Games for Your Mind

Games for Your Mind is not just a collection of recreational logic puzzles and games, as the title might suggest, it is much richer than that.

 

The leitmotif of this book is that it is difficult “to draw a clear line with amusing puzzles on one side, and difficult mathematical and philosophical questions on the other.” 

 

The author suggests the word empuzzlement to designate the process through which dry discussions of difficult and abstract concepts are transformed into engaging puzzles. Two great masters in this art of empuzzlement were Lewis Carroll and Raymond Smullyan.

 

Lewis Carroll, better remembered as the author of Alice in Wonderland, was in fact a professional mathematician, who integrated puzzles into his scholarly work on logic.  Carroll empuzzled the central principles of Aristotelian logic and Part II of the book is dedicated to his (non-fictional) work.

 

Raymond Smullyan, according to Wikipedia, “was an American mathematician, magician, concert pianist, logician, Taoist, and philosopher”. As a logician, he popularized Gödel’s incompleteness theorems, through a variety of puzzles involving knights (who always tell the truth) and knaves (who always lie). Many of those puzzles are presented and explained throughout the book.

 

There are basically two kinds of chapters in the book: those presenting topics in the history of logic (e.g. Chapter 3 on Aristotle’s syllogism), and those built around a series of puzzles (e.g. Chapter 7: Liars and Truthtellers). The solutions to the puzzles are given at the end of each chapter. The puzzles were chosen by the author for their interest as pedagogical tools, rather than as purely recreational amusements. Each of them is a ‘microcosm’ of some milestone in the history of logic.

 

The final chapter is a short history of fiction works, typically detective stories, where the solutions of seemingly unsolvable puzzles play a crucial role. Obviously, Sherlock Holmes and Hercule Poirot are part of this gallery, but we also meet less known fictional characters (I never heard about some of them), especially from the so-called Golden Age of crime novels in the ‘30s. This is a truly delightful chapter, and the topic would deserve an entire book on its own.

 

Rosenhouse has succeeded in writing a book that is informative and entertaining at the same time, in a style that is lively and engaging, and accessible to a general audience.  It is a real pleasure to read. 

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Fabio Mainardi (fabio.mainardi@rd.nestle.com) works as senior data scientist at Nestlé Research, Lausanne. After a PhD in number theory, he has been working as applied mathematician in R&D divisions of different companies. His mathematical interests include statistical models, probability, discrete mathematics and optimization theory.