The Grammar of Science (1903)

Of all the travels made by man since the voyages of Dante, this new exploration along the shores of Multiplicity and Complexity promised to be the longest, though as yet it had barely touched two familiar regions⁠—race and sex. Even within these narrow seas the navigator lost his bearings and followed the winds as they blew. By chance it happened that Raphael Pumpelly helped the winds; for, being in Washington on his way to Central Asia he fell to talking with Adams about these matters, and said that Willard Gibbs thought he got most help from a book called the Grammar of Science, by Karl Pearson. To Adams’s vision, Willard Gibbs stood on the same plane with the three or four greatest minds of his century, and the idea that a man so incomparably superior should find help anywhere filled him with wonder. He sent for the volume and read it. From the time he sailed for Europe and reached his den on the Avenue du Bois until he took his return steamer at Cherbourg on December 26, he did little but try to find out what Karl Pearson could have taught Willard Gibbs.

Here came in, more than ever, the fatal handicap of ignorance in mathematics. Not so much the actual tool was needed, as the right to judge the product of the tool. Ignorant as one was of the finer values of French or German, and often deceived by the intricacies of thought hidden in the muddiness of the medium, one could sometimes catch a tendency to intelligible meaning even in Kant or Hegel; but one had not the right to a suspicion of error where the tool of thought was algebra. Adams could see in such parts of the Grammar as he could understand, little more than an enlargement of Stallo’s book already twenty years old. He never found out what it could have taught a master like Willard Gibbs. Yet the book had a historical value out of all proportion to its science. No such stride had any Englishman before taken in the lines of English thought. The progress of science was measured by the success of the Grammar, when, for twenty years past, Stallo had been deliberately ignored under the usual conspiracy of silence inevitable to all thought which demands new thought-machinery. Science needs time to reconstruct its instruments, to follow a revolution in space; a certain lag is inevitable; the most active mind cannot instantly swerve from its path; but such revolutions are portentous, and the fall or rise of half-a-dozen empires interested a student of history less than the rise of the Grammar of Science, the more pressingly because, under the silent influence of Langley, he was prepared to expect it.

For a number of years Langley had published in his Smithsonian Reports the revolutionary papers that foretold the overthrow of nineteenth-century dogma, and among the first was the famous address of Sir William Crookes on psychical research, followed by a series of papers on Roentgen and Curie, which had steadily driven the scientific lawgivers of Unity into the open; but Karl Pearson was the first to pen them up for slaughter in the schools. The phrase is not stronger than that with which the Grammar of Science challenged the fight: “Anything more hopelessly illogical than the statements with regard to Force and Matter current in elementary textbooks of science, it is difficult to imagine,” opened Mr. Pearson, and the responsible author of the “elementary textbook,” as he went on to explain, was Lord Kelvin himself. Pearson shut out of science everything which the nineteenth century had brought into it. He told his scholars that they must put up with a fraction of the universe, and a very small fraction at that⁠—the circle reached by the senses, where sequence could be taken for granted⁠—much as the deep-sea fish takes for granted the circle of light which he generates. “Order and reason, beauty and benevolence, are characteristics and conceptions which we find solely associated with the mind of man.” The assertion, as a broad truth, left one’s mind in some doubt of its bearing, for order and beauty seemed to be associated also in the mind of a crystal, if one’s senses were to be admitted as judge; but the historian had no interest in the universal truth of Pearson’s or Kelvin’s or Newton’s laws; he sought only their relative drift or direction, and Pearson went on to say that these conceptions must stop: “Into the chaos beyond sense-impressions we cannot scientifically project them.” We cannot even infer them: “In the chaos behind sensations, in the ‘beyond’ of sense-impressions, we cannot infer necessity, order or routine, for these are concepts formed by the mind of man on this side of sense-impressions”; but we must infer chaos: “Briefly chaos is all that science can logically assert of the supersensuous.” The kinetic theory of gas is an assertion of ultimate chaos. In plain words, Chaos was the law of nature; Order was the dream of man.

