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"Cogwheels of the Mind: The Story of Venn Diagrams" by A.W.F. Edwards
One of the most humble books telling the history about Venn Diagrams, John Venn himself and the developments that came along with it!
May the Fourth be with you all!
Some books deserve a chance to be read. Because we buy and review books that are used, this copy happened to be a former library book. According to the stamp card, this was never checked out from the library—not once. Despite the populace's low-brow interest in Mathematics, it makes us wonder: What does this mean for authors who write about Math? Illiteracy is already a problem here in the United States and so reading something of interest makes this book appeal to a niche audience, which is a strange thing to say since Mathematics should be for everyone. Anyway, we're thankful this website exists shining light to books, Math books especially, giving them the chance they deserve. People get a chance to live, express and become themselves, shouldn't books be given the same treatment?
(For those new here, we don't do a "TBR"—"to be read" listing—nor do we mark a book as "DNF"—"did not finish"—here on The Seeds of Books. We read all the books we buy and review them accordingly, but on behalf of us, we want to thank those among the "BookTok" community for normalizing not finishing books you buy and read. It's like walking away from someone the moment they start talking to you then posting on social media telling people about it. It's very disrespectful to the author[s] after all the hard work they put into writing and getting their book[s] published.)
Reading the Foreword by Ian Stewart was a treat. Sharing his brief story in how he got into Mathematics and briefly explaining the power of Venn Diagrams was nice. We see the Foreword section as "opening act" for the main event so to speak, and Stewart who's also an author, did a great job introducing readers to this great book.
The book starts with a gentle history and survey in the development of such diagrams. Author Edwards told it as best as he could mentioning that there aren't much written about the main man himself, John Venn. Readers will learn about sets drawn out with respect to the famous intersecting circles, but get more and more complex when representing sets more than four and five. How complex? Let's just say that the diagrams couldn't be properly represented by just circles, let alone squares to which such diagrams were tested during its development. The coolest thing about what readers will learn about these Venn Diagrams in the more advanced areas? Author Edwards himself made contributions and shares how he was able to go about doing it.
Along with learning about its development are illustrations in how these diagrams look, seeing how the sets intersect within one another. The cool part is seeing how these sets intersect another set once without crossing it twice! Another cool thing was Edwards showed flags of countries in how their designs represent the disjoint and intersectionality of these diagrams. Not only the countries' flags, but you will better understand that such designs can also be found in a basketball and tennis ball in terms of the sets' borders crossing other sets. The more you read through the book, the more it may sound like making geometrical drawings with respect to sets in connection with one another, but the results look visually beautiful. Oh, and yes, there is mention of the yin-yang style of diagramming.
Last two chapters goes through some diagrams that even I, myself, haven't heard much about until now, and that is the Boolean Cube. We all know what a Boolean is in computer programming and Mathematical Logic, but this one was a neat feature in contrast to Venn diagrams. Yes, it's a cube drawn with two different iterations on a 2D paper, but displays the elements of sets just as neatly. Reading on it, as mentioned by the author himself, it gets more and more complex when introducing additional sets to the point where Graph Theory will need to help organize such diagrams. However, while it's easy to dive deeper into Graph Theory, how each vertex and sides are supposed to coincide with one another means veering into the topic that's too advanced for the book (we have learned and studied a bit of it last year). In addition, there were more diagrams crafted and introduced which ended up looking like lotuses; it's really pretty, actually. Just goes to show how visually pleasing and beautiful Mathematics can be...because it is!
This short but simple book is a great historical and developmental account of Venn diagrams, the Edwards-Venn Diagrams, its continual editions and advancements. Whether you're a student or self-learner of Mathematics, curious to learn about the accounts of Venn diagrams, and/or have a huge liking to Logic, Set Theory, Graph Theory or the artistic side of Mathematics, we think you'll get mileage of knowledge and information from this book! The fact that this was written by Edwards himself, who contributed developments of such diagrams makes this book a treat to have in your library/collection.
We did mention earlier that this was a former library book that was never checked out. There isn't a stamp as to when this book appeared at the time, but this was from the Kishwaukee College Library, located in Malta, Illinois. Not sure if it's the waning interest in Mathematics, or that math books only appeal to a niche audience, but these are one of those "diamond in the rough" books—books you never hear much about until someone shares and talks about it. On the other hand, we have plenty to say about the declining interest in Mathematics as well as illiteracy here in the United States and likely the world, but let's digress.
It's not a perfect book, as some parts get a bit heavy and confusing on the side of describing sets and its intersectionality. That's not much of a negative, but for those with little to no experience in the subject might get lost reading them throughout this book.
This isn't a rare book by any means, but it's one that gets overlooked and passed on. We'd recommend it if you enjoy Mathematics on the history and development side, especially if it ties with your favorite areas in relation to Logic, Combinatorics, Graph Theory or even Geometry. It's guaranteed to please.
UPDATE (02-01-2026 at 8:16PM): Edited and fixed grammatical errors.
- One of the most underrated/overlooked Math books in existence today.
