection that Leonardo has to make against the poet, is che non ha potestà in un medesimo tempo di dire diverse cose, “that he has not the power of saying several things at one and the same time“; but it must be the aim of Art to waken that Harmony of many tones which lies slumbering in the human soul, and that must take place with lightning rapidity, like an inspiration of the Deity: for armonia non s'ingenera se non in istanti, nei quali le proportionalità degli obietti si fan vedere, o'udire. “Harmony cannot be bred otherwise than in instants in which the relative proportions of things are seen or heard.“ Here, obviously, it is the plastic artist who is master, for he alone reveals his whole work in one single moment, and that is why Leonardo speaks of his art as a Divinity, una Deità. But the musician too gives in every moment a multiform perfect Harmony, while on the contrary the word-poet is forced to build up bit by bit, l'una parte nasce dall' altra successivamente, e non nasce la succedente, se l'antecedente non muore, “one part is born from the other in succession, and the following part is not born unless the previous part is dead.“ It is not my intention here to discuss the aesthetic doctrines of Leonardo: I

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have only felt compelled to show you with what a passionate bias this clear-sighted man paid respect to the Eye, and, beside the Eye, to the direct impressions of the senses in general as opposed to all mere reflection. The point of contact with Richard Wagner is clear, and in any other connection would give occasion to useful considerations.
    Here, however, we have one immediate and special interest — Leonardo, the man whose Eye at once reminded us of Goethe's Eye, is not only the antipodes of Goethe in respect to the scientific observation of Nature, but he comes very near to refusing altogether to recognise as true art that very art in which Goethe rendered immortal services. From the point of view which we are for the moment adopting, Goethe and Leonardo stand so far apart that we should hardly bring them into relationship, were it not for Kant who holds out the hand to both. For as a matter of fact, Kant, whom a while ago we found to be of so near kin to Leonardo that the two viewed from the distant Goethe appeared like brothers, now, seen from point of view of Leonardo's aesthetics, seems to move close up to Goethe. In this method of constructing “parcel-wise“ — una parte nasce dall' altra — we were able to discover a characteristic of Kant's method of perception; now it is Leonardo who shows us, that it is equally characteristic of every professor of the art of thinking, even of the Poet — and instinctively these words, una parte nasce dall' altra, call to our recollection Goethe's Doctrine of Metamorphosis. Of course Goethe examines nature with an Eye differing from that of Kant, yet he too is forced to construct, and in order to put the phenomena of nature perspicuously into form and to embody them in his memory, he cannot help allowing one part to arise from another. That is the exact purport of Metamorphosis. Practically there is, then, in Goethe's intellectual personality, exactly as in

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Kant's, a preponderant quality that we might well indicate with Kant as “understanding“ in contradistinction to “Sense,“ or perhaps still better as Reason (in the Kantian sense of “the whole higher power of recognition,“) in contradistinction to the power of observation. In both these men, Goethe and Kant, — however various may have been the sources at which they drew their impressions, — the insistence upon the idea of dallying with theory forms a common feature. However different from the path trodden by Kant may be that by which Goethe reached his Ideas, — he is only quite at borne, only quite the master, quite the creator, in that domain which Kant calls the Higher Power as opposed to a Lower Power; while Leonardo looks upon this so-called Lower Power as the Higher Power, and takes no account of any knowledge that has not, “born of the experience of the senses, made its way through mathematical exposition, and found its final conclusion in experiment.“ That is why he exhorts us to put no faith in authors who have wished by the force of imagination alone to make themselves interpreters between nature and man: non vi fidate degli autori che anno solo colla imaginatione voluto farsi interprete fra la natura all' uomo, and warns us not to give ourselves up to those things of which the human mind is incapable and which cannot be demonstrated by any natural example: Quelle cose di che la mente umana non è capace e non si possono dimostrare per nessuno esemplo naturale. As you see, Leonardo will only accept in relation to Nature the most strict empiricism knitting together effect and cause, whereas formation by Ideas as practised by Goethe, and defended by Kant, seemed to him to be idle imagination, or as he also called it bugiarda scientia, a science of lies.
    Here then we discover how far-reaching is the difference between Goethe and Leonardo; for it is not merely con-

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cerned with art alone, but extends to the whole method of contemplating nature. In the previous lecture we saw that Goethe was working with ideas when he believed himself to be in possession of experiences: that at once gives you an example of the dominant power of Reason — of the Higher Power of Recognition in contradistinction to empirical contemplation. For, as we saw in our investigation of the doctrine of metamorphosis, Ideas are certainly something seen, but not empirically seen; in other words, they are not given to us by mere experience. It is true that they are rooted in Impressions of the senses, though that is only the field which gives them nourishment: the air which surrounds them is that of Reason, and the daylight in which we see them, radiates from within out of a focus imaginarius.
    There is a saying of Kant's which will render us good service at this moment: for it describes exactly what it is that divides Goethe and Leonardo, and at the same time affords us a deep insight into Kant's own method of seeing; by abstract study we might perhaps have failed altogether in understanding his view; but in the light and shade of Leonardo's and Goethe's methods, his view stands out in plastic form. Kant is speaking of the essential nature of the Poet. After having, in diametrical opposition to Leonardo, assigned the highest of all artistic rank to the art of Poetry, he gives the poet the credit of encouraging “a free, personal and independent Power, untrammelled and unhampered, of observing and judging Nature as phenomenon, according to views which She herself affords neither to the senses nor to the understanding, and therefore to make use of her in the interests, and for the Schematisation of that which is transcendental“ (i.e. beyond the senses). The poet, then, teaches us to look upon Nature from points of view which direct experience does not offer us, and opens up in us a power to make use of what is clear to our Senses for the benefit

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of the schematisation of that which transcends them. This definition of the poet gives us an exact idea of Goethe's position in regard to Nature. In his method of observation there is a continual exchange between that with which the senses furnish us and that in which the experience of the senses only acts as a spring-board. Goethe is a good, trusty and, where necessary, a sober observer of Nature; in spite of which it is in the noblest sense of the word a poetical longing — I must add a yearning and a formative power — which impels him to observation: he wishes to put in practice that “free, personal and independent power,“ and unconsciously he flies far beyond the boundaries of empirical experience. His Orphische Urworte with its last line:

Ein Flügelschlag!  Und hinter uns Aeonen!

“One stroke of the wings! And behind us aeons!“ appeared first in the Morphologie of which the masterly Athroismos belongs to the osteology, and here in the midst of illustrations of bones and comparative tables he cries out:


Nimm vom Munde der Muse,
Dass du schauest, nicht schwärmst, die liebliche volle Gewissheit.

