THE ART OF THINKING

The Dance of Life by Havelock Ellis is part of the HackerNoon Books Series. You can jump to any chapter in this book here. THE ART OF THINKING

III. THE ART OF THINKING

IHerbert Spencer pointed out, in his early essay on “The Genesis of Science,” that science arose out of art, and that even yet the distinction is “purely conventional,” for “it is impossible to say when art ends and science begins.” Spencer was here using “art” in the fundamental sense according to which all practice is of the nature of art. Yet it is of interest to find a thinker now commonly regarded as so prosaic asserting a view which to most prosaic people seems fanciful. To the ordinary solid man, to any would-be apostle of common sense, science—and by “science” he usually means applied science—seems the exact opposite of the vagaries and virtuosities that the hard-headed homme moyen sensuel is accustomed to look upon as “art.”Yet the distinction is modern. In classic times there was no such distinction. The “sciences”—reasonably, as we may now see, and not fancifully as was afterwards supposed—were “the arts of the mind.” In the Middle Ages the same liberal studies—grammar, logic, geometry, music, and the rest—could be spoken of either as “sciences” or as “arts,” and for Roger Bacon, who in the thirteenth century was so 69genuine a man of science, every branch of study or learning was a “scientia.” I am inclined to think that it was the Mathematical Renaissance of the seventeenth century which introduced the undue emphasis on the distinction between “science” and “art.” “All the sciences are so bound together,” wrote Descartes, the banner-bearer of that Renaissance, in his “Règles pour la Direction de l’Esprit,” “that it is much easier to learn them all at once than to learn one alone by detaching it from the others.” He added that we could not say the same of the arts. Yet we might perhaps say of arts and sciences that we can only understand them all together, and we may certainly say, as Descartes proceeded to say of the sciences alone, that they all emanate from the same focus, however diversely coloured by the media they pass through or the objects they encounter. At that moment, however, it was no doubt practically useful, however theoretically unsound, to overemphasise the distinction between “science,” with its new instrumental precision, and “art.” At the same time the tradition of the old usage was not completely put aside, and a Master of “Arts” remained a master of such sciences as the directors of education succeeded in recognising until the middle of the nineteenth century. By that time 70the development of the sciences, and especially of the physical sciences, as “the discovery of truth,” led to a renewed emphasis on them which resulted in the practical restriction of the term “art” to what are ordinarily called the fine arts. More formally, science became the study of what were supposed to be demonstrable and systematically classifiable truths regarding the facts of the world; art was separated off as the play of human impulses in making things. Sir Sidney Colvin, in the “Encyclopædia Britannica,” after discussing the matter (which Mill had already discussed at length in his “Logic” and decided that the difference is that Science is in the Indicative Mood and Art in the Imperative Mood), concluded that science is “ordered knowledge of natural phenomena and of the relations between them,” or that “Science consists in knowing, Art consists in doing.” Men of science, like Sir E. Ray Lankester, accepted this conclusion. That was as far as it was possible to go in the nineteenth century.But the years pass, and the progress of science itself, especially the sciences of the mind, has upset this distinction. The analysis of “knowing” showed that it was not such a merely passive and receptive method of recognising “truth” as scientists had innocently supposed. This is probably admitted now by the Realists among philosophers as well as by the Idealists. Dr. Charles Singer, perhaps our most learned historian of science, now defines science, no longer as a body of 71organized knowledge, but as “the process which makes knowledge,” as “knowledge in the making”; that is to say, “the growing edge between the unknown and the known.” As soon as we thus regard it, as a making process, it becomes one with art. Even physical science is perpetually laying aside the “facts” which it thought it knew, and learning to replace them by other “facts” which it comes to know as more satisfactory in presenting an intelligible view of the world. The analysis of “knowing” shows that this is not only a legitimate but an inevitable process. Such a process is active and creative. It clearly partakes at least as much of the nature of “doing” as of “knowing.” It involves qualities which on another plane, sometimes indeed on the same plane, are essentially those involved in doing. The craftsman who moulds conceptions with his mind cannot be put in a fundamentally different class from the craftsman who moulds conceptions with his hand, any more than the poet can be put in a totally different class from the painter. It is no longer possible to deny that science is of the nature of art.So it is that in the fundamental sense, and even, it will have to be added, in a sense that comprehends the extravagancies of wild variations from the norm, we have to recognise that the true man of science is an artist. Like the lunatic, the lover, the poet (as a great physician, Sir William Osler, has said), the student is “of imagination all compact.” It was by his “wonderful imagination,” it has been well pointed out, that Newton was constantly discovering new tracks and new processes in the region of the unknown. The extraordinary various life-work of Helmholtz, who initiated the valuation of beauty on a physiological basis, scientifically precise as it was, had, as Einstein has remarked, an æsthetic colouring. “There is no such thing as an unimaginative scientific man,” a distinguished professor of mechanics and mathematics declared some years ago, and if we are careful to remember that not every man who believes that his life is devoted to science is really a “scientific man,” that statement is literally true. It is not only true of the scientific man in the special sense; it is also true of the philosopher. In every philosopher’s work, a philosophic writer has remarked, “the construction of a complete system of conceptions is not carried out simply in the interests of knowledge. Its underlying 73motive is æsthetic. It is the work of a creative artist.” The intellectual lives of a Plato or a Dante, Professor Graham Wallas from a different standpoint has remarked, “were largely guided and sustained by their delight in the sheer beauty of the rhythmic relation between law and instance, species and individual, or cause and effect.”That remark, with its reference to the laws and rhythm in the universe, calls to mind the great initiator, so far as our knowledge extends back, of scientific research in our European world. Pythagoras is a dim figure, and there is no need here to insist unduly on his significance. But there is not the slightest doubt about the nature of that significance in its bearing on the point before us. Dim and legendary as he now appears to us, Pythagoras was no doubt a real person, born in the sixth century before Christ, at Samos, and by his association with that great shipping centre doubtless enabled to voyage afar and glean the wisdom of the ancient world. In antiquity he was regarded, Cicero remarks, as the inventor of philosophy, and still to-day he is estimated to be one of the most original figures, not only of Greece, but the world. He is a figure full of interest from many points of view, 74however veiled in mist, but he only concerns us here because he represents the beginning of what we call “science”—that is to say, measurable knowledge at its growing point—and because he definitely represents it as arising out of what we all conventionally recognise as “art,” and as, indeed, associated with the spirit of art, even its most fantastic forms, all the way. Pythagoras was a passionate lover of music, and it was thus that he came to make the enormously fruitful discovery that pitch of sound depends upon the length of the vibrating chord. Therein it became clear that law and spatial quantity ruled even in fields which had seemed most independent of quantitative order. The beginning of the great science of mechanics was firmly set up. The discovery was no accident. Even his rather hostile contemporary Heraclitus said of Pythagoras that he had “practised research and inquiry beyond all other men.” He was certainly a brilliant mathematician; he was, also, not only an astronomer, but the first, so far as we know, to recognise that the earth is a sphere,—so setting up the ladder which was to reach at last to the Copernican conception,—while his followers took the further step of affirming that the earth was not the centre of our cosmic system, but concentrically related. So that Pythagoras may not only be called the Father of Philosophy, but, with better right the Father of Science in the modern exact sense. Yet he remained fundamentally an artist even in the conventional sense. His free play of imagination 75and emotion, his delight in the ravishing charm of beauty and of harmony, however it may sometimes have led him astray,—and introduced the reverence for Number which so long entwined fancy too closely with science,—yet, as Gomperz puts it, gave soaring wings to the power of his severe reason.One other great dim figure of early European antiquity shares with Pythagoras the philosophic dominance over our world, and that is the Platonic Socrates, or, as we might perhaps say, the Socratic Plato. And here, too, we are in the presence of a philosopher, if not a scientist, who was a supreme artist. Here again, also, we encounter a legendary figure concealing a more or less real human person. But there is a difference. While all are agreed that, in Pythagoras we have a great and brilliant figure dimly seen, there are many who consider that in Socrates we have a small and dim figure grown great and brilliant in the Platonic medium through which alone he has been really influential in our world, for without Plato the name of Socrates would have scarcely been mentioned. The problem of the Pythagorean legend may be said to be settled. But the problem of the Socratic legend is still under discussion. We cannot, moreover, quite put it aside as merely of academic interest, for its solution, if ever reached, would touch that great vital problem of art 76in the actual world with which we are here throughout concerned.If one examines any large standard history of Greece, like Grote’s to mention one of the oldest and best, one is fairly sure to find a long chapter on the life of Socrates. Such a chapter is inserted, without apology, without explanation, without compunction, as a matter of course, in a so-called “history,” and nearly every one, even to-day, still seems to take it as a matter of course. Few seem to possess the critical and analytical mind necessary for the examination of the documents on which the “history” rests. If they approached this chapter in a questioning spirit, they might perhaps discover that it was not until about half a century after the time of the real Socrates that any “historical” evidence for the existence of our legendary Socrates begins to appear. Few people seem to realise that even of Plato himself we know nothing certain that 77could not be held in a single sentence. The “biographies” of Plato began to be written four hundred years after his death. It should be easy to estimate their value.There are three elements—one of them immeasurably more important than the other two—of which the composite portrait of our modern Socrates is made up: Xenophon, Plato, the dramatists. To the contribution furnished by the first, not much weight is usually attached. Yet it should really have been regarded as extremely illuminating. It suggests that the subject of “Socrates” was a sort of school exercise, useful practice in rhetoric or in dialectics. The very fact that Xenophon’s Socrates was so reminiscent of his creator ought to have been instructive. It has, however, taken scholars some time to recognise this, and Karl Joël, who spent fifteen of the 78best years of his life over the Xenophontic Socrates, to discover that the figure was just as much a fiction as the Platonic Socrates, has lately confessed that he thinks those years rather wasted. It might have been clear earlier that what Plato had done was really just the same thing so far as method was concerned, though a totally different thing in result because done by the most richly