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Mandatory recommendation for Gödel, Escher, Bach: An Eternal Golden Braid [1] by Douglas Hofstadter. Now I know most HNers are no stranger to this book, but if

Mandatory recommendation for Gödel, Escher, Bach: An Eternal Golden Braid [1] by Douglas Hofstadter. Now I know most HNers are no stranger to this book, but if you haven't read it I encourage you to pick up a copy. A lot of people will say that it "changed the way they think about everything" without going into much more detail, so I'll just tell you how it did so for me. I've always been an analytical thinker, but the most useful thing this book did for me was teach me how to think mathematically. It showed me there was immense beauty in mathematical thought. [1] http://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach http://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach

presidentender 13y ago
It's a good read, but you have to be careful with it, because it can take up a lot of your time and you'll quickly run into diminishing returns. Hofstadter is smarter than I am, and I know he's smarter than I am, so I'm never sure whether I've understood anything properly. It's a perfectly laid Dunning-Kruger trap, and it ensnares probably too much of my processor time when I fall into it.
- jonnathanson 13y ago
  The problem with reading Hofstadter is that, because he's so brilliant and so lucid, you'll often find yourself readily him uncritically: thoroughly convinced by anything he's saying, and simply absorbing it all. Some of his books, the aforementioned in particular, are works of insight and genius. Others, such as his recent book on metaphor-as-thought, are speculative steps onto a bit thinner ice. (Note: I realize Hofstadter and his colleagues have spent decades exploring metaphor-based AI, and that there might be something quite real to it -- but he doesn't make a convincing case for the sufficiency of this hypothesis, though he insists it's there).
6cxs2hd6 13y ago
GEB high on my list of books that I own on dead trees, but also want on Kindle. Even if it didn't qualify for Amazon's deal to get it cheaper if you already bought it from them -- even if I had to pay a lot for it. Yeah, I know it's not an ideal format for Kindle, e.g. the illustrations and... a few other features I won't give away here. But still. What a great thing to have at-hand anytime you wanted to dive in and read part of it. Sigh.
jfb 13y ago
For anyone looking for a brief, accessible explanation of the proof itself, I cannot recommend the Nagel and Newman [1] highly enough. [1] http://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/0814758371/ref=sr_1_1?ie=UTF8&qid=1380563150&sr=8-1&keywords=nagel+newman http://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/081475837...
- alok-g 13y ago
  While I loved the first few chapters of the book, and they were mind-opening, I found the explanation of the proof unsatisfactory. As I recall, it was mentioned in the preface that the book will give a complete outline of the actual proof. I did not find this to be the case, the outline seemed to jump quite a bit from one thought to another leaving me with more questions about the proofs than answers. I still do not understand the proofs (though I now nearly understand an analogous result in computer science via Jeff Ulmann's book).
  - jfb 13y ago
    I has been a few decades since I read it for the first time, so I may be glossing it in my mind.
Tycho 13y ago
Even if it doesn't have a profound effect on your perspective or if you find the conclusions uninteresting, the journey itself is very informative. Read if you don't already have much exposure to: first order logic / predicate calculus; formal systems; DNA; Escher and Bach; number theory; Goedel's incompleteness theorem; Turing machines; neuroscience; information theory...
eli_gottlieb 13y ago
Is it really that great? I started reading it when in college, got tired of lugging a huge dead-tree book around in my bag, and eventually just sort of put it down. Maybe I didn't get far enough in to hit the parts that would be interesting to someone who's already long-since done basic programming and math?
- laxatives 13y ago
  It definitely blew my mind when I first read it, but I think its also gained a big cult following creating a lot of hype. I thought about it a lot for a few months after I read it, but I certainly haven't thought about it in over a year and it definitely hasn't shaped the way I think about things now (at least not that I'm aware of). If you haven't taken the math behind it, its awesome and you should definitely read the first 14 chapters if you're interested. But after that, its basically a bunch of Hofstatdler's musings on DNA and AI, a lot of which seems outdated and like a lot of speculation (the book was published ~25 years ago). Then again, most books I've read I forget about much sooner than a few months. If you want a good read, go for it, but its not some holy grail that will change your life forever.
- breckinloggins 13y ago
  It's probably not that earth-shattering if you already have an appreciation for the beauty of mathematical patterns and thought, but if you're a 19 year old college kid like I was who thought he hated math, it will definitely cause you to rethink your position. Keith Devlin's popular mathematics works also have much the same appeal.
- dionidium 13y ago
  I started reading it when in college, got tired of lugging a huge dead-tree book around in my bag, and eventually just sort of put it down. That it was heavy in your bag isn't really saying much about the book. Are you familiar with Russell's Paradox? If reading about Russell's Paradox for the first time demands that you work it around in your head for the next hour as though some outside force is compelling you to understand its implications, then the book is probably for you. If that sounds miserable, then it probably isn't.
joe_the_user 13y ago
It annoying having GEB discussion be the top thread in a discussion about a rigorous or accessible exposition of Goedels' theorem. If those who don't find GEB tedious, overblown and overlong would to agree it's just not about Goedel's theorem. I mean really not. It's about self-reference and stuff. But it absolutely not any kind of exposition of Goedel's theorem at all, just stop. And I read it as a kid. I've picked it up recently, I have a degree in advanced math. I kind of like Hofstadter's take on AI. But I think GEB is just terrible. I mean, it has long, clever discussions that half-explain thing so I think it makes people feel like they sort of understand things. But have to say I think it gives the opposite of a solid math approach by never being fully clear, concise or complete.
- chii 13y ago
  if you have a degree in advanced maths, i would postulate the book isn't written for people like you. Its a laymen's book, written for the general public with no indepth knowledge of maths - and yet it manages to both inform, and pique the interest of readers. Sure, it isn't vigorous like one would have to be for a published scientific paper, but a normal person don't read that sort of thing anyway.
  - joe_the_user 13y ago
    I first encountered GEB when my mother read it to me and my sister when we were my sister was nine and I was fourteen. I assume GEB may be both informing and interest piquing for some people. For us, it just didn't ever get clear about what it was about and was mostly frustrating for that reason. Maybe none of us were "normal".

