22 ms·

Gödel, Escher, Bach: an in-depth explainer

430 points by behnamoh 4y ago

guenthert 4y ago
All I get is "Error: TypeError: Object.fromEntries is not a function" (Chrome on a Chromebook). Gosh, I yearn for the times when people used HTML to create web sites ...
danbmil99 4y ago
An incredible piece of work. Shaped my life trajectory in many ways. Introduced me to thinkers like Daniel Dennett and Stanislaw Lem. Every generation or so a book comes along that, in retrospect, seems almost clairvoyant. This is one of those books.
- pjmorris 4y ago
  I was introduced to both Dennett and Lem through 'The Mind's I: Fantasies And Reflections On Self & Soul', an anthology edited by Hofstadter and Dennett that I chanced upon in the university library. I recognized Hofstadter from GEB. I found 'I' very digestible, I admit that I still haven't finished GEB. It beckons me from the bookshelf.
- danbmil99 4y ago
  Other posters correct, those authors were mentioned in the Mind's I, but I never would have read that unless I started with GDB
  - danbmil99 4y ago
    G. E. B.
craggyjaggy 4y ago
Maybe one day I'll try reading it again and actually finish it, but so far I couldn't do it. Everything is fascinating and mind blowing don't get me wrong, but I feel like there is always this weird pretentious atmosphere going on. I don't know how to describe it, but by the end of the first half reading GEB was not fun anymore.
- mejutoco 4y ago
  You can skip the alternating socratic parts and it is much lighter :P I think Zen and the art of motorcycle repair has a similar structure with Socratic dialogs interspersed.
- scrame 4y ago
  It is for sure pretentious, he's a cloistered academic classic music nerd that appreciates art exclusively through rigid structure. He's also aware of that and tries to explore that. The second half is weird too, because it describes the academic work he does in the future, but is a stab in the dark compared to the documentarian aspect of the first half. Think of it like forming a hypothesis: GEB: This is what we can see. EGB: This is what I think it means.
- andybak 4y ago
  I've never understood why people think it's pretentious. It joyous and innocent. It's someone laying out the shiny baubles they love and inviting anyone passing to take a look.
- polytely 4y ago
  I don't really get why it would be pretentious, like it's not pretending to be smarter than it is. It doesn't seem to me that the author is showing off for the sake of showing off, but rather that he is not hiding his joy and love for the themes discussed in the book.
mtreis86 4y ago
I wonder how experienced the author of GEB is with psychedelics, that book always felt fairly trippy to me.
- mistrial9 4y ago
  commitment to the material in that depth is not the product of drugs
  - widowlark 4y ago
    Thank you so much for saying this, I find this misconception deeply insulting
    - mxkopy 4y ago
      It's not an insult. Psychedelics can profoundly change how someone perceives things. GEB has that sort profound shift in POV that many would associate with psychedelics.
      - Brusco_RF 4y ago
        Getting hit in the head can also change how someone perceives things. I think the above commenter was expressing frustration with the popular notion that taking drugs is some sort of shortcut to understanding consciousness, dynamic systems, etc
        andybak 4y ago
        "Shortcut" is overstating it. It can steer one's thinking in a direction that makes those topics seem more relevant or interesting. This in itself can be very valuable. > Getting hit on the head Well - there are recorded cases of brain damage unlocking abilities and aptitudes (albeit with great rarity). So probably not recommended. But rest assured, psychedelics are less painful, cause less damage and have a higher probability of beneficial effects.
        4y ago
thanatos519 4y ago
Why read this when GEB is its own in-depth explainer?
- karaterobot 4y ago
  For one thing, I read GEB and found it difficult to follow. No doubt there is more in GEB than in this article, but without this less lengthy summary I couldn't get at it, life and attention being what they are. If I returned to the book now, I bet I'd understand more of what was already in it.
  - kfarr 4y ago
    Yeah this article is an excellent summary and I'd recommend people read it before the book instead of after
- scrame 4y ago
  One word: double-acrostic.
- quickthrower2 4y ago
  So is XKCD but it has the explainer site / wiki.
- stavros 4y ago
  Unfortunately, we can't prove that GEB can explain itself.
kenjackson 4y ago
Is there a good book that is similar in spirit, but doesn't require the maturity of GEB? I know an 8th grader that would be a great target, but I don't know if they have the mathematical/logical maturity to get through it.
- pseudosudoer 4y ago
  While I'm not sure it requires "less maturity", DH released a subsequent book titled "I am a strange loop" which is an attempt to condense his ideas from GEB.
- squeaky-clean 4y ago
  It depends on what you mean by "a similar spirit" I suppose. One thing Hofstadter didn't like about GEB was he felt too many people didn't see his central theme among the many other ideas there. His 2007 book, "I Am A Strange Loop" is a bit of an answer to this. It's mostly the same ideas in GEB about the self and strange loops, but without all the meandering and interludes. It's been a while but I remember it being less logic/mathy than GEB. I did enjoy it. But the meandering and the interludes are part of the enjoyment of GEB. So if you're looking for another book to capture that spirit of GEB, I'm drawing a blank, hopefully someone else knows one. Barely related recommendation, but I remember reading "A Brief History of Time" around that age. Very doable for a young teen if they have a passion for that sort of topic.
  - denton-scratch 4y ago
    > people didn't see his central theme Ah - interesting. It took me several readings to tease-out what I thought the central theme was. As it happens, it led to a position that I objected to (and still object to). So discovering that central theme brought the book down a peg or two in my estimation. I still think it's one of the most entertaining books of popsci that I've ever opened.
- stinkytaco 4y ago
  Zen and the Art of Motorcycle Maintenance comes to mind immediately. It works on several levels and is very accessible as a result. If you wanted to stray from the spirit of GEB into narrative prose, there are a number of books I could recommend, especially in science fiction.
tootallgavin 4y ago
G.E.B is hegelian philosophy without one mention to Hegel and more mechanic than organic Anyone read the Phenomenology of Spirit and notice the same ideas?
