HN Books @HNBooksMonth

I was just re-reading this book last night. https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden...

⬐ lacker

That book is where I first learned about Gödel's incompleteness theorem. Definitely a good book!

I spent a while when I first read it trying to understand Gödel numbering, all the stuff where you multiply prime numbers together, 11 stands for (, that sort of thing. It wasn't until far later that I realized all of that was just a mathematician in the 1930's trying to explain how a string of characters could be encoded as a binary number, something that modern computer programmers more or less take for granted.

For a detailed perspective on how the proof works, I highly recommend Ernest Nagel and James Newman's book Gödel's Proof [0], mentioned in the article. Alternatively, Gödel Escher Bach by Douglas Hofstader is a classic which serves as a great (and more accessible) introduction to the proof [1].

[0] https://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/081...

[1] https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden...

There's so much more to CS theory than big O notation and you're in for a treat if you check out any of the below - happy to share more if people are interested.

1. https://www.amazon.com/Computational-Complexity-Approach-San...

2. https://www.amazon.com/Quantum-Computing-since-Democritus-Aa...

3. https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden...

4. https://www.amazon.com/Introduction-Theory-Computation-Micha...

Look, I know, it's cool, and like, it has the potential to help. But trying to tech/math your way into a better democracy isn't very likely because people are assholes; you have to make incentives for the assholery to fight itself, it's not easy. Hofstader in Godel Escher Bach goes WAY into why that is from a math/physics/art/music point of view, you should read it (maybe you have already), it's like 6 bucks. https://www.amazon.com/gp/offer-listing/0465026567/ref=tmm_p...

I'm not confounding bitcoins with marxism and that mess of history. I'm just saying that there are things out there that were good in theory, but the applications of the theory are just plain terrible, marxism is a famous example of that.

⬐ andrepd

>But trying to tech/math your way into a better democracy isn't very likely because people are assholes

That's ridiculous. So we can't do anything, whatsoever, to improve our society and our systems, because eh people are assholes or whatever? That's nonsense. Of course we can improve our systems, our laws, our government, and of course mathematics and technology can help. For example, our voting systems are woeful because they are holdovers from a time when nobody thought about these things from a mathematical point of view (and nobody still does: "let's just vote for people and let the person with the most votes win" sounds perfectly simple and correct for 99% of the population). But we can do much better, and it can objectively improve our democracy a whole lot.

Will applying mathematics and technology to democracy fundamentally change and transcend human nature? Duh, of course not, but nobody claimed it will. There's plenty between implementing an utopia and going nothing at all.

⬐ Balgair

> So we can't do anything, whatsoever, to improve our society and our systems, because eh people are assholes or whatever?

Yes, that is correct. Also, me and Mr. Strawman could use some more hay, do you have any?

> ...and nobody still does...

This is what I'm talking about. Trying to force math/tech onto a democracy/republic where the voting population doesn't understand it cannot end well. The voter will be suspicious, and rightfully so, of the process if they do not understand it. This is especially true if there is any corruption in the system at all. Since we know men are not angels, then the vast majority of voters must have belief in the processes as we all know men do become devils. Democracy demands this faith to work. Yes, we can make the system mathematically better, but if that comes at the cost of the faith in democracy, then it's mute. Even with the system we have now, simple as it is, there is already a large lack of faith in it by a lot of the US, and this is already a threat to idea of self-determination.

If this seems interesting to you, I would suggest reading: "Gödel, Escher, Bach: An Eternal Golden Braid" [1]

[1] https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden...

⬐ edem

Came here to suggest this book. You were faster.

⬐ mrkgnao

I think Westworld naming the next episode "The Well-Tempered Clavier" could, somehow, lead to a resurgence in interest in GEB -- lots of people on /r/westworld seem to be interested, for sure! (For one, I've heard that the show's creators have admitted that they are creatively indebted to the book in some ways.)

⬐ jyriand

I think it might have something to do with the structure of the fugue.

> a contrapuntal composition in which a short melody or phrase (the subject) is introduced by one part and successively taken up by others and developed by interweaving the parts.

⬐ ThomPete

Westworld also did some interesting hints to "The Origin of Consciousness in the Breakdown of the Bicameral Mind" by Julian Jaynes a book that if you haven't read it yet you should. It's up there with GEB.

1. https://www.amazon.com/Concepts-Techniques-Models-Computer-P...

2. https://www.amazon.com/Big-Book-Concepts-MIT-Press/dp/026263...

3. https://www.amazon.com/Gödel-Escher-Bach-Eternal-Golden/dp/0...

⬐ solipsism

Is it a HN feature that cuts off long URLs unless you click Reply to isolate the comment? Actually even after isolating the comment the URLs are cut off (but not quite as short). Highly annoying.

