I love GEB. It is a masterpiece. But it is important to realize before diving into it that one of the things that makes it a masterpiece is that it is literary, that is, that it contains a wealth of detail that is, strictly speaking, unnecessary to the main point. Drawing a parallel between GEB and James Joyce's Ulysses is actually quite a good analogy. Indeed, Ulysses is almost nothing but "unnecessary detail", to the extent that it makes the book all but unreadable (which, I think, is no small part of its appeal). If you're waiting for either GEB or Ulysses to hurry up and get to the mother fucking point, you're going to be waiting a long time. In that regard, both books are good for techies to read because every now and then it's good to read something that drags you out of your comfort zone and futzes around in all kinds of obscure nooks and crannies before getting to the mother fucking point -- if indeed it ever does. Getting to the point can be important, but there is more to life (and literature).
I love Ulysses and metafiction in general, but when people apply this kind of writing style to philosophy it drives me a bit up the wall. Philosophy at the end of the day is about arguing a point; it isn't about producing an aesthetic experience.
So why would you abuse your reader by making it a pain in the ass to figure out what you mean? I know there are some fancy arguments around stretching limits of language, but none of them seemed all that sensible to me. The only advantage I see to obscurantist writing is that it makes it impossible to critique the philosophers work. Any critique will just be met by the response that you didn't fully understand the author's argument. The Searle/Derrida debates are a great example of this. The upshot is that people spend all their time debating what you actually mean. Which I guess is good for the philosopher's brand, but doesn't advance knowledge much.
This isn't to say that you can't have beautiful writing in philosophy. I think Gaston Bachelard is a great example of both an elegant writer and a clear writer.
That being said, people really really love GEB, so it probably is worth reading regardless of these misgivings. One of these days I'll get to it.
> So why would you abuse your reader by making it a pain in the ass to figure out what you mean?
I think this statement is both wrong and irrelevant.
Wrong: if you look into GEB, you notice that is has many chapters. And each chapter works on some topic --- and the chapters itself aren't a pain in the ass to figure out what they mean. Not at all. Each chapter transports its goal quite nicely and timely.
Irrelevant: this book is not an academical paper. It's a book meant to amuse you, to enlighten you, to sharpen your thinking skills. An academic paper describing just how Gödel's work works can be a *LOT* thinner --- but, usually, is also a lot dryer.
It's actually the case that this book gives you many good things that help you to understand (and accept or dismiss) such academic papers easier. But even here, mind the "many", if you expect "all" from the book, then you'll be dissatisfied.
I also wouldn't say that GEB is a philosophical book, at least not in the way modern philosophy is understood. If you see it as a book dedicated to like ("philo") wisdom ("sophie"), then it is. But so are most after books in the IT field.
> So why would you abuse your reader by making it a pain in the ass to figure out what you mean?
A psychonaout or a shaman would argue some insights are only available on a drug infused spiritual trip.
Musicians talk of flow.
That state of discombobulation you dislike is not to meant to furnish you with answers but rather with new dots to notice and connect on your own. Not everything is a mathematical proof.
I think the real reason this sort of style isn't attractive is because many try to emulate it who lack the talent and then it truly is noise. It is a lot to ask from a reader and the value is rarely there that is well observed.
But sometimes the payoff is worth it. GBE resonates with a lot of people.
Hahah the whole point of op is that there is value in not always having a point, but meandering, especially for techies. Are you set an proving him right?
I think it'd be more fair to say that GEB is just philosophical navel-gazing with the appearance of some deep philosophical truth... When the actual truth is they cheaped out on editorial staff :D
I got it, and read a portion of it. It was a meandering and badly written mess with no point. It felt like Seinfeld in science-ish form.
I can imagine it being received differently today, but I read it twice in the 80s. It blew my mind. Now you can’t swing a stick without hitting some referent or concept in its pages, but that’s the internet age, efficiently routing the arcane to hypernerds worldwide. It’s made the whole world boring.