- svnt 4y ago
  The ideas and what a modern reading brings to them can be difficult to disentangle. A more charitable take might be that because emergence is fractal that there are uncountable ways not involving Hegel to arrive at and express a similar underlying idea.
- scrame 4y ago
  I love this comment.
- nextaccountic 4y ago
  > Anyone read the Phenomenology of Spirit and notice the same ideas? Can you elaborate? I've had some friends talk about Hegel with me but I never understood much of it
  - tootallgavin 4y ago
    https://www.youtube.com/watch?v=9Z1zY39EKbs https://www.youtube.com/watch?v=9Z1zY39EKbs That is an interpretation of the Phenomenology of Spirit. Hegel and Hofstadter seem to be trying to find "spirit". To keep it simple, spirit can be defined by the "I" aka self-consciousness (but it could also be an ant colony, the Church, the State, the biosphere, etc... all the way up to "God"). Hegel tries to notice the becoming of the notion of the Concept (which could be noticed as the basic thought-tool) into (and through) the notion of the "I". Hofstadter is trying to do something similar but instead of the Concept as the base (or starting point), he uses the Axiom. Hofstadter then tries to discover if "I" (or "spirit") can emerge from a system of axioms. Please Note: In order to keep it short I gloss over about 1500 pages of Hegel's & Hofstadter's works.
davesque 4y ago
I've read GEB over many years rather in the way someone would read the Bible. I pick it up from time to time and enjoy chewing on one or two chapters of material. But I've yet to figure out if the book actually has a specific thesis. I know it's all about the power of interpretation and the way in which interpreting a formal system as self-referencing has the effect of completely blowing up the intended design of that system. But can someone sum up how this connects to consciousness beyond the obvious way in which consciousness plays the role of the interpreter? Or is that itself the thesis of the book? Or maybe that consciousness is the originator of self-reference? Bottom line is that I think the thesis can be summed up in a few sentences, but apparently it takes a whole 800 page book to get to the point. Would love other people's thoughts on what that point is ultimately. By the way, as salty as I sound about it, I love GEB. So don't get me wrong :).
- pvarangot 4y ago
  The book is about... should I call it golemization? the emergence of a being from a summation of non-being things. Few people get it like that and I think it's a problem with the book. It's taken as more of a funny and poignant popular science dive into some aspects of logic and computability. Hofstadter expands on "I Am a Strange Loop" which I think you should read if you are interested into what was his take with GEB.
- MonkeyMalarky 4y ago
  Metamagical Themas is worth checking out for that style of reading as it is a compilation of his essays. One can pick and choose any to read but there's overarching themes that bring them together too.
  - scrame 4y ago
    100%, not just the collection of columns, but that he has postscripts for it. He manahes to keep things accessible over a few columns rather than the overly sprawling GEB (which I've read a few times, and still revisit pieces) or his later personal works, which involve a lot of personal grief in the guise of discussions of cognitive studies.
- 4y ago
svat 4y ago
IMO, to read GEB for its content would be missing the point: what I think is the greatest thing about the book is that it's simply, purely, Hofstadter having fun. The linked post says "GEB is really idiosyncratic in a way no one can imitate", but I'd put it as: it's a deeply personal book. The author's personality shines through in a way I had not encountered before in a mathematics text, and so the book was a revelation for me. Hofstadter's actual thesis/intent with the book, and what he has to say about Gödel numbering (note: the book goes over Gödel's theorem and some implications, but Hofstadter's real interest is less in Gödel's theorem than in the proof technique—Gödel numbering—that Gödel used, because he is tickled by the self-reference), or Escher or Bach for that matter, are not really what make the book most worthwhile. What matters is the marriage of form and content, the perfect puns that seem to be set up several hundred pages apart, the way you'd be reading another dialogue before suddenly realizing that the lines are spelling out an acrostic, the satisfaction of things working themselves out perfectly (even the puns) (a feeling similar to the satisfying tying-together of the plots of certain novels, some of Wodehouse's included), and so on. Very few authors can write about technical topics in a way their personality shines through. (Knuth is another IMO, except with the personality staying in second place to the technical content, while with Hofstadter it's the other way around!) (Or non-technical writing: did you know about Hofstadter's translation of Eugene Onegin? He learnt Russian just to be able to read and translate that poem (see https://archive.nytimes.com/www.nytimes.com/books/97/07/20/reviews/hofstadter-translation.html https://archive.nytimes.com/www.nytimes.com/books/97/07/20/r... https://www.tralalit.de/en/2018/07/25/a-tale-of-two-or-so-translations/ https://www.tralalit.de/en/2018/07/25/a-tale-of-two-or-so-tr... https://www.york.ac.uk/depts/maths/histstat/pml1/onegin/ https://www.york.ac.uk/depts/maths/histstat/pml1/onegin/ for the story, and https://archive.nytimes.com/www.nytimes.com/books/99/09/12/reviews/990912.12louriet.html https://archive.nytimes.com/www.nytimes.com/books/99/09/12/r... for the very negative NYT review) and the result is amazing for exactly the reasons the reviewer complains about: yes it can't stand alone and it's best read alongside a "real" translation say Falen's, but throughout you can see Hofstadter having fun with his word games, and somehow his personality shines through even in just the way he's choosing to translate Pushkin; it's so amazing how he manages to have so many things just work out. “Till his creditors cast their nyet's”)
- patcon 4y ago
fredgrott 4y ago
The real neat thing is if you compare the full series from the author of GEB to the famous math person named Penrose as they both cover different sides of the same argument and at times beautiful math as well. Short take...our reality is a mesh between two different math desc, one is micro and one is not. The only problem is we still have no idea how nature bridges between those two different mathematic systems and that leads us down some very interesting rabbit holes: 1. String Theory and multiple worlds, except they are on micro basis, i.e. you cannot see them even with an electron microscope. 2. Tim travel at electron part level but not atom level. among other interesting things.