“Take from the mouth of the muse the sweet full certainty that thou art seeing and under no delusion.“ So it is the Muse that is to be our guardian goddess in the domain of the investigation of nature. Goethe, indeed, in certain moments is fully conscious of his own method of procedure; for in his legacy of notes upon natural science we find the following most noteworthy passage: “Phantasy is far nearer to nature than the senses: the latter are in nature, the former hovers over her. Phantasy can hold its own with nature, the senses are mastered by her.“ There you see at work the free, personal power, of which Kant spoke; at the same time you see the exact opposite of Leonardo's convictions and principles. For


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according to Leonardo all forms of knowledge are vain and full of errors, — vane e piene di errori, — unless they be created from the experience of the senses and tested by scientific experiment. Leonardo is such a strict empiric, that he goes so far as to warn the artist that he must know no other aim than to gareggiare colla natura, — literally “to compete with nature.“ How differently the Eyes of Goethe and Leonardo work we see not only in the Doctrines to which their method of Seeing gives occasion, but also in the success of their activity. Not only can Leonardo say of himself, “in painting I can stand comparison with any other man, be he who he may,“ 13 while Goethe, after toiling for years, is obliged to confess the contrary, but Leonardo's contributions to science are throughout of a different nature from those of Goethe. I am far from underrating Goethe's doctrine of metamorphosis, — his doctrine of colour, — his other scientific thoughts; rather am I deeply convinced that his whole method of observing Nature possesses for the culture of the human intellect a significance of which we are only just beginning to be aware. In many respects Goethe is even now hardly born. But this significance is one of culture and not of true science in the strict sense of the word. Goethe will teach us “to cast a free Eye upon the wide field of nature“ — a free Eye, that is to say the Eye of the conscious human creator, who no longer stands in dull obedience at the command of idle Matter, but who is able “to hold his own with Nature“: and that means at the same time the eye of the man who is no longer dazzled by his own compelling hallucinations, but who, thanks to Kant's efforts, has won together with his own freedom, the freedom of Nature. All this, — to which I propose to return to-day, so soon as our observations shall have ripened sufficiently, — we can perceive, and yet must admit that it was Goethe's part to excite and spur on exact natural science rather than really to

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further it himself: while Leonardo, on the contrary, who saw as a schematiser, and thought as a mechanician, was such a master of the art of gaining knowledge, that in his guesses he anticipated the triumphant course of our natural history. As Kant proclaimed to us, “experience alone is the fountain of truth in the observation of Nature.“ Leonardo knew that full well: gareggiare colla natura, “to compete with nature“ — that was his maxim not only in art, but also in science; it was his delight and the cause of his success. That the earth revolves is no symbolical idea, like Goethe's doctrine of metamorphosis, but a concrete theory; that the blood is chased from the heart through the veins, is not, like the discovery of the intermaxillary bone, an inference from an a priori admission, but a fact discovered by painstaking autopsy and observation. In respect of pure natural science, I think we may say that Leonardo surpassed Goethe almost as much as he did in painting. He knows the only true method: one sees that in him at once: and that says everything. Observation, experiment, mathematical calculation, — these are the three principles which he again and again impresses as the foundation of all knowledge. If beyond this we remember that he devoted a passionate interest to the technics of instruments (he built himself a sort of telescope for the observation of the moon a century before Galilei), we must admit that he possessed all the qualities which go to make the born investigator of Nature.
    By working up with more and more sharpness the contrast between Leonardo and Goethe, we have now reached the critical point, that is to say the point where we shall be rewarded if we sink a deep shaft, confident of coming upon a vein of the precious metal of discernment. Whoso thoroughly understands the difference between the value for science set upon mathematics by Leonardo and that set by Goethe, has gained much, not only in the

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estimate of the two great intellects, but for his own thought-life in general. At the same time this point is one of those which are of primary importance for the understanding of the intellect of Kant. For if a little while ago we saw Kant near — very near to Goethe — we see him quickly move back to Leonardo as soon as stress is laid not upon Art and Idea, but upon Science and Mathematics. Here it is not only the analogy of qualities between Leonardo and Kant which is dominant, — as it was just now in the case of the observation of schematising, — but a true close kinship in the whole manner of looking upon the universe. There, at a great distance, Goethe stands aloof.
    I have already spoken of Leonardo's love for mathematics; but I must still claim your patience for a few moments. Non mi legga chi non è matematico, “let no man read me who is not a mathematician“! Such forcible language as this should be enough! but we have still got to learn that in Leonardo this is no question of a mere predilection, nor even of an instrument indispensable to the practical artist, but the insight of a philosopher into the essence of the human intellect. “The man who undervalues mathematics nourishes himself upon confusion,“ says Leonardo, chi biasima la somma certezza della matematica, si pasce di confusione e mai porrà silentio alle contraditioni delle soffistiche scientie, colle quali s'inpara uno eterno gridore. “For truth and the power of knowledge are contained in the mathematical sciences.“ That is a very important saying, “the power of knowledge.“ Goethe would not have subscribed to it: Kant would have done so with both hands. And because practical knowledge is joined to the mathematical way of thinking, therefore Leonardo lays down the dogma that “no human investigation can lay claim to be considered as true science unless it will stand the test of mathematical demonstration.“ For the criterion of

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true science — vera scientia — is incontrovertible certainty, and knowledge in the sense of certainty is only afforded by mathematics. The consequence of this is that nessuna certezza è, dove non si puo applicare una delle scientie matematiche over che non sono unite con esse matematiche, — therefore no investigation can lay the foundation of true science, unless it can and does follow the path of mathematical exposition, that is Leonardo's impregnable conviction. It is with the clear recognition of the relationship between mathematics and knowledge that this miracle of a man forestalled Kant, in the same way that in his discoveries he anticipated Copernicus and Harvey. In one of his ripest works, Die Anfangsgründe der Naturwissenschaft, Kant writes in the same way, “I maintain that in every special nature-doctrine there will be found only so much exact science as it contains of mathematics.“ Certainly Kant, the thinker, analysed more exactly than Leonardo. The whole tenour of Kant's general philosophy teaches us to distinguish between “exact“ and “inexact“ science; he has shown us that a science which rests upon empirical observation alone, is only worthy of the name and dignity of a “science,“ so far as it does not deviate from experience, ordering its discovered facts systematically, and dissecting them in accordance with the relationship between cause and effect; but that such science should preferably be called systematic art (giving as an example the chemistry of his time), because the apodictic certainty of any true knowledge needs something more than empirical experience. This Something, which Kant calls the “Pure Part,“ is exactly that inner, human code of laws, which, in so far as it touches intuitive vision, is called mathematics. Nothing, with the single exception of mathematics, gives apodictic certainty, and apodictic certainty alone can be called knowledge in the strict sense of the word. Therefore, the more

