It remains still to mention the corresponding difference, which is very deep and has never yet been properly appreciated, between Classical and modern mathematics. The former conceived of things _as they are_, as _magnitudes_, timeless and purely present, and so it proceeded to Euclidean geometry and mathematical statics, rounding off its intellectual system with the theory of conic sections. We conceive things as they _become_ and _behave_, as _function_, and this brought us to dynamics, analytical geometry and thence to the Differential Calculus.[9] The modern theory of functions is the imposing marshalling of this whole mass of thought. It is a bizarre, but nevertheless psychologically exact, fact that the physics of the Greeks—being statics and not dynamics—neither knew the use nor felt the absence of the time- element, whereas we on the other hand work in thousandths of a second. The one and only evolution-idea that is timeless, ahistoric, is Aristotle’s entelechy. This, then, is our task. We men of the Western Culture are, with our historical sense, an exception and not a rule. World-history is _our_ world picture and not all mankind’s. Indian and Classical man formed no image of a world in progress, and perhaps when in due course the civilization of the West is extinguished, there will never again be a Culture and a human type in which “world-history” is so potent a form of the waking consciousness. ----- Footnote 7: From Homer to the tragedies of Seneca, a full thousand years, the same handful of myth-figures (Thyestes, Clytæmnestra, Heracles and the like) appear time after time without alteration, whereas in the poetry of the West, Faustian Man figures, first as Parzeval or Tristan, then (modified always into harmony with the epoch) as Hamlet, Don Quixote, Don Juan, and eventually Faust or Werther, and now as the hero of the modern world-city romance, but is always presented in the atmosphere and under the conditions of a particular century. Footnote 8: It was about 1000 A.D. and therefore contemporaneously with the beginning of the Romanesque style and the Crusades—the first symptoms of a new Soul—that Abbot Gerbert (Pope Sylvester II), the friend of the Emperor Otto III, invented the mechanism of the chiming wheel- clock. In Germany too, the first tower-clocks made their appearance, about 1200, and the pocket watch somewhat later. Observe the significant association of time measurement with the edifices of religion. Footnote 9: Newton’s choice of the name “fluxions” for his calculus was meant to imply a standpoint towards certain metaphysical notions as to the nature of time. In Greek mathematics time figures not at all. ----- VI