nathias 4y ago
GEB is one of the best works of modern philosophy, I don't think the reviewer gets the point, the story of formal systems and the structures that determine them are used as an analog for other systems that aren't formal to try and shed light on the process of ontological emergence of intelligence. If you are at least a bit interested in philosophy and computation, you should read GEB at least once.
adamnemecek 4y ago
The underlying idea is the idea of fixed points (aka spectra, diagonalizations, embedding, invariants, braids). By fixed point I mean something like the "Lawvere's fixed point theorem". https://ncatlab.org/nlab/show/Lawvere%27s+fixed+point+theorem https://ncatlab.org/nlab/show/Lawvere%27s+fixed+point+theore... I have a linkdump on this https://github.com/adamnemecek/adjoint https://github.com/adamnemecek/adjoint I also have a discord https://discord.gg/mr9TAhpyBW https://discord.gg/mr9TAhpyBW
- Workaccount2 4y ago
  Maybe an ELI5 of "fixed points"?
  - adamnemecek 4y ago
    A solution of any computational problem.
  - Jtsummers 4y ago
    General definition (courtesy of the wiki): A fixed point (sometimes shortened to fixpoint, also known as an invariant point) is a value that does not change under a given transformation. So x is a fixed point of a function f if f(x) = x. This can be generalized to various kinds of things in mathematics, but as an algebraic example: f(x) = x^2 1 and 0 are fixed points: f(1) = 1^2 = 1 f(0) = 0^2 = 0 https://en.wikipedia.org/wiki/Fixed_point_(mathematics) https://en.wikipedia.org/wiki/Fixed_point_(mathematics)
  - emmelaich 4y ago
    Perhaps not an explanation per se, but examples -- If you have two rulers and and compress one, then you when you lay them together there will be one point which is exactly at the same point. Likewise, if you have two paper chessboards, and scrunch one up, there will be at least one square* which is exactly over the top of the intact one. This also gives an intuition for the difficulty of actually finding the fixed point, even though you know there is one. * more precisely not only a square, but an exact, dimensionless point. (afaik)
jstanley 4y ago
> Gödel's Incompleteness Theorem: any sufficiently rich formal system, together with an interpretation, has strings which are true but unprovable. This is only half of it! Gödel's Incompleteness Theorem states that any sufficiently rich formal system, together with an interpretation, either has strings which are true but unprovable or has strings which are provable but untrue. Either is possible! In practice people prefer to have true things that can't be proven rather than provable things that are untrue. But either is possible.
- pdonis 4y ago
  > or has strings which are provable but untrue. Where are you getting this from?
- slowhand09 4y ago
  Careful lest you be shot with a crab cannon.
- SkyBelow 4y ago
  Is there a distinction between saying a system has something that is provable and untrue and saying the system is self contradictory (and the more generalized layman interpretation that the system is wrong).
  - layer8 4y ago
    See https://en.wikipedia.org/wiki/Consistency https://en.wikipedia.org/wiki/Consistency. Under the syntactic definition of consistency, a self-contradiction simply means that a particular statement and its logical negation can both be proved in the system. That doesn’t say anything about the truth of the statement.
    - teawrecks 4y ago
      But isn't something defined as true in a system iff it can be proven in said system? So the only way "proven but untrue" makes sense is if there is a contradiction, no?
2-718-281-828 4y ago
is here somebody who also got the impression that the book is somewhat overrated?
- honkler 4y ago
  yes me
Lwepz 4y ago
For those interested, here is a talk by Gemma De La Cuevas that tackles those fascinating tangled hierarchies: https://www.youtube.com/watch?v=0Q2gF1PImZw https://www.youtube.com/watch?v=0Q2gF1PImZw
- anthk 4y ago
  "Las Cuevas".
dinobones 4y ago
Am I the only one who did not find this book that interesting? I studied CS so it just felt like reading my class textbooks again, except with random trippy stories in between that try to shoehorn theory into a poor metaphor. The fundamentals of CS (strings, automata, graphs) are elementary building blocks. This is by design. You can apply them to almost anything. Almost everything "is a graph", or "recursion" if you formulate them to be so.
- ampersand3 4y ago
  I started GEB a couple of weeks ago and I have to agree to some extend (I also have a CS background). The information density is low and the authors style of writing feels very self-indulgent and even pretentious. In the foreword of the recent edition he portrays himself as a very petty, narrow-minded and unpleasant person. But at the same time, when it really gets going I can't help but being swept away and entertained by the unfiltered enthusiasm he displays and the work he has done to put it to paper. It's like a conversation with a very exhausting but at the same time very interesting person. It's like trying to put that tingling in the back of the brain when some kind of insight looms in words. I feel like it's probably best read as a curious psychograph of a nerd in the seventies who is deeply interested in theoretical computer science and its implications on awareness and (artificial) intelligence. Not as a scientific non-fiction-book which is trying to educate the reader or trying to make a strong argument for something
- climate-code 4y ago
  The point isn't that everything is recursive - the point is that systems that are recursive / self-referential cause breakdowns in logic (they are incomplete). This is a deep philosophical insight - it rhymes with the Buddhist idea of no-self - the problems that arise because we hold onto a false sense of self.
- xiaolingxiao 4y ago
  I read it before studying cs and I thought it was fascinating and made me want to study it. After studying it at the grad school level I re read it and found the book somewhat pedantic. It’s a bit like the black swan in the regard: it package advanced under grad level stem topics with colorful anecdotes and musings.
spindle 4y ago
There was a very good (charitable) takedown of some of the content of GEB referenced on Hacker News a few months ago, but I can't find it :-( Can anyone help please?
JasonFruit 4y ago
