Rembrandt’s paintings and again the dark tone-worlds of Beethoven’s quartets; in the regular polyhedrons of Euclid, the Parthenon sculptures and the pyramids of Old Egypt, the Nirvana of Buddha, the aloofness of court-customs under Sesostris, Justinian I and Louis XIV, in the God- idea of an Æschylus, a Plotinus, a Dante; and in the world-embracing spatial energy of modern technics. ----- Footnote 66: That is, “it is impossible to part a cube into two cubes, a biquadrate into two biquadrates, and generally any power above the square into two powers having the same exponent.” Fermat claimed to possess a proof of the proposition, but this has not been preserved, and no general proof has hitherto been obtained.—_Tr._ Footnote 67: Thus Bishop Berkeley’s _Discourse addressed to an infidel mathematician_ (1735) shrewdly asked whether the mathematician were in a position to criticize the divine for proceeding on the basis of faith.—_Tr._ Footnote 68: From the savage conjuror with his naming-magic to the modern scientist who subjects things by attaching technical labels to them, the form has in no wise changed. See Vol. II, pp. 116 et seq., 322 et seq. Footnote 69: See Vol. II, pp. 137 et seq. ----- XII To return to mathematics. In the Classical world the starting-point of every formative act was, as we have seen, the ordering of the “become,” in so far as this was present, visible, measurable and numerable. The Western, Gothic, form-feeling on the contrary is that of an unrestrained, strong-willed far-ranging soul, and its chosen badge is pure, imperceptible, unlimited space. But we must not be led into regarding such symbols as unconditional. On the contrary, they are strictly conditional, though apt to be taken as having identical essence and validity. Our universe of infinite space, whose existence, for us, goes without saying, simply does not exist for Classical man. It is not even capable of being presented to him. On the other hand, the Hellenic cosmos, which is (as we might have discovered long ago) entirely foreign to our way of thinking, was for the Hellene something self-evident. The fact is that the infinite space of our physics is a form of very numerous and extremely complicated elements tacitly assumed, which have come into being only as the copy and expression of _our_ soul, and are actual, necessary and natural only for _our_ type of waking life. The simple notions are always the most difficult. They are simple, in that they comprise a vast deal that not only is incapable of being exhibited in words but does not even need to be stated, because _for men of the particular group_ it is anchored in the intuition; and they are difficult because for all alien men their real content is _ipso facto_ quite inaccessible. Such a notion, at once simple and difficult, is our specifically Western meaning of the word “space.” The whole of our