endowed of poet-philosophers, the most consummate of artists. For that is probably how we ought to regard Plato, and not, like some, as merely a great mystificator. It is true that Plato was the master of irony, and that “irony,” in its fundamental meaning, is, as Gomperz points out, “pleasure in mystifying.” But while Plato’s irony possesses a significance which we must always keep before us, it is yet only one of the elements of his vast and versatile mind.It is to the third of these sources that some modern investigators are now inclined to attach primary significance. It was on the stage—in the branch of drama that kept more closely in touch with life than that which had fallen into the hands of the prose dialecticians and rhetoricians—that we seem to find the shadow of the real Socrates. But he was not the Socrates of the dramatic dialogues of Plato or even of Xenophon; he was a minor Sophist, an inferior Diogenes, yet a remarkable figure, arresting and disturbing, whose idiosyncrasies were quite perceptible to the crowd. It was an original figure, hardly the embodiment of a turning-point in philosophy, but fruitful of great possibilities, 79so that we could hardly be surprised if the master of philosophic drama took it over from real life and the stage for his own purposes.To make clear to myself the possible way—I am far from asserting it was the actual way—in which our legendary Socrates arose, I sometimes think of Chidley. Chidley was an Australian Sophist and Cynic, in the good sense of both these words, and without doubt, it seems to me, the most original and remarkable figure that has ever appeared in Australia, of which, however, he was not a native, though he spent nearly his whole life there. He was always poor, and like most philosophers he was born with a morbid nervous disposition, though he acquired a fine and robust frame. He was liable not only to the shock of outward circumstances but of inward impulses; these he had in the past often succumbed to, and only slowly and painfully gained the complete mastery over as he gained possession of his own philosophy. For all his falls, which he felt acutely, as Augustine and Bunyan as well as Rousseau felt such lapses, there was in him a real nobility, an even ascetic firmness and purity of character. I never met him, but I knew him more intimately, perhaps, than those who came in contact with him. For many years I was in touch with him, and his last letter was written shortly before his death; he always felt I ought to be persuaded of the truth he had to reveal and never quite understood my sympathetic attitude of scepticism. He had devoured all the philosophic literature 80he could lay hold of, but his philosophy—in the Greek sense, as a way of life, and not in our modern sense as a system of notions—was his own: a new vision of Nature’s simplicity and wholeness, only new because it had struck on a new sensibility and sometimes in excessive and fantastic ways, but he held his faith with unbending devotion, and never ceased to believe that all would accept the vision when once they beheld it. So he went about the streets in Sydney, clad (as a concession to public feeling) in bathing drawers, finding anywhere he could the Stoa which might serve for him, to argue and discuss, among all who were willing, with eager faith, keen mind, and pungent speech. A few were won, but most were disturbed and shocked. The police persistently harassed him; they felt bound to interfere with what seemed such an outrage on the prim decency of the streets; and as he quietly persisted in following his own course, and it was hard to bring any serious charge against him, they called in the aid of the doctors, and henceforth he was in and out of the asylum instead of the prison. No one need be blamed; it was nobody’s fault; if a man transgresses the ordinary respectable notions of decency, he must be a criminal, and if he is not a criminal, he must be a lunatic; the social organisation takes no account of philosophers; the philosophic Hipparchia and her husband must not nowadays consummate their marriage in public, and our modern philosophers meekly agree that philosophy is to have nothing to do with a life. Every one in the 81case seems to have behaved with due conventional propriety, just as every one behaved around the deathbed of Tolstoy’s Ivan Ilitch. It was Chidley’s deathbed they were preparing, and he knew it, but he unflinchingly grasped the cup they held out to him and drank it to the dregs. He felt he could do no other. There was no fabled hemlock in it, but it was just as deadly as though it had been accompanied by all the dramatic symbolisation of a formal condemnation to death, such as had really been recorded (Plato well knew) in old Athenian annals. There was no Plato in Sydney. But if there had been, it is hard to conceive any figure more fit for the ends of his transforming art. Through that inspiring medium the plebeian Sophist and Cynic, while yet retaining something of the asperity of his original shape, would have taken on a new glory, his bizarreries would have been spiritualised and his morbidities become the signs of mystic possession, his fate would have appeared as consecrated in form as it genuinely was in substance, he would have been the mouthpiece, not only of the truths he really uttered, but of a divine eloquence on the verge of which he had in real life only trembled, and, like Socrates in the hands of Plato, he would have passed, as all the finest philosophy passes at last, into music. So in the end Chidley would have entered modern history, just as 82Socrates entered ancient history, the Saint and Martyr of Philosophy.If it should so be that, as we learn to see him truly, the figure of the real Socrates must diminish in magnitude, then—and that is the point which concerns us here—the glory of the artist who made him what he has become for us is immensely enhanced. No longer the merely apt and brilliant disciple of a great master, he becomes himself master and lord, the radiant creator of the chief figure in European philosophy, the most marvellous artist the world has ever known. So that when we look back at the spiritual history of Europe, it may become possible to say that its two supreme figures, the Martyr of Philosophy and the Martyr of Religion, were both—however real the two human persons out of which they were formed—the work of man’s imagination. For there, on the one hand, we see the most accomplished of European thinkers, and on the other a little band of barbarians, awkwardly using just the same Greek language, working with an unconscious skill which even transcends all that conscious skill could have achieved, yet both bearing immortal witness to the truth that the human soul only lives truly in art and can only be ruled through art. So it is that in art lies the solution of the conflicts 83of philosophy. There we see Realism, or the discovery of things, one with Idealism, or the creation of things. Art is the embodied harmony of their conflict. That could not be more exquisitely symbolised than by these two supreme figures in the spiritual life of Europe, the Platonic Socrates and the Gospel Jesus, both alike presented to us, it is so significant to observe, as masters of irony.There has never again been so great an artist in philosophy, so supreme a dramatist, as Plato. But in later times philosophers themselves have often been willing to admit that even if they were not, like Plato, dramatists, there was poetry and art in their vocation. “One does not see why the sense for Philosophy should be more generally diffused than that for poetry,” remarked Schelling, evidently regarding them as on the same plane. F. A. Lange followed with his memorable “History of Materialism,” in which the conception of philosophy as a poetic art was clearly set forth. “Philosophy is pure art,” says in our own days a distinguished thinker who is in especially close touch with the religious philosophy of the East. “The thinker works with laws of thought and scientific facts in just the same sense as the musical composer with tones. He must find accords, he must think out sequences, he must set the part in a necessary relation to the whole. But for that he needs art.” Bergson regards 84philosophy as an art, and Croce, the more than rival of Bergson in popular esteem, and with interesting points of contact with the French philosopher, though his standpoint is so different, has repeatedly pointed out—as regards Nietzsche, for instance, and even as regards a philosopher to whom he is so closely related as Hegel—that we may read philosophy for its poetic rather than its historic truth. Croce’s position in this matter is not, indeed, easy to state quite simply. He includes æsthetics in philosophy, but he would not regard philosophy as an art. For him art is the first and lowest stratum in the mind, not in rank, but in order, and on it the other strata are laid and combine with it. Or, as he elsewhere says, “art is the root of our whole theoretic life. Without root there can be neither flower nor fruit.” But for Croce art is not itself flower or fruit. The “Concept” and other abstractions have to be brought in before Croce is satisfied that he has attained reality. It may, perhaps, indeed, be permitted, even to an admirer of the skill with which Croce spreads out such wide expanses of thought, to suggest that, in spite of his anxiety to keep close to the concrete, he is not therein always successful, and that he tends to move in verbal circles, as may perhaps happen to a philosopher who would reduce the philosophy 85of art to the philosophy of language. But, however that may be, it is a noteworthy fact that the close relationship of art and philosophy is admitted by the two most conspicuous philosophers of to-day, raised to popular eminence in spite of themselves, the Philosopher of Other-worldliness and the Philosopher of This-worldliness.If we turn to England, we find that, in an age and a land wherein it was not so easy to make the assertion as it has now more generally become, Sir Leslie Stephen, in harmony, whether or not he knew it, with F. A. Lange, wrote to Lord Morley (as he later became) in the last century: “I think that a philosophy is really made more of poetry than of logic; and the real value of both poetry and philosophy is not the pretended reasoning, but the exposition in one form or other of a certain view of life.” It is, we see, just what they have all been saying, and if it is true of men of science and philosophers, who are the typical representatives of human thinking, it is even true of every man on earth who thinks, ever since the day when conscious thinking began. The world is an unrelated mass of impressions, as it first strikes our infant senses, falling at random on the sensory mechanism, and all appearing as it were on the same plane. For an infant the moon is no farther away than his mother’s breast, even though he possesses an inherited mental apparatus fitted to coördinate and distinguish the two. It is only when we begin to think, that we can arrange these 86unrelated impressions into intelligible groups, and thinking is thus of the nature of art.All such art, moreover, may yet be said to be an invention of fictions. That great and fundamental truth, which underlies so much modern philosophy, has been expounded in the clearest and most detailed manner by Hans Vaihinger in his “Philosophie des Als Ob.”IIHans Vaihinger is still little known in England; and that is the more remarkable as he has always been strongly attached to English thought, of which his famous book reveals an intimate knowledge. In early life he had mixed much with English people, for whom he has a deep regard, and learnt to revere, not only Darwin, but Hume and J. S. Mill, who exerted a 87decisive influence on his own philosophic development. At the beginning of his career he projected a history of English philosophy, but interest in that subject was then so small in Germany that he had regretfully to abandon his scheme, and was drawn instead, through no active effort on his part, to make the study of Kant the by-product of his own more distinctive work, yet it was a fitting study, for in Kant he saw the germs of the doctrine of the “as if,” that is to say, the practical significance of fiction in human life, though that is not the idea traditionally associated with Kant, who, indeed, was not himself clear about it, while his insight was further darkened by his reactionary tendencies; yet Vaihinger found that it really played a large part in Kant’s work and might even be regarded as his special and personal way of regarding things; he was not so much a metaphysician, Vaihinger remarks, as a metaphorician. Yet even in his Kantian studies the English influence