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 geneticist A. W. F. Edwards
provides an accessible and engaging history of the Venn diagram, its
reception and evolution, and its presence in such objects and images as
Christian iconography, tennis balls, and flags which provide a rich
source of Venn diagrams for Edwards, including those of Switzerland,
Poland, and Japan (all one-set Venn diagrams), Greenland (a two-set Venn
diagram), and Maryland (a three-set device).
Edwards begins with a sketch of Venn's life, his discovery of the
three-circle design while developing a series of lectures on symbolic
logic at Cambridge University, and the publication of his find in an
1880 paper, and, more influentially, his 1881 book, Symbolic Logic.
Edwards discusses the rival diagrammatic scheme invented by Charles
Dodgson, better known as Lewis Carroll, who also developed a board game
based on his design. The author also recreates famous Venn diagrams from
history, including Winston Churchill's of 1948 depicting the mutual
interests of the British Empire, a united Europe, and the
English-speaking world, with the United Kingdom located at the
intersection.
Edwards goes on to show how different shapes can be linked together to
form artistically beautiful and mathematically important, multi-set Venn
diagrams, including the author's own influential Adelaide variation. And
he delineates the possibilities for expanding the analytic power of
these diagrams far beyond those first appreciated by Venn. Edwards even
tells readers how to draw complex Venn diagrams on a spherical surface
to create "Vennis balls." For anyone interested in mathematics or its
history, Cogwheels of the Mind is invaluable and compelling reading.
