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Journal of World History 10.1 (1999) 218-220

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The Measure of Reality: Quantification and Western Society, 1250-1600. By Alfred W. Crosby. New York: Cambridge University Press, 1996. Pp. xii + 245. $24.95 (cloth); $14.95 (paper).

In 1560 Peter Bruegel the Elder produced a picture called Temperance that portrayed musicians, builders, astronomers, gunners, and money-changers all engaged in activities that involved keeping time, counting, and measuring. The musicians were reading from a written score, and the men with the money were writing down figures in books.

That picture is the first illustration in Alfred Crosby's new book, The Measure of Reality, and it announces two themes, which he brings together in a highly stimulating way. One is the application of number and measurement to everything from architecture and maps to music, from accountancy and astronomy to army drill. European culture developed strongly in this direction, Crosby shows, between the end of the Middle Ages and the scientific revolution, preparing the ground not only for the emergence of modern science, but also for a "tempered" or disciplined attitude in every aspect of life.

The other lesson from the Bruegel picture is that all these measuring and numbering activities are related to a visual understanding of the world, with even music read from visual patterns on the page. Some polyphonic compositions were so complex, Crosby says, that they could be appreciated only by the eye and not by the ear. Thus he offers an [End Page 218] exciting synthesis that links both the invention of musical notation and the Renaissance techniques of pictorial perspective to the emergence of modern science.

As a book on the history of ideas in western Europe, this is a most valuable and interesting work, and I have only one small reservation: that the author does not fully explain the geometrical methods of medieval architectural work, which allowed builders to use geometrical constructions in place of measurements. Had he discussed this, there would be less surprise in the observation that medieval thinkers did mathematics without quantification and in "the absence of actual measurement" (p. 67). It would also then be possible to recognize that the introduction of measuring rods and rules marked off in fractions of an inch (or other units) was itself a minor revolution.

In Bruegel's picture, all the instruments being used for linear measurement are of the medieval type, adapted to geometrical methods. This confirms what is known from other evidence: that in 1560 some artisans in northern Europe were still using the old methods. At the same time, though, Leonard and Thomas Digges (among others) were discussing the greater precision that could be attained by combining geometrical methods with scale measurement, and part of their work was eventually published as "A Geometrical Practice Named Panto-metria." Crosby quotes this prominently from a second source (p. 1) without fully explaining that the transition from geometry-based concepts to measuring rods and scales was still incomplete.

This is a minor oversight in an otherwise brilliant perspective of European intellectual history, and if Crosby had left the matter there, one would feel only gratitude for the insights the book offers. However, Crosby also says that he is seeking "explanations for the amazing success of European imperialism" (p. ix), and hence of Western domination of the modern world. He sees the Europeans' number skills and visual abilities as the key to their capacity to organize people and capital in exploring and colonizing the rest of the world.

When considering Crosby's work in this wider context, I find it impossible to accept that so Eurocentric a book can really explain very much. If the links among visualization, measurement, and mathematics were critical for world history, it must surely be obligatory to discuss how far those links developed in other cultures, not just in the West. If Crosby had done this in detail rather than just asserting that "the West in the sixteenth century was unique" (p. 238), he might have been surprised by how far some societies had developed "visualization...