was felt, for Vaihinger’s work has here been to take up the Neo-Kantism of F. A. Lange and to develop it in an empirical and positivistic direction.There was evidently something in Vaihinger’s spirit that allied him to the English spirit. We may see that in his portrait; it is not the face of the philosophic dreamer, the scholarly man of the study, but the eager, forceful head of the practical man of action, the daring adventurer, the man who seems made to struggle with the concrete things of the world, the kind of man, that 88is to say, whom we consider peculiarly English. That, indeed, is the kind of man he would have been; that is the kind of life, a social life full of activity and of sport, that he desired to lead. But it was impossible. An extreme and lifelong short-sightedness proved a handicap of which he has never ceased to be conscious. So it came about that his practical energy was, as it were, sublimated into a philosophy which yet retained the same forceful dynamic quality.For the rest, his origin, training, and vocation seem all to have been sufficiently German. He came, like many other eminent men, out of a Swabian parsonage, and was himself intended for theology, only branching off into philosophy after his university career was well advanced. At the age of sixteen he was deeply influenced, as so many others have been, by Herder’s “Ideen zur Geschichte der Menschheit”; that not only harmonised with his own tendency at the time towards a mixed theism and pantheism, but it first planted within him the conception of evolution in human history, proceeding from an animal origin, which became a fundamental element of his mental constitution. When a year later he came across Darwin’s doctrines he felt that he knew them beforehand. These influences were balanced by that of Plato, through whose “Ideas” he caught his first glimpse of an “As-If world.” A little later the strenuous training of one of his teachers in the logical analysis of Latin syntax, especially in the use of the conjunctions, furnished the 89source from which subsequently he drew that now well-known phrase. It was in these years that he reached the view, which he has since definitely advocated, that philosophy should not be made a separate study, but should become a natural part and corollary of every study, since philosophy cannot be fruitfully regarded as a discipline by itself. Without psychology, especially, he finds that philosophy is merely “a methodic abstraction.” A weighty influence of these days was constituted by the poems and essays of Schiller, a Swabian like himself, and, indeed, associated with the history of his own family. Schiller was not only an inspiring influence, but it was in Schiller’s saying, “Error alone is life, and knowledge is death,” that he found (however unjustifiably) the first expression of his own “fictionalism,” while Schiller’s doctrine of the play impulse as the basis of artistic creation and enjoyment seemed the prophecy of his own later doctrine, for in play he saw later the “as if” as the kernel of æsthetic practice and contemplation.At the age of eighteen Vaihinger proceeded to the Swabian University of Tübingen and here was free to let his wide-ranging, eager mind follow its own impulses. He revealed a taste for the natural sciences and with this the old Greek nature philosophers, especially Anaximander, for the sake of their anticipations of modern evolutionary doctrines. Aristotle also occupied him, later Spinoza, and, above all, Kant, though 90it was chiefly the metaphysical antinomies and the practical reason which fascinated him. As ever, it was what made for practice that seemed mostly to concern him. Schelling, Hegel, and Schleiermacher, the official German idealists, said nothing to him. He turned from them to Schopenhauer, and thence he drew the pessimisms, the irrationalism, and the voluntarism which became permanent features of his system of thought. The irrationalism, as he himself points out, was completely opposed to all early influences on him, but it lay in his own personal circumstances. The contrast between his temperamental impulse to energetic practical action in every direction, and the reserve, passivity, and isolation which myopia enforced, seemed to him absolutely irrational and sharpened his vision for all the irrationality of existence. So that a philosophy which, like Schopenhauer’s, truthfully recognised and allowed for the irrational element in existence came like a revelation. As to Vaihinger’s pessimism, that, as we might expect, is hardly of what would be generally considered a pessimistic character. It is merely a recognition of the fact that most people are over-sanguine and thereby come to grief, whereas a little touch of pessimism would have preserved them from much misery. Long before the Great War, Vaihinger felt that many Germans were over-sanguine regarding the military power of their Empire, and of Germany’s place in the world, and that such optimism might easily conduce to war and disaster. In 1911 he 91even planned to publish anonymously in Switzerland a pamphlet entitled “Finis Germaniæ,” with the motto “Quos Deus vult perdere, prius dementat,” and was only prevented by a sudden development of the eye-trouble. Vaihinger points out that an unjustified optimism had for a long time past led in the politics of Germany—and also, he might have said, of the countries later opposed to her—to lack of foresight, over-haste, and arrogance; he might have added that a very slight touch of pessimism would also have enabled these countries, on both sides, to discover the not very remote truth that even the victors in such a contest would suffer scarcely less than the conquered. In early life Vaihinger had playfully defined Man as a “species of ape afflicted by megalomania”; he admits that, whatever truth lies behind the definition, the statement is somewhat exaggerated. Yet it is certainly strange to observe, one may comment, how many people seem to feel vain of their own ungratified optimism when the place where optimism most flourishes is the lunatic asylum. They never seem to pause to reflect on the goal that lies ahead of them, though there must be few who on looking back cannot perceive what terrible accidents they might have foreseen and avoided by the aid of a little pessimism. When the gods, to ruin a man, first make him mad, they do it, almost invariably, by making him an optimist. One might hazard the assertion that the chief philosophic distinction between classic antiquity and modern 92civilisation is the prevalence in the latter of a facile optimism; and the fact that of all ancient writers the most popular in modern times has been the complacently optimistic (or really hedonistic) Horace is hardly due to his technical virtuosity. He who would walk sanely amid the opposing perils in the path of life always needs a little optimism; he also needs a little pessimism.Reference has been made to Vaihinger’s devouring appetite for knowledge. This, indeed, was extraordinary, and of almost universal range. There seem to have been few fields with which he failed to come in touch, either through books or by personal intercourse with experts. He found his way into all the natural sciences, he was drawn to Greek archæology and German philosophy; he began the study of Sanscrit with Roth. Then, realising that he had completely neglected mathematics, he devoted himself with ardour to analytic geometry and infinitesimals, a study which later he found philosophically fruitful. Finally, in 1874, he may be said to have rounded the circle of his self-development by reading the just published enlarged and much improved edition of F. A. Lange’s “History of Materialism.” Here he realised the presence of a spirit of the noblest order, equipped with the widest culture and the finest lucidity of vision, the keenest religious radicalism combined with large-hearted tolerance and lofty moral equilibrium, all manifested in a completed master-work. Moreover, 93the standpoint of F. A. Lange was precisely that which Vaihinger had been independently struggling towards, for it brought into view that doctrine of the place of fiction in life which he had already seen ahead. It is not surprising that he should generously and enthusiastically acclaim Lange as master and leader, though his subsequent work is his own, and has carried ideas of which Lange held only the seeds to new and fruitful development.It was in 1876-77 that Vaihinger wrote his book, a marvellous achievement for so youthful a thinker, for he was then only about twenty-five years of age. A final revision it never underwent, and there remain various peculiarities about the form into which it is cast. The serious failure in eyesight seems to have been the main reason for delaying the publication of a work which the author felt to be too revolutionary to put forth in an imperfect form. He preferred to leave it for posthumous publication.But the world was not standing still, and during the next thirty years many things happened. Vaihinger found the new sect of Pragmatists coming into fashion with ideas resembling his own, though in a cruder shape, which seemed to render philosophy the “meretrix theologorum.” Many distinguished thinkers were working towards an attitude more or less like his own, 94especially Nietzsche, whom (like many others even to-day) he had long regarded with prejudice and avoided, but now discovered to be “a great liberator” with congenial veins of thought. Vaihinger realised that his conception was being independently put forward from various sides, often in forms that to him seemed imperfect or vicious. It was no longer advisable to hold back his book. In 1911, therefore, “Die Philosophie des Als Ob” appeared.The problem which Vaihinger set out to solve was this: How comes it about that with consciously false ideas we yet reach conclusions that are in harmony with Nature and appeal to us as Truth? That we do so is obvious, especially in the “exact” branches of science. In mathematics it is notorious that we start from absurdities to reach a realm of law, and our whole conception of the nature of the world is based on a foundation which we believe to have no existence. For even the most sober scientific investigator in science, the most thoroughgoing Positivist, cannot dispense with fiction; he must at least make use of categories, and they are already fictions, analogical fictions, or labels, which give us the same pleasure as children receive when they are told the “name” of a thing. Fiction is, indeed, an indispensable supplement to logic, or even a part of it; whether we are working inductively or deductively, both ways hang closely together with fiction; and axioms, though they seek to be primary verities, are more akin to fiction. If we had 95realised the nature of axioms, the doctrine of Einstein, which sweeps away axioms so familiar to us that they seem obvious truths, and substitutes others which seem absurd because they are unfamiliar, might not have been so bewildering.Physics, especially mathematical physics, Vaihinger explains in detail, has been based, and fruitfully based, on fictions. The infinite, infinitely little or infinitely great, while helpful in lightening our mental operations, is a fiction. The Greeks disliked and avoided it, and “the gradual formation of this conception is one of the most charming and instructive themes in the history of science,” indeed, one of the most noteworthy spectacles in the history of the human spirit; we see the working of a logical impulse first feeling in the dark, gradually constructing ideas fitted to yield precious service, yet full of hopeless contradictions, without any relation to the real world. That absolute space is a fiction, Vaihinger points out, is no new idea. Hobbes had declared it was only a phantasma; Leibnitz, who agreed, added that it was merely “the idolum of a few modern Englishmen,” and called time, extension, and movement “choses idéales.” Berkeley, in attacking the defective conceptions of the mathematicians, failed to see that it was by means of, and not in spite of, these logically defective conceptions that they attained logically valuable results. All the marks of fiction were set up on the mathematician’s pure space; it was impossible and unthinkable: yet it proved useful and fruitful.96The tautological fiction of “Force”—an empty reduplication of the fact of a succession of relationships—is one that we constantly fall back on with immense satisfaction and with the feeling of having achieved something; it has been a highly convenient fiction which has aided representation and experience. It is one of the most famous, and also, it must be added, one of the most fatal of fantasies. For when we talk of, for instance, a “life-force” and