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Cover image of Cogwheels of the Mind
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Cogwheels of the Mind

The Story of Venn Diagrams

A. W. F. Edwards
foreword by Ian Stewart

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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...

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.

Reviews

Reviews

Edwards arrives with this pleasing little history about who John Venn was, why he conceived of the diagram, and the properties that lie secreted beneath such a seemingly simple mathematical object... A world-class authority, Edwards... proves himself wholly accessible to anyone interested in reading about mathematics.

Deserves to become a minor classic and may well go on to make many friends for mathematics.

Entertaining.

Edwards is a charming if earnest guide, and the many illustrations of the beautiful cogwheels will fascinate and satisfy.

The kind of book that I can imagine giving to a wide range of readers: any junior high student would be able to follow the mathematics, and most professors would find it interesting... I found it to be a nice—if light—read, and it is well worth a look.

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About

Book Details

Publication Date
Status
Available
Trim Size
7
x
9.25
Pages
128
ISBN
9780801874345
Illustration Description
12 color illus.
Table of Contents

Foreword
Preface
Chapter 1. John Venn and His Logic Diagram
Chapter 2. Rings, Flags, and Balls
Chapter 3. Five and More Sets
Chapter 4. The Gray Code, Binomial Coefficients, and the Revolving-Door

Foreword
Preface
Chapter 1. John Venn and His Logic Diagram
Chapter 2. Rings, Flags, and Balls
Chapter 3. Five and More Sets
Chapter 4. The Gray Code, Binomial Coefficients, and the Revolving-Door Algorithm
Chapter 5. Cosine Curves and Sine Curves
Chapter 6. Ironing the Hypercube
Chapter 7. Diagrams with Rotational Symmetry
Appendix 1. Metrical Venn Diagrams
Appendix 2. A Rotatable Edwards–Venn Diagram
References
Index

Author Bios
Featured Contributor

A. W. F. Edwards

A. W. F. Edwards is, like John Venn before him, a fellow of Gonville and Caius College, Cambridge. He is the author of Likelihood and Pascal's Arithmetical Triangle, both available from Johns Hopkins.