No one means all he says, and yet very few say all they mean, for words are slippery and thought is viscous; but since Bacon and Newton, English thought had gone on impatiently protesting that no one must try to know the unknowable at the same time that everyone went on thinking about it. The result was as chaotic as kinetic gas; but with the thought a historian had nothing to do. He sought only its direction. For himself he knew, that, in spite of all the Englishmen that ever lived, he would be forced to enter supersensual chaos if he meant to find out what became of British science⁠—or indeed of any other science. From Pythagoras to Herbert Spencer, everyone had done it, although commonly science had explored an ocean which it preferred to regard as Unity or a Universe, and called Order. Even Hegel, who taught that every notion included its own negation, used the negation only to reach a “larger synthesis,” till he reached the universal which thinks itself, contradiction and all. The Church alone had constantly protested that anarchy was not order, that Satan was not God, that pantheism was worse than atheism, and that Unity could not be proved as a contradiction. Karl Pearson seemed to agree with the Church, but everyone else, including Newton, Darwin and Clerk Maxwell, had sailed gaily into the supersensual, calling it:⁠—

“One God, one Law, one Element,
And one far-off, divine event,
To which the whole creation moves.”

Suddenly, in 1900, science raised its head and denied.

Yet, perhaps, after all, the change had not been so sudden as it seemed. Real and actual, it certainly was, and every newspaper betrayed it, but sequence could scarcely be denied by one who had watched its steady approach, thinking the change far more interesting to history than the thought. When he reflected about it, he recalled that the flow of tide had shown itself at least twenty years before; that it had become marked as early as 1893; and that the man of science must have been sleepy indeed who did not jump from his chair like a scared dog when, in 1898, Mme. Curie threw on his desk the metaphysical bomb she called radium. There remained no hole to hide in. Even metaphysics swept back over science with the green water of the deep-sea ocean and no one could longer hope to bar out the unknowable, for the unknowable was known.

The fact was admitted that the uniformitarians of one’s youth had wound about their universe a tangle of contradictions meant only for temporary support to be merged in “larger synthesis,” and had waited for the larger synthesis in silence and in vain. They had refused to hear Stallo. They had betrayed little interest in Crookes. At last their universe had been wrecked by rays, and Karl Pearson undertook to cut the wreck loose with an axe, leaving science adrift on a sensual raft in the midst of a supersensual chaos. The confusion seemed, to a mere passenger, worse than that of 1600 when the astronomers upset the world; it resembled rather the convulsion of 310 when the Civitas Dei cut itself loose from the Civitas Romae, and the Cross took the place of the legions; but the historian accepted it all alike; he knew that his opinion was worthless; only, in this case, he found himself on the raft, personally and economically concerned in its drift.

English thought had always been chaos and multiplicity itself, in which the new step of Karl Pearson marked only a consistent progress; but German thought had affected system, unity, and abstract truth, to a point that fretted the most patient foreigner, and to Germany the voyager in strange seas of thought alone might resort with confident hope of renewing his youth. Turning his back on Karl Pearson and England, he plunged into Germany, and had scarcely crossed the Rhine when he fell into libraries of new works bearing the names of Ostwald, Ernst Mach, Ernst Haeckel, and others less familiar, among whom Haeckel was easiest to approach, not only because of being the oldest and clearest and steadiest spokesman of nineteenth-century mechanical convictions, but also because in 1902 he had published a vehement renewal of his faith. The volume contained only one paragraph that concerned a historian; it was that in which Haeckel sank his voice almost to a religious whisper in avowing with evident effort, that the “proper essence of substance appeared to him more and more marvellous and enigmatic as he penetrated further into the knowledge of its attributes⁠—matter and energy⁠—and as he learned to know their innumerable phenomena and their evolution.” Since Haeckel seemed to have begun the voyage into multiplicity that Pearson had forbidden to Englishmen, he should have been a safe pilot to the point, at least, of a “proper essence of substance” in its attributes of matter and energy: but Ernst Mach seemed to go yet one step further, for he rejected matter altogether, and admitted but two processes in nature⁠—change of place and interconversion of forms. Matter was Motion⁠—Motion was Matter⁠—the thing moved.