its élan, or whatever other dainty term we like to apply to it, we are not only summarily mingling together many separate phenomena, but we are running the risk that our conception may be taken for something that really exists. There is always temptation, when two processes tend to follow each other, to call the property of the first to be followed by the other its “force,” and to measure that force by the magnitude of the result. In reality we only have succession and coexistence, and the “force” is something that we imagine.We must not, therefore, treat our imagination with contempt as was formerly the fashion, but rather the reverse. The two great periods of English Philosophy, Vaihinger remarks, ended with Ockham and with Hume, who each took up, in effect, the fictional point of view, but both too much on the merely negative side, without realising the positive and constructive value of fictions. English law has above all realised it, even, he adds, to the point of absurdity. Nothing is so precious as fiction, provided only one chooses the right 97fiction. “Matter” is such a fiction. There are still people who speak with lofty contempt of “Materialism”; they mean well, but they are unhappy in their terms of abuse. When Berkeley demonstrated the impossibility of “matter,” he thought he could afford to throw away the conception as useless. He was quite wrong; it is logically contradictory ideas that are the most valuable. Matter is a fiction, just as the fundamental ideas with which the sciences generally operate are mostly fictions, and the scientific materialisation of the world has proved a necessary and useful fiction, only harmful when we regard it as hypothesis and therefore possibly true. The representative world is a system of fictions. It is a symbol by the help of which we orient ourselves. The business of science is to make the symbol ever more adequate, but it remains a symbol, a means of action, for action is the last end of thinking.The “atom,” to which matter is ultimately reduced, is regarded by Vaihinger as equally a fiction, though it was at first viewed as an hypothesis, and it may be added that since he wrote it seems to have returned to the stage of hypothesis. But when with Boscovich the “atom” was regarded as simply the bearer of energy, it became “literally a hypostatised nothing.” We have 98to realise at the same time that every “thing” is a “summatory fiction,” for to say, as is often said, that a “thing” has properties and yet has a real existence apart from its properties is obviously only a convenient manner of speech, a “verbal fiction.” The “force of attraction,” as Newton himself pointed out, belongs to the same class of summatory fictions.Vaihinger is throughout careful to distinguish fiction alike from hypothesis and dogma. He regards the distinction as, methodologically, highly important, though not always easy to make. The “dogma” is put forward as an absolute and unquestionable truth; the “hypothesis” is a possible or probable truth, such as Darwin’s doctrine of descent; the “fiction” is impossible, but it enables us to reach what for us is relatively truth, and, above all, while hypothesis simply contributes to knowledge, fiction thus used becomes a guide to practical action and indispensable to what we feel to be progress. Thus the mighty and civilising structure of Roman law was built up by the aid of what the Romans themselves recognised as fictions, while in the different and more flexible system of English laws a constant inspiration to action has been furnished by the supposed privileges gained by Magna Carta, though we now recognise them as fictitious. Many of our ideas tend to go through the three stages of Dogma, Hypothesis, and Fiction, sometimes in that order and sometimes in the reverse order. Hypothesis especially presents a state of labile stability which is 99unpleasant to the mind, so it tends to become either dogma or fiction. The ideas of Christianity, beginning as dogmas, have passed through all three stages in the minds of thinkers during recent centuries: the myths of Plato, beginning as fiction, not only passed through the three stages, but then passed back again, being now again regarded as fiction. The scientifically valuable fiction is a child of modern times, but we have already emerged from the period when the use of fiction was confined to the exact sciences.Thus we find fiction fruitfully flourishing in the biological and social sciences and even in the highest spheres of human spiritual activity. The Linnæan and similar classificatory systems are fictions, even though put forward as hypotheses, having their value simply as pictures, as forms of representation, but leading to contradictions and liable to be replaced by other systems which present more helpful pictures. There are still people who disdain Adam Smith’s “economic man,” as though proceeding from a purely selfish view of life, although Buckle, forestalling Vaihinger, long ago explained that Smith was deliberately making use of a “valid artifice,” separating facts that he knew to be in nature inseparable—he based his moral theory on a totally different kind of man—because so he could reach results approximately true to the observed phenomena. Bentham also adopted a fiction for his own system, though believing it to be an hypothesis, and Mill criticised it as being “geometrical”; the 100criticism is correct, comments Vaihinger, but the method was not thereby invalidated, for in complicated fields no other method can be fruitfully used.The same law holds when we approach our highest and most sacred conceptions. It was recognised by enlightened philosophers and theologians before Vaihinger that the difference between body and soul is not different from that between matter and force,—a provisional and useful distinction,—that light and darkness, life and death, are abstractions, necessary, indeed, but in their application to reality always to be used with precaution. On the threshold of the moral world we meet the idea of Freedom, “one of the weightiest conceptions man has ever formed,” once a dogma, in course of time an hypothesis, now in the eyes of many a fiction; yet we cannot do without it, even although we may be firmly convinced that our acts are determined by laws that cannot be broken. Many other great conceptions have tended to follow the same course. God, the Soul, Immortality, the Moral World-Order. The critical hearers understand what is meant when these great words are used, and if the uncritical misunderstand, that, adds Vaihinger, may sometimes be also useful. For these things are Ideals, and all Ideals are, logically speaking, fictions. As Science leads to the Imaginary, so Life leads to the Impossible; without them we cannot reach the heights we are born to scale. “Taken literally, however, our most valuable conceptions are worthless.”101When we review the vast field which Vaihinger summarises, we find that thinking and existing must ever be on two different planes. The attempt of Hegel and his followers to transform subjective processes into objective world-processes, Vaihinger maintains, will not work out. The Thing-in-Itself, the Absolute, remains a fiction, though the ultimate and most necessary fiction, for without it representation would be unintelligible. We can only regard reality as a Heraclitean flux of happening—though Vaihinger fails to point out that this “reality” also can only be an image or symbol—and our thinking would itself be fluid if it were not that by fiction we obtain imaginary standpoints and boundaries by which to gain control of the flow of reality. It is the special art and object of thinking to attain existence by quite other methods than that of existence itself. But the wish by so doing to understand the world is both unrealisable and foolish, for we are only trying to comprehend our own fictions. We can never solve the so-called world-riddle because what seem riddles to us are merely the contradictions we have ourselves created. Yet, though the way of thinking cannot be the way of being, since they stand on such different foundations, thinking always has a kind of parallelism with being, and though we make our reckoning with a reality that we falsify, yet the practical result tends to come out right. Just because thinking is different from reality, its forms must also be different in order to correspond 102with reality. Our conceptions, our conventional signs, have a fictive function to perform; thinking in its lower grades is comparable to paper money, and in its higher forms it is a kind of poetry.Imagination is thus a constitutive part of all thinking. We may make distinctions between practical scientific thinking and disinterested æsthetic thinking. Yet all thinking is finally a comparison. Scientific fictions are parallel with æsthetic fictions. The poet is the type of all thinkers: there is no sharp boundary between the region of poetry and the region of science. Both alike are not ends in themselves, but means to higher ends.Vaihinger’s doctrine of the “as if” is not immune from criticism on more than one side, and it is fairly obvious that, however sound the general principle, particular “fictions” may alter their status, and have even done so since the book was written. Moreover, the doctrine is not always quite congruous with itself. Nor can it be said that Vaihinger ever really answered the question with which he set out. In philosophy, however, it is not the attainment of the goal that matters, it is the things that are met with by the way. And Vaihinger’s philosophy is not only of interest because it presents so clearly and vigorously a prevailing tendency in modern thought. Rightly understood, it supplies a fortifying influence to those who may have seen their cherished spiritual edifice, whatever it may be, fall around them and are tempted to a mood of disillusionment. 103We make our own world; when we have made it awry, we can remake it, approximately truer, though it cannot be absolutely true, to the facts. It will never be finally made; we are always stretching forth to larger and better fictions which answer more truly to our growing knowledge and experience. Even when we walk, it is only by a series of regulated errors, Vaihinger well points out, a perpetual succession of falls to one side and the other side. Our whole progress through life is of the same nature; all thinking is a regulated error. For we cannot, as Vaihinger insists, choose our errors at random or in accordance with what happens to please us; such fictions are only too likely to turn into deadening dogmas: the old vis dormitiva is the type of them, mere husks that are of no vital use and help us not at all. There are good fictions and bad fictions just as there are good poets and bad poets. It is in the choice and regulation of our errors, in our readiness to accept ever-closer approximations to the unattainable reality, that we think rightly and live rightly. We triumph in so far as we succeed in that regulation. “A lost battle,” Foch, quoting De Maistre, lays down in his “Principes de Guerre,” “is a battle one thinks one has lost”; the battle is won by the fiction that it is won. It is so also in the battle of life, in the whole art of living. Freud regards dreaming as fiction that helps us to sleep; thinking we may regard as fiction that helps us to live. Man lives by imagination.104IIIYet what we consider our highest activities arise out of what we are accustomed to regard as the lowest. That is, indeed, merely a necessary result of evolution; bipeds like ourselves spring out of many-limbed creatures whom we should now regard as little better than vermin, and the adult human creature whose eyes, as he sometimes imagines, are fixed on the stars, was a few years earlier merely a small animal crawling on all fours. The impulse of the philosopher, of the man of science, of any ordinary person who sometimes thinks about seemingly abstract or disinterested questions—we must include the whole range of the play of thought in response to the stimulus of curiosity—may seem at the first glance to be a quite secondary and remote product of the great primary instincts. Yet it is not difficult to bring this secondary impulse into direct relation with the fundamental primary instincts, even, and perhaps indeed chiefly, with the instinct of sex. On the mental side—which is not, of course, its fundamental side—the sexual instinct is mainly, perhaps solely, a reaction to the stimulus of curiosity. Beneath that mental surface the really active force is a physiologically based instinct urgent towards action, but the boy or girl who first becomes conscious of the mental stimulus is unaware of the instinct it springs from, and may even disregard as unimportant its specific