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we have of mathematics, the more we have of exact Science.
    You see what a true and deep-reaching kinship exists between the methods of observation of these two men, who at first sight seemed so diametrically opposed to one another. Kant, absolutely devoid of all artistic gifts, has yet the power of recognising the fundamental significance of form and measurement in the building up of human knowledge; and in many of his works, and more especially in Die Metaphysischen Anfangsgründe der Naturwissenschaft, proves himself to be a genius of the first quality in the despotic domain of this schematic manner of Seeing; Leonardo, the artist, the painter of the Last Supper and the Mona Lisa, is none the less devoted to mathematics and mechanics; he compares the influence upon the intellect of their incontrovertible certainty, with that of light upon the Eye, and with the exaggeration of the hot-blooded artistic temperament, he utters the opinion that here alone lies the certainty of knowledge.
    We have to deal here with a true harmony between the dispositions of the two men. And as a matter of fact this harmony reveals itself exactly where Goethe misses fire — for we may legitimately here speak of a miss-fire as well in art as in philosophy. So far as art is concerned we may well overlook the position, inasmuch as Goethe himself bitterly felt his own failure. But in the matter of philosophy he was not so clearly conscious, and that is what has led us and him to a condition in which the pascersi di confusione has gained great force. That Goethe despised mathematics is of course the foolish twaddle of the titmice that chirp on every twig of life; a single sentence of his suffices to refute it: “no one can set a higher value on mathematics than I do, for mathematics afford precisely that which it has been denied to me to accomplish.“ 14 So he too felt that here something had

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been “denied to him,“ and how highly he often valued this “something denied“ is shown by a sentence in the Farbenlehre, the Doctrine of Colour, a passage where any irritation against the mathematicians might have been excused, and where in spite of that Goethe declares mathematics to be “one of the noblest organs of mankind.“ Still we must admit that Goethe was not only deficient in the power of practising mathematics, but was even unable fully to appreciate the essence of the science in its inevitable influence upon the human intellect. “It is a mistake to imagine,“ he exclaims pettishly, “that when I have discovered the mathematical equation for a phenomenon I know all about it that is worth knowing, and can consider the whole matter as sufficiently dealt with and to be laid on the shelf.“ 15 What does he mean? The function of mathematics is to apprehend, to prove according to the laws of motion, to reduce clearly to a science — just as Albrecht Dürer did for the outer form of the human body, and as Leonardo tried to do for the mechanism of the circulation of the blood in its inner parts. “The book of Nature is written in the language of mathematics,“ says Galilei. Goethe, on the other hand, finds a contradiction between the phenomenon observed and the mathematical scheme. For this sentiment he has to thank the pure power of his sight; but instead of allowing himself to be taught by Kant that if Image and Scheme do not exactly tally, it is due to the essential quality of the human intellect; 16 instead of recognising with Leonardo the fact that mathematical representation is the necessary organ of everything which can be called Science in the sense of exact knowledge, and that what he, Goethe, is striving after is not Science but something different, that is to say a glorified Contemplation, — that World of the Eye of which we spoke in the previous lecture, — and that this World demands ideal exposition; instead of all this, Goethe obstinately

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works himself up into the unfortunate idea that there can be an unmathematical science, — that the employment of mathematics must be kept within bounds, and that they must be relegated to a narrow domain in the Study of Nature, etc. Science and art, — so he maintains, — have “fallen into pitiable error through the wrongful employment of mathematics.“ 17 When we remember that Goethe's unmathematical dicta, of which we could cite many, are chiefly in the department of optics, and when we consider what a famous advance mathematical optics have made since Goethe's time, and what a wide outlook upon comprehensive knowledge has been opened up in this very direction in our days by the work of Maxwell and Hertz; when we realise the present importance of spectral analysis to astronomy, chemistry, and physics; and then when we see Goethe ridiculing the spectrum as little more than a mere puerility of Newton's, we must feel that however much the great observer of nature and Poet may have the right to view Nature in his own fashion, he is yet lacking in the understanding of the mathematical method of exact science. And this is the more striking when we find in Leonardo, two hundred years before Newton, a few but astonishingly correct remarks about the colours of the spectrum, and when we think of Kant's high estimate of the undulation theory of Huyghens, we have then the experimental proof that if we follow Goethe in the path of science, we advance no further in the exact sciences, whereas by following the mathematical path, which he detested and which Kant looked upon as the only right way, we have advanced from one theoretical and practical attainment to another.
    What, then, is the essence of the mathematical method? That is a question which it is impossible for us here to shirk, otherwise we should neither understand correctly Leonardo's extreme way of viewing Nature, nor Goethe's,

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nor should we understand why Kant's philosophical critique enables him to do justice to both these antagonistic views. I shall try to answer the question at once in as few and as simple words as possible, leaning indeed upon Kant, but without making him responsible for my free and illustrative exposition; we shall deal more precisely with the matter in observations to be added hereafter.
    So soon as we thoughtfully, — I use the word “thoughtful“ in contradistinction to passive contemplation, — so soon as we thoughtfully approach Nature and construct that “unity of objects“ without which she would no longer be Nature but Chaos, every single conjunction, arrange it as we may, means Motion. Think only of the commonest perceptions of any Bodies that you please, which you, innocent of any attempt at philosophising, simply join together, thinking in contemplative consciousness, something in the same way as the herdsman watches his grazing herd. Either the objects are at rest, and then our mind must move in order to perceive them, whereby we arrive at Form, or our mind is at rest and the objects move before it and then we arrive at Number: in most cases the two sorts of conjunction will take place simultaneously; and as you see, whether we direct our observation to the proximity in space, or to the sequence in Time, Motion is always at the bottom of it. Motion, says Kant, is that which unites space and time, and motion conceived, that is to say grasped by Reason, is Mathematics. If we look at the still geometrical figures in our school-books, we sometimes think that here is the very emblem of rest; but in the next lecture we shall see how the great Descartes laid the foundation of the higher mathematics, when he taught us to set free into Motion every resting Form, whereby we attain a second gift, namely, the power to convert every species of Motion into a visible, permanent Form.

