Cogwheels of the Mind: The story of Venn diagrams by A. W. F. Edwards, Johns Hopkins University Press, 拢17/$25, ISBN 0801874343 Reviewed by Ben Longstaff
IN Manhattan you can eat 鈥減izza Venn鈥�: one half with capers, one half with anchovies, but arranged so that one quarter has both toppings, and one quarter has neither. Of course, it would be far nicer to forget the anchovies altogether, but that鈥檚 not the point. The idea of a Venn diagram is to represent classes or sets, and show where they intersect.
Pizza fans excluded, most people are probably more familiar with Venn diagrams as drawings of overlapping circles. In this case there would be two: one for each topping, presumably inside a larger one labelled 鈥渕argherita鈥�. Cogwheels of the Mind is the story of these curious objects and their discoverer, 19th-century logician John Venn. It is told by A. W. F. Edwards, who is a fellow of Gonville and Caius, the same University of Cambridge college at which Venn taught. (We might even have had Dodgson diagrams: another Cambridge resident, Charles Dodgson, was inspired to create his own version.)
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Although massively popular, Venn diagrams hit something of a brick wall for want of a simple way to show more than just a few sets without getting into a hopeless mess. Edwards鈥檚 own delightful solution 鈥� the cogwheels of the title 鈥� was first published in this very magazine (7 January 1989, p 51), and triggered something of a Venn renaissance.
Yes, it鈥檚 a slightly esoteric subject, but why not? Edwards is a charming if earnest guide, and the many illustrations of the beautiful cogwheels will fascinate and satisfy.