A student of history had no need to understand these scientific ideas of very great men; he sought only the relation with the ideas of their grandfathers, and their common direction towards the ideas of their grandsons. He had long ago reached, with Hegel, the limits of contradiction; and Ernst Mach scarcely added a shade of variety to the identity of opposites; but both of them seemed to be in agreement with Karl Pearson on the facts of the supersensual universe which could be known only as unknowable.

With a deep sigh of relief, the traveller turned back to France. There he felt safe. No Frenchman except Rabelais and Montaigne had ever taught anarchy other than as path to order. Chaos would be unity in Paris even if child of the guillotine. To make this assurance mathematically sure, the highest scientific authority in France was a great mathematician, M. Poincaré of the Institut, who published in 1902 a small volume called La Science et l’Hypothèse, which purported to be relatively readable. Trusting to its external appearance, the traveller timidly bought it, and greedily devoured it, without understanding a single consecutive page, but catching here and there a period that startled him to the depths of his ignorance, for they seemed to show that M. Poincaré was troubled by the same historical landmarks which guided or deluded Adams himself: “[In science] we are led,” said M. Poincaré, “to act as though a simple law, when other things were equal, must be more probable than a complicated law. Half a century ago one frankly confessed it, and proclaimed that nature loves simplicity. She has since given us too often the lie. Today this tendency is no longer avowed, and only as much of it is preserved as is indispensable so that science shall not become impossible.”

Here at last was a fixed point beyond the chance of confusion with self-suggestion. History and mathematics agreed. Had M. Poincaré shown anarchistic tastes, his evidence would have weighed less heavily; but he seemed to be the only authority in science who felt what a historian felt so strongly⁠—the need of unity in a universe. “Considering everything we have made some approach towards unity. We have not gone as fast as we hoped fifty years ago; we have not always taken the intended road; but definitely we have gained much ground.” This was the most clear and convincing evidence of progress yet offered to the navigator of ignorance; but suddenly he fell on another view which seemed to him quite irreconcilable with the first: “Doubtless if our means of investigation should become more and more penetrating, we should discover the simple under the complex; then the complex under the simple; then anew the simple under the complex; and so on without ever being able to foresee the last term.”

A mathematical paradise of endless displacement promised eternal bliss to the mathematician, but turned the historian green with horror. Made miserable by the thought that he knew no mathematics, he burned to ask whether M. Poincaré knew any history, since he began by begging the historical question altogether, and assuming that the past showed alternating phases of simple and complex⁠—the precise point that Adams, after fifty years of effort, found himself forced to surrender; and then going on to assume alternating phases for the future which, for the weary Titan of Unity, differed in nothing essential from the kinetic theory of a perfect gas.

Since monkeys first began to chatter in trees, neither man nor beast had ever denied or doubted Multiplicity, Diversity, Complexity, Anarchy, Chaos. Always and everywhere the Complex had been true and the Contradiction had been certain. Thought started by it. Mathematics itself began by counting one⁠—two⁠—three; then imagining their continuity, which M. Poincaré was still exhausting his wits to explain or defend; and this was his explanation: “In short, the mind has the faculty of creating symbols, and it is thus that it has constructed mathematical continuity which is only a particular system of symbols.” With the same light touch, more destructive in its artistic measure than the heaviest-handed brutality of Englishmen or Germans, he went on to upset relative truth itself: “How should I answer the question whether Euclidian Geometry is true? It has no sense!⁠ ⁠… Euclidian Geometry is, and will remain, the most convenient.”

Chaos was a primary fact even in Paris⁠—especially in Paris⁠—as it was in the Book of Genesis; but every thinking being in Paris or out of it had exhausted thought in the effort to prove Unity, Continuity, Purpose, Order, Law, Truth, the Universe, God, after having begun by taking it for granted, and discovering, to their profound dismay, that some minds denied it. The direction of mind, as a single force of nature, had been constant since history began. Its own unity had created a universe the essence of which was abstract Truth; the Absolute; God! To Thomas Aquinas, the universe was still a person; to Spinoza, a substance; to Kant, Truth was the essence of the “I”; an innate conviction; a categorical imperative; to Poincaré, it was a convenience; and to Karl Pearson, a medium of exchange.

