Magical Mathematics [and the converse]
“The two of us have been mixing entertainment with mathematics for most of our lives.” (page xi)
When I learned that Persi Diaconis and Ron Graham had co-authored a book on the mathematics of magic, the Book Editor of CHANCE immediately asked Princeton University Press for a copy! Even though I am not at all interested in card tricks. Nor in juggling. (The title is a wee confusing to [a non-native speaker like] me as it sounds as focussing on the magics of mathematics rather than the converse.)
Once the book had arrived, I showed the book to my wife and she started reading it right away, going over the first chapter prior to giving it back. Later, on a plane trip between Phoenix and Minneapolis, I happened to sit next to a professional magician, The Amazing Hondo!, who started chatting with me and telling me about his work and some of his tricks. He knew about Persi as a magician but was surprised he was equally famous among mathematicians. Hondo showed me a few (impressive) sleights of hand and explained a nice mathematical trick (based on creating apparent randomness while always extracting the same number of cards from the pile). As I happened to have the book with me, he took a look at it, commenting on one trick, and wrote down the reference. I have had a few other occurrences of how the book attracted the attention of non-magicians and/or non-mathematicians: this illustrates the appeal of the concept of this book for a very wide audience and, of course, once one starts reading the book, the attaction is increased manyfold. It is indeed a very entertaining book, with a fairly easy mathematical level, and it is also a beautiful product, with wide margins, fancy (but readable) fonts, photographs, and graphs or tables in the margins.
“Both of our worlds have a dense social structure: thousands of players turning ideas over and over.” (page xi)
The entertaining and cosy style of Mathematical Magics (oops, Magical Mathematics!) does not mean it is an easy read. First, conceptualising the card manipulations requires a good analytic mind if one does not have a deck of cards available. Second, the connections with mathematics involve several subfields and not only combinatorics. Like de Bruijn sequences and graphs, the Mandelbrot set, Penrose tiling. And even Bayesian analysis for reversible Markov chains (p.42) and the I Ching… The last chapters are however less directly related to maths (even though Chapter 10 about great mathematical magicians includes connections with topology).
Interestingly (for us academics), the book mentions a (Banff) BIRS 2004 workshop relating to magics via de Bruijn sequences and Gray codes. With the traditional picture in front of the (old) BIRS building. (Another item of information, IBM stands for International Brotherhood of Magicians!)
“We hope that our book will shine a friendly light on the corners of the world that are our homes.” (page xii)
One of the complaints I share with my wife about Magical Mathematics is that some of the tricks are not explained in full enough detail. At least for some non-native speakers like us. For instance, during my skiing break in the Alps, Paul my nephew and I tried the Gilbreath principle and could not make it work without forcing the perfect riffle-shuffle one card at a time. The sentence “the shuffle doesn’t have to be carefully done” (p.63) set us on the wrong track. On pages 106 and 107, two 1500′s books in French are quoted with one typo (sont versus font, but at the time s and f were typed quite similarly), a missing s in Inventions, and without the accents: I wonder whether or not accents existed at the time. (It seems they did not, as seen on the originals here and there.) The comment on Heeffer’s 1624 (French) book is confusing [to me] in that Heeffer is a current math historian working on a 1624 book by Jean Leurechon. (The accents are not there in the 1624 edition.)
Overall, this is a wonderful book, potentialy enjoyable by a large range of individuals. (Precision: I read half of it flying over the beauty of sunsetted Greenland and the other half in a chalet next to the ski slopes. So I was in a mellow spirit!) The order behind the apparent randomness of card tricks becomes clearer and clearer to the naïve reader like me.And the warmth and communal spirit of the magician community transpires through the last chapters. (Note there is a $1000 reward posted within the book!)