presidentender 13y ago

It's a good read, but you have to be careful with it, because it can take up a lot of your time and you'll quickly run into diminishing returns. Hofstadter is smarter than I am, and I know he's smarter than I am, so I'm never sure whether I've understood anything properly. It's a perfectly laid Dunning-Kruger trap, and it ensnares probably too much of my processor time when I fall into it.

jonnathanson 13y ago
The problem with reading Hofstadter is that, because he's so brilliant and so lucid, you'll often find yourself readily him uncritically: thoroughly convinced by anything he's saying, and simply absorbing it all. Some of his books, the aforementioned in particular, are works of insight and genius. Others, such as his recent book on metaphor-as-thought, are speculative steps onto a bit thinner ice. (Note: I realize Hofstadter and his colleagues have spent decades exploring metaphor-based AI, and that there might be something quite real to it -- but he doesn't make a convincing case for the sufficiency of this hypothesis, though he insists it's there).

6cxs2hd6 13y ago

GEB high on my list of books that I own on dead trees, but also want on Kindle. Even if it didn't qualify for Amazon's deal to get it cheaper if you already bought it from them -- even if I had to pay a lot for it. Yeah, I know it's not an ideal format for Kindle, e.g. the illustrations and... a few other features I won't give away here. But still. What a great thing to have at-hand anytime you wanted to dive in and read part of it. Sigh.

jfb 13y ago

For anyone looking for a brief, accessible explanation of the proof itself, I cannot recommend the Nagel and Newman [1] highly enough. [1] http://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/0814758371/ref=sr_1_1?ie=UTF8&qid=1380563150&sr=8-1&keywords=nagel+newman http://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/081475837...