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    But just in the same way as these higher mathematics proceed from the union of Geometry and Arithmetic, so it is only by further, and, as closer observation shows, powerful conjunctions of space and time, that a really intelligible and logical Nature comes into existence for us, and it is from these conjunctions that we realise the ideas of the inter-relationship of various perceptions, — of the interchangeability of phenomena, — of causative cohesion. Thus, for example, the relationship between cause and effect signifies a twofold Motion in space and time. You will find that set forth with unsurpassable lucidity in the fourth paragraph of Schopenhauer's principal work, to which I refer you. 18 And with further investigation and thought you will understand how Kant arrives at the definition, “Matter is that which is movable,“ and at the assertion that space can only be filled by motion. And that you may not think that I am leading you on to the pin-points of the most abstract philosophy, but that, on the contrary, you may understand that I am dealing here with the concrete and necessary apprehension of Nature by human intelligence, I will call your attention to the fact that our modern physics, however antimetaphysical may be their attitude in their empirical delusion, learn to recognise Kant's standpoint as the only justifiable one, and that the little globules of atoms are only preserved as a deduction and a help for coarser intellects, whereas Lord Kelvin and other leading spirits among the mathematical physicists speak of “centres of energy,“ and by atoms understand gyrating motion. Lord Armstrong, * in his book Electric Movements in Air and Water, asserts that there is no ground for looking upon Matter as anything else but Motion. Even the hypothetical aether he rejects as super-

    * I purposely cite English investigators because no others, not even Italians and Frenchmen, are so far removed from the influence of German metaphysics.

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fluous, and is of opinion that “empty space would do just as well, if we only chose to conceive a continuity of interacting motions.“ 19
    I think that this sketch, slight as it is, will suffice to make you understand and accept Kant's apodictic assertion, “natural science is throughout a doctrine of Motion, either pure or applied.“
    But here comes in a second important consideration, not, like the first one, composed of physical elements, but purely philosophical. The highest code of this science of Motion is not perceived as a fact in Nature, but is rooted in the essence of Reason. It is we ourselves, we men, who have no other possibility of comprehending Matter, that is to say, when we aim at a comprehension of Nature which shall be logical, thoughtful, and capable of founding an apodictic certainty of knowledge; — it is we ourselves, I say, who are unable to comprehend Matter otherwise than as Motion, and for whom in consequence of this every vera scientia, every absolute certainty is bound to result in a doctrine of motion either pure or applied. The human understanding works out the analysis of Motion by its special gift of schematic experience which we call mathematics. It is by mathematics that the human intellect assimilates and digests that which is foreign to it and outside of its ken. Much is rejected, but what remains from that time forth becomes possessed of a humanly comprehensible form. That is what Kant means when he says, “the highest law of Nature must lie in ourselves, that is to say in our understanding.“ To put it rather roughly, but in a way suited to the present standpoint of our study, Nature gives the facts, the human understanding gives the laws. To formulate this let me once more bring forward words of Kant's, “the human understanding does not create its laws out of Nature, but imposes them upon her.“ At the first blush this remark will perhaps strike you as

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strongly paradoxical, but it will suffice for the present if you to a certain extent clearly grasp these two things: all exact Science, in the true and strict meaning of the word, resolves itself into a Doctrine of Motion. All Doctrine of Motion is mathematics, and so far human. To try to escape from a law of our true Being is nothing less than an attempt to creep out of our own skin. We may well therefore praise the acuteness of the great Leonardo, who had so rightly and energetically grasped the fundamental law of all exact investigation — in opposition to whom when a man comes forward, even should he be a Goethe, and exclaims, Friends! I will teach you a Science that shall be unmathematical, — then we recognise and acknowledge the fact that the great man is entangled in deep error. Indeed, the error is twofold, first inasmuch as his definition of Science cannot be called adequate, and secondly because he does not rightly grasp the essence of mathematics, and their law-giving function in reference to all that constitutes causal conjunction, and that means Nature as it exists in our thoughts.
    Quite another question is whether that which Goethe strove after, that is to say an unmathematical, and to that extent un-logical and therefore unscientific comprehension of Nature, is not, say what you will, entitled to a profound measure of justification. Here, too, is a question that we must not leave unanswered, for it is of weighty importance in the understanding of Kant. But in order to answer that question we must do as we did in our former lecture; we must undertake an excursus which will furnish us with the indispensable and self-evident material. If you were minded without any further preparation to plunge headlong into Kant's abstract-analytical method of thought, I suspect that it would be very difficult for you to bring a vivid understanding to bear upon his exegesis of an unmathematical

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conception of Nature, what he calls “Nature as exposition“ — whereas starting from Goethe you are at once in a position to understand Kant, and so will be able to delight in the unexampled profundity of the most powerful of all thinkers. We must then take heart and undertake an examination of the relationship between exact Mathematical Science, to which alone Leonardo assigned any value, and Goethe's comprehension of Nature. In the main this excursus will result in a comparison of physical optics and Goethe's doctrine of colour; there are, however, some general remarks with which we have to set out, and which will weave themselves into our exposition as it progresses.

 * * * * * *

    The difficulty which at the outset attaches to our task is the fact that Goethe himself was devoid of any theoretical consciousness of his own procedure, one might even say of his own aim. His own saying, “a man has never gained so much ground as when he does not know whither the way leads,“ is true of himself; for while he believed that he was doing no more than lending a hand in contemporary investigations of nature, he was in reality founding a new method. That is the naked truth, the unrecognised truth which seems to have foundered without leaving a trace, yet not for ever, in the noise and dust of the vulgar riot of our successful mechanical science. There are moments in the activities of great intellects where they render superlative services: that is when they do not quite understand themselves, when they enter the lists to do battle passionately for some impossible assertion, in spite of being gifted with a keener sight than their fellows, and with more consequential thought than their censors: for it is just here where they entangle themselves in a mass of contradictions, that they work like an unconscious natural force, paving


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the way for future knowledge: here the intellect collects itself into an avalanche ready to sweep clean all the tidy paths of human frivolity, or like a volcano bursts the too heavily weighted crust in which the idleness of tens of centuries has imprisoned the bright fiery element of the soul of man. Only consider Goethe, that noble man! Is it thinkable that he with his brilliant eyes should have looked in the light during a whole lifetime, and have seen nothing true? Yet, as I know that here I shall at once be tilting against unbelief and contradiction, I will quote the words of a pioneer in exact natural science, the admittedly greatest physiologist of the nineteenth century, Johannes Müller. He was what Louis Agassiz, Clerk Maxwell, and Heinrich Hertz (but with their exceptions a dwindling number of our famous natural investigators) were, a really lofty intellect of permanent importance. Here is what Müller says with reference to Goethe's essay on the skeletons of rodents, — “It is impossible to point to anything similar which comes up to this projection sketched from the centre of the organisation. Unless I am mistaken there lies in this outline the foreshadowing of a distant ideal of natural history.“ Remember these words “the foreshadowing of a distant ideal“! And Müller, the exact investigator of nature, prizes the awakening of this foreshadowing so highly, that on the next page he pronounces the judgment, that Goethe has “reached the greatest“ not only as artist, but also as investigator. 20 Here, too, is a judgment which should never be forgotten. For we moderns have grown up under the nourishing showers of pseudo-scientific platitudes; Rudolf Virchow alone dared forty years ago to take Goethe as investigator publicly under his protection, a weighty witness indeed, upon whose exactitude and unimaginativeness no man will cast a doubt, but who unfortunately was not competent altogether to lift the veil of misunderstanding: for to that end would

