3-2015 When Satan meets Cantor -- A book review

Satan, Cantor, and Infinity, and Other Mind-Boggling Puzzles, Raymond M Smullyan (Pub.: Dover Publications, Mineola, New York)

Raymond Smullyan, the master story-teller, wears many feathers on his cap : mathematician, logician, concert pianist, stage magician, amateur astronomer, puzzle master, teacher. He often mixes his talents, and creates amazing books on logic and puzzles, which often call for profound reasoning and mathematical deduction. His book, “Satan, Cantor and Infinity: Mind-Boggling Puzzles (by Raymond M. Smullyan) ” is one such masterpiece.

In this book, Raymond Smullyan takes a puzzle-based perspective on the principles underlying the works of mathematician Georg Cantor, particularly on infinity. His fascinating riddles involve probability, certainty, time, and infinity, and they unfold amidst a landscape populated by honorable knights, lying knaves, quick-witted robots, and other fanciful characters. This 270+ pages tome, explains 25 puzzles, grouped into 7 parts. Each puzzle is as intriguing as the other, and demonstrates the inventive genius of the author. Using an imaginary sorcerer who is really a logician, Smullyan takes us on a tour of logic and mathematics, including Godel’s famous theorem. Which brings us to the pioneering discoveries of Georg Cantor. Each puzzle is not linked to any other in the book, and so the reader may peruse the contents in any order.

I chose to read the last part of the book (part 6) which had a tantalising title “A journey into infinity”. This part carries a puzzzle, or rather an introspection “What is infinity ?” A very lucid conversation involving the Sorcerer, talks about infinity and the famous “Hilbert’s hotel problem”. This lead me to my favourite concept – paradoxes. I also found in part 5 “The envelopes paradox”. I had written about this paradox, in this very journal “Gonit Sora”, some time ago.

The book has its fair share of puzzles involving truth-tellers (knights) and liars (knaves). It has therefore several interesting examples of the usage of Goodman’s principle.

Smullyan not only unveils his puzzles in his own fascinating style. He also gives clues/solutions to most of his puzzles. But wait ! You need to ponder well, before you can grasp the puzzle or its solution (my experience) . Finally, this book is not for the mathematically weak-minded. A good knowledge of Cantor’s set theory, and the works of Zermelo, Fraenkel, Russel, Godel, and Lewis Caroll, would make reading this book, a lot more enjoyable. My closing remark would be that rather than using this book for entertainment, it can also be a valuable and innovative tool for understanding mathematics and logic.

Smullyan beautifully sums up his thoughts as follows: “The moral of the story is that even fallen angels might benefit from a good course in mathematical logic.”

An autograph or a kiss ?

Raymond Smullyan teaches a clever and honest method of earning a kiss. See ::

http://server3.pianosociety.com/protected/smullyan-rambles.mp4

He teaches a less elegant way to plant a kiss. See ::
http://blog.tanyakhovanova.com/?p=235

In case you are wondering who this pervert Raymond Smullyan is, look at my blog entry "The Hardest Logic Puzzle Ever " (given below).


partha

The Hardest Logic Puzzle Ever

The Hardest Logic Puzzle Ever -- by Raymond Smullyan

I have just received a book on logic puzzles, by Raymond Smullyan. Smullyan would be best described as the craziest and most gifted person in this world. He is a mathematician, a concert pianist, logician, writer, magician, conjurer, raconteur, all packed in one. Here is a masterpiece which I found on the Internet :

In 1992, George Boolos called the following "the hardest logic puzzle ever". I figured that people here would especially like it. It's certainly a Raymond Smullyan inspired puzzle and goes as follows.

"Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are 'da' and 'ja', in some order. You do not know which word means which."

Just for the sake of clarity, George Boolos gives the following four clarifications: (1) It could be that one god gets asked more than one question (and thus, some god is not asked any question at all). (2) What the second question is, and to which god it is put, may depend on the answer to the first question (likewise, for the third question). (3) Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely. (4) Random will answer 'da' or 'ja' when asked any yes-no question.

Good luck!

partha

PS: The person who solves the above puzzle will be declared as the "second Smullyan", in this blog. You can email me your ssolutions.

PPS : To know more about Raymond Smullyan, visit ::
http://en.wikipedia.org/wiki/Raymond_Smullyan

PPPS: A solution is here.

PPPPS: This problem is described here