physiological manifestations. The child is only conscious of new 105curiosities, and these it persistently seeks to satisfy at any available or likely source of information, aided by the strenuous efforts of its own restlessly active imagination. It is in exactly the same position as the metaphysician, or the biologist, or any thinker who is faced by complex and yet unsolved problems. And the child is at first baffled by just the same kind of obstacles, due, not like those of the thinker, to the silence of recalcitrant Nature, but to the silence of parents and teachers, or to their deliberate efforts to lead him astray.Where do babies come from? That is perhaps for many children the earliest scientific problem that is in this way rendered so difficult of solution. No satisfying solution comes from the sources of information to which the child is wont to appeal. He is left to such slight imperfect observations as he can himself make; on such clues his searching intellect works and with the aid of imagination weaves a theory, more or less remote from the truth, which may possibly explain the phenomena. It is a genuine scientific process—the play of intellect and imagination around a few fragments of observed fact—and it is undoubtedly a valuable discipline for the childish mind, though if it is too prolonged it may impede or distort natural development, and if the resulting theory is radically false it may lead, as the theories of scientific adults sometimes lead, if not speedily corrected, to various unfortunate results.A little later, when he has ceased to be a child and 106puberty is approaching, another question is apt to arise in the boy’s mind: What is a woman like? There is also, less often and more carefully concealed, the corresponding curiosity in the girl’s mind. Earlier this question had seemed of no interest; it had never even occurred to ask it; there was little realisation—sometimes none at all—of any sexual difference. Now it sometimes becomes a question of singular urgency, in the solution of which it is necessary for the boy to concentrate all the scientific apparatus at his command. For there may be no ways of solving it directly, least of all for a well-behaved, self-respecting boy or a shy, modest girl. The youthful intellect is thus held in full tension, and its developing energy directed into all sorts of new channels in order to form an imaginative picture of the unknown reality, fascinating because incompletely known. All the chief recognised mental processes of dogma, hypothesis, and fiction, developed in the history of the race, are to this end instinctively created afresh in the youthful individual mind, endlessly formed and re-formed and tested in order to fill in the picture. The young investigator becomes a diligent student of literature and laboriously examines the relevant passages he finds in the Bible or other ancient primitive naked books. He examines statues and pictures. Perhaps he finds some old elementary manual of anatomy, but here the long list of structures with Latin names proves far more baffling than helpful to the youthful investigator who can in no possible way 107fit them all into the smooth surface shown by the statues. Yet the creative and critical habit of thought, the scientific mind generated by this search, is destined to be of immense value, and long outlives the time when the eagerly sought triangular spot, having fulfilled its intellectual function, has become a familiar region, viewed with indifference, or at most a homely tenderness.That was but a brief and passing episode, however permanently beneficial its results might prove. With the achievement of puberty, with the coming of adolescence, a larger and higher passion fills the youth’s soul. He forgets the woman’s body, his idealism seems to raise him above the physical: it is the woman’s personality—most likely some particular woman’s personality—that he desires to know and to grasp.A twofold development tends to take place at this age—in those youths, that is to say, who possess the latent attitude for psychic development—and that in two diverse directions, both equally away from definite physical desire, which at this age is sometimes, though not always, at its least prominent place in consciousness. On the one hand there is an attraction for an idealised person—perhaps a rather remote person, for such most easily lend themselves to idealisation—of the opposite (or occasionally the same) sex, it may sometimes for a time even be the heroine of a novel. Such an ideal attraction acts as an imaginative and emotional ferment. The imagination is stimulated to 108construct for the first time, from such material as it has come across, or can derive from within, the coherent picture of a desirable person. The emotions are trained and disciplined to play around the figure thus constructed with a new impersonal and unselfish, even self-sacrificing, devotion. But this process is not enough to use up all the energies of the developing mind, and the less so as such impulses are unlikely by their very nature to receive any considerable degree of gratification, for they are of a nature to which no adequate response is possible.Thus it happens in adolescence that this new stream of psychic energy, emotional and intellectual, generated from within, concurrently with its primary personal function of moulding the object of love, streams over into another larger and more impersonal channel. It is, indeed, lifted on to a higher plane and transformed, to exercise a fresh function by initiating new objects of ideal desire. The radiant images of religion and of art as well as of science—however true it may be that they have also other adjuvant sources—thus begin to emerge from the depths beneath consciousness. They tend to absorb and to embody the new energy, while its primary personal object may sink into the background, or at this age even fail to be conscious at all.This process—the process in which all abstract thinking is born as well as all artistic creation—must to some slight extent take place in every person whose mental activity is not entirely confined to the immediate 109objects of sense. But in persons of more complex psychic organisation it is a process of fundamental importance. In those of the highest complex organisation, indeed, it becomes what we term genius. In the most magnificent achievements of poetry and philosophy, of art and of science, it is no longer forbidden to see the ultimate root in this adolescent development.To some a glimpse of this great truth has from time to time appeared. Ferrero, who occupied himself with psychology before attaining eminence as a brilliant historian, suggested thirty years ago that the art impulse and its allied manifestations are transformed sexual instinct; the sexual impulse is “the raw material, so to speak, from which art springs”; he connected that transformation with a less development of the sexual emotions in women; but that was much too hasty an assumption, for apart from the fact that such transformation could never be complete, and probably less so in women than in men, we have also to consider the nature of the two organisms through which the transformed emotions would operate, probably unlike in the sexes, for the work done by two machines obviously does not depend entirely upon feeding them with the same amount of fuel, but also on the construction of the two engines. Möbius, a brilliant and original, if not erratic, German psychologist, who was also concerned with the question of difference in the amount of sexual energy, regarded the art impulse as a kind of sexual secondary character. That is to say, no doubt,—if we develop 110the suggestion,—that just as the external features of the male and his external activities, in the ascending zoölogical series, have been developed out of the impulse of repressed organic sexual desire striving to manifest itself ever more urgently in the struggle to overcome the coyness of the female, so on the psychic side there has been a parallel impulse, if of later development, to carry on the same task in forms of art which have afterwards acquired an independent activity and a yet further growth dissociated from this primary biological function. We think of the natural ornaments which adorn male animals from far down in the scale even up to man, of the additions made thereto by tattooing and decoration and garments and jewels, of the parades and dances and songs and musical serenades found among lower animals as well as Man, together with the love-lyrics of savages, furnishing the beginnings of the most exquisite arts of civilisation.It is to be noted, however, that these suggestions introduce an assumption of male superiority, or male inferiority—according to our scheme of values—which unnecessarily prejudices and confuses the issue. We have to consider the question of the origin of art apart from any supposed predominance of its manifestations in one sex or the other. In my own conception—put forward a quarter of a century ago—of what I called auto-erotic activities, it was on such a basis that I sought to place it, since I regarded those auto-erotic phenomena as arising from the impeded spontaneous 111sexual energy of the organism and extending from simple physical processes to the highest psychic manifestations; “it is impossible to say what finest elements in art, in morals, in civilisation generally, may not really be rooted in an auto-erotic impulse,” though I was careful to add that the transmutation of sexual energy into other forms of force must not be regarded as itself completely accounting for all the finest human aptitudes of sympathy and art and religion.It is along this path, it may perhaps be claimed,—as dimly glimpsed by Nietzsche, Hinton, and other earlier thinkers,—that the main explanation of the dynamic process by which the arts, in the widest sense, have come into being, is now chiefly being explored. One thinks of Freud and especially of Dr. Otto Rank, perhaps the most brilliant and clairvoyant of the younger investigators who still stand by the master’s side. In 1905 Rank wrote a little essay on the artist in which this mechanism is set forth and the artist placed, in what the psycho-analytic author considers his due place, between the ordinary dreamer at one end and the neurotic subject at the other, the lower forms of art, such as myth-making, standing near to dreams, and the higher forms, such as the drama, philosophy, and the founding of religions, near to psycho-neurosis, but all possessing a sublimated life-force which has its root in some modification of sexual energy.112It may often seem that, in these attempts to explain the artist, the man of science is passed over or left in the background, and that is true. But art and science, as we now know, have the same roots. The supreme men of science are recognisably artists, and the earliest forms of art, which are very early indeed,—Sir Arthur Evans has suggested that men may have drawn before they talked,—were doubtless associated with magic, which was primitive man’s science, or, at all events, his nearest approximation to science. The connection of the scientific instinct with the sexual instinct is not, indeed, a merely recent insight. Many years ago it was clearly stated by a famous Dutch author. “Nature, who must act wisely at the risk of annihilation,” wrote Multatuli at the conclusion of his short story, “The Adventures of Little Walter,” “has herein acted wisely by turning all her powers in one direction. Moralists and psychologists have long since recognised, without inquiring into the causes, that curiosity is one of the main elements of love. Yet they were only thinking of sexual love, and by raising the two related termini in corresponding wise on to a higher plane I believe that the noble thirst for knowledge springs from the same soil in which noble love grows. To press through, to reveal, to possess, to direct, and to ennoble, that is the task and the longing, alike of the lover and the natural discoverer. So that every Ross or Franklin is a Werther of the Pole, and whoever is in love is a Mungo Park of the spirit.”113IVAs soon as we begin to think about the world around us in what we vainly call a disinterested way—for disinterest is, as Leibnitz said, a chimera, and there remains a superior interest—we become youths and lovers and artists, and there is at the same time a significant strain of sexual imagery in our thought. Among ourselves this is not always clear; we have been dulled by the routine of civilisation and the artificial formalities of what is called education. It is clear in the mythopœic creation of comparative primitive thought, but in civilisation it is in the work of men of genius—poets, philosophers, painters, and, as