Every socially awkward person who obsesses about their intellect is an in-depth explainer of Goedel, Escher, Bach. It's a fun read, and clever enough, but the relation between the work of the three is pretty shallow, and if you understand only what the book contains, you haven't gotten very deep into their valuable work. The book is more an act of self-indulgence on the author's part, or at best a tribute to the brilliance of his subjects, than a profound intellectual achievement in itself.
- svat 4y ago
  > The book is more an act of self-indulgence on the author's part That's precisely what it is. And what makes it valuable too: such works of blatant self-indulgence are not very common in mathematics (at least, while remaining enjoyable to read). > than a profound intellectual achievement in itself Sure. I would call the book an artistic achievement in the intellectual realm: it talks about ideas, but is art. To put it another way: everyone knows "mathematics is not a spectator sport" — this is usually said in the sense of "you can't learn mathematics unless you do it yourself", which is true enough, but it's also a loss in the sense that there's no equivalent of sitting back and watching a game, watching someone play with ideas and do mathematics. This book comes close. How good the quality of the game is, and whether you'll learn anything from watching the game, is debatable (probably not much), but the experience itself is unusual, which makes the existence of this book a happy circumstance.
- mhneu 4y ago
  Agree (on sentence 2 and 3.) Gödel, Escher, Bach doesn't go very deep.
KhoomeiK 4y ago
I almost upvoted and then noticed it links to the AI Alignment Forum. Even a broken clock...
eointierney 4y ago
I gotta say that Godel's work is perhaps the most misrepresented in (common, non-mathematical) culture of foundational mathematical proofs. Just read the proofs. They're not that difficult. Their consequences are wonderful. Enjoy brilliance
nicholast 4y ago
The book is not just about the ideas, it is about the tapestry of how it was presented. It was a new form of literature. The whole document was its own strange loop.
racl101 4y ago
My uncle had this book. Talk about a fascinating book that I barely understand even 5%. But then again I tried to read it when I was in high school. So maybe I understand more in older age.
niccl 4y ago
The other Hofstadter gem is Fluid Concepts and Creative Analogies.
mod50ack 4y ago
I have read the book. But if your concern is a simple explanation of Gödel, read Nagel and Newman. I spent an afternoon on that in undergrad and woke up the next morning content. Went on to learn much more later, of course.
paulpauper 4y ago
Sometimes I think I am smart and then am reminded that this books exists and the author was only 30 when he wrote it. crazy
llamataboot 4y ago
Like the Zen Masters the author thinks DH has a problem with, I rather think that the point of GEB is to be read by a person at a certain point in spacetime who experiences it a certain way, though I appreciate the logic, it misses the strange loop.
intrasight 4y ago
GEB was very influential in my pursuing a career in math and software. Interesting and seemingly not widely known is that Hofstadter's "Fluid Concepts and Creative Analogies" was the first book sold on Amazon.com.
enviclash 4y ago
Thanks for pointing me towards this fantastic book. About the review, it says nothing about Bach (once only) or Escher (just the figures), so how does it capture clearly or comprehensively the book?
kfarr 4y ago
Intellectually poor man's attempt at a summary of the summary: Part 1 - math proof that a formal system when evaluated by an agent "breaking out of the system" can use that system to prove itself inconsistent. ("f* up" the internal logic of that system by feeding it into itself) Part 2 - ironically, to be conscious you have to have an awareness of your own system (a "strange loop") but you'll never be able to understand yourself as proven in part 1.
- itronitron 4y ago
  Seems like Part 2 makes a giant assumption.
galaxyLogic 4y ago
Certainly everybody believes that Godel's theorems are true. But I wonder if its' Achilles heel is the notion of "stepping outside" of the formal system. Can we formalize what "stepping outside" means? How can we be sure we have done it correctly? When we step "outside" and do reasoning, are we doing it following the formal logic? Which logic? Are there rules as to what kind of inferences are NOT allowed when reasoning "outside of the system"? In other words when we "reason outside of the formal system" we are using English. Can we trust the logic of English is "correct"? Can a formal system really do self-reference? It's just strings. WE can give an interpretation to formal sentences but when we interpret a given sentence as referring to "itself" doesn't it really refers to the interpretation, not to "itself" but its interpretation? When natural language refers to the formal system doesn't it really just refer to what the formal system "means" in the natural language, not to the formal system itself as such?
- lmm 4y ago
  We can absolutely reason formally from outside a formal system, by embedding it in a larger one, and this is a very standard and normal technique that anyone working seriously in this area does all the time. E.g. you work in ZFC + some large cardinal assumption that allows you to construct a model of ZFC inside that system, and then reason formally about ZFC there. > WE can give an interpretation to formal sentences but when we interpret a given sentence as referring to "itself" doesn't it really refers to the interpretation, not to "itself" but its interpretation? Indeed it can't - see e.g. Löb's theorem. A formal system can manipulate a set of rules that might happen to be its own rules, but it can never "know" that those are in fact its own rules. Which makes sense when you think about it.
  - galaxyLogic 4y ago
    Yes, very interesting point. It can not know that they are its own rules. BUT we can know that. Therefore we the meta-level can reason about the subject more than it can of itself. For example the subject-system can not mechanically prove that it is looking at its own ruleset. So the term "unprovable" should probably best be always qualified with: in which system. There are facts about systems which the system itself can not prove. Statements like that can be expressed in some formalized subset of English and proven following the rules of that formalized English. What is that "formalized English" that we use in our reasoning? Or does it not matter?
martopix 4y ago
GEB is art, in the sense that it's really literary. In this sense an "explainer" cannot really capture what it is about and why it's interesting. Reading a summary of the story of Hamlet, no matter how "in-depth", is not interesting.
nathan_compton 4y ago
Isn't the uh book kind of an in-depth explainer of itself?

