IV
The task of world-knowing—for the man of the higher Cultures a need, seen as a duty, of expressing his own essence—is certainly in every case the same, though its process may be called science or philosophy, and though its affinity to artistic creation and to faith-intuition may for one be something felt and for another something questionable. It is to present, without accretions, that form of the world-picture which to the individual in each case is proper and significant, and for him (so long as he does not compare) is in fact “the” world.
The task is necessarily a double one, in view of the distinction between “Nature” and “History.” Each speaks its own form-language which differs utterly from that of the other, and however the two may overlap and confuse one another in an unsifted and ambiguous world-picture such as that of everyday life, they are incapable of any inner unity.
Direction and Extension are the outstanding characters which differentiate the historical and the scientific (naturhaft) kind of impressibility, and it is totally impossible for a man to have both working creatively within him at the same time. The double meaning of the German word “Ferne” (distance, farness) is illuminating. In the one order of ideas it implies futurity, in the other a spatial interval of standing apart, and the reader will not fail to remark that the historical materialist almost necessarily conceives time as a mathematical dimension, while for the born artist, on the contrary,—as the lyrics of every land show us—the distance-impressions made by deep landscapes, clouds, horizon and setting sun attach themselves without an effort to the sense of a future. The Greek poet denies the future, and consequently he neither sees nor sings of the things of the future; he cleaves to the near, as he belongs to the present, entirely.
The natural-science investigator, the productive reasoner in the full sense of the word, whether he be an experimenter like Faraday, a theorist like Galileo, a calculator like Newton, finds in his world only directionless quantities which he measures, tests and arranges. It is only the quantitative that is capable of being grasped through figures, of being causally defined, of being captured in a law or formula, and when it has achieved this, pure nature-knowledge has shot its bolt. All its laws are quantitative connexions, or as the physicist puts it, all physical processes run a course in space, an expression which a Greek physicist would have corrected—without altering the fact—into “all physical processes occur between bodies” conformably to the space-denying feeling of the Classical soul.
The historical kind of impression-process is alien to everything quantitative, and affects a different organ. To World-as-Nature certain modes of apprehension, as to World-as-History certain other modes, are proper. We know them and use them every day, without (as yet) having become aware of their opposition. There is nature-knowledge and there is man-knowledge; there is scientific experience and there is vital experience. Let the reader track down this contrast into his own inmost being, and he will understand what I mean.
All modes of comprehending the world may, in the last analysis, be described as Morphology. The Morphology of the mechanical and the extended, a science which discovers and orders nature-laws and causal relations, is called Systematic. The Morphology of the organic, of history and life and all that bears the sign of direction and destiny, is called Physiognomic.
V
In the West, the Systematic mode of treating the world reached and passed its culminating-point during the last century, while the great days of Physiognomic have still to come. In a hundred years all sciences that are still possible on this soil will be parts of a single vast Physiognomic of all things human. This is what the “Morphology of World-History” means. In every science, and in the aim no less than in the content of it, man tells the story of himself. Scientific experience is spiritual self-knowledge. It is from this standpoint, as a chapter of Physiognomic, that we have just treated of mathematics. We were not concerned with what this or that mathematician intended, nor with the savant as such or his results as a contribution to an aggregate of knowledge, but with the mathematician as a human being, with his work as a part of the phenomenon of himself, with his knowledge and purposes as a part of his expression. This alone is of importance to us here. He is the mouthpiece of a Culture which tells us about itself through him, and he belongs, as personality, as soul, as discoverer, thinker and creator, to the physiognomy of that Culture.
Every mathematic, in that it brings out and makes visible to all the idea of number that is proper to itself and inborn in its conscious being, is, whether the expression-form be a scientific system or (as in the case of Egypt) an architecture, the confession of a Soul. If it is true that the intentional accomplishments of a mathematic belong only to the surface of history, it is equally true that its unconscious element, its number-as-such, and the style in which it builds up its self-contained cosmos of forms are an expression of its existence, its blood. Its life-history of ripening and withering, its deep relation to the creative acts, the myths and the cults of the same Culture—such things are the subject-matter of a second or historical morphology, though the possibility of such a morphology is hardly yet admitted.