Its probably pretty telling to be reading a book on the history of Venn diagrams at the beach, but I took the chance and started A.W.F. Edwards' Cogwheels of the Mind: The Story of Venn Diagrams a few weeks ago. A delightful, short (about a hundred pages, with many diagrams) history of the graphical approach by John Venn. Which links well with the algebra of Bernoulli, whose algebra led to computing, and is being used very actively in the computer you are staring at. It also has survived as a much-taught methodology in schools from kindergarten upwards. Perhaps I am a bit optimistic, but I believe a large number of eighth graders could draw one. Its perhaps the most beautiful and simplest example of visualization of complex ideas. The book also carefully reviews the extension of Venn diagrams into greater numbers of classifications, and Edwards further work in the area. Although the book is short, it does require some willingness to think through his examples. A strong graphical intuition is desirable.
One of the reviewers at Amazon suggested that the book should have gone further, comparing Venn diagrams to other diagrammatic methods, but I disagree ... this is an example of a 'just enough' monograph, rich in both in the history and its implication regards the way we think about hard problems. It sufficed at the beach. It did inspire me to look at the other methods mentioned. In an appendix, Edwards suggests its extension into statistical domains.
Another reviewer questioned if there was an audience for such a book. Well, besides myself, there are others who like to see popular mathematics well written, and prefer the proofs to be left in the references for now. No, it won't make the NYT best-seller list, but it did enlighten me.
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