The historian never stopped repeating to himself that he knew nothing about it; that he was a mere instrument of measure, a barometer, pedometer, radiometer; and that his whole share in the matter was restricted to the measurement of thought-motion as marked by the accepted thinkers. He took their facts for granted. He knew no more than a firefly about rays⁠—or about race⁠—or sex⁠—or ennui⁠—or a bar of music⁠—or a pang of love⁠—or a grain of musk⁠—or of phosphorus⁠—or conscience⁠—or duty⁠—or the force of Euclidian geometry⁠—or non-Euclidian⁠—or heat⁠—or light⁠—or osmosis⁠—or electrolysis⁠—or the magnet⁠—or ether⁠—or vis inertiae⁠—or gravitation⁠—or cohesion⁠—or elasticity⁠—or surface tension⁠—or capillary attraction⁠—or Brownian motion⁠—or of some scores, or thousands, or millions of chemical attractions, repulsions or indifferences which were busy within and without him; or, in brief, of Force itself, which, he was credibly informed, bore some dozen definitions in the textbooks, mostly contradictory, and all, as he was assured, beyond his intelligence; but summed up in the dictum of the last and highest science, that Motion seems to be Matter and Matter seems to be Motion, yet “we are probably incapable of discovering” what either is. History had no need to ask what either might be; all it needed to know was the admission of ignorance; the mere fact of multiplicity baffling science. Even as to the fact, science disputed, but radium happened to radiate something that seemed to explode the scientific magazine, bringing thought, for the time, to a standstill; though, in the line of thought-movement in history, radium was merely the next position, familiar and inexplicable since Zeno and his arrow: continuous from the beginning of time, and discontinuous at each successive point. History set it down on the record⁠—pricked its position on the chart⁠—and waited to be led, or misled, once more.

The historian must not try to know what is truth, if he values his honesty; for, if he cares for his truths, he is certain to falsify his facts. The laws of history only repeat the lines of force or thought. Yet though his will be iron, he cannot help now and then resuming his humanity or simianity in face of a fear. The motion of thought had the same value as the motion of a cannonball seen approaching the observer on a direct line through the air. One could watch its curve for five thousand years. Its first violent acceleration in historical times had ended in the catastrophe of 310. The next swerve of direction occurred towards 1500. Galileo and Bacon gave a still newer curve to it, which altered its values; but all these changes had never altered the continuity. Only in 1900, the continuity snapped.

Vaguely conscious of the cataclysm, the world sometimes dated it from 1893, by the Roentgen rays, or from 1898, by the Curie’s radium; but in 1904, Arthur Balfour announced on the part of British science that the human race without exception had lived and died in a world of illusion until the last year of the century. The date was convenient, and convenience was truth.

The child born in 1900 would, then, be born into a new world which would not be a unity but a multiple. Adams tried to imagine it, and an education that would fit it. He found himself in a land where no one had ever penetrated before; where order was an accidental relation obnoxious to nature; artificial compulsion imposed on motion; against which every free energy of the universe revolted; and which, being merely occasional, resolved itself back into anarchy at last. He could not deny that the law of the new multiverse explained much that had been most obscure, especially the persistently fiendish treatment of man by man; the perpetual effort of society to establish law, and the perpetual revolt of society against the law it had established; the perpetual building up of authority by force, and the perpetual appeal to force to overthrow it; the perpetual symbolism of a higher law, and the perpetual relapse to a lower one; the perpetual victory of the principles of freedom, and their perpetual conversion into principles of power; but the staggering problem was the outlook ahead into the despotism of artificial order which nature abhorred. The physicists had a phrase for it, unintelligible to the vulgar: “All that we win is a battle⁠—lost in advance⁠—with the irreversible phenomena in the background of nature.”

All that a historian won was a vehement wish to escape. He saw his education complete; and was sorry he ever began it. As a matter of taste, he greatly preferred his eighteenth-century education when God was a father and nature a mother, and all was for the best in a scientific universe. He repudiated all share in the world as it was to be, and yet he could not detect the point where his responsibility began or ended.