Thanks for the context. I'd recently tried reading GEB but couldn't get into it much since I already knew the formal version of the concepts it discusses about. I also have experience of an earlier time when expert knowledge was much less accessible, and where I treasured books like this that tried to compress every ambition within them, since they brought a lot of threads for further edification together in them.
Do you have substantive critique? Because the fellow you're responding to is giving substance to his criticism, the parent comment is giving substance, the article is giving substance, and whether GEB has substance is apparently up for debate. If the person you're replying to is deadset on proving the parent right, you are dead set on proving nothing. Please tell us what you disagree with, and the particulars of why, or maybe leave the discussion to the adults.
OP: In that regard, both books are good for techies to read because every now and then it's good to read something that drags you out of your comfort zone and futzes around in all kinds of obscure nooks and crannies before getting to the mother fucking point -- if indeed it ever does. Getting to the point can be important, but there is more to life (and literature).
Commentor: Philosophy at the end of the day is about arguing a point; it isn't about producing an aesthetic experience. (Even though this statement directly against original post, it's so obvious to author that he does not feel the need to explain, but goes on a tangent how bad the writing is)
Me: Hahah the whole point of op is that there is value in not always having a point, but meandering...
Response: It was a meandering and badly written mess with no point.
Me: ...
You: Leave it to the adults.
Me: ...
You: You're not making a point!!!
(Considering the nature of the first comment and assuming you didnt do it on purpose, you ending with blaming me I'm not making a point is poetic to be honest)
I don't consider "there is value in not always having a point, but meandering" to be itself a point, mainly because you don't give a reason to suppose that that is the case or a reasonable case to consider. It seems itself to be rather meandering, circling a value and a raison d'etre without specifying either. It's the specification that makes it worth considering, as adults do know.
Ah, nobody reads Kant anymore; and even if they do, they tend to read just the first critique, stick to the analytic and focus on the "important" sections. You have to read the whole thing! And then, if you're so privileged, and you have to time, nothing is more fruitful than going on towards the Groundwork for Metaphysics of Morals, and the Critique of the Power of Judgement. And once you've read that last book, maybe you will begin to understand Derrida. Or even better, you will begin to understand how to critique him.
Philosophy is defined by the human experience, it is asking questions that do not have readily proveable answers, of answers that are heavily contextual to the individual. The probability of the answers weighed in the individuals head. These probabilities and likeliness to believe more of one philosophy over the other is often primarily from the details.
Details are important because they are little parts that support the likelihood of the larger point being true. If the details don't work it's likely because the theory is innacurate.
> Philosophy at the end of the day is about arguing a point; it isn't about producing an aesthetic experience.
I'd argue that point. Nietzsche's "Also Sprach Zarathustra" (Thus Spoke Zarathustra) comes to my mind first. Art contains and conveys truth.
Nietzsche's work is also a good example about why it's foolish to argue too much about what an author meant. He wasn't always clear in his thoughts - just like us all - and his thinking changed considerably anyway.
> Philosophy at the end of the day is about arguing a point; it isn't about producing an aesthetic experience.
So why would you abuse your reader by making it a pain in the ass to figure out what you mean?
This is a funny thing to say about a discipline that was more or less founded by Plato, who was notably obscurantist if not outright esoteric.
In any case, philosophy is not always about making a point and there is not always a point to be made. Sometimes it's just asking questions.
This hasn't been my experience of Plato at all. I've always found his dialogs to be written with a surprising clarity. Is there a work in particular you're thinking of?
When philosophy starts with a real observation (...then words, then discussion), obscurantism is appropriate and expected. Because words can only fit a real observation badly.
When philosophy starts with words, a clear point is expected, for the obvious reasons.
What part of Plato are you referring to? Republic is honestly written at a 10th grade English reading level. The most esoteric work of Plato is Timaeus, but most people do not see that as a foundational text in Western philosophy.