- Short but excellent book into the history and development of Venn Diagrams.
- Author Edwards himself made contributions in the diagram's development.
- Beautiful illustrations of the diagrams, looking more like art than mathematical diagrams.
- Perfect book whose story will appeal to students, professors, reseachers and self-learners alike.
- Some information discussed may be too confusing and dense for the layperson.
PROFILE |
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|---|---|
| Title | Cogwheels of the Mind: The Story of Venn Diagrams |
| Author(s) | A.W.F. Edwards (foreword by Ian Stewart) |
| Description | [FRONT FLAP] Used today in spheres of life as diverse as busines 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 (a rich source of Venn diagrams)—including those of Switzerland, Poland, and Japan (all one-set Venn diagram); and Maryland (a three-set device). Edawrds 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, in his 1881 book, Symbolic Logic, Edwards discusses the rival diagrammatic scheme invented by Charles Dodgson, better known as Lewis Carroll, who 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. [BACK FLAP] Edwards goes on to show how different shapes can be linked 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. |
| Dedication | -- |
| ISBN / Bar code number | 0-8018-7434-3 / 9 780801 874345 90000 |
| Book Dimensions | Width: 7.25″ (7 ¼″) |
| Height: 9.56″ (9 9/16″) | |
| Depth: 0.62″ | |
| Page Count | 132 |
| Contents | Foreword, Preface, 1. John Venn and His Logic Diagram 1 John Venn, 1834-1923. Logic Diagrams, Euler's circles. Venn diagrams. Boolean algebra. Binary labeling. Churchill's Venn diagram. Earlier diagrams. W. Stanley Jevons. H.J.S. Smith. 2. Rings, Flags, and Balls 17 Precursors of the pattern. The Trinity. Borromean rings. Lewis Carroll's diagram. The Game of Logic. Two-colorable property. The flag of Greenland, and the arms of Maryland. The diagram on a sphere. The globe. Projections. Tennis balls and basketballs. 3. Five and More Sets 29 Adding sets. C.S. Pierce. Venn's attempt. Lewis Carroll's attempt. Edward's solution. Other solutions: Grünbaum's, Humphries's, Fisher and Koh's. 4. The Gray Code, Binomial Coefficients, and the Revolving-Door Algorithm 47 Edwards's form maps a Gray code. Alternative forms. The binomial coefficients represented by necklaces of regions. The revolving-door algorithm. Jevons again. 5. Cosine Curves and Sine Curves 61 The linear diagram. C.A.B. Smith's variant maps the binary code. Martin Gardner's "proof" that π = 2. Hybrid diagrams. The rotatable diagram. 6. Ironing the Hypercube 77 The dual diagram maps the hypercube. The maximal planar subgraph. The Karnaugh map. The Hamming code. Hamilton circuits. 7. Diagrams with Rotational Symmetry 84 Leibniz's divisibility theorem and Henderson symmetry. Grünbaum's symmetrical five-set diagram. Polar symmetry. Edward's family of seven-set diagrams with rotational and polar symmetry. More diagrams. Appendix 1. Metrical Venn Diagrams 95 Appendix 2. A Rotatable Edwards-Venn Diagram 101 References 105 Index 109 |
| Frontispiece | Portrait of John Venn by C.E. Brock, 1899. By kind permission of the Master and Fellows of Gonville and Caius College, Cambridge. |
| Jacket Design | Brian Barth |
| Author Photograph | -- |
| Published | 2004 |
| Publisher | The Johns Hopkins University Press 2715 North Charles Street Baltimore, Maryland 21218-4363 www.press-jhu.edu) |
| Copyright | © 2004 A.W.F. Edwards All rights reserved, Published 2004 |
| Printed in | Printed in the United States of America on acid-free paper |
| Book Format | Hardcover |
| Quoted Reviews |
"Cogwheels of the Mind is not only interesting but inviting. Edwards' penetrating insight into the contentious history of John Venn and his diagram is fascinating. Read it!" —Jack Kuipers, Calvin College "You simply cannot be knowledgeable of Venn diagrams until you have read Professor Edwards' delightful book. It is a real treat for the logical mind." —Paul J. Nahin, author of Oliver Heaviside: The Life, and Times of an Electrical Genius of the Victorian Age |
| Best Seller's List | -- |
| Other | 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. 9 8 7 6 5 4 3 2 1 Edwards, A.W.F. (Anthony William Fairbank), 1935— Cogwheels of the mind : the story of Venn diagrams / A.W.F. Edwards. p. cm. Includes bibliographical references and index. ISBN 0-8018-7434-3 (hardcover : alk. paper) A catalog record for this book is available from the British Library. |
| Library of Congress Cataloging-in-Publication Data | 1. Venn diagrams |
| 2. Logic, Symbolic, and mathematical. | |
| I. Title. | |
| CIP Number | -- |
| LC Control Number | 2003010633 |
| LC Call Number | QA248.E28 2004 |
| DDC Call Number | 511.3'3—dc21 |
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