Used today in spheres of life as diverse as business strategy, creative writing, medicine, computer science, and theoretical physics, Venn diagrams possess fascinating properties. The basic Venn diagram is both elegantly simple--three overlapping circles that intersect to create eight distinct areas--and conceptually innovative. Devised by English logician John Venn (1834-1923) to visually represent complex logical propositions and algebraic statements, the diagrams drew the excited interest of both scholars and the general public.

In Cogwheels of the Mind, statistician and...