First, the "reading level" of Plato depends on the translation, but that's not what I"m talking about. The way most people are exposed to Plato, they're assigned to read his most straight forward texts, but his dialogues are full of mysticism and ideas that he only hints at in the dialogues (particularly in Timaeus and Parminedes) which his students expanded on later. Plato was skeptical of the written word as a means of transmitting ideas and sort of held some ideas back exclusively for his students at the academy who continued to develop them.
platon didn't speak english, because english wouldn't exist for fifteen more centuries, so he didn't write the republic at any english reading level. the various english translations of it vary greatly in their clarity and readability
i agree that the timaios is platon's most esoteric surviving work, and it's full of enormous amounts of nonsense, but i think it's still reasonably clearly written. sadly, it is a foundational text in not only western philosophy but eastern philosophy as well, and it took twenty centuries for most thinkers to reject most of its erroneous dogmas
This. Philosophy is the grandparent of math. And if there is a point to math, then that there always has to be a proofable point.
I think the problem is a cultural conflict between sub-concious problemsolvers and "concious" problem solvers. The later expect a algorithm , step by step instruction from the former, who when this is demanded, use there subconcious to produce a plausible story. When asked for there inspirations to deduce the process yourself, you get a crows nest of shiny things, bits and pieces, not making a reasonable whole - but they infuriatingly at the end of day do.
Why not accept that there are things you can not directly communicate with and if you are hellbent on becoming such a thing, there is no step-by-step instruction.
> I know there are some fancy arguments around stretching limits of language, but none of them seemed all that sensible to me.
Did you read Robert Kegan "The Evolving Self"? It was pretty popular at HN some time ago. Robert Kegan stretching limits of language and he's got a reason: he introduces some notions like "culture of embeddedness" that you just can't define in a way like dictionaries do, one cannot simply get to a point. Kegan uses another approach, he gives his reader an experience that makes her to understand "culture of embeddedness".
Philosophy by definition deals with uncategorised (or poorly categorised) aspects of our world, with aspects that have no good language to talk about them. Anything that was categorised to a point when there is an accepted language to talk about it is not a philosophy, it is a science or something. Philosophy makes first attempts to categorise and when philosophers found a way then a new branch of science emerges.
When you try to talk about uncategorised things, you just can't talk about it. For example, lets assume that there are no widely accepted categorisation of colors, but you've developed one including names for colors like "blue", "red", "magenta" and so on. How you could communicate your ideas to others? The only way I know is to point to different examples of blue and say "blue", point to red and say "red". You need to lead your audience through experiences of blue/red/magenta while they train their neurons to classify them and only then you can refer to their experiences with words "blue", "red", "magenta" to convey the idea that they always appear in a rainbow in the same sequence. While you keep pointing at different colors saying their names, your audience will probably think, that it takes too long for you to get to a point.
I didn't read GEB, so I cannot say how this reason to "stretch limits of language" relates to it, but you've sad that you know no good reason for such stretching, and I hope that now you know at least one reason for it.
Personally, I believe that the distinction between "unnecessary detail" and "the point" is mostly subjective and in the mind of the reader.
The point of a book is to get the reader to reach a certain understanding. Every brain is different and while one literary path might get some readers to that destination, other paths may be required for others. But there is no singular point of understanding that exists solely at the end of that path. The path itself is what builds that understanding.
Part of the art of writing is covering a large enough space of multiple paths to get most readers there without too many of them getting lost.
There is a very clear distinction between details and main point. If you assume that there is no main point in a text, you negate all that the writer is trying to communicate.
Maybe I've been reading books the wrong way my whole life, but I never assume there's a singular "main point" in the text. I mean, why would one waste time writing 100 or 1000 page text circling around some single point for the reader to guess, instead of spelling it clearly up front, and then arguing for it?
Often, writing is like a connect-the-dots drawing where those points are the written details and the point is the overall shape. Yes, there is a "main point" that is not those details. But it's the details that convey it. Subtract all of them, and the shape disappears.
