Satan, Cantor, and Infinity

If readers risk brain cramps from these 200-plus puzzles, problems, and paradoxes, the challenging brain-teasers will teach them something about critical thinking.

Raymond Smullyan is the veteran mathematician and writer (THE LADY OR THE TIGER?, FIRST ORDER LOGIC, ALICE IN PUZZLE-LAND) who juggles logic and “magic” in an animated, accessible manner that’s also quite entertaining.

Here, he sets up a loose narrative structure around which to list his demanding questions. Guided by “the Sorcerer,” readers experience an adventure on the Island of Knights and Knaves, where the Sorcerer maintains a castle and a witch doctor threatens the peace, where Princess Annabelle has been imprisoned and her suitor Alexander seeks to rescue her.

In this delightful maze of honest knights and lying knaves, intelligent robots and even smarter computers, the Sorcerer reflects on mathematician Georg Cantor and provides dozens of questions and quizzes about time and change, infinity and probability and reality.

By using this fictional framework and anecdotes such as the title story, the Sorcerer/Smullyan creates a flowing book that should appeal to mature logicians and some young players of Dungeons and Dragons.

Using syllogistic reasoning and Holmesian deduction, code-breaking and math exercises, many readers may realize that they’re using intellectual muscles that have almost atrophied. The infrequent rewards of achieving some solution are balanced by occasional confusion and frustration—even discomfort. But, as they say, “No pain, no gain.” And, perhaps in Smullyan’s case, “... no brain.”