we have to recognise, men of science—that this trait is most conspicuously manifested. To realise this it is sufficient to contemplate the personality and activity of one of the earliest great modern men of science, of Leonardo da Vinci. Until recent times it would have seemed rather strange so to describe Leonardo da Vinci. He still seemed, as he was in his own time, primarily a painter, an artist in the conventionally narrow sense, and as such one of the greatest, fit to paint, as Browning put it, one of the four walls of the New Jerusalem. Yet even his contemporaries who so acclaimed him were a little worried about Leonardo in this capacity. He accomplished so 114little, he worked so slowly, he left so much unfinished, he seemed to them so volatile and unstable. He was an enigma to which they never secured the key. They failed to see, though it is clearly to be read even in his face, that no man ever possessed a more piercing concentration of vision, a more fixed power of attention, a more unshakable force of will. All that Leonardo achieved in painting and in sculpture and in architecture, however novel or grandiose, was, as Solmi, the highly competent Vincian scholar has remarked, merely a concession to his age, in reality a violence done to his own nature, and from youth to old age he had directed his whole strength to one end: the knowledge and the mastery of Nature. In our own time, a sensitive, alert, widely informed critic of art, Bernhard Berenson, setting out with the conventional veneration for Leonardo as a painter, slowly, as the years went by and his judgment grew more mature, adopted a more critical attitude, bringing down his achievements in art to moderate dimensions, yet without taking any interest in Leonardo as a stupendous artist in science. We may well understand that vein of contempt for the crowd, even as it almost seems the hatred for human society, the spirit of Timon, which runs across Leonardo’s writings, blended, no doubt inevitably blended, with his vein of human sweetness. This stern devotee of knowledge declared, like the author of “The Imitation of Christ,” that “Love conquers all things.” There is here no discrepancy. The man who poured a contemptuous 115flood of irony and denunciation over the most sacred social institutions and their most respectable representatives was the same man—the Gospels tell us—who brooded with the wings of a maternal tenderness over the pathos of human things.When, indeed, our imagination plays with the idea of a future Overman, it is Leonardo who comes before us as his forerunner. Vasari, who had never seen Leonardo, but has written so admirable an account of him, can only describe him as “supernatural” and “divine.” In more recent times Nietzsche remarked of Leonardo that “there is something super-European and silent in him, the characteristic of one who has seen too wide a circle of things good and evil.” There Nietzsche touches, even though vaguely, more nearly than Vasari could, the distinguishing mark of this endlessly baffling and enchanting figure. Every man of genius sees the world at a different angle from his fellows, and there is his tragedy. But it is usually a measurable angle. We cannot measure the angle at which Leonardo stands; he strikes athwart the line of our conventional human thought in ways that are sometimes a revelation and sometimes an impenetrable mystery. We are reminded of the saying of Heraclitus: “Men hold some things wrong and some right; God holds all things fair.” The dispute as to whether he was above all an artist or a man of science is a foolish and even unmeaning dispute. In the vast orbit in which Leonardo moved the distinction had little or no existence. 116That was inexplicable to his contemporaries whose opinions Vasari echoes. They could not understand that he was not of the crowd of makers of pretty things who filled the workshops of Florence. They saw a man of beautiful aspect and fine proportions, with a long curled beard and wearing a rose-coloured tunic, and they called him a craftsman, an artist, and thought him rather fantastic. But the medium in which this artist worked was Nature, the medium in which the scientist works; every problem in painting was to Leonardo a problem in science, every problem in physics he approached in the spirit of the artist. “Human ingenuity,” he said, “can never devise anything more simple and more beautiful, or more to the purpose, than Nature does.” For him, as later for Spinoza, reality and perfection were the same thing. Both aspects of life he treats as part of his task—the extension of the field of human knowledge, the intension of the power of human skill; for art, or, as he called it, practice, without science, he said, is a boat without a rudder. Certainly he occupied himself much with painting, the common medium of self-expression in his day, though he produced so few pictures; he even wrote a treatise on painting; he possessed, indeed, a wider perception of its possibilities than any artist who ever lived. “Here is the creator of modern landscape!” exclaimed Corot before Leonardo’s pictures, and a remarkable description he has left of the precise effects of colour and light produced when a woman in white 117stands on green grass in bright sunshine shows that Leonardo clearly apprehended the plein-airiste’s problem. Doubtless it will prove possible to show that he foresaw still later methods. He rejected these methods because it seemed to him that the artist could work most freely by moving midway between light and darkness, and, indeed, he, first of painters, succeeded in combining them—just as he said also that Pleasure and Pain should be imaged as twins since they are ever together, yet back to back because ever contrary—and devised the method of chiaroscuro, by which light reveals the richness of shade and shade heightens the brightness of light. No invention could be more characteristic of this man whose grasp of the world ever involved the union of opposites, and the opposites both apprehended more intensely than falls to the lot of other men.Yet it is noteworthy that Leonardo constantly speaks of the artist’s function as searching into and imitating Nature, a view which the orthodox artist anathematises. But Leonardo was not the orthodox artist, not even, perhaps, as he is traditionally regarded, one of the world’s supreme painters. For one may sympathise with Mr. Berenson’s engaging attempt—unconvincing as it has seemed—to “expose” Leonardo. The drawings Mr. Berenson, like every one else, admires whole-heartedly, but, save for the unfinished “Adoration,” which he regards as a summit of art, he finds the paintings mostly meaningless and repellent. 118He cannot rank Leonardo as an artist higher than Botticelli, and concludes that he was not so much a great painter as a great inventor in painting. With that conclusion it is possible that Leonardo himself would have agreed. Painting was to him, he said, a subtle invention whereby philosophical speculation can be applied to all the qualities of forms. He seemed to himself to be, here and always, a man standing at the mouth of the gloomy cavern of Nature with arched back, one hand resting on his knee and the other shading his eyes, as he peers intently into the darkness, possessed by fear and desire, fear of the threatening gloom of that cavern, desire to discover what miracle it might hold. We are far here from the traditional attitude of the painter; we are nearer to the attitude of that great seeker into the mysteries of Nature, one of the very few born of women to whom we can ever even passingly compare Leonardo, who felt in old age that he had only been a child gathering shells and pebbles on the shore of the great ocean of truth.It is almost as plausible to regard Leonardo as primarily an engineer as primarily a painter. He offered his services as a military engineer and architect to the Duke of Milan and set forth at length his manifold claims which include, one may note, the ability to construct what we should now, without hesitation, describe as “tanks.” At a later period he actually was appointed architect and engineer-general to Cæsar Borgia, and in this capacity was engaged on a variety 119of works. He has, indeed, been described as the founder of professional engineering. He was the seer of coming steam engines and of steam navigation and transportation. He was, again, the inventor of innumerable varieties of ballistic machines and ordnance, of steam guns and breech-loading arms with screw breech-lock. His science always tended to become applied science. Experience shows the road to practice, he said, science is the guide to art. Thus he saw every problem in the world as in the wide sense a problem in engineering. All nature was a dynamic process of forces beautifully effecting work, and it is this as it were distinctive vision of the world as a whole which seems to give Leonardo that marvellous flair for detecting vital mechanism in every field. It is impossible even to indicate summarily the vast extent of the region in which he was creating a new world, from the statement, which he set down in large letters, “The sun does not move,” the earth being, he said, a star, “much like the moon,” down to such ingenious original devices as the construction of a diving-bell, a swimming-belt, and a parachute of adequate dimensions, while, as is now well known, Leonardo not only meditated with concentrated attention on the problem of flight, but realised scientifically the difficulties to be encountered, and made ingenious attempts to overcome them in the designing of flying-machines. It is enough—following expert scientific guidance—to enumerate a few points: he studied botany in the biological 120spirit; he was a founder of geology, discovering the significance of fossils and realising the importance of river erosion; by his studies in the theories of mechanics and their utilization in peace and war he made himself the prototype of the modern man of science. He was in turn biologist in every field of vital mechanism, and the inaugurator before Vesalius (who, however, knew nothing of his predecessor’s work) of the minute study of anatomy by direct investigation (after he had found that Galen could not be relied on) and post-mortem dissections; he nearly anticipated Harvey’s conception of the circulation of the blood by studying the nature of the heart as a pump. He was hydraulician, hydrographer, geometrician, algebraist, mechanician, optician. These are but a few of the fields in which Leonardo’s marvellous insight into the nature of the forces that make the world and his divining art of the methods of employing them to human use have of late years been revealed. For centuries they were concealed in notebooks scattered through Europe and with difficulty decipherable. Yet they are not embodied in vague utterances or casual intuitions, but display a laborious concentration on the precise details of the difficulties to be overcome; nor was patient industry in him, as often happens, the substitute for natural facility, for 121he was a person of marvellous natural facility, and, like such persons, most eloquent and persuasive in speech. At the same time his more general and reflective conclusions are expressed in a style combining the maximum of clarity with the maximum of concision,—far, indeed, removed from the characteristic florid redundancy of Italian prose,—which makes Leonardo, in addition to all else, a supreme master of language.Yet the man to whom we must credit these vast intellectual achievements was no abstracted philosopher shut up in a laboratory. He was, even to look upon, one of the most attractive and vivid figures that ever walked the earth. As has sometimes happened with divine and mysterious persons, he was the natural child of his mother, Caterina, of whom we are only told that she was “of good blood,” belonging to Vinci like Ser Piero the father, and that a few years after Leonardo’s birth she became the reputable wife of a citizen of his native town. Ser Piero da Vinci was a notary, of a race of notaries, but the busiest notary in Florence and evidently a man of robust vigour; he married four times and his youngest child was fifty years the junior of Leonardo. We hear of the extraordinary physical 122strength of Leonardo himself, of his grace and charm, of his accomplishments in youth, especially in singing and playing on the flute, though he had but an elementary school education. Except for what he learnt in the workshop of the many-sided but then still youthful Verrocchio, he was his own schoolmaster, and was thus enabled to attain that absolute emancipation from authority and tradition which made him indifferent even to the Greeks, to whom he was most akin. He was left-handed; his