alok-g 13y ago
While I loved the first few chapters of the book, and they were mind-opening, I found the explanation of the proof unsatisfactory. As I recall, it was mentioned in the preface that the book will give a complete outline of the actual proof. I did not find this to be the case, the outline seemed to jump quite a bit from one thought to another leaving me with more questions about the proofs than answers. I still do not understand the proofs (though I now nearly understand an analogous result in computer science via Jeff Ulmann's book).
- jfb 13y ago
  I has been a few decades since I read it for the first time, so I may be glossing it in my mind.

Tycho 13y ago

Even if it doesn't have a profound effect on your perspective or if you find the conclusions uninteresting, the journey itself is very informative. Read if you don't already have much exposure to: first order logic / predicate calculus; formal systems; DNA; Escher and Bach; number theory; Goedel's incompleteness theorem; Turing machines; neuroscience; information theory...

eli_gottlieb 13y ago

Is it really that great? I started reading it when in college, got tired of lugging a huge dead-tree book around in my bag, and eventually just sort of put it down. Maybe I didn't get far enough in to hit the parts that would be interesting to someone who's already long-since done basic programming and math?

laxatives 13y ago
It definitely blew my mind when I first read it, but I think its also gained a big cult following creating a lot of hype. I thought about it a lot for a few months after I read it, but I certainly haven't thought about it in over a year and it definitely hasn't shaped the way I think about things now (at least not that I'm aware of). If you haven't taken the math behind it, its awesome and you should definitely read the first 14 chapters if you're interested. But after that, its basically a bunch of Hofstatdler's musings on DNA and AI, a lot of which seems outdated and like a lot of speculation (the book was published ~25 years ago). Then again, most books I've read I forget about much sooner than a few months. If you want a good read, go for it, but its not some holy grail that will change your life forever.
breckinloggins 13y ago
It's probably not that earth-shattering if you already have an appreciation for the beauty of mathematical patterns and thought, but if you're a 19 year old college kid like I was who thought he hated math, it will definitely cause you to rethink your position. Keith Devlin's popular mathematics works also have much the same appeal.
dionidium 13y ago
I started reading it when in college, got tired of lugging a huge dead-tree book around in my bag, and eventually just sort of put it down. That it was heavy in your bag isn't really saying much about the book. Are you familiar with Russell's Paradox? If reading about Russell's Paradox for the first time demands that you work it around in your head for the next hour as though some outside force is compelling you to understand its implications, then the book is probably for you. If that sounds miserable, then it probably isn't.

joe_the_user 13y ago

It annoying having GEB discussion be the top thread in a discussion about a rigorous or accessible exposition of Goedels' theorem. If those who don't find GEB tedious, overblown and overlong would to agree it's just not about Goedel's theorem. I mean really not. It's about self-reference and stuff. But it absolutely not any kind of exposition of Goedel's theorem at all, just stop. And I read it as a kid. I've picked it up recently, I have a degree in advanced math. I kind of like Hofstadter's take on AI. But I think GEB is just terrible. I mean, it has long, clever discussions that half-explain thing so I think it makes people feel like they sort of understand things. But have to say I think it gives the opposite of a solid math approach by never being fully clear, concise or complete.

chii 13y ago
if you have a degree in advanced maths, i would postulate the book isn't written for people like you. Its a laymen's book, written for the general public with no indepth knowledge of maths - and yet it manages to both inform, and pique the interest of readers. Sure, it isn't vigorous like one would have to be for a published scientific paper, but a normal person don't read that sort of thing anyway.
- joe_the_user 13y ago
  I first encountered GEB when my mother read it to me and my sister when we were my sister was nine and I was fourteen. I assume GEB may be both informing and interest piquing for some people. For us, it just didn't ever get clear about what it was about and was mostly frustrating for that reason. Maybe none of us were "normal".