## Book Review: The Riddle of Scheherazade And Other Amazing Puzzles, Ancient and Modern

The Riddle of Scheherazade And Other Amazing Puzzles, ancient and Modern, by Raymond Smullyan

This book is really two books in one.  The first book is a series of thematically related chapters that serves to continue Edgar Allen Poe’s continuation of the story of Scheherazade in the 1001 Arabian Nights, where the lovely young woman saves her life by a series of puzzles that amuse the sultan.  The second book is a book on “coercive logic” and the ways in which people are compelled to do things by accepting the challenge of answering questions.

As this book is full of riddles, some more explanation of the precise contents of this book would be worthwhile, if one is the type of person who (like me) enjoys riddles and puzzles of a logical type.  The book begins by commenting that it is a continuation of Edgar Allen Poe’s “The Thousand-and-Second Tale of Scheherazade,” giving an unusual sort of literary provenance to what is a popularly accessible logic and math book.  The second chapter is a set of riddles related to the supposed setting.  The third chapter is a set of riddles about Hassan’s mules and camels, as well as other questions of amount and distance.  The fourth chapter looks at some ancient western puzzles where a king on a hunting expedition is outsmarted by his knights who keep on changing the numbers of people present in the rooms without his knowledge, as well as some Egyptian and Hindu puzzles about numbers and bees.  The fifth chapter brings some questions in probabilities about the jewel chests of a certain Abdul, chapter six examines a lot of robberies of Abdul by some of Ali Baba’s forty thieves, and the seventh chapter contains more puzzles of a miscellaneous nature.  In chapter eight there are a series of logic puzzles about the Mazdaysians and Aharmanites (the former who never lie and the latter who never tell the truth).  These riddles continue in the ninth chapter as well.  The tenth chapter contains more numerical and algebraic riddles, while the eleventh chapter introduces and develops the idea of the metapuzzle, where outside information allows previously insoluble problems to be solved.  The twelfth chapter relates the story of Al-Kazir and his love for the sultan’s daughters, while the final chapter of the first book shows Scheherazade using coercive logic to compel the sultan to save her life, marry her, and make lots of of babies [1].

Up to this point, the book has been an amusing sort of collection of historical riddles (with the answers in the back) that serves to amuse the mathematically literate and somewhat logical reader, but these games come with a twist.  It is to be assumed that the reader of this book is interested by intellectual word games and somewhat skilled in the phrasing of questions to lead to desired answers, because this is where the book becomes considerably more intriguing, entering the realms of human psychology (which coercive logic is really a study in) as well as some of the more hazy edges of logic and mathematics.  The first half of the book is really just a subtle way of examining these far deeper philosophical matters without making the point too blunt.

Coercive logic is not itself a new phenomenon, as I thought of several biblical examples as I was reading the book (which itself makes reference to a few of the Bible’s riddles–such as the “all Cretans are liars” and Solomon’s riddle of the two prostitutes).  What makes coercive logic coercive is that every answer is a trap–and so the only way to avoid the coercion is to refuse to answer, but a person who is intoxicated with their own powers of intellect and logic is not likely to avoid the trap.  After introducing the concept the author examines “left and right handed coercion” where all people write truthful statements with their dominant hand (I am left handed, for example) and write false statements with their weaker hand before writing a chapter which would force anyone who answered a given question to give the questioner a million dollars (this is why such logic is coercive–if you let others define the terms of the game, you have to assume they are going to be smart enough to win).

After making the point sufficiently well, the book then includes a chapter on “variable” liars that tell the truth some days consistently and lie consistently other days (as opposed to the variable liars who change from one moment to the next that we are all more familiar with).  Then there is a chapter with a series of riddles about Japanese and Chinese binary responder machines, a chapter of riddles about the planets Oron and Seth (where people always speak what is accurate on their home planet and say nothing accurately on another planet), a chapter with riddles about twins who can only be distinguished by the fact that one tells the truth in the normal state and lies consistently in the altared state and the other twin does the reverse, and another chapter that elaborates on this with riddles about two twins who lie on one day of a three day cycle and tell the truth on the other two days.

After these riddles are done the book enters its home stretch with some historical problems, including a special set of Godelian problems in one chapter, and closing with a chapter on some strange paradoxes (including the so-called Cretan paradox referenced in Titus 1) which attempt to show how problems can be consistent and inconsistent at the same time.  It is clear that the author of this book is fascinated by puzzles and riddles and paradoxes, but aside from pointing out some of the hazards of letting other people define the rules of the game, and examining the limitations of human reasoning, it is unclear what the author’s larger point is.  Given that the author’s body of work includes a lot of Taoist and philosophical writings, it appears as if there is more than meets the eye with this particular book, but only the subtle reader will understand that underneath the book’s jovial and joking sort of manner there lies a serious warning about not trusting one’s own intuition when dealing with the trickery of others.  It is a warning well-heeded when dealing with those who seek to entrap with coercive logic.

[1]  I’m not making this up:  “Epilogue:  These days, one seldom ends stories happily; one rarely writes that the couple lived happily ever after.  However, if I am to be truthful and give an accurate account of my secret source, then I have to inform you that the king and Scheherazade did live happily ever after–very happily, in fact.  They had many beautiful and bright children who grew up to become makers of all sorts of puzzles, which have come down to us through the ages.”

Raymond Smullyan, The Riddle of Scheherazade And Other Amazing Puzzles, Ancient and Modern, (New York, NY:  Alfred A. Knopf, 1997), 80-81.