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have been required that philosophical training which Virchow abominated, so that his fine words raised a great storm of dust at the time, but soon died away leaving no influence behind them. 21
    In these days every tiny two-legged wheel in the great machine of science thinks himself justified in shrugging his shoulders over Goethe as an investigator of Nature. I happen to possess an autograph letter from one of these celebrities, who rates his professorial dignity at a height which entitles him to allow himself the following judgment of Goethe: “his conception of Nature is just what an easy-going aesthete and collector of curiosities might make up out of his walks abroad.“ This is the audacity of a man of middling capacity whom the schoolmaster's rod and the sting of hunger have raised by luck to the degree of Doctor of Philosophy, and finally up the three steps of the Professorial Chair! A man whose fame may perhaps live through two or three editions of our encyclopaedias, dares to speak in this way of the princely intellect of a Goethe, of that god-like Eye which for more than half a century never ceased in the thoughtful contemplation of Nature, of a man of whom a Johannes Müller could pronounce the opinion that as an investigator he “reached the greatest.“
    But enough of this. If I were to talk myself into a state of indignation over the intellectual decay resulting from the narrow empiricism of a tyrannical science which has fallen a prey to the overlearned Philistines, I should not readily come to an end. The reaction has already begun; there are good men and true of a younger generation at work on behalf of Goethe the investigator, and what is more important than the influence of these individuals is the fact that a universal necessity, a cultural need that cannot be put aside, is forcing us to enter upon the road which Goethe has pointed out to us as the “foreshadowing of a distant ideal,“ unless we

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wish to fall into crass barbarism. A leading spirit among the living antimetaphysical empirics, Ernst Mach, has disclosed what is the next thing to be annihilated, and if his object was to serve the ends of a purely mechanical barbarism he has not been far out: our languages! In the interest of “science“ they are to be abolished in order to make room for an abstract international language! 22 The ideal which floats before the learned professor is the Chinese system of writing, because, being entirely ideographic, it throws overboard all ballast of expression of the finer emotions. 23 After that grammar and history are to be “laid aside.“ Add to this the simplification of the Alphabet, and supplement it with algebraical formulae and chemical symbols, and you will have collected together all that Professor Mach deems essential in a language. He is not far out. A science which only concerns itself with abstract Ghosts, is at no single point in contact with life. Goethe's desire, by means of his doctrine of colour, parenthetically “to enrich language and so facilitate the communication of the higher conceptions among the friends of Nature,“ from this point of view must signify the ne plus ultra of folly. And when Mach, in conclusion, expresses the hopeful opinion that the English language is in a fair way to reach that ideal, we will not ignore the tiny grain of truth which has crept into this Hellish dream, worthy of one of Breughel's Witches'-sabbaths, and join the standard of those who hold no inheritance more sacred than that of their mother-tongue. The richer, the more illogical, the more incomprehensible a language, the better does it hold up the mirror to Nature. The men who have attempted to rob us of our language, have, so far as in them lay, robbed us of Nature; has not Lord Armstrong taught us that science needs no more than the assumption of empty space (vide supra)? In contradistinction to which the man whose genius was rooted

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in the sovereign and creative mastery of language, — in his much-despised teaching of nature followed the one object, to give us side by side with his immortal poems that which was their one eternal Source, visible, inexhaustible Nature with all the wealth of its many forms.
    Goethe, as I said before, did not possess a critically analytical consciousness of his new method, and hence it is that his judgment as to the relationship between his way of investigation and that of true science, is hazy and easily misleading.
    Sometimes his insight is clear enough, for example when he cites the attraction which in his youthful days Spinoza exercised over him, and adds, “the mathematical method was the very opposite of my poetical method of thought and exposition.“ This, of course, is a general statement; the mathematical method, dear to the Jewish Thinker, seems to Goethe to be in opposition to his own poetical method of thought. And yet when we come to deal with the special investigation of Nature there are passages of decisive import which may be brought into court. I select one from the year 1826, which possesses the importance of a composition with mathematics. Goethe writes, “It was not long before I was compelled, in deference to my own capabilities and relations, to claim the right to view, to investigate, and to comprehend Nature in her simplest, most secret beginnings as in her highest and most striking creations without the co-operation of mathematics. That has been my contention through life. Any service that I may have rendered in that way is open to all: how it may appeal to others remains to be seen.“ 24 Is not this perfectly clear? “In deference to my own capabilities“ — that points to the capabilities which are “in opposition to“ Mathematics. And Goethe claims the right to view, to investigate, and to comprehend Nature in accordance with these capabilities. To view, to investigate, to com-
 
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prehend, that is a perfect programme for a personal system of Natural Philosophy. Further on in the same disquisition Goethe says in so many words that “a new point of view justifies new opinions.“ This recognition explains the many passages in which Goethe declares, with no trace of bitterness, that his method of contemplating Nature “is incomprehensible to the Professors, for the simple reason that they think otherwise“; it is in these passages that he confesses in regard to the first great congresses of German works on natural history, that they furnished nothing which could in the slightest degree touch, or move, or excite him, no new encouragement, no new gift, — and this was the man who “for fifty years had been passionately devoted to the observation of nature“; for among the German natural scientists there was “not one that showed so much as the slightest approach to his own way of thinking.“ 25 And there are other passages which come under this category, in which Goethe in his last years, — as, for example, in the essay on the rodents quoted above — instead of as was his wont portraying his efforts in the domain of morphology in the bright colours of the successful investigators, all at once “feels most vividly that his honest endeavours in the observation of nature, were only presentiments and not pioneering.“ All this leaves nothing to be wished for in the way of clearness and true insight. In such moments Goethe is so fully conscious that he cannot see eye to eye with the men of true science, that he claims it as a right to dare to investigate in his own way, and admits that this way is something which continues to be incomprehensible to them, indeed that he is dealing with a “new standpoint,“ — with something in the future, — of which the significance remains half veiled even to himself.
    Physics simply do not recognise the fundamental ideas of Goethe's Doctrine of Colour. So from the stand-

