…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!
……一站式搞定大量内容的好方法。《The Night is Large》也很赞，但数学比重没那么多。我还没看到有人推荐 Smullyan 呢。我觉得《The Lady or the Tiger》是经典，但我真的很喜欢《Forever Undecided》。
…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.
……给你答案，但要做到这一点，你必须构造出某种自指。（就像哥德尔那样！）如果你喜欢思考这类事情，Raymond Smullyan 写过很多精彩的作品——更通俗的入门我推荐比如《Forever Undecided》或《To Mock a Mockingbird》，想看形式化严谨推导的可以看《First-Order Logic》。
…answer for you, but to do so you need to develop some kind of self-reference. (Like Godel!) If you like thinking about this sort of thing, Raymond Smullyan has a lot of great writing - I'd recommend eg Forever Undecided or To Mock a Mockingbird for a more informal treatment, or First-Order Logic for a formal one.
…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
……通俗入门的好办法——而且能让你充分被里面的各种大坑吓醒。读完之后也看看这篇善意的批评：http://sockpuppet.org/blog/2013/07/22/applied-practical-cryp... Raymond Smullyan 写的《Forever Undecided》。一本有趣的“哥德尔谜题指南”。已经绝版了，但亚马逊上有二手书。Scott Aaronson 写的《Quantum Computing since Democritus》。很有趣的概览，但需要对 P/NP、量子……有一定了解
…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…
我最喜欢的 Smullyan 的书已经绝版了：《Forever Undecided: A Puzzle Guide to Gödel》。大学时哥德尔的悖论理论把我彻底迷住了，二十年后的今天我依然忍不住觉得它向我们传达了某种启示——而不是某些人所做的那种文字游戏式的联想……
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…
……由图灵机模拟），那你可能想看看《Gödel, Escher, Bach》，Hofstadter 在里面讨论了第二不完备性定理如何适用于图灵机。你也许还会喜欢 Smullyan 的《Forever Undecided》。它通过谜题带你建立起直觉，去理解不完备性定理对人类知识及其局限性意味着什么。退一步讲，拿来当消遣读物也很棒。祝好！
…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!
……一站式搞定大量内容的好方法。《The Night is Large》也很赞，但数学比重没那么多。我还没看到有人推荐 Smullyan 呢。我觉得《The Lady or the Tiger》是经典，但我真的很喜欢《Forever Undecided》。
…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.
……给你答案，但要做到这一点，你必须构造出某种自指。（就像哥德尔那样！）如果你喜欢思考这类事情，Raymond Smullyan 写过很多精彩的作品——更通俗的入门我推荐比如《Forever Undecided》或《To Mock a Mockingbird》，想看形式化严谨推导的可以看《First-Order Logic》。
…answer for you, but to do so you need to develop some kind of self-reference. (Like Godel!) If you like thinking about this sort of thing, Raymond Smullyan has a lot of great writing - I'd recommend eg Forever Undecided or To Mock a Mockingbird for a more informal treatment, or First-Order Logic for a formal one.
……并不是真正写给普通大众读者的。不管你同不同意，这都是个极具吸引力的论点，看得我头皮发麻。关于哥德尔的其他好资料还有：- Nagel 和 Newman 写的《Gödel's Proof》- Smullyan 写的《Forever Undecided》
…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
……通俗入门的好办法——而且能让你充分被里面的各种大坑吓醒。读完之后也看看这篇善意的批评：http://sockpuppet.org/blog/2013/07/22/applied-practical-cryp... Raymond Smullyan 写的《Forever Undecided》。一本有趣的“哥德尔谜题指南”。已经绝版了，但亚马逊上有二手书。Scott Aaronson 写的《Quantum Computing since Democritus》。很有趣的概览，但需要对 P/NP、量子……有一定了解
…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…
我最喜欢的 Smullyan 的书已经绝版了：《Forever Undecided: A Puzzle Guide to Gödel》。大学时哥德尔的悖论理论把我彻底迷住了，二十年后的今天我依然忍不住觉得它向我们传达了某种启示——而不是某些人所做的那种文字游戏式的联想……
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…