For any given reader, some of those detail points won't resonate with them and will be basically ignored. But as long as there are enough other details, they will still trace the right shape and get the overall point.
A big part of the art of writing is figuring out which constellation of details will lead to the right shape being traced in the minds of as many readers as possible.
> Indeed, Ulysses is almost nothing but "unnecessary detail", to the extent that it makes the book all but unreadable
I was always apprehensive of reading Ulysses… until I did. And then I read some basic analysis of it and then read it again and now I’m slightly baffled why people find it _that_ difficult. Yes it’s not at all typical but it’s really not that hard and it’s definitely no Finnegan’s Wake. Now that’s a challenge!
I mean lots of the lore is just residual 16 year old’s getting into reading stuff. You read l’Estranger (translated), decide you’re an intellectual, and so have a go at Ulysses cos it’s the hardest one and so suitable for you, an intellectual. The internet has been a good transmission vector for the sentiment.
If your ideas about cooking come from watching Masterchef (analogously), you might treat the idea of making a beurre blanc as a similar act of conquest, triumph in the face of splitting adversity whilst a thousand-voice choir crescendos in the background as you whisk. But a million french housewives happily made it for decades having never been told it’s impossible, and indeed knowing better that it isn’t.
To be sure, you certainly didn't mean it this way, but for the sake of the poor guy who has seen GEB touted as one of these books that "every programmer/computer scientist/CS major has to read" and sees your post in the same light:
You don't have to read GEB. You will be a fine techie without reading it. And you'll be a fine person in general without reading it. There is no spiritual revelation you can only get from GEB or some important technical knowledge that you'll get that you wouldn't get from a normal CS degree program. Try it out and see if you enjoy Hofstadter's writing - if you do, you might be in for a really enlightening and enjoyable experience. If you don't, no worries - your time is better spent elsewhere - there is no need to put yourself through the pain of slogging through a >700 page book that you don't enjoy. There are many other perfectly fine entry points for learning about topics in computer science, cognitive science, or philosophy of mind.
Right. And to be sure, GEB might have Godel in the name, but it's not really a book about Godel's incompleteness theorems. It mentions them, but that is not really the main thrust of the book. It's not a book about Godel, Escher, and/or Bach, really (though of course it discusses the ideas of these three people a lot). Hofstadter, if I recall correctly, even says as much (or something along these lines) in the preface.
So of course, there are more to-the-point resources for the technical concepts that Hofstadter employs. It's an understandable misconception to have when people so often say GEB is a must-read for techies and when it has a name that includes "Godel". So remember - GEB is about Hofstadter trying to argue for a point about a particular thesis (how the mind ("I") arises from the brain), and to that end, he employs many different concepts (many of which are from computer science) and explains them poetically (at least, a lot of people think so). But teaching you these concepts is just a secondary, even tertiary, goal of his. If you find his writing engaging, it might be a more fun way to learn about that stuff - but if not, don't worry, GEB wasn't primarily written to teach you anyway. I'm sure even the biggest GEB fans will agree.
It sounds like you're making a distinction between the plot and the theme.
I'd argue the plot is entirely about Godel's incompleteness theorem. It's not just "mentioned in passing", the entire book is centered around a series of increasingly complex explanations that culminate in explaining the actual theorem itself.
But just like a good novel is way, way more than just the plot, GEB is way more than just the Godel incompleteness theorem.
Personally I didn't really find any other thesis or theme that compelling. However, I absolutely loved the clever ways in which he illustrated each concept. Others may have appreciated other aspects of it, and that's great too. Many people can enjoy the book for different reasons.
The Godel proof chapter feels like the apotheosis of the book. The rest almost feels tacked on, e.g. the whole dna-computing ... , even the "strange loops" part, which I would not think is the main crux of the book.
I shouldn't have said "mentioned" to insinuate "mentioned in passing", you are right. But no, though it plays a central role in his argument, GEB is not about Godel's incompleteness theorem (I believe Hofstadter even says as much in the preface, and he laments that readers didn't get the overall point of the book - though I don't have my copy with me to confirm, so I might be misremembering exactly what he says).