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point of physics it is impossible to judge of this theory. Goethe starts precisely at the point where Physics leave off. It is evidence of a quite superficial appreciation of the matter when people go on talking of Goethe's relation to Newton and modern Physics, and at the same time take no thought of the fact, that these two are entirely different. 26
    Unfortunately it is Goethe himself who with the utmost impressiveness and vehemence has spoken about his so-called relations to Newton, and not to Newton alone, but to exact natural science in general. Did you remark in the above-quoted solemn declaration the five simple words, “without the co-operation of mathematics“? That is where the evil fountain of misunderstanding still continues to flow. It is not without the co-operation of mathematics, but in opposition to mathematics that Goethe observes, investigates, and comprehends Nature. The mathematical method and Goethe's method may run parallel to one another, but can never coalesce: no compromise between them is possible: they cannot at one time work together and at another time without one another.
    One instance will serve better than a hundred to show you how deeply this misunderstanding penetrated in Goethe's case. One month after that fundamental declaration in which the practised eye alone can detect the blemish of the “without co-operation,“ he says to Eckermann: “surely it is not the mathematicians who invented the metamorphosis of plants? I worked it out without mathematics, and the mathematicians have been forced to admit it.“ If these words are correctly reported, they are valid proof that we must trust to our own powers in order to see clearly in this matter; Goethe, the herald and founder, leaves us in the lurch as to the true understanding of his work. Mathematics and metamorphosis! This would have been the place to show that we are

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dealing with two dissimilar and irreconcilable subjects which nowhere come into contact with one another. The first lecture has shown you what was Goethe's idea of metamorphosis; we must admit that, like every human acceptation, it implies the conception of Motion; but instead of trusting itself like the sailor to the stream, it hovers like an eagle in the empyrean from which the living hurrying flood is at once Motion and Rest: Motion, so far as its law of existence is concerned, Rest as regards form. Mathematics (and in a wider sense all true science, inasmuch as it everywhere obeys the one impulse to be converted into mathematics) have no other power and function than the analysis of the condition of Becoming; * even that which is at rest they must set free into motion, otherwise they have no hold upon it. Goethe's efforts, on the contrary, do not tend towards analytical knowledge, but towards the most intensive contemplation, — “the world of the eye,“ the law of which is not Becoming, but Being. That accounts for the peculiar permeation of that which is simultaneous and that which is successive which has sometimes puzzled us, as indeed it puzzled Goethe himself. For while science, whose whole essence depends upon the understanding of cause and effect, recognises Being as an almost imaginary point between something which has been growing and something which is yet to be, the Eye, on the other hand, although not blind to successive alterations, can manifestly never perceive the condition of progression or process of “Becoming,“ otherwise than as locked up in a condition of Being. This will suffice for the moment to show the absurdity of Goethe's outcry against the mathematicians. How was any mathematician, as such, to discover Meta-

    * There is, so far as I can see, no single English word in common use which accurately conveys the meaning of the German Werden as opposed to Sein. Werden is the process of coming into Being — i.e. a transition state; Sein is Being — i.e. an accomplished fact. I shall translate Werden throughout the book as “Becoming,“ or “coming into being.“ — R.

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morphosis? He would have been a poor mathematician. Nor do the words, “I discovered this without mathematics,“ hit the nail on the head any better, though Goethe rarely fails us in that respect. And as regards the closing remark, “they have been forced to admit it,“ that is simply based upon error. Goethe's doctrine of metamorphosis has been as much repudiated by Science as were his anti-mathematical optics. It may be admitted that the repudiation was not so unanimous and immediate, but only because in the domain of Biology the complication is far greater, so that room is afforded for endless misunderstandings. But open any reliable contemporary book on botany, for instance, Julius Sachs' History of Botany (chapter 4), and you will find Goethe's doctrine of metamorphosis unconditionally refuted. Sachs shows how Goethe was continually wavering between fact and idea, and he reveals the mischief of which hangers-on laid the foundation during long years, while they, instead of turning to account the thought of metamorphosis “in the deeper sense of idealistic Philosophy,“ introduced it into exact science, which was impossible without “combining the highest abstractions with the most careless and rawest empiricism, and in a measure with quite false observations.“ The doctrine of metamorphosis has been quite as much a hindrance as a help to the science of the nineteenth century. That is the judgment of a scientist whose right to be heard cannot be called in question. You see how peculiarly connected it is with the words “they have been forced to admit it.“ But the great confusion which to this day has existed between Goethe's doctrine of metamorphosis and exact science, is due, as I said before, to the nature of the subject. All the sciences are striving towards mathematics; yet Biology, in contradistinction to Physics, is still far from having reached the mark. And here we must depend upon a schooling of the sense of sight, otherwise the subject will not be seen at

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all. We may observe, but we shall not take notice. That was why before Goethe's time comparative anatomy dragged out a miserable existence; men like Kaspar Friedrich Wolff died unknown. Goethe, with several others around him like Camper and Oken, was the first powerfully to excite the imagination, and so compelled it to take notice of what was seen. Here alone lies the significance for science of a doctrine of metamorphosis. The whole of Goethe's natural science might be called “an introduction to the art of seeing.“ Nor is that a small thing to say; for phantastic imaginings do not teach the art of seeing, but on the contrary lead to those false observations which Sachs blamed; on the other hand, there is a Something which Goethe by a happy inspiration called the “exact phantasy of the senses.“ 27 This phantasy is — as the word describes it — something felt by the senses, not abstract; it rests upon very accurate Seeing, and the unsurpassable exactness of many of Goethe's observations is attested by Müller and Helmholtz, by Virchow and Gegenbaur, by Sachs and Ferdinand Cohn; here, however, exact Phantasy must be allied to exact Seeing. Scientific hypotheses all pass away, but Goethe's Doctrine of Metamorphosis and Doctrine of Colour will never pass away: they stand as firmly as the facts which they mirror in Reason. Hence the importance of Goethe's ideas in Zoology and Botany. Science has used his thoughts as she uses the ophthalmoscope, in order to see into the depths, to discover facts; but, only as tools, not as an organ. It is true that the Doctors of the theory of evolution delight in tracing their pedigree to Goethe, but that is the innocence of the elderly child that would do better to search for an ancestry in Moses, Sanchoniathon, Thales, and Empedocles; venerable men who historically would render it better service, and are also more in sympathy with its intellectual culture.
     But in order exhaustively to lay bare the relationship