430 points by behnamoh 4y ago

All I get is "Error: TypeError: Object.fromEntries is not a function" (Chrome on a Chromebook). Gosh, I yearn for the times when people used HTML to create web sites ...

danbmil99 4y ago

An incredible piece of work. Shaped my life trajectory in many ways. Introduced me to thinkers like Daniel Dennett and Stanislaw Lem. Every generation or so a book comes along that, in retrospect, seems almost clairvoyant. This is one of those books.

pjmorris 4y ago
I was introduced to both Dennett and Lem through 'The Mind's I: Fantasies And Reflections On Self & Soul', an anthology edited by Hofstadter and Dennett that I chanced upon in the university library. I recognized Hofstadter from GEB. I found 'I' very digestible, I admit that I still haven't finished GEB. It beckons me from the bookshelf.
danbmil99 4y ago
Other posters correct, those authors were mentioned in the Mind's I, but I never would have read that unless I started with GDB
- danbmil99 4y ago
  G. E. B.

craggyjaggy 4y ago

Maybe one day I'll try reading it again and actually finish it, but so far I couldn't do it. Everything is fascinating and mind blowing don't get me wrong, but I feel like there is always this weird pretentious atmosphere going on. I don't know how to describe it, but by the end of the first half reading GEB was not fun anymore.

mejutoco 4y ago
You can skip the alternating socratic parts and it is much lighter :P I think Zen and the art of motorcycle repair has a similar structure with Socratic dialogs interspersed.
scrame 4y ago
It is for sure pretentious, he's a cloistered academic classic music nerd that appreciates art exclusively through rigid structure. He's also aware of that and tries to explore that. The second half is weird too, because it describes the academic work he does in the future, but is a stab in the dark compared to the documentarian aspect of the first half. Think of it like forming a hypothesis: GEB: This is what we can see. EGB: This is what I think it means.
andybak 4y ago
I've never understood why people think it's pretentious. It joyous and innocent. It's someone laying out the shiny baubles they love and inviting anyone passing to take a look.
polytely 4y ago
I don't really get why it would be pretentious, like it's not pretending to be smarter than it is. It doesn't seem to me that the author is showing off for the sake of showing off, but rather that he is not hiding his joy and love for the themes discussed in the book.

mtreis86 4y ago

I wonder how experienced the author of GEB is with psychedelics, that book always felt fairly trippy to me.

mistrial9 4y ago
commitment to the material in that depth is not the product of drugs
- widowlark 4y ago
  Thank you so much for saying this, I find this misconception deeply insulting
  - mxkopy 4y ago
    It's not an insult. Psychedelics can profoundly change how someone perceives things. GEB has that sort profound shift in POV that many would associate with psychedelics.
    - Brusco_RF 4y ago
      Getting hit in the head can also change how someone perceives things. I think the above commenter was expressing frustration with the popular notion that taking drugs is some sort of shortcut to understanding consciousness, dynamic systems, etc
      - andybak 4y ago
        "Shortcut" is overstating it. It can steer one's thinking in a direction that makes those topics seem more relevant or interesting. This in itself can be very valuable. > Getting hit on the head Well - there are recorded cases of brain damage unlocking abilities and aptitudes (albeit with great rarity). So probably not recommended. But rest assured, psychedelics are less painful, cause less damage and have a higher probability of beneficial effects.
      - 4y ago

thanatos519 4y ago

Why read this when GEB is its own in-depth explainer?

karaterobot 4y ago
For one thing, I read GEB and found it difficult to follow. No doubt there is more in GEB than in this article, but without this less lengthy summary I couldn't get at it, life and attention being what they are. If I returned to the book now, I bet I'd understand more of what was already in it.
- kfarr 4y ago
  Yeah this article is an excellent summary and I'd recommend people read it before the book instead of after
scrame 4y ago
One word: double-acrostic.
quickthrower2 4y ago
So is XKCD but it has the explainer site / wiki.
stavros 4y ago
Unfortunately, we can't prove that GEB can explain itself.

kenjackson 4y ago

Is there a good book that is similar in spirit, but doesn't require the maturity of GEB? I know an 8th grader that would be a great target, but I don't know if they have the mathematical/logical maturity to get through it.

pseudosudoer 4y ago
While I'm not sure it requires "less maturity", DH released a subsequent book titled "I am a strange loop" which is an attempt to condense his ideas from GEB.
squeaky-clean 4y ago
It depends on what you mean by "a similar spirit" I suppose. One thing Hofstadter didn't like about GEB was he felt too many people didn't see his central theme among the many other ideas there. His 2007 book, "I Am A Strange Loop" is a bit of an answer to this. It's mostly the same ideas in GEB about the self and strange loops, but without all the meandering and interludes. It's been a while but I remember it being less logic/mathy than GEB. I did enjoy it. But the meandering and the interludes are part of the enjoyment of GEB. So if you're looking for another book to capture that spirit of GEB, I'm drawing a blank, hopefully someone else knows one. Barely related recommendation, but I remember reading "A Brief History of Time" around that age. Very doable for a young teen if they have a passion for that sort of topic.
- denton-scratch 4y ago
  > people didn't see his central theme Ah - interesting. It took me several readings to tease-out what I thought the central theme was. As it happens, it led to a position that I objected to (and still object to). So discovering that central theme brought the book down a peg or two in my estimation. I still think it's one of the most entertaining books of popsci that I've ever opened.
stinkytaco 4y ago
Zen and the Art of Motorcycle Maintenance comes to mind immediately. It works on several levels and is very accessible as a result. If you wanted to stray from the spirit of GEB into narrative prose, there are a number of books I could recommend, especially in science fiction.

