thinking “as the art of spending good words in babble” (die Kunst, wortreich zu schwatzen), and why even to-day the lecture-room philosopher has not a word to say about Goethe’s philosophy. Every logical operation is capable of being _drawn_, every system a _geometrical_ method of handling thoughts. And therefore Time either finds no place in the system at all, or is made its victim. This is the refutation of that widely-spread misunderstanding which connects time with arithmetic and space with geometry by superficial analogies, an error to which Kant ought never to have succumbed—though it is hardly surprising that Schopenhauer, with his incapacity for understanding mathematics, did so. Because the living act of numbering is somehow or other related to time, number and time are constantly confused. But numbering is not number, any more than drawing is a drawing. Numbering and drawing are a becoming, numbers and figures are things become. Kant and the rest have in mind now the living act (numbering) and now the result thereof (the relations of the finished figure); but the one belongs to the domain of Life and Time, the other to that of Extension and Causality. _That_ I calculate is the business of organic, _what_ I calculate the business of inorganic, logic. Mathematics as a whole—in common language, arithmetic and geometry— answers the _How?_ and the _What?_—that is, the problem of the Natural order of things. In opposition to this problem stands that of the _When?_ of things, the specifically historical problem of destiny, future and past; and all these things are comprised in the word _Chronology_, which simple mankind understands fully and unequivocally. Between arithmetic and geometry there is no opposition.[112] Every kind of number, as has been sufficiently shown in an earlier chapter, belongs entirely to the realm of the extended and the become, whether as a Euclidean magnitude or as an analytical function; and to which heading should we have to assign the cyclometric[113] functions, the Binomial Theorem, the Riemann surfaces, the Theory of Groups? Kant’s scheme was refuted by Euler and d’Alembert before he even set it up, and only the unfamiliarity of his successors with the mathematics of their time—what a contrast to Descartes, Pascal and Leibniz, who evolved the mathematics of _their_ time from the depths of their own philosophy!—made it possible for mathematical notions of a relation between time and arithmetic to be passed on like an heirloom, almost uncriticized.