peculiar method of writing long raised the suspicion that it was deliberately adopted for concealment, but it is to-day recognised as simply the ordinary mirror-writing of a left-handed child without training. This was not the only anomaly in Leonardo’s strange nature. We now know that he was repeatedly charged as a youth on suspicion of homosexual offences; the result remains obscure, but there is some reason to think he knew the inside of a prison. Throughout life he loved to surround himself with beautiful youths, though no tradition of license or vice clings to his name. The precise nature of his sexual temperament remains obscure. It mocks us, but haunts us from out of his most famous pictures. There is, for instance, the “John the Baptist” of the Louvre, which we may dismiss with the distinguished art critic of to-day as an impudent blasphemy or brood over long, without being clearly able to determine into what obscure region of the Freudian Unconscious Leonardo had here adventured. Freud himself has 123devoted one of his most fascinating essays to a psychoanalytic interpretation of Leonardo’s enigmatic personality. He admits it is a speculation; we may take it or leave it. But Freud has rightly apprehended that in Leonardo sexual passion was largely sublimated into intellectual passion, in accordance with his own saying, “Nothing can be loved or hated unless first we have knowledge of it,” or, as he elsewhere said, “True and great love springs out of great knowledge, and where you know little you can love but little or not at all.” So it was that Leonardo became a master of life. Vasari could report of him—almost in the words it was reported of another supreme but widely different figure, the Jesuit saint, Francis Xavier—that “with the splendour of his most beautiful countenance he made serene every broken spirit.” To possess by self-mastery the sources of love and hate is to transcend good and evil and so to possess the Overman’s power of binding up the hearts that are broken by good and evil.Every person of genius is in some degree at once man, woman, and child. Leonardo was all three in the extreme degree and yet without any apparent conflict. The infantile strain is unquestioned, and, apart from the problem of his sexual temperament, Leonardo was a child even in his extraordinary delight in devising fantastic toys and contriving disconcerting tricks. His more than feminine tenderness is equally clear, alike in his pictures and in his life. Isabella d’Este, in 124asking him to paint the boy Jesus in the Temple, justly referred to “the gentleness and sweetness which mark your art.” His tenderness was shown not only towards human beings, but to all living things, animals and even plants, and it would appear that he was a vegetarian. Yet at the same time he was emphatically masculine, altogether free from weakness or softness. He delighted in ugliness as well as in beauty; he liked visiting the hospitals to study the sick in his thirst for knowledge; he pondered over battles and fighting; he showed no compunction in planning devilish engines of military destruction. His mind was of a definitely realistic and positive cast; though there seems no field of thought he failed to enter, he never touched metaphysics, and though his worship of Nature has the emotional tone of religion, even of ecstasy, he was clearly disdainful of the established religions, and perpetually shocked “the timid friends of God.” By precept and by practice he proclaimed the lofty solitude of the individual soul, and he felt only contempt for the herd. We see how this temper became impressed on his face in his own drawing of himself in old age, with that intent and ruthless gaze wrapped in intellectual contemplation of the outspread world.Leonardo comes before us, indeed, in the end, as a figure for awe rather than for love. Yet, as the noblest type of the Overman we faintly try to conceive, Leonardo is the foe, not of man, but of the enemies of man. The great secrets that with clear vision his stern grip 125tore from Nature, the new instruments of power that his energy wrought, they were all for the use and delight of mankind. So Leonardo is the everlasting embodiment of that brooding human spirit whose task never dies. Still to-day it stands at the mouth of the gloomy cavern of Nature, even of Human Nature, with bent back and shaded eyes, seeking intently to penetrate the gloom beyond, with the fear of that threatening darkness, with the desire of what redeeming miracle it yet perchance may hold.VThat Leonardo da Vinci was not only supremely great in science, but the incarnation of the spirit of science, the artist and lover of Nature, is a fact it is well to bear in mind. Many mistakes would be avoided if it were more clearly present to consciousness. We should no longer find the artists in design absurdly chafing under what they considered the bondage of the artists in thought. It would no longer be possible, as it was some years ago, and may be still, for a narrow-minded pedagogue like Brunetière, however useful in his own field, to be greeted as a prophet when he fatuously proclaimed what he termed “the bankruptcy of science.” Unfortunately so many of the people who masquerade under the name of “men of science” have no sort of title to that name. They may be doing good and honest work by accumulating in little cells the facts which others, more truly inspired by the spirit of science, 126may one day work on; they may be doing more or less necessary work by the application to practical life of the discoveries which genuine men of science have made. But they themselves have just as much, and no more, claim to use the name of “science” as the men who make the pots and dishes piled up in a crockery shop have to use the name of “art.” They have not yet even learnt that “science” is not the accumulation of knowledge in the sense of piling up isolated facts, but the active organisation of knowledge, the application to the world of the cutting edge of a marvellously delicate instrument, and that this task is impossible without the widest range of vision and the most restless fertility of imagination.Of such more genuine men of science—to name one whom by virtue of several common interests I was sometimes privileged to come near—was Francis Galton. He was not a professional man of science; he was even willing that his love of science should be accounted simply a hobby. From the standpoint of the ordinary professional scientific man he was probably an amateur. He was not even, as some have been, a learned amateur. I doubt whether he had really mastered the literature of any subject, though I do not doubt that that mattered little. When he heard of 127some famous worker in a field he was exploring, he would look up that man’s work; so it was with Weismann in the field of heredity. And, as I would note with a smile in reading his letters, Galton was not able to spell Weismann’s name correctly. His attitude in science might be said to be pioneering much like that of the pioneers of museums in the later seventeenth and earlier eighteenth centuries, men like Tradescant and Ashmole and Evelyn and Sloane: an insatiable curiosity in things that were only just beginning, or had not yet begun, to arouse curiosity. So it was that when I made some personal experiments with the Mexican cactus, mescal (Anhalonium Lewinii), to explore its vision-producing qualities, then quite unknown in England, Galton was eagerly interested and wanted to experiment on himself, though ultimately dissuaded on account of his advanced age. But, on this basis, Galton’s curiosity was not the mere inquisitiveness of the child, it was coördinated with an almost uniquely organised brain as keen as it was well-balanced. So that on the one hand his curiosity was transformed into methods that were endlessly ingenious and inventive, and on the other it was guided and held in check by inflexible caution and good sense. And he knew how to preserve that exquisite balance without 128any solemnity or tension or self-assertion, but playfully and graciously, with the most unfailing modesty. It was this rare combination of qualities—one may see it all in his “Inquiries into Human Faculty”—which made him the very type of the man of genius, operating, not by profession or by deliberate training, but by natural function, throwing light on the dark places of the world and creating science in out-of-the-way fields of human experience which before had been left to caprice or not even perceived at all. Throughout he was an artist and if, as is reported, he spent the last year of his life chiefly in writing a novel, that was of a piece with the whole of his marvellous activity; he had never been doing anything else. Only his romances were real.Galton’s yet more famous cousin, Charles Darwin, presents in equal purity the lover and the artist in the sphere of Nature and Science. No doubt there were once many obtuse persons to whom these names seemed scarcely to fit when applied to Darwin. There have been people to whom Darwin scarcely seemed a man of genius, merely a dry laborious pedestrian student of facts. He himself even—as many people find it difficult to forget—once lamented his indifference to poetry and art. But Darwin was one of those elect persons in whose subconscious, if not in their conscious, nature is implanted the realisation that “science is poetry,” and in a field altogether remote from the poetry and art of convention he was alike 129poet and artist. Only a man so endowed could from a suggestion received on reading Malthus have conceived of natural selection as a chief moulding creative force of an infinite succession of living forms; so also of his fantastic theory of pangenesis. Even in trifling matters of experiment, such as setting a musician to play the bassoon in his greenhouse, to ascertain whether music affected plants, he had all the inventive imagination of poet or of artist. He was poet and artist—though I doubt if this has been pointed out—in his whole attitude towards Nature. He worked hard, but to him work was a kind of play, and it may well be that with his fragile health he could not have carried on his work if it had not been play. Again and again in his “Life and Letters” we find the description of his observations or experiments introduced by some such phrase as: “I was infinitely amused.” And he remarks of a biological problem that it was like a game of chess. I doubt, indeed, whether any great man of science was more of an artist than Darwin, more consciously aware that he was playing with the world, more deliciously thrilled by the fun of life. That man may well have found “poetry and art” dull who himself had created the theory of sexual selection which made the whole becoming of life art and the secret of it poetry.130It is not alone among biologists, from whose standpoint it may be judged easier to reach, since they are concerned with living Nature, that we find the attitude of the lover and the artist. We find it just as well marked when the man of genius plays in what some might think the arid field of the physicist. Faraday worked in a laboratory, a simple one, indeed, but the kind of place which might be supposed fatal to the true spirit of science, and without his researches in magnetic electricity we might have missed, with or without a pang, those most practical machines of our modern life, the dynamo and the telephone. Yet Faraday had no practical ends in view; it has been possible to say of him that he investigated Nature as a poet investigates the emotions. That would not have sufficed to make him the supreme man of science he was. His biographer, Dr. Bence Jones, who knew him well, concludes that Faraday’s first great characteristic was his trust in facts, and his second his imagination. There we are brought to the roots of his nature. Only, it is important to remember, these two characteristics were not separate and distinct. In themselves they may be opposing traits; it was because in Faraday they were held together in vital tension that he became so potent an instrument of research into Nature’s secrets. Tyndall, who was his friend and fellow worker, seems to have perceived this. “The force of his imagination,” wrote Tyndall, “was enormous,”—he “rose from the smallest beginnings to the greatest ends,” 131from “bubbles of oxygen and nitrogen to the atmospheric envelope of the earth itself,”—but “he bridled it like a mighty rider.” Faraday himself said to the same effect: “Let the imagination go, guarding it by judgment and principles, but holding it in and directing it by experiment.” Elsewhere he has remarked that in youth he was, and he might have added that he still remained, “a very lively imaginative person and could believe in the ‘Arabian