tootallgavin 4y ago

G.E.B is hegelian philosophy without one mention to Hegel and more mechanic than organic Anyone read the Phenomenology of Spirit and notice the same ideas?

svnt 4y ago
The ideas and what a modern reading brings to them can be difficult to disentangle. A more charitable take might be that because emergence is fractal that there are uncountable ways not involving Hegel to arrive at and express a similar underlying idea.
scrame 4y ago
I love this comment.
nextaccountic 4y ago
> Anyone read the Phenomenology of Spirit and notice the same ideas? Can you elaborate? I've had some friends talk about Hegel with me but I never understood much of it
- tootallgavin 4y ago
  https://www.youtube.com/watch?v=9Z1zY39EKbs https://www.youtube.com/watch?v=9Z1zY39EKbs That is an interpretation of the Phenomenology of Spirit. Hegel and Hofstadter seem to be trying to find "spirit". To keep it simple, spirit can be defined by the "I" aka self-consciousness (but it could also be an ant colony, the Church, the State, the biosphere, etc... all the way up to "God"). Hegel tries to notice the becoming of the notion of the Concept (which could be noticed as the basic thought-tool) into (and through) the notion of the "I". Hofstadter is trying to do something similar but instead of the Concept as the base (or starting point), he uses the Axiom. Hofstadter then tries to discover if "I" (or "spirit") can emerge from a system of axioms. Please Note: In order to keep it short I gloss over about 1500 pages of Hegel's & Hofstadter's works.

davesque 4y ago

I've read GEB over many years rather in the way someone would read the Bible. I pick it up from time to time and enjoy chewing on one or two chapters of material. But I've yet to figure out if the book actually has a specific thesis. I know it's all about the power of interpretation and the way in which interpreting a formal system as self-referencing has the effect of completely blowing up the intended design of that system. But can someone sum up how this connects to consciousness beyond the obvious way in which consciousness plays the role of the interpreter? Or is that itself the thesis of the book? Or maybe that consciousness is the originator of self-reference? Bottom line is that I think the thesis can be summed up in a few sentences, but apparently it takes a whole 800 page book to get to the point. Would love other people's thoughts on what that point is ultimately. By the way, as salty as I sound about it, I love GEB. So don't get me wrong :).

pvarangot 4y ago
The book is about... should I call it golemization? the emergence of a being from a summation of non-being things. Few people get it like that and I think it's a problem with the book. It's taken as more of a funny and poignant popular science dive into some aspects of logic and computability. Hofstadter expands on "I Am a Strange Loop" which I think you should read if you are interested into what was his take with GEB.
MonkeyMalarky 4y ago
Metamagical Themas is worth checking out for that style of reading as it is a compilation of his essays. One can pick and choose any to read but there's overarching themes that bring them together too.
- scrame 4y ago
  100%, not just the collection of columns, but that he has postscripts for it. He manahes to keep things accessible over a few columns rather than the overly sprawling GEB (which I've read a few times, and still revisit pieces) or his later personal works, which involve a lot of personal grief in the guise of discussions of cognitive studies.
4y ago

svat 4y ago

IMO, to read GEB for its content would be missing the point: what I think is the greatest thing about the book is that it's simply, purely, Hofstadter having fun. The linked post says "GEB is really idiosyncratic in a way no one can imitate", but I'd put it as: it's a deeply personal book. The author's personality shines through in a way I had not encountered before in a mathematics text, and so the book was a revelation for me. Hofstadter's actual thesis/intent with the book, and what he has to say about Gödel numbering (note: the book goes over Gödel's theorem and some implications, but Hofstadter's real interest is less in Gödel's theorem than in the proof technique—Gödel numbering—that Gödel used, because he is tickled by the self-reference), or Escher or Bach for that matter, are not really what make the book most worthwhile. What matters is the marriage of form and content, the perfect puns that seem to be set up several hundred pages apart, the way you'd be reading another dialogue before suddenly realizing that the lines are spelling out an acrostic, the satisfaction of things working themselves out perfectly (even the puns) (a feeling similar to the satisfying tying-together of the plots of certain novels, some of Wodehouse's included), and so on. Very few authors can write about technical topics in a way their personality shines through. (Knuth is another IMO, except with the personality staying in second place to the technical content, while with Hofstadter it's the other way around!) (Or non-technical writing: did you know about Hofstadter's translation of Eugene Onegin? He learnt Russian just to be able to read and translate that poem (see https://archive.nytimes.com/www.nytimes.com/books/97/07/20/reviews/hofstadter-translation.html https://archive.nytimes.com/www.nytimes.com/books/97/07/20/r... https://www.tralalit.de/en/2018/07/25/a-tale-of-two-or-so-translations/ https://www.tralalit.de/en/2018/07/25/a-tale-of-two-or-so-tr... https://www.york.ac.uk/depts/maths/histstat/pml1/onegin/ https://www.york.ac.uk/depts/maths/histstat/pml1/onegin/ for the story, and https://archive.nytimes.com/www.nytimes.com/books/99/09/12/reviews/990912.12louriet.html https://archive.nytimes.com/www.nytimes.com/books/99/09/12/r... for the very negative NYT review) and the result is amazing for exactly the reasons the reviewer complains about: yes it can't stand alone and it's best read alongside a "real" translation say Falen's, but throughout you can see Hofstadter having fun with his word games, and somehow his personality shines through even in just the way he's choosing to translate Pushkin; it's so amazing how he manages to have so many things just work out. “Till his creditors cast their nyet's”)

patcon 4y ago

fredgrott 4y ago

The real neat thing is if you compare the full series from the author of GEB to the famous math person named Penrose as they both cover different sides of the same argument and at times beautiful math as well. Short take...our reality is a mesh between two different math desc, one is micro and one is not. The only problem is we still have no idea how nature bridges between those two different mathematic systems and that leads us down some very interesting rabbit holes: 1. String Theory and multiple worlds, except they are on micro basis, i.e. you cannot see them even with an electron microscope. 2. Tim travel at electron part level but not atom level. among other interesting things.

