[172]. Which, inasmuch as it has been detached from time, is able to employ mathematical symbols. These rigid figures signify for us a destiny of yore. But their meaning is other than mathematical. Past is not a cause, nor Fate a formula, and to anyone who handles them, as the historical materialist handles them, mathematically, the past event as such, as an actuality that has lived once and only once, is invisible.
[173]. That is, not merely conclusions of peaces or deathdays of persons, but the Renaissance style, the Polis, the Mexican Culture and so forth—are dates or data, facts that have been, even when we possess no representation of them.
[174]. See Vol. II, pp. 403 et seq., 589 et seq.
[175]. The formation of hypotheses in Chemistry is much more thoughtless, owing to the less close relation of that science to mathematics. A house of cards such as is presented to us in the researches of the moment on atom-structure (see, for example, M. Born, Der Aufbau der Materie, 1920) would be impossible in the near neighbourhood of the electro-magnetic theory of light, whose authors never for a moment lost sight of the frontier between mathematical vision and its representation by a picture, or of the fact that this was only a picture.
[176]. There is no difference essentially between these representations and the switchboard wiring-diagram.
[177]. Goethe’s theory of colour openly controverted Newton’s theory of light. A long account of the controversy will be found in Chapter IX of G. H. Lewes’s Life of Goethe—a work that, taken all in all, is one of the wisest biographies ever written. In reading his critique of Goethe’s theory, of course, it has to be borne in mind that he wrote before the modern development of the electro-magnetic theory, which has substituted a merely mathematical existence for the Newtonian physical existence of colour-rays as such in white light. Now, this physical existence was just what, in substance, Goethe denied. What he affirmed, in the simpler language of his day, was that white light was something simple and colourless that becomes coloured through diminutions or modifications imposed upon it by “darkness.” The modern physicist, using a subtler hypothesis than Newton’s and a more refined “balance” than that which Lewes reproaches Goethe for “flinging away,” has found in white light, not the Newtonian mixture of colour-rays, but a surge of irregular wave-trains which are only regularized into colour-vibrations through being acted upon by analysers of one sort and another, from prisms to particulate matter. This necessity of a counter-agent for the production of colour seems—to a critical outsider at any rate—very like the necessity of an efficient negative principle or “opaque” that Goethe’s intuitive interpretation of his experiments led him to postulate. It is this that is the heart of the theory, and not the “simplicity” of light per se.
So much it seems desirable to add to the text and the reference, in order to expand the author’s statement that “both were right.” For Lewes, with all his sympathetic penetration of the man and real appreciation of his scientific achievement, feels obliged to regard his methods and his theory as such as “erroneous.” And it is perhaps not out of place in this book to adduce an instance of the peculiar nature and power of intuitive vision (which entirely escapes direct description) in which Vision frankly challenges Reason on its own ground, meets with refutation (or contempt) from the Reason of its day, and yet may come to be upheld in its specific rightness (its rightness as vision, that is, apart from its technical enunciation by the seer) by the Reason of a later day.—Tr.
[180]. The word dimension ought only to be used in the singular. It means extension but not extensions. The idea of the three directions is an out-and-out abstraction and is not contained in the immediate extension-feeling of the body (the “soul”). Direction as such, the direction-essence, gives rise to the mysterious animal sense of right and left and also the vegetable characteristic of below-to-above, earth to heaven. The latter is a fact felt dream-wise, the former a truth of waking existence to be learned and therefore capable of being transmuted. Both find expression in architecture, to wit, in the symmetry of the plan and the energy of the elevation, and it is only because of this that we specially distinguish in the “architecture” of the space around us the angle of 90° in preference, for example, to that of 60°. Had not this been so, the conventional number of our “dimensions” would have been quite different.