Nights’ as easily as in the ‘Encyclopædia’.” But he soon acquired almost an instinct for testing facts by experiment, for distrusting such alleged facts as he had not so tested, and for accepting all the conclusions that he had thus reached with a complete indifference to commonly accepted beliefs. (It is true he was a faithful and devout elder in the Sandemanian Church, and that is not the least fascinating trait in this fascinating man.) Tyndall has insisted on both of these aspects of Faraday’s mental activity. He had “wonderful vivacity,” he was “a man of excitable and fiery nature,” and “underneath his sweetness was the heat of a volcano.” He himself believed that there was a Celtic strain in his heredity; there was a tradition that the family came from Ireland; I cannot find that there are any Faradays, or people of any name resembling Faraday, now in Ireland, but Tyndall, being himself an Irishman, liked to believe that the tradition was sound. It would only account for the emotionally vivacious side of this nature. There was also the other side, on which Tyndall 132also insists: the love of order, the extreme tenacity, the high self-discipline able to convert the fire within into a clear concentrated glow. In the fusion of these two qualities “he was a prophet,” says Tyndall, “and often wrought by an inspiration to be understood by sympathy alone.” His expansive emotional imagination became the servant of truth, and sprang into life at its touch. In carrying out physical experiments he would experience a childlike joy and his eyes sparkled. “Even to his latest days he would almost dance for joy at being shown a new experiment.” Silvanus Thompson, in his book on Faraday, insists (as Tyndall had) on the association with this childlike joy in imaginative extravagance of the perpetual impulse to test and to prove, “yet never hesitating to push to their logical conclusions the ideas suggested by experiment, however widely they might seem to lead from the accepted modes of thought.” His method was the method of the “Arabian Nights,” transferred to the region of facts.Faraday was not a mathematician. But if we turn to Kepler, who moved in the sphere of abstract calculation, we find precisely the same combination of characteristics. It was to Kepler, rather than to Copernicus, that we owe the establishment of the heliocentric theory of our universe, and Kepler, more than any man, was the precursor of Newton. It has been said that if Kepler had never lived it is difficult to conceive who could have taken his place and achieved his special 133part in the scientific creation of our universe. For that pioneering part was required a singular blend of seemingly opposed qualities. Only a wildly daring, original, and adventurous spirit could break away from the age-long traditions and rigid preconceptions which had ruled astronomy for thousands of years. Only an endlessly patient, careful, laborious, precise investigator could set up the new revolutionary conceptions needed to replace these traditions and preconceptions. Kepler supplied this rare combination of faculties. He possessed the most absurdly extravagant imagination; he developed a greater regard for accuracy in calculation than the world had ever known. He was willing to believe that the earth was a kind of animal, and would not have been surprised to find that it possessed lungs or gills. At the same time so set was he on securing the precise truth, so patiently laborious, that some of his most elaborate calculations were repeated, and without the help of logarithms, even seventy times. The two essential qualities that make the supreme artist in science have never been so clearly made manifest as in Kepler.Kepler may well bring us to Einstein, the greatest pioneer in the comprehension of the universe since his day, and, indeed, one who is more than a pioneer, since he already seems to have won a place beside Newton. It is a significant fact that Einstein, though he possesses an extremely cautious, critical mind, and is regarded as conspicuous for his common sense, has a 134profound admiration for Kepler, whom he frequently quotes. For Einstein also is an imaginative artist.Einstein is obviously an artist, even in appearance, as has often been noted by those who have met him; “he looks far more the musician than the man of science,” one writes, while those who know him well say that he is “essentially as much an artist as a discoverer.” As a matter of fact he is an artist in one of the most commonly recognised arts, being an accomplished musician, a good violinist, it is said, while improvisation on the piano, he himself says, is “a necessity of his life.” His face, we are told, is illumined when he listens to music; he loves Bach and Haydn and Mozart, Beethoven and Wagner much less, while to Chopin, Schumann, and the so-called romantics in music, as we might anticipate, he is indifferent. His love of music is inborn; it developed when, as a child, he would think out little songs “in praise of God,” and sing them by himself; music, Nature, and God began, even 135at that early age, to become a kind of unity to him. “Music,” said Leibnitz, “is the pleasure the human soul experiences from counting without being aware that it is counting.” It is the most abstract, the most nearly mathematical of the arts—we may recall how music and mathematics had their scientific origin together in the discovery of Pythagoras—and it is not surprising that it should be Einstein’s favorite art. It is even more natural that, next to music, he should be attracted to architecture—the art which Goethe called “frozen music”—for here we are actually plunged into mechanics, here statics and dynamics are transformed into visible beauty. To painting he is indifferent, but he is drawn to literature, although no great reader. In literature, indeed, it would seem that it is not so much art that he seeks as emotion; in this field it is no longer the austerely architectonic that draws him; thus he is not attracted to Ibsen; he is greatly attracted to Cervantes as well as Keller and Strindberg; he has a profound admiration for Shakespeare, but is cooler towards Goethe, while it would seem that there is no writer to whom he is more fervently attached than the most highly emotional, the most profoundly disintegrated in nervous organisation of all great writers, Dostoievsky, especially his masterpiece, “The Brothers Karamazov.” “Dostoievsky 136gives me more than any scientist, more than Gauss.” All literary analysis or æsthetic subtlety, it seems to Einstein, fails to penetrate to the heart of a work like “The Karamazovs,” it can only be grasped by the feelings. His face lights up when he speaks of it and he can find no word but “ethical satisfaction.” For ethics in the ordinary sense, as a system, means little to Einstein; he would not even include it in the sciences; it is the ethical joy embodied in art which satisfies him. Moreover, it is said, the keynote of Einstein’s emotional existence is the cry of Sophocles’ Antigone: “I am not here to hate with you, but to love with you.” The best that life has to offer, he feels, is a face glowing with happiness. He is an advanced democrat and pacifist rather than (as is sometimes supposed) a socialist; he believes in the internationality of all intellectual work and sees no reason why this should destroy national characteristics.Einstein is not—and this is the essential point to make clear—merely an artist in his moments of leisure and play, as a great statesman may play golf or a great soldier grow orchids. He retains the same attitude in the whole of his work. He traces science to its roots in emotion, which is exactly where art also is rooted. Of Max Planck, the physicist, for whom he has great admiration, Einstein has said: “The emotional condition which fits him for his task is akin to that of a devotee or a lover.” We may say the same, it would seem, of Einstein himself. He is not even to be included, 137as some might have supposed, in that rigid sect which asserts that all real science is precise measurement; he recognises that the biological sciences must be largely independent of mathematics. If mathematics were the only path of science, he once remarked, Nature would have been illegible for Goethe, who had a non-mathematical, even anti-mathematical, mind, and yet possessed a power of intuition greater than that of many an exact investigator. All great achievements in science, he holds, start from intuition. This he constantly repeats, although he adds that the intuition must not stand alone, for invention also is required. He is disposed to regard many scientific discoveries commonly regarded the work of pure thought as really works of art. He would have this view embodied in all education, making education a free and living process, with no drilling of the memory and no examinations, mainly a process of appeal to the senses in order to draw out delicate reactions. With his end, and even for the sake of acquiring ethical personality, he would have every child learn a handicraft, joinery, bookbinding, or other, and, like Élie Faure, he has great faith in 138the educational value of the cinema. We see that behind all Einstein’s activity lies the conception that the physicist’s work is to attain a picture, “a world-picture,” as he calls it. “I agree with Schopenhauer,” Einstein said at a celebration in honour of Planck in 1918, “that one of the most powerful motives that attract people to science and art is the longing to escape from everyday life with its painful coarseness and desolating bareness, and to break the fetters of their own ever-changing desires. It impels those of keener sensibility out of their personal existences into the world of objective perception and understanding. It is a motive force of like kind to that which drives the dweller in noisy confused cities to restful Alpine heights whence he seems to have an outlook on eternity. Associated with this negative motive is the positive motive which impels men to seek a simplified synoptic view of the world conformable to their own nature, overcoming the world by replacing it with this picture. The painter, the poet, the philosopher, the scientist, all do this, each in his own way.” Spengler has elaborately argued that there is a perfect identity of physics, mathematics, religion, and great art. We might fairly be allowed to point to Einstein as a lofty embodiment of that identity.Here, where we reach the sphere of mathematics, we are among processes which seem to some the most inhuman of all human activities and the most remote 139from poetry. Yet it is here that the artist has the fullest scope for his imagination. “Mathematics,” says Bertrand Russell in his “Mysticism and Logic,” “may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.” We are in the imaginative sphere of art, and the mathematician is engaged in a work of creation which resembles music in its orderliness, and is yet reproducing on another plane the order of the universe, and so becoming as it were a music of the spheres. It is not surprising that the greatest mathematicians have again and again appealed to the arts in order to find some analogy to their own work. They have indeed found it in the most various arts, in poetry, in painting, in sculpture, although it would certainly seem that it is in music, the most abstract of the arts, the art of number and of time, that we find the closest analogy. “The mathematician’s best work is art,” said Mittag-Lefler, “a high and perfect art, as daring as the most secret dreams of imagination, clear and limpid. Mathematical genius and artistic genius touch each other.” And Sylvester wrote in his “Theory of Reciprocants”: “Does it not seem as if Algebra had attained to the dignity of a fine art, in which the workman has a free hand to develop his conceptions, as in a musical theme or a subject for painting? It has reached a point in which every properly developed algebraical composition, like a skilful landscape, is expected to suggest the notion of an infinite distance lying beyond the limits 140of the canvas.” “Mathematics, rightly viewed,” says Bertrand Russell again, “possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture.... The true spirit of delight, the exaltation, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.”The mathematician has reached the highest rung on the ladder of human thought. But it is the same ladder which we have all of us been always ascending, alike from the infancy of the individual and the infancy of the race. Molière’s Jourdain had been speaking prose for more than forty years without knowing it. Mankind has been thinking poetry throughout its long career and remained equally ignorant.

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