You should edit and put the titles before the links.

⬐ selmat

Updated as new comment since two hours already elapsed

[1] Concepts, Techniques, and Models of Computer Programming (MIT Press) - URL: https://www.amazon.com/Concepts-Techniques-Models-Computer-P...

[2] The Big Book of Concepts (MIT Press) - URL: https://www.amazon.com/Big-Book-Concepts-MIT-Press/dp/026263...

[3] Gödel, Escher, Bach: An Eternal Golden Braid - URL: https://www.amazon.com/Gödel-Escher-Bach-Eternal-Golden/dp/0...

"I want to find the absolutely crazy-to-grasp book of all times."

Gödel, Escher, Bach - An Eternal Golden Braid, by Douglas Hofstadter. Anytime I start reading a story which contains recursiveness my mind will feel warped and stuck in a loop at times.

http://amzn.to/1KijebX (affiliate link)

http://www.amazon.com/gp/product/0465026567 (non affiliate link)

There's nothing about the idea of physical consciousness that says it has to be a continuum -- there could just be some critical mass or qualitative attribute of brains that puts us "over the threshold", so to speak. Nobody can give any kind of a definitive answer. For ideas about a "continuum" of consciousness, you might read Phi:

http://www.amazon.com/Phi-A-Voyage-Brain-Soul-ebook/dp/B0078...

Or for other views, you might check out V.S Ramachandran (neuroscience): http://www.amazon.com/Brief-Tour-Human-Consciousness-Imposto...

Jeff Hawkins (computer science): http://www.amazon.com/On-Intelligence-Jeff-Hawkins/dp/080507...

Hofstadter (mathematics, cognitive science): http://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/...

Those are some of my favorite popular-press books on the subject.

⬐ astrocyte

* Read Jeff Hawkins (On intelligence)

* Have GEB (Covered enough of it)

My point was to bring out the implicit belief that there is :

> Some critical mass or qualitative attribute of brains that puts us "over the threshold"

> If consciousness is indeed a variable quantity, then every single able bodied adult human has more "units" of consciousness than, say, a dog.

> The variation within a species is also probably pretty small compared to the gap between species.

None of which are proven in any scientific way yet many believe it to be the truth. We haven't even resolved what consciousness let alone its range of existence.

> Just like intelligence, the amount of consciousness that a person has is not a measure of their value.

And yet, one draws lines to distinguish human intelligence/consciousness from that say of a dog.

This reminds me of Godel's incompleteness theorem - which I'll poorly present as: Any system that is sufficiently complex and complete will contain legal assertions that will disprove or destroy the system. (Those that do not are not complete).

http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_the... http://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/...

⬐ sp332

I don't want to be condescending, but that isn't what the theorem says. (I'm not even sure it's true.) Incompleteness means there is a true statement, that cannot be proved true inside the system.

⬐ gohrt

And the contrapositive is that any sufficiently complex complete system is inconsistent.

⬐ sp332

Oh man, brokentone was right this whole time. Sorry brokentone!

⬐ brokentone

I'm only able to flirt with the edges of understanding this deep philosophy/math, so I can see correlations, but not defend them

⬐ kbd

> ... will contain legal assertions...

Well, the comments state that to make this happen he had to "[exploit] a bug in the UTF-7 decoder". So, not legal assertions.

⬐ brokentone

It parses, thus it is legal.

⬐ jerf

Neither throwing an exception nor having a perfectly-deterministic buggy behavior is what Godel was referring to. This shouldn't remind you of anything related to the incompleteness theorem, because it's completely unrelated.

⬐ anaphor

Not completely unrelated: https://en.wikipedia.org/wiki/G%C3%B6del_numbering but what he/she was talking about is unrelated.

Not sure if this is the right direction or not. In different ways they are all, essentially, about programming...

http://www.amazon.com/Code-Language-Computer-Hardware-Softwa...

http://www.amazon.com/Elements-Computing-Systems-Building-Pr...

http://www.amazon.com/Structure-Interpretation-Computer-Prog...

http://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/...

http://www.amazon.com/Pragmatic-Programmer-Journeyman-Master...

Good luck!

⬐ dlf

Ditto on "Code." As a non-programmer learning to program, it was everything I needed to know to wrap my head around how everything actually works.

⬐ syedkarim

This is absolutely the right direction--thanks! The one book on the list that might get kicked back is "Structure and Interpretation of Computer Programs". Too bad, since it's probably the most concrete. This is a great starting point, thanks again.

Godel, Escher, and Bach

http://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/...

http://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/...

