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490 The decisive event, however, was the invention — "contemporary" with that of the Classical coin about 650 — of double-entry book-keeping by Fra Luca Pacioli in 1494. Goethe calls this in Wilhelm Meister "one of the finest discoveries of the human intellect," and indeed its author may without hesitation be ranked with his contemporaries Columbus and Copernicus. To the Normans we owe our modes of reckoning and to the Lombards our book-keeping. These, be it observed, were the same two Germanic stocks which created the two most suggestive juristic works of the early Gothic, and whose longing into distant seas gave the impulses for the two discoveries of America. "Double-entry book-keeping is born of the same spirit as the system of Galileo and Newton. ... With the same means as these, it orders the phenomenon into an elegant system, and it may be called the first Cosmos built up on the basis of a mechanistic thought. Double-entry book-keeping discloses to us the Cosmos of the economic world by the same method as later the Cosmos of the stellar universe was unveiled by the great investigation of natural philosophy. ... Double-entry book-keeping rests on the basic principle, logically carried out, of comprehending all phenomena purely as quantities."

Double-entry book-keeping is a pure Analysis of the space of values, referred to a co-ordinate system, of which the origin is the "Firm." The coinage of the Classical world had only permitted of arithmetical compilations with value-magnitudes. Here, as ever, Pythagoras and Descartes stand opposed. It is legitimate for us to talk of the "integration" of an undertaking, and the graphic curve is the same optical auxiliary to economics as it is to science. The Classical economy-world was ordered, like the cosmos of Democritus, according to stuff and form. A stuff, in the form of a coin, carries the economic movement and presses against the demand-unit of equal value-quantity at the place of use. Our economy-world is ordered by force and mass. A field of money-tensions lies in space and assigns to every object, irrespective of its specific kind, a positive or negative effect-value, which is represented by a book-entry. "Quod non est in libris, non est in mundo." But the symbol of the functional money thus imagined, that which alone may be compared with the Classical coin, is not the actual book-entry, nor yet the share-voucher, cheque, or note, but the act by which the function is fulfilled in writing, and the rôle of the value-paper is merely to be the generalized historical evidence of this act.

Yet side by side with this the West, in its unquestioning admiration of the Classical, has gone on striking coins, not merely as tokens of sovereignty, but in the belief that this evidenced money was money corresponding in reality to