Satan, Cantor, and Infinity and Other Mind-Bogglin

Professor Smullyan's book Satan, Cantor, and Infinity, is an excellent mathematical novel, extremely readable for everybody from elementary schoolboys(girls) to first class college (university) students. The story concerns three major personalities - The Sorcerer living in the Knight-Knave Island and Princess Annabelle with her suitor. As in many books of professor Smullyan the first half of the story is devoted to various puzzles about knights (truth-tellers) and knaves (liars). The third chapter takes place on the island of robots. The puzzles of self-constructive and self-destructive robots throw light on problem of languages, which allow self-reference, and the famous Gödel's theorems. This chapter may be harder to catch and the reader is recommended to consult another professor Smullyan's book, Forever Undecided. In the rest of the book are introduced Zeno's paradoxes concerning the problem of continuity and change (with these paradoxes are discussed the most elementary ideas of infinitesimal calculus), envelope paradox (a kind of paradox of rationality), ant the set-theoretic paradoxes (Burry's paradox, Mannoury's paradox, Russell's paradox and Cantor's paradox). The basic ideas of set theory are introduced in the form of problems of a prisoner in the Hell - Satan gives the prisoner opportunity to save himself(herself) if he(she) puzzles out an integer which Satan wrote on the paper closed in an envelope. Story also introduces the famous Continuum problem - the set theoretic problem formulated by the founder of set theory Georg Cantor in the 19th century and unsolved to our times (or at least unsolved by the more modest set theoretic principles not using some hypotheses concerning large cardinals). The story concludes with a nice Zwicker's hypergame paradox and a legend about a gifted student of Cantor imprisoned in Hell, who outwits the Great Satan. The entire book is written in non-technical style and really is a MATHEMATICAL NOVEL, maybe a mathematical fairy tale, not a textbook. (I would only like to know if professor Smullyan is really going to fulfill his promise given in the book that he will try to present more calculus ideas in the future.) Well, the book is very delightful reading for these days - the Good defeats the Evil even in this story, even in the realm of mathematics!

Before you start reading this book, prepare to have your logic bone tweaked, tickled and annoyed. There is no one better than Raymond Smullyan at creating logic puzzles that will intrigue, infuriate and stretch your mind to slightly beyond its limits. The last chapter, a dialog between Satan and a student of Cantor, could be the basis of a book and is a true work of genius. I read it twice, not because I didn't understand it, but because I enjoyed it so much. The other sections of the book cover many facets of logic, including lists of superb problems about people from the planet Og, where green northerners always tell the truth and red northerners always lie. However, green southerners always lie and red southerners always tell the truth. Similar to the knights and knaves problems, most can be solved using a simple table. Solutions to the problems are given at the end of each chapter. Raymond Smullyan seems to exist at a different logical level than the rest of us. His problems are at times fiendishly clever, although not beyond the capacity of someone willing to think a bit. This is a case where you can expand your mind by showing how limited it was before.

This is a VERY good book some puzzles are easier and some harder, but all of them have an answer. hours of fun! when you are done go back and see if you can do some of the harder puzzles without peeking at the answer.

Smullyan has produced another terrific collection of puzzles and problems, bound to engage those readers with an interest in logic and mathematics. The puzzles are very approachable, and the reader who spends a few minutes working them out will be highly rewarded for his efforts. This is a must-read for all indoctrinated Smullyan fans, and a great introduction for new readers to Smullyan's world of mind-bending brain exercises.