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When asked to list minds that made the Renaissance and the revolutions in invention and technology that created the modern world, academics will usually name artists, writers, and early scientists. To this list should be added another important category: bookkeepers. In the emergence of Europe from medieval superstition and the intellectual ruts of Christian Neoplatonism, much depended on the rise of commerce and with it, bookkeeping. Bookkeeping is, after all, just another way of quantifying the world, in terms of that great simplifier of human reality, money. In chronicling the history of thought, philosophers tend to stress the contribution to science of the likes of Galileo and Hobbes, people who ingrained in the Western mind the distinction between secondary and primary qualities, between the appearance of smells, colors, and tastes, and such underlying, quantifiable realities as mass and momentum. But the early bookkeepers also helped the Europeans shake their medieval habits of thought, especially the prevailing notion that everything in the Creator’s scheme of the universe had divinely conferred upon it an intrinsic value. In a sense, the rise of bookkeepers with their mercantile secularism throws new light on an old joke: before the advent of accountancy, medieval intellectuals knew the value of everything and the price of nothing.

These meditations have been provoked by a captivating new book. Alfred W. Crosby’s The Measure of Reality (Cambridge University Press, $24.95) spells out the factors that stimulated the new way of thinking that began in the late Middle Ages to replace the qualitative and theological view of reality. On the old model, all was understood in narrative, even dramatic terms: “God and Purpose loom over all.” For [End Page 500] example, more important than the mere utilitarian value was the sym-bolic meanings of numbers. Seven, being the sum of the first odd number and the first even number, was perfect; ten, the number of commandments, symbolized law. The study of these meanings was for Augustine, as for many later minds, “the science of numbers.” Geography was qualitative, holding that the peoples of the Indies, governed by slow-moving Saturn, were slow moving. Europeans, on the other hand, lived in the land of the seventh climate, that of the moon, which revolves around the earth faster than any other body. Therefore, Europeans are the most active people. Maps were designed not geometrically, but to show what was near and far, important and unimportant. Their representation of geographic reality was, as Crosby says, “for sinners, not navigators.”

In contrast to all this, the New Model emphasized “precision, quanti-fication of physical phenomena, and mathematics.” The aim of this thinking was panometry, the will to measure everything. The new approach, in Crosby’s description, was simply this: reduce what you are trying to think about to the minimum required by its definition; visualize it on paper, or at least in your mind, “be it the fluctuation of wool prices at the Champagne fairs or the course of Mars through the heavens, and divide it, either in fact or in imagination, into equal quanta.” Measuring, then, becomes a matter of counting the quanta. However simplified (or oversimplified) this quantitative representation of reality is, it at least has the virtue of being precise; moreover, you can manipulate it and experiment with it. Today, the refrain from postmodern theorists is that “science just proves whatever it wants to” and that its “objectivity” is an illusion. But manipulating numbers doesn’t mean fiddling with them: as Crosby points out, a quantitatively represented reality “possesses a sort of independence from you,” and it has a capacity to accomplish something “verbal representation rarely does: contradict your fondest wishes and elbow you on to more efficacious speculation.”

The comparison with “verbal representation” is telling, for I suspect quantification makes it easier to set up tests of intellectual honesty. If you can devise explanatory hypotheses over a domain, and if they can be used to make predictions which don’t pan out, predictions which, no matter their attractiveness, don’t jibe with the numbers, then you are on the way to productive science. We live in an age accustomed to wisecracks...

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pp. 500-511
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