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