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between Goethe's conception of Nature by means of the “Phantasy of the senses“ and the mathematically exact Science of Nature, we must avail ourselves of a concrete example. For this Optics and the Doctrine of Colour must serve our purpose. Naturally it is not possible for me here to dive into the mysteries of optics, nor indeed would any man be able to give an exposition of Goethe's doctrine of colour with greater brevity than he did himself. That immortal work is all Perception and pure Perception; the least learned of men can study it paragraph by paragraph, and see step by step what Goethe saw. Here sight and understanding are identical. One would imagine that every man would lay hold upon it. And since Helmholtz, whom I may well quote here as the universally honoured representative of the mathematical anti-Goethe science, has expressly affirmed, “the experiments which Goethe cites in his Doctrine of Colour are accurately observed, and vividly described; as to their correctness there is no dispute,“ 28 no one who might wish to read this forbidden book need tremble for his scientific salvation. Exact, correct observations, which have moreover earned the praise of a genuine university professor as being vividly described, can certainly harm no man. But I know that it is all of no use; no human being can be induced to read the Doctrine of Colour. This glorious child of a demi-god is like a sleeping Brünnhilde waiting for the dawn of the new day which shall bring the hero to awaken her. We can therefore only deal with a few leading principles: that however will suffice to enable you to grasp the difference between “Nature as Mathematics“ and “Nature as Exposition,“ and never again to fall into doubt as to the right of the latter to assert its right to a place side by side with the former. In this connection Goethe, Leonardo, and Kant, each in his own special individuality, will arise before your eyes.

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    The first paragraph in Helmholtz's Optics consists of a definition of light, set forth as follows: “Light is looked upon by the majority of physicists as a peculiar form of motion of a hypothetical medium, the Light-aether; and we will accept this view of the undulation-theory which very fully accounts for all Phenomena.“ Here you have in a nutshell the whole method of mathematical-mechanical science. The storied words of the dying poet, “more light!“ are often cited in and out of season. What would our sensitive souls have said if Goethe had called out “more special motive-form of the hypothetical medium!“ Do not, however, believe that with this poor joke I wish to cast ridicule upon the optical definition; no less a man than René Descartes is responsible for the conception that light must be looked upon as Motion, and indeed as the motion of an invisible medium pervading the universe. It is the acceptation of this theory that has made optics the most perfect of all sciences: I only wished to call your attention to the fact that the first law of all science — if science is to be exact, — is the abolition of that which is visible, or if not in so many words of that which is visible, in any case the abolition of that which is practically seen, in favour of an abstract, mathematically available, altogether unfelt and schematic representation. In the same work (p. 268) Helmholtz actually reproaches Goethe with the fact that “in his studies in natural history he starts upon the principle of never abandoning the domain of that which is visible to the senses.“ From the point of view of science, then, it is a mistake to dwell upon that which is visible to the senses; for, as Helmholtz goes on to say, “Every physical exegesis must rise to the level of all those Forces which can naturally never be objects perceptible to the senses, but are only objects of the apprehensive understanding.“ These so-called Forces are purely creatures of the imagination: even the most sober anti-philosophical

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Science now admits that they only exist in our heads: and for that very reason they are unable to make use of the perception of the senses as such, but have to replace them by a sensibility of the imagination. 29 What is then seen is, as one of the greatest men of genius among the physicists, Heinrich Hertz, admits, a delusion from which it is impossible to exact “any conformity with things.“ 30 The very first step then leads from concrete perception to the abstract, and until that has been attained no Science is exact. To the unlearned, to the men of simple thoughts, Light would seem to be the most concrete of all perceivable things. And yet here you have a definition of Light which thrusts aside all perception; for looked at exactly it contains only two propositions, of which the one says “Light is Light-aether,“ an idea which reminds one of the “I am that I am“ of Jehovah, and must be dealt with by the logicians; while the second adds the assertion that “Light is motion.“ Now since the most cursory reflection has already sufficed to teach us that the conception of Nature as Motion is an irrefutable requisite of the human intellect, — that is to say that it is not a law of Nature but of our brain, — and inasmuch as Leonardo as a keen thinker even in his day recognised the justice of this principle, — it follows that the above definition is neither more nor less than an universal metaphysical postulate. Since then, as you know, certain leading Physicists have also declared against the hypothetical medium, the aether, as superfluous. In their minds Light is nothing but abstract motion in empty space.
    But now let us, please, read a little further in Helmholtz. We come to the Scheme. As Kant acutely remarked, “The subjective principle of Nature precedes the objective, the combination precedes that which is combined.“ That “which is complex must be supplied by ourselves,“ for we can investigate “only that which we

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Light-aetherhave ourselves supplied.“ Now in optics we supply a great deal. 31
    Following the advice of Helmholtz, let us attempt to represent the “peculiar form of motion of the hypothetical medium“ with the help of a wet thread which we shall hold in our fingers and allow to hang down freely, moving to and fro.
    Here you see the diagram; the line from A to B is the thread when not in motion; so the tiny particles of Light-aether follow one another in a straight line so long as they are not in motion: and here the dotted line shows you how the so-called waves behave as soon as a particle of aether begins to rock backwards and forwards at the top point A. And what is the reason of the movements of this same particle? Here again we have something peculiar. Helmholtz writes, “exactly as the movement of the single particles of the thread takes place, so would be the movement of a succession of aether-particles along which a ray of light should transmit itself.“ If then we have above received a definition of Light containing nothing more than the abstract admission that Light is motion, the Light-ray is at once introduced as an hypostasis transmitting itself along the particles of Light-aether, and so causing their motion. And whilst light is, according to the definition, a movement of waves, the Light-ray is, according to the mathematical definition, “a perpendicular line.“ Here we seem to have got into something like a witches' caldron! Let us just imagine that the sun is at noon: the world is steeped in light: how many rays are we to reckon there? Certainly more