nathias 4y ago

GEB is one of the best works of modern philosophy, I don't think the reviewer gets the point, the story of formal systems and the structures that determine them are used as an analog for other systems that aren't formal to try and shed light on the process of ontological emergence of intelligence. If you are at least a bit interested in philosophy and computation, you should read GEB at least once.

adamnemecek 4y ago

The underlying idea is the idea of fixed points (aka spectra, diagonalizations, embedding, invariants, braids). By fixed point I mean something like the "Lawvere's fixed point theorem". https://ncatlab.org/nlab/show/Lawvere%27s+fixed+point+theorem https://ncatlab.org/nlab/show/Lawvere%27s+fixed+point+theore... I have a linkdump on this https://github.com/adamnemecek/adjoint https://github.com/adamnemecek/adjoint I also have a discord https://discord.gg/mr9TAhpyBW https://discord.gg/mr9TAhpyBW

Workaccount2 4y ago
Maybe an ELI5 of "fixed points"?
- adamnemecek 4y ago
  A solution of any computational problem.
- Jtsummers 4y ago
  General definition (courtesy of the wiki): A fixed point (sometimes shortened to fixpoint, also known as an invariant point) is a value that does not change under a given transformation. So x is a fixed point of a function f if f(x) = x. This can be generalized to various kinds of things in mathematics, but as an algebraic example: f(x) = x^2 1 and 0 are fixed points: f(1) = 1^2 = 1 f(0) = 0^2 = 0 https://en.wikipedia.org/wiki/Fixed_point_(mathematics) https://en.wikipedia.org/wiki/Fixed_point_(mathematics)
- emmelaich 4y ago
  Perhaps not an explanation per se, but examples -- If you have two rulers and and compress one, then you when you lay them together there will be one point which is exactly at the same point. Likewise, if you have two paper chessboards, and scrunch one up, there will be at least one square* which is exactly over the top of the intact one. This also gives an intuition for the difficulty of actually finding the fixed point, even though you know there is one. * more precisely not only a square, but an exact, dimensionless point. (afaik)

jstanley 4y ago

> Gödel's Incompleteness Theorem: any sufficiently rich formal system, together with an interpretation, has strings which are true but unprovable. This is only half of it! Gödel's Incompleteness Theorem states that any sufficiently rich formal system, together with an interpretation, either has strings which are true but unprovable or has strings which are provable but untrue. Either is possible! In practice people prefer to have true things that can't be proven rather than provable things that are untrue. But either is possible.

pdonis 4y ago
> or has strings which are provable but untrue. Where are you getting this from?
slowhand09 4y ago
Careful lest you be shot with a crab cannon.
SkyBelow 4y ago
Is there a distinction between saying a system has something that is provable and untrue and saying the system is self contradictory (and the more generalized layman interpretation that the system is wrong).
- layer8 4y ago
  See https://en.wikipedia.org/wiki/Consistency https://en.wikipedia.org/wiki/Consistency. Under the syntactic definition of consistency, a self-contradiction simply means that a particular statement and its logical negation can both be proved in the system. That doesn’t say anything about the truth of the statement.
  - teawrecks 4y ago
    But isn't something defined as true in a system iff it can be proven in said system? So the only way "proven but untrue" makes sense is if there is a contradiction, no?

2-718-281-828 4y ago

is here somebody who also got the impression that the book is somewhat overrated?

honkler 4y ago
yes me

Lwepz 4y ago

For those interested, here is a talk by Gemma De La Cuevas that tackles those fascinating tangled hierarchies: https://www.youtube.com/watch?v=0Q2gF1PImZw https://www.youtube.com/watch?v=0Q2gF1PImZw

anthk 4y ago
"Las Cuevas".

dinobones 4y ago

Am I the only one who did not find this book that interesting? I studied CS so it just felt like reading my class textbooks again, except with random trippy stories in between that try to shoehorn theory into a poor metaphor. The fundamentals of CS (strings, automata, graphs) are elementary building blocks. This is by design. You can apply them to almost anything. Almost everything "is a graph", or "recursion" if you formulate them to be so.

ampersand3 4y ago
I started GEB a couple of weeks ago and I have to agree to some extend (I also have a CS background). The information density is low and the authors style of writing feels very self-indulgent and even pretentious. In the foreword of the recent edition he portrays himself as a very petty, narrow-minded and unpleasant person. But at the same time, when it really gets going I can't help but being swept away and entertained by the unfiltered enthusiasm he displays and the work he has done to put it to paper. It's like a conversation with a very exhausting but at the same time very interesting person. It's like trying to put that tingling in the back of the brain when some kind of insight looms in words. I feel like it's probably best read as a curious psychograph of a nerd in the seventies who is deeply interested in theoretical computer science and its implications on awareness and (artificial) intelligence. Not as a scientific non-fiction-book which is trying to educate the reader or trying to make a strong argument for something
climate-code 4y ago
The point isn't that everything is recursive - the point is that systems that are recursive / self-referential cause breakdowns in logic (they are incomplete). This is a deep philosophical insight - it rhymes with the Buddhist idea of no-self - the problems that arise because we hold onto a false sense of self.
xiaolingxiao 4y ago
I read it before studying cs and I thought it was fascinating and made me want to study it. After studying it at the grad school level I re read it and found the book somewhat pedantic. It’s a bit like the black swan in the regard: it package advanced under grad level stem topics with colorful anecdotes and musings.

spindle 4y ago

There was a very good (charitable) takedown of some of the content of GEB referenced on Hacker News a few months ago, but I can't find it :-( Can anyone help please?