But anyway - you and anyone else of course are free to enjoy Hofstadter's explanations of Godel's incompleteness theorem - maybe you even think that it is the best/most interesting/most fun/most insightful explanation. I just mean to say that Hofstadter isn't writing this book primarily to explain technical concepts - his explanations are a means to an end. So someone who struggles to get through this book shouldn't feel bad - its main goal was never to be a "must-read for programmers" anyway.
Never understood this logical jump in reductio ad absurdum argument. "If one finds a contradiction, therefore the initial premise is wrong". The argument always assumes a binary state, either true or false. It excludes another valid state which is "undefined". The premise of the video above is effectively to prove that one can't build a machine that is capable of resolving a paradox. As if computers have limited capabilities and that they are uncapable to reason the way humans can. But that's not true. If you allow a machine to produce 3 answers, "yes", "true" and "unresolvable", then it is very much possible to build such a machine that produces such output, i.e. detects that a problem is indeed a paradox. By simply implementing this reductio ad absurdum algorithm.
The halting problem asks, "Is it possible to write a program which correctly outputs YES or NO to the halting question for every possible input which is the code of a program?"
The binary requirement comes from the question, not a failure to think differently. The consequences of binary requirement with completeness (correct output for every input) is the point.
If you modify the question as you suggest, to output UNRESOLVABLE in exactly the cases where the input is a paradox, that doesn't work either. It is not possible to reliably detect every self-referential paradox, for reasons analogous to (but more complicated than) it not being possible to reliably say for every program if it will eventually halt.
Even so, it is possible to write a program which outputs UNRESOLVABLE in cases where that particular implementation of a halt-test program gets stumped and gives up despite there being another correct answer it hasn't found, or when it detects specific patterns. But that's more about hitting arbitrary limits of a particular implementation, so not as interesting theoretically. It is what you'd do in practice, if someone asked you to write a halting detector in the real world.
The halting problem computation model has unlimited memory. Sometimes people say this means you can "solve" the halting problem in practice because real machines have bounded memory, therefore finite states, which must eventually repeat if a program does not halt. But this isn't really a solution, because the halt-test program needs exponentially more memory than the input program would be allowed if run. However you look at it, that is not "in practice", it is prevented by computational inaccessibility, and it also doesn't satisfy the principle of the halting problem, which is to ask if halt-test can be written in the same kind of universal programming system as the programs it analyses. (Besides, you can run programs with unlimited memory, by always being willing to pause, upgrade machine, and resume, whenever current memory is filled.)
When analysed with denotational semantics, there actually is a third output called "bottom" (⊥) which means "mathematical value representing doesn't terminate". But even using mathematical approaches, there is no way to calculate when that's the output for all possible inputs to a correct halt-test function.
although, as schoen and jlokier have patiently explained, you're mistaken about the halting problem, it's a productive and interesting mistake, and others have taken your line of thinking a great deal further than you have even begun to imagine! you may be interested in reading about their work: https://en.wikipedia.org/wiki/Intuitionistic_logic
In fact, there is an obvious way how to build a machine that tells whether the program will stop or not. One only needs to track all the states that the machine was in, and if a program enters a state that was already encountered before then it's obviously stuck. And there are only that many permutations of possible states that machine can be in. So a number (time) can be given of when the result will be guaranteed to be found (which of course could be beyond physical resources of the universe, but mathematics are fine not to take those into account)
This is totally true for some models of computation (including some studied in academic computer science), but it's not true for the models of computation that the halting problem applies to, like the Turing machine, which explicitly has an infinite tape and therefore has the potential for an unbounded number of machine states.
In fact, this unboundedness is a core part of what makes these models of computation so expressive. In the Gödel's incompleteness theorem analogy, you can say "there is an integer such that ..." or "there is no integer such that ...". In the Turing machine model, you can write programs that search for counterexamples to mathematical claims. Because these programs are written to try every integer, you can only tell if they eventually halt by yourself resolving the mathematical claim.
