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.”

2-2015 My own corner on the web

Now, I have my own corner, on the web. The new URL for my website is ::
http://drpartha.org.in/index.htm

You can navigate down to all my pages starting from the above page.

Bookmark this page, and let all your friends know about this new site. If you own or administer a website, please add a link to the above page from your site.

Thanks, partha

1-2015 When did it all start ?

On Christmas Day (25 Dec.) I posed myself the question >> "When was Jesus born ?" . More out of curiosity and perplexion as a maths teacher. The question was repeated and published on the Internet, for all the world to answer ::

http://partha-the-prof.blogspot.in/2012/01/32012-when-was-jesus-christ-born.html

http://partha-the-prof.blogspot.in/2012/01/82012-when-was-jc-born-sequel.html

Now, almost three years later, I get a clue from someone who knows more than me on these matters :: http://aristean.org/birthmay23.htm

Then, why did someone start the confusion with 25 Dec. ?

There is also confusion on the :

date of crucifixion of JC

The whole question is much more fundamental, and of serious tenor when we ask "When exactly did CE start ?" Are we following a calendar which is of questionable origin ?

I am still confused.

partha

3-2014 It takes a leader to recognise a leader

It takes a leader to recognise a leader

TeX Users Group (TUG) endorses the free ebook LLL - Let's Learn LaTeX. TUG is the ultimate authority in matters related to TeX and LaTeX. TUG has listed LLL amongst the top tutorial resources in LaTeX. TUG has also published an announcement regarding LLL, in its flagship journal TUGBOAT.

What more are you waiting for ?

Start now, take a look at :: http://www.freewebs.com/profpartha/teachlatex.htm

2-2014 Finding a new home for the Taj Mahal

The LaTeX masterpiece I made, can now be accessed from :: http://drpartha.org.in/profpartga/teachlatex.htm

Take a look at the Synopsis first.

partha

1 / 2014 It takes time to create a masterpiece

I have just now uploaded my LaTeX magnum opus "Let's Learn LaTeX" to https://sites.google.com/site/drpartha/Home/LLL.zip. It took more than three years of patient study and experimentation, to create all the contents. It took more than a month to find out the ideal way to publish the masterpiece. I yet do not know how many centuries it will need for people to take notice. Maybe it will be archeologists who will discover this masterpiece buried under the pile of debris called the w-w-web. Maybe I wont be alive then, to answer your queries. So, hurry up and start the learning.

64 / 2013 Course Chronicle (crypto - v4)

Crypto - v4 Course Chronicle
Course website : profpartha.webs.com/cryptov4.htm
Course Instructor : Prof. S. Parthasarathy (drpartha@gmail.com)
Each session = 90 min. approx

Session #	Date	Events
34,35	2014-01-12	Final exam.
32,33	2014-01-08	Closure. Debriefing. Exam announcement and instructions. Course feedback and speakout. Salute the giants. Videos: 1. Alan Turing 2. Claude Shannon
30, 31	2014-01-03	Misc. concepts and tools: Leet, one-way encryption, steganography, Hamming, Chaffing and winnowing, secure wipe/shred, ethical hacking, practice what you preach.
28, 29	2014-01-02	SSL at work. Detailed overview of SSL. Downloading and importing CA root certificate, and CRL. CRL vs OCSP. Videos : 1. The web is down 2. DDOS 3. How SSL works
26, 27	2014-01-01	Network security tools. PKI. TCP/IP. IPV4 vs IPV6. IPSEC. Other tools.
24, 25	2013-12-27	Principles of Authentication, Identity authentication, content authentication, zero-knowledge authentication, challenge-response authentication, biometric authentication, passwords. Strong passwords. Demo of password meters. Video: What are smart cards ?
22, 23	2013-12-26	Security enhanced Linux, Multi-level security, BIOS password, Bootloader password, Login password, secure coding tools, Discretionary access control,  Mandatory access control, Physical verification of GPG fingerprints of students keys.
20, 21	2013-12-25	Number theory -- DL problem. Overview of RSA algorithm. Mid course review. The Indian angle.
18, 19	2013-12-20	Fundamental concepts in number theory, Peano's axioms, What are Numbers ?, Divisibility, quotient, remainder, modulo arithmetic, properties of modulo arithmetic, Fermat's little theorem, Euler's generalisation, modulo inverse, Prime numbers, co-primes, Euler's totient function, GCD, Euclidean algorithm, extended Euclidean algorithm.
16, 17	2013-12-16	Cryptographic standards. Block ciphers, Feistel structures. DES, 3DES, AES. ECB, CBC modes, S box, P box. Overview of Blowfish, IDEA. Video -- Key strength and brute force attacks. Exercise 5, 5a, 5b
13, 14, 15	2013-12-13	GPG Command examples. Export keys. Import keys. Secure key distribution. Exercises : 4a, 4b, 4c -- importing keys securely
12, 13	2013-12-09	GPG introduction. Command examples. Demo: Creating GPG key pairs.
9, 10, 11	2013-12-06	Pig pen cipher, Block ciphers, Feistel networks. Hash digests, MAC and HMAC, principles of hash digests, properties of hash digests, md family vs. sha family, sha3, digital signatures, properties and usage, demos of md5sum and shasum, "How to build a fortress" Video: Diffie Helman key exchange -- paints analogy Exercise #3: Subscribe Schneier's cryptogram newsletter.
7, 8	2013-12-02	Symm. key crypto contd., ROT13, XOR, Vigenere cipher, trap-door functions, factoring problem, discrete logarithm problem. Video: Locked box analogy Demo: Doing it with zip. Doing it with vi Exercise #2: Symmetric encryption with zip.
5, 6	2013-11-28	Elements of cryptography, terminology, encryption vs. decryption, Why Alice and Bob should go on a holiday, Caesar's cipher, symmetric keys, key exchange problem, concepts of asymmetric key cryptography, public key vs. private key. Videos: Ronald Rivest, Bruce Schneier.
3,4	2013-11-27	e-security: risks, threats, remedies. Simple examples. Exercises #1a, #1b, #1c. Handout DVD distributed to the class.
1, 2	2013-11-21	Start crypto-v4 course. Take off lecture. Security questionnaire.
0	2013-11-10 to 2013-11-20	Political disturbances. KU closed due to strikes.

63/2013 You need help ?

You need more info. ? You need help ?

If you want help, and you expect people to help you, ask. But, ask wisely and with some sense of decency and responsibility.

Learn how you can prove that you deserve being helped.

partha

62/2013 A sequel to the sequel

This is a sequel to my post 61/2013. My final and definive response to the cynical, xenophobic and puerile comments made by some of you, is here.

61/2013 Cryptography has Indian roots

Conents removed for editing and updates