V
That 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, may 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.”[[47]] 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 some 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.[[48]] 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 any 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 poet 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.[[49]]
It 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,” from “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 also 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 part 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 profound admiration for Kepler, whom he frequently quotes. For Einstein also is an imaginative artist.[[50]]
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 at 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.[[51]] 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 gives 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, as 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.[[52]] 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,[[53]] he has great faith in the 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.[[54]] 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 from 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 of 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.