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than you would see in the halo of a Byzantine Madonna's head. Does this raise a smile? And yet here is no joke, but your faith is bespoken for the following proposition: “we can in such cases consider the movement of the particles of aether inside a ray approximately as an isolated mechanical Whole, progressing independently of the movements of the neighbouring rays.“ You perceive that the rays are an altogether material conception. The possibility that innumerable rays running side by side do not take up the lateral movements of the aether-particles, so that for the very superabundance of light-rays there is no light, is a question which you must settle for yourselves, for to that Physics afford no answer. If we had the wave-movement alone, or the rectilinear movement alone (which latter movement laid the foundation of the whole optics of Newton who knew nothing of any wave-movement), then in that case our power of conception would at least possess a possible illusion; but to our mathematical Physics both conceptions are indispensable: Light is a rectilinear movement which does not spread itself like sound in all directions, and in spite of that Light is at the same time a wave, or undulatory movement. It is only by the conjunction of these two contradictory hypotheses that all phenomena can be exhaustively and mathematically reduced to a Scheme. The great mathematician d'Alembert calls attention to the fact that the so-called “cloudlessness“ of Mathematics really only holds good where they deal with the wholly Abstract, but that the richer the evidence of the senses to which you apply them, the darker become the conceptions upon which you base their operations. 32 You see here how true are his words. Mathematical Physics are practical, useful, infallible, grand, bewildering — I would gladly grant their right to all the laudatory Predicates in the Dictionary, — with one exception, clear. Whoever in agreement with d'Alembert searches

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into their foundations, will find them obscure. When Goethe wished to lay before a friend a few ideas concerning light he began by storming against the unhappy conception of the Rays. “There is absolutely no question of Rays, — they are an abstraction invented to explain the phenomenon in its greatest simplicity, an abstraction worked up, built upon, or rather piled up, until the whole matter at last became muddled into incomprehensibility.“ But let us leave the so-called Rays and return to our Waves, only following the exposition so far until we meet a practical conception clear to the senses, so as to justify the belief that we are floating down from the cloudy Olympus of hypothetical constructions, and are setting foot upon the solid ground of empirics.
    And here I would crave your attention: the time has come for us, as Kant taught us, “to supply the synthesis.“ In proportion as I move the thread more or less violently, so the serpentine line which it forms in the air will show greater or lesser curves; in the same way the aether-particles in the Light-aether, in proportion to the violence of their motion, will deviate more or less from their original position, — in other words, the Waves will be higher or lower: this variation in the height of the Waves is known as the Amplitude of Wave-motion. Besides the height of the Waves their length has to be taken into consideration. The distance between a1 and a2, from wave-crest to wave-crest, or from b1 to b2, from wave-valley to wave-valley, may vary in length: that is called the Wave-length. Thirdly, the movement of each aether-particle, which can be imagined as rocking to and fro, may take place with varying speed: that is called the Duration of oscillation. Pray hold fast to the conception that we must admit in these Waves a varying height, length, and duration of oscillation. And inasmuch as thought, as the saying goes, pays no duty, we may besides all this assume various directions of motion.

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Once more let us consider the wet thread. I can move my hand from right to left and from left to right, and then the single particles of the string which is curving into waves will also move rectilinearly to and fro; the same holds good with the aether-particles; in this case we say that the light is “rectilinearly polarised.“ But just as I move my hand rectilinearly from left to right, I might equally move it in a right line to and fro from front to back; I must therefore assume at least two directions of oscillation, and indeed might, if necessary, assume as many more as I please; in the simplest case we speak of two perpendicular directions of waves mutually polarised. Again, I might move my hand in a circle or in an ellipse. In that case the single particle of the string would, instead of a straight line, describe a circular line, or an elliptic line from one wave-crest to another, or from one wave-valley to the next: here too we must assume the same of the Light-aether particles; in the one case we speak of circular polarised light, in the other of elliptic polarised light. There are several other complications, but for our present purpose this is sufficient. We can therefore conceive waves of varying amplitude (that is to say height), waves of different length, waves of different duration of oscillation, waves rectilinearly polarised, perpendicularly polarised in opposition, circularly polarised, and elliptically polarised. But now I have to make a last and highest demand upon your imagination. Represent to yourselves all these differences with all their various prepositions as before, “with,“ “in,“ “upon,“ etc. — high waves and low waves, short and long, swift and slow in their oscillations, in endless gradations, pressing upon one another in all directions, — and in addition the aether-particles in various straight lines, and also working through each other in circles and ellipses: and then do you know what you have arrived at? Why, the Natural Light of the Physicists, as the

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sun, the candle, the match brings it into existence! This again is a serious matter. Cross-examine Helmholtz: he will furnish you with information. “Natural light,“ he writes, “is a uniform compound of all sorts of differently polarised Light,“ moreover, “it contains wave-features of an endless number of continually intermingling values of oscillatory duration.“
    It seems to me that we have fairly carried out Kant's behests as to ourselves supplying the synthesis. Yet I must here insert a remark. Nothing would be more unjustifiable than to ridicule this Scheme of the physicists, far rather would I with complete confidence vote with Kant that such intellectual constructions are “the pride of human reason.“ It is only by degrees that the monstrous complexity of the illusion established itself, as new phenomena, which it was necessary to incorporate in the one great Scheme, gradually became known, new ones have cropped up since Helmholtz's time: as for instance the Röntgen Rays, which compelled the conclusion that the oscillations do not only take place perpendicularly to the direction of transmission, but also parallel to it; that is to say as if we were not only to move our wet thread to and fro rectilinearly and in a circular line, but also from top to bottom and conversely from bottom to top, — not only therefore in the direction of floor and ceiling, but also in the direction of the room's walls. There will always be new additional matter coming to the front, until in the end the Scheme of Undulation will become useless by reason of its growing and alarming complication, and then some genius will enrich us with a new Image which will combine Light, radiating energy, chemical agency, electricity, magnetism, in one single practical scheme paving the way for new discoveries. The new theory is already at hand, widely developed, only lacking as yet a presentation as Image. 33 Enthusiastic admiration is the due of those men who like

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Democritus and Descartes and Kant endow the human brain with such schematic and creative illusions; and unquestionable recognition is the meed of those men of exact Science who, like Newton and Helmholtz, by their scorn of fatigue, their gift of observation, acuteness, power of sensitiveness, and talent, not only enrich the treasury of knowledge, — adding to the already existing thoughts of genius which they have inherited, — but also render to mankind services of imperishable value. One need only think of the ophthalmoscope! The depreciation of exact science, as we meet with it here and there in the works of various fanatics and obscurantists, makes one so indignant because it denies manifest demonstrable services which every lamp-cleaner can see even if he cannot understand them; whereas the depreciation of philosophy and art is pardonable where it is due to stupidity or faulty education. We must have no misunderstanding upon this point. The one thing against which I defend myself is this, that an invisible church served by a priesthood of narrow-minded, arrogant, and intolerant professors, who under the honourable title of “learned“ enjoy a quite unjustified respect, — since learning and power of judgment by no means of necessity go hand in hand 34 — that these enemies of nature, this tribe of fanatics should seize upon my unders