JasonFruit 4y ago

Every socially awkward person who obsesses about their intellect is an in-depth explainer of Goedel, Escher, Bach. It's a fun read, and clever enough, but the relation between the work of the three is pretty shallow, and if you understand only what the book contains, you haven't gotten very deep into their valuable work. The book is more an act of self-indulgence on the author's part, or at best a tribute to the brilliance of his subjects, than a profound intellectual achievement in itself.

svat 4y ago
> The book is more an act of self-indulgence on the author's part That's precisely what it is. And what makes it valuable too: such works of blatant self-indulgence are not very common in mathematics (at least, while remaining enjoyable to read). > than a profound intellectual achievement in itself Sure. I would call the book an artistic achievement in the intellectual realm: it talks about ideas, but is art. To put it another way: everyone knows "mathematics is not a spectator sport" — this is usually said in the sense of "you can't learn mathematics unless you do it yourself", which is true enough, but it's also a loss in the sense that there's no equivalent of sitting back and watching a game, watching someone play with ideas and do mathematics. This book comes close. How good the quality of the game is, and whether you'll learn anything from watching the game, is debatable (probably not much), but the experience itself is unusual, which makes the existence of this book a happy circumstance.
mhneu 4y ago
Agree (on sentence 2 and 3.) Gödel, Escher, Bach doesn't go very deep.

KhoomeiK 4y ago

I almost upvoted and then noticed it links to the AI Alignment Forum. Even a broken clock...

eointierney 4y ago

I gotta say that Godel's work is perhaps the most misrepresented in (common, non-mathematical) culture of foundational mathematical proofs. Just read the proofs. They're not that difficult. Their consequences are wonderful. Enjoy brilliance

nicholast 4y ago

The book is not just about the ideas, it is about the tapestry of how it was presented. It was a new form of literature. The whole document was its own strange loop.

racl101 4y ago

My uncle had this book. Talk about a fascinating book that I barely understand even 5%. But then again I tried to read it when I was in high school. So maybe I understand more in older age.

niccl 4y ago

The other Hofstadter gem is Fluid Concepts and Creative Analogies.

mod50ack 4y ago

I have read the book. But if your concern is a simple explanation of Gödel, read Nagel and Newman. I spent an afternoon on that in undergrad and woke up the next morning content. Went on to learn much more later, of course.

paulpauper 4y ago

Sometimes I think I am smart and then am reminded that this books exists and the author was only 30 when he wrote it. crazy

llamataboot 4y ago

Like the Zen Masters the author thinks DH has a problem with, I rather think that the point of GEB is to be read by a person at a certain point in spacetime who experiences it a certain way, though I appreciate the logic, it misses the strange loop.

intrasight 4y ago

GEB was very influential in my pursuing a career in math and software. Interesting and seemingly not widely known is that Hofstadter's "Fluid Concepts and Creative Analogies" was the first book sold on Amazon.com.

enviclash 4y ago

Thanks for pointing me towards this fantastic book. About the review, it says nothing about Bach (once only) or Escher (just the figures), so how does it capture clearly or comprehensively the book?

kfarr 4y ago

Intellectually poor man's attempt at a summary of the summary: Part 1 - math proof that a formal system when evaluated by an agent "breaking out of the system" can use that system to prove itself inconsistent. ("f* up" the internal logic of that system by feeding it into itself) Part 2 - ironically, to be conscious you have to have an awareness of your own system (a "strange loop") but you'll never be able to understand yourself as proven in part 1.

itronitron 4y ago
Seems like Part 2 makes a giant assumption.

galaxyLogic 4y ago

Certainly everybody believes that Godel's theorems are true. But I wonder if its' Achilles heel is the notion of "stepping outside" of the formal system. Can we formalize what "stepping outside" means? How can we be sure we have done it correctly? When we step "outside" and do reasoning, are we doing it following the formal logic? Which logic? Are there rules as to what kind of inferences are NOT allowed when reasoning "outside of the system"? In other words when we "reason outside of the formal system" we are using English. Can we trust the logic of English is "correct"? Can a formal system really do self-reference? It's just strings. WE can give an interpretation to formal sentences but when we interpret a given sentence as referring to "itself" doesn't it really refers to the interpretation, not to "itself" but its interpretation? When natural language refers to the formal system doesn't it really just refer to what the formal system "means" in the natural language, not to the formal system itself as such?

lmm 4y ago
We can absolutely reason formally from outside a formal system, by embedding it in a larger one, and this is a very standard and normal technique that anyone working seriously in this area does all the time. E.g. you work in ZFC + some large cardinal assumption that allows you to construct a model of ZFC inside that system, and then reason formally about ZFC there. > WE can give an interpretation to formal sentences but when we interpret a given sentence as referring to "itself" doesn't it really refers to the interpretation, not to "itself" but its interpretation? Indeed it can't - see e.g. Löb's theorem. A formal system can manipulate a set of rules that might happen to be its own rules, but it can never "know" that those are in fact its own rules. Which makes sense when you think about it.
- galaxyLogic 4y ago
  Yes, very interesting point. It can not know that they are its own rules. BUT we can know that. Therefore we the meta-level can reason about the subject more than it can of itself. For example the subject-system can not mechanically prove that it is looking at its own ruleset. So the term "unprovable" should probably best be always qualified with: in which system. There are facts about systems which the system itself can not prove. Statements like that can be expressed in some formalized subset of English and proven following the rules of that formalized English. What is that "formalized English" that we use in our reasoning? Or does it not matter?

martopix 4y ago

GEB is art, in the sense that it's really literary. In this sense an "explainer" cannot really capture what it is about and why it's interesting. Reading a summary of the story of Hamlet, no matter how "in-depth", is not interesting.

nathan_compton 4y ago

Isn't the uh book kind of an in-depth explainer of itself?