As history unveiled itself in the new order, man’s mind had behaved like a young pearl oyster, secreting its universe to suit its conditions until it had built up a shell of nacre that embodied all its notions of the perfect. Man knew it was true because he made it, and he loved it for the same reason. He sacrificed millions of lives to acquire his unity, but he achieved it, and justly thought it a work of art. The woman especially did great things, creating her deities on a higher level than the male, and, in the end, compelling the man to accept the Virgin as guardian of the man’s God. The man’s part in his Universe was secondary, but the woman was at home there, and sacrificed herself without limit to make it habitable, when man permitted it, as sometimes happened for brief intervals of war and famine; but she could not provide protection against forces of nature. She did not think of her universe as a raft to which the limpets stuck for life in the surge of a supersensual chaos; she conceived herself and her family as the centre and flower of an ordered universe which she knew to be unity because she had made it after the image of her own fecundity; and this creation of hers was surrounded by beauties and perfections which she knew to be real because she herself had imagined them.

Even the masculine philosopher admired and loved and celebrated her triumph, and the greatest of them sang it in the noblest of his verses:⁠—

“Alma Venus, coeli subter labentia signa
Quae mare navigerum, quae terras frugiferenteis
Concelebras⁠ ⁠…

Quae quondam rerum naturam sola gubernas,
Nec sine te quidquam dias in luminis oras
Exoritur, neque fit laetum neque amabile quidquam;
Te sociam studeo!”

Neither man nor woman ever wanted to quit this Eden of their own invention, and could no more have done it of their own accord than the pearl oyster could quit its shell; but although the oyster might perhaps assimilate or embalm a grain of sand forced into its aperture, it could only perish in face of the cyclonic hurricane or the volcanic upheaval of its bed. Her supersensual chaos killed her.

Such seemed the theory of history to be imposed by science on the generation born after 1900. For this theory, Adams felt himself in no way responsible. Even as historian he had made it his duty always to speak with respect of everything that had ever been thought respectable⁠—except an occasional statesman; but he had submitted to force all his life, and he meant to accept it for the future as for the past. All his efforts had been turned only to the search for its channel. He never invented his facts; they were furnished him by the only authorities he could find. As for himself, according to Helmholz, Ernst Mach, and Arthur Balfour, he was henceforth to be a conscious ball of vibrating motions, traversed in every direction by infinite lines of rotation or vibration, rolling at the feet of the Virgin at Chartres or of M. Poincaré in an attic at Paris, a centre of supersensual chaos. The discovery did not distress him. A solitary man of sixty-five years or more, alone in a Gothic cathedral or a Paris apartment, need fret himself little about a few illusions more or less. He should have learned his lesson fifty years earlier; the times had long passed when a student could stop before chaos or order; he had no choice but to march with his world.

Nevertheless, he could not pretend that his mind felt flattered by this scientific outlook. Every fabulist has told how the human mind has always struggled like a frightened bird to escape the chaos which caged it; how⁠—appearing suddenly and inexplicably out of some unknown and unimaginable void; passing half its known life in the mental chaos of sleep; victim even when awake, to its own ill-adjustment, to disease, to age, to external suggestion, to nature’s compulsion; doubting its sensations, and, in the last resort, trusting only to instruments and averages⁠—after sixty or seventy years of growing astonishment, the mind wakes to find itself looking blankly into the void of death. That it should profess itself pleased by this performance was all that the highest rules of good breeding could ask; but that it should actually be satisfied would prove that it existed only as idiocy.

Satisfied, the future generation could scarcely think itself, for even when the mind existed in a universe of its own creation, it had never been quite at ease. As far as one ventured to interpret actual science, the mind had thus far adjusted itself by an infinite series of infinitely delicate adjustments forced on it by the infinite motion of an infinite chaos of motion; dragged at one moment into the unknowable and unthinkable, then trying to scramble back within its senses and to bar the chaos out, but always assimilating bits of it, until at last, in 1900, a new avalanche of unknown forces had fallen on it, which required new mental powers to control. If this view was correct, the mind could gain nothing by flight or by fight; it must merge in its supersensual multiverse, or succumb to it.