If you enjoyed this article, and haven't read "Gödel, Escher, Bach: An Eternal Golden Braid" by Doug Hofstadter yet, then stop reading HN immediately and order yourself a copy:

http://www.amazon.com/G%C3%83%C2%B6del-Escher-Bach-Eternal-G...

Having read this book would, in a fair world, be worth more on your CV/resumé than a large proportion of comp-sci degrees.

Even better, go out of your front door to a real bookshop and get them to order you one. Who knows, you might speak to someone! BONUS!

Well, there are some related topics on Quora: http://www.quora.com/Randomness?q=random and http://www.quora.com/What-are-some-good-books-on-random-proc...

You can actually ask your question there as well in case this question gets unnoticed on HN; Quora people are very smart and pretty responsive

see http://en.wikipedia.org/wiki/Stochastic_process, http://en.wikipedia.org/wiki/Random_walk and do a search for Random Processes or Stochastic Processes on Amazon bookstore

Read about Entropy: http://en.wikipedia.org/wiki/Entropy A good book on Information theory can help you put it in context: http://www.amazon.com/s/ref=nb_sb_ss_c_1_18?url=search-alias...

Check out GMP http://gmplib.org/

If you're philosophically inclined read some existentialists, they deal a lot with irrationality and chaos: http://en.wikipedia.org/wiki/Existentialism

If you're financially inclined read Random Walk Down Wall Street: http://www.amazon.com/Random-Walk-Down-Wall-Street/dp/039331 and the Black Swan: http://www.amazon.com/Black-Swan-Impact-Highly-Improbable/dp... you may want to check out his other book as well, it is rather non-technical: http://www.amazon.com/Fooled-Randomness-Hidden-Chance-Market...

To learn more on how Wall Street deals with the stock market randomness read some books on Time Series analysis and forecasting, e.g the classic http://www.amazon.com/Time-Analysis-Forecasting-Probability-...

If you are a data scientist in heart read this great Q&A thread: http://www.quora.com/How-do-I-become-a-data-scientist

I wish I could help you with a link to a clear non-technical introductory article but this is all I've got. As random as it gets:)

Probably some good introductory book on science will fit the bill, science after all deals primarily with randomness. You may want to check out http://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/...

⬐ drewse

Also, since it looks like you're like you've been on HN for a while, do you know how I can add this to the questions section? Some posts start with "Ask HN:"

[I'll delete this comment once the issue's been resolved]

⬐ helwr

Just put "Ask HN:" in the title

⬐ drewse

Thanks, but I guess I can't change that now.

⬐ drewse

Thank you very much! You are extremely helpful and supplied me with a lot of material to look over! Some of these books or topics are only covered by big textbooks, which is not exactly what I was looking for (I think it was unclear in my original post), but you did help introduce me to some new topics and fields where randomness takes place.

Also, it's nice to be reminded about Quora. I've heard of it before, but hadn't thought about it in a while. I might try it and give it a go!

Very much relevant to anybody who found this interesting: http://www.amazon.com/Godel-Escher-Bach-Eternal-Golden/dp/04...

I found it in a used bookstore for $5 once, totally by accident. It's probably the best nonfiction book I've ever started (I unfortunately never bothered to finish, which isn't so good. It's still in my backpack in case I ever get stuck anywhere...).

⬐ RevRal

Sure, you can get by in life without having finished reading GEB. But to me, a life having not read GEB is not a life worth living.

MIT's OpenCourseWare is an excellent way for him to study CS on his own while in high school.

I would recommend, at 14, getting him utterly hooked on the mindset of CS and related subjects. Godel, Escher, Bach, etc. If you can get him fascinated with the field, he'll find all the information he needs on his own better than any list of required reading you'll get.

http://ocw.mit.edu/OcwWeb/web/home/home/index.htm

http://www.amazon.com/dp/0465026567

Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid http://www.amazon.com/Godel-Escher-Bach-Eternal-Golden/dp/04...

⬐ steveplace

It's taken me 6 months to get through 1/3 of the book.

If you want a good feel for this stuff, try downloading and going through this course, "NAND to Tetris": (Link is not the course, but a talk about it.)

http://video.google.com/videoplay?docid=7654043762021156507

The book is only $26, last I looked. The course software is all Open Source.

You'll see how digital logic is used to construct components like logic units and memory, which is then used to construct a computer, for which you create a computer language, which you then use to write an operating system, and finally, you program games on it.

This will then give you the wherewithal to really understand Godel-Escher-Bach:

http://www.amazon.com/Godel-Escher-Bach-Eternal-Golden/dp/04...

If you want, you can read the book first, but then go through the course and read it again. The 1st time you read it, much of it will be lost on you, but the 2nd time, you'll have many Ah-HA! moments.

One key is Automata Theory. Understand that, and you can understand what you are trying to ask about.