Forever undecided

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1. abrax3141Sep 2022
   Smullyan's "Forever Undecided", and Ernest Nagel's "Gödel's Proof" are the best explanations available, to my mind. I find GEB to be bloated, if all that one is interested in is Gödel. (There is much more to recommend GEB, but if all you want is Gödel's proof, see one of the above.)
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2. pjungwirJul 2020
   I second this! Gardner would be something more recreational and fun than a lot else out there. The Colossal Book of Mathematics is a good way to get a lot in one place. The Night is Large is also great but less math-focused.

   I don't see any recommendations for Smullyan yet. The Lady or the Tiger is the classic I think, but I really loved Forever Undecided.

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3. pjungwirFeb 2017
   My favorite Smullyan book is out of print: Forever Undecided: A Puzzle Guide to Gödel. Gödel's paradoxical theory hooked me in college, and after twenty years I still can't help but feel that it has a message for us---not in the word-play associations that some philosophers mistreat such things, but more in its implications for the human mind and artificial intelligence, along the lines that Roger Penrose explores. I've read Franzén's rejection of all attempts to "apply" Gödel's proof, and yet, I keep coming back to the idea that we can see our way "out" of these limited systems.

   Anyway, Smullyan's book is a real treat. In the later chapters he even goes beyond Gödel. I've never completely figured out how much of that is Smullyan and how much is other published research.

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4. TelmoMenezesAug 2015
   Sure, and abductive reasoning can be formalized in certain modal logics with Kripke semantics.

   What Gödel tells us is that, as long as you have a sufficiently powerful formal system, you cannot prove the consistency of the system itself. Modal logics are no exception.

   If you are a computationalist (that is to say, you believe that the human mind can be emulated by a Turing machine), then you might want to take a look at Gödel, Escher, Bach, where Hofstadter discusses how the second incompleteness theorem applies to Turing machines.

   You might also enjoy "Forever Undecided" by Smullyan. It uses puzzles to guide you to an intuition about what the incompleteness theorems means to human knowledge and its limitations. In the worst case it's a fun read.

   Peace!

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5. pjungwirMay 2015
   The Tufte book is a pleasure but hard to tote to the beach. If you try to carry it on a plane they might charge you extra. :-) Some other ideas:

   Managing the Professional Service Firm by David Maister. I can't keep this one on my shelf because I keep giving it away.

   Cryptography Engineering by Bruce Schneier. Very accessible. Probably not very practical if you're not building a cryptosystem, but it's a nice way to get a lay understanding---and scare you enough about how many pitfalls there are. When you finish read this loving criticism also: http://sockpuppet.org/blog/2013/07/22/applied-practical-cryp...

   Forever Undecided by Raymond Smullyan. Fun "puzzle guide to Gödel". Out of print but Amazon has used copies.

   Quantum Computing since Democritus by Scott Aaronson. Fun survey but requires some familiarity with P/NP, quantum mechanics, linear algebra.

   Programmers at Work by Susan Lammers. Interviews with computer pioneers. Interesting to see how they think and what they have in common.

   Time Management for System Administrators by Thomas Limoncelli. Short, easy read with lots of practical advice for all of us.

   The Mac is Not a Typewriter by Robin Williams. Very slim. Learn the difference between hyphens, en-dashes, and em-dashes.

   If you do product design you might enjoy a slow musing read through Apple's original Human Interface Guidelines.

   Those last three combined probably weigh half of the Tufte book.

   Have a nice vacation! :-)

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6. pjungwirDec 2014
   I came here to say the same thing. I was really interested in Gödel's Incompleteness Theorem in college, and around 22 I had the same idea as Penrose: that if the mind could be simulated on a computer, it would be a formal system in Gödel's terminology, yet the mystery of the Incompleteness Theorem is that we can work out when things are true or false despite limitations of formal systems. Penrose takes that nugget and tries to develop a rigorous argument against general AI or a mind that is explainable by purely Newtonian mechanics. At least that's my understanding. I only made it about half way through the book, because it is not really aimed at a general reader. Agree or not, it's a pretty fascinating argument, one which makes my head spin.

   Some other nice resources on Godel are:

       - Gödel's Proof by Nagel and Newman
       - Forever Undecided by Smullyan

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