Cogwheels of the Mind

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. Booklist Deserves to become a minor classic and may well go on to make many friends for mathematics. -- Jeremy Gray Nature 2004 Entertaining. Boston Sunday Globe Edwards is a charming if earnest guide, and the many illustrations of the beautiful cogwheels will fascinate and satisfy. -- Ben Longstaff New Scientist 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. -- Darren Glass MAA Online Many excellent and graphically exciting illustrations of Venn diagrams transform what might have been a simple math book into one that shows that mathematics can generate pictures that could be considered... in the forefront of modern art. School Library Journal Give this book to any youngster with an enquiring mind, and watch delight develop. -- John Haigh Significance 2004 There is a nice balance between personal anecdotes, history, aesthetics and attention to detail... The overall result should become something of a classic. -- B. I. Henry The Physicist Venn diagrams are familiar as pictorial representations of relationships among sets, and statistician Edwards discusses their development... He shows how to interlink shapes to form beautiful Venn diagrams. Choice 2004 I heartily recommend it for readers interested in knowing more about John Venn and the geometric properties of Venn diagrams. It will also be appreciated by those interested in the process of mathematical discovery. -- Frank Ruskey American Scientist An insightful history of the diagrams. Scientific American 2004 Lovely little book... which should not be summarized. It should be bought and enjoyed first-hand. It is a book in which mathematics and its history are combined in a lovely autobiographical account of a voyage of discovery. The mathematics is interesting, the history is interesting, the personal account is interesting, and the book, with its elegant full-colour pictures and diagrams is beautifully produced. The author and his publisher are to be warmly thanked and congratulated. -- Peter M. Neumann British Society for the History of Mathematics Bulletin 2004 A short book, with a fittingly large number of illustrations, it summarizes a wealth of logical and geometric ideas. -- Rob Hardy The Times of Acadiana 2005 If you have an interest in the history of mathematical ideas and the creative process of mathematicians, then I recommend this book. -- John Wilkins Mathematics Teacher 2005 Edwards' fascinating study relates this invention to the study of mathematics, scientific thought, graphic design, and modern art. School Library Journal 2005 A very short readable book on attempts to physically represent the intersection of any number of sets. -- Jim Kiernan Convergence 2005 There is no better place to start than with Cogwheels of the Mind. -- Frank Ruskey American Scientist 2005 This is a wonderful book which should be taken simply for what it is, the story of the Venn-Edwards diagrams. -- Amirouche Moktefi Review of Modern Logic 2005 An engaging, very readable, and profusely illustrated account. Historia Mathematica 2006 An easy, friendly, and enlightening book to read... Would be of particular interest to college professors, especially those involved in teaching a History of Mathematics class and/or a Graph theory class. -- Darlinda Cassel School Science and Mathematics 2007

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.

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 EdwardsVenn Diagram References Index