For example, we can write a program that tests the Goldbach conjecture or the 3n+1 conjecture by brute force. Determining if these programs' search through all integers will halt or not is equivalent to resolving the status of these conjectures!
Here's an example of a Python program whose halting behavior -- if run on a hypothetical Python interpreter with infinite RAM and the ability to make use of it -- is currently unknown. It looks for counterexamples to the 3n+1 conjecture, and it tries every integer to see if it's a counterexample.
start = i = 1
visited = []
while True:
if i in visited:
if 1 not in visited:
break
else:
print(start, visited)
visited = []
start += 1
i = start
continue
visited.append(i)
if i % 2:
i = 3*i + 1
else:
i //= 2
On an actual computer's Python interpreter, I believe this will eventually halt with a MemoryError exception (although I'm not at all sure that you can actually run it long enough to hit that, as it will probably take many years!), failing to resolve the mathematical question. That potential for the MemoryError is why it matters whether your model has infinite memory or not!
(You can make a considerably more memory-efficient version of this which should be able to search much further before hitting a MemoryError, but I don't expect it changes the ultimate fate of the program when run on a real physical computer.)
When systems (think "automated" systems like computer programs, mathematical axioms, formal systems, etc, where conclusions can be drawn/calculated "mechanically" from a few starting points) get large enough, they gain the ability to become self-referential. That is, they become expressive enough to encode statements about themselves. A hallmark of this are "incompleteness theorems" like those of Godel or the Turing halting problem.
The book argues that these "strange loops" (of a system onto itself) are behind the emergence of intelligence and consciousness, because physical matter itself gives rise to human intelligence, albeit being a mechanical system.
I can appreciate a book being obscure or dragging things out when it is trying to give the reader an aesthetic experience. But this point seem to be one that would easiest be communicated clearly and succinctly.
Or is the point "there is so much mystery in these systems that perhaps there is room for an explanation for consciousness"? Maybe then I would be more sympathetic.
Or perhaps I should just read the book before condemning it :)
the point of the book is to give supporting evidence and guide the reader to the conclusion through testimony of thought and historical anecdote.
in other words, GEB tries to coax the reader into a eureka moment, which is exactly why it has so many fans; it convinced each and every one of us that we were genius for just a split second.
Good summary. Examples of GEB’s “fluff” are missing from this comment section, so I wanted to jump in and add one of my favorite. Bach encoded his own name in music notes in a piece, and when discussing that, Hofstadter encodes a sentence in the first letter of each paragraph in that chapter.
GEB’s point is that self-reference - the ability for a system to “talk about itself” - is crucial for conciousness and for real artificial intelligence.
I've heard about this book so many times and was interested to read it. But I know that as a non native English reader, my track record against reading English proses is very poor, and looks like lots of value of the book is exactly in the prose? Maybe I'll have to skip this one, unless some brave souls have already translated it.
It's Indonesian, which as I have guessed, doesn't have one at least as far as I google it. But it's astonishing that this kind of book have so many translations! Even into Chinese, wow! I guess it's truly one of most influential book.
And the translations are actually very good, since Douglas Hofstadter worked directly with translators to ensure that as much of the wordplays and Easter eggs as possible are preserved (of which there are a lot)
But if memory serves the translators of the Italian version removed a whole chapter of it (I might have to check details because I am far from both my author-signed English edition and the Italian one I bought many years later).
The Dutch translation of GEB is excellent. I think others, e.g. the French, are also quite good/excellent, potentially because Hofstadter himself was quite involved in the translation process. Hell, much of GEB and especially his later books discuss translation extentensively, so it would be strange if there were authorized translations of GEB that were somehow lacking in quality.
Crucially the French translation was significantly rewritten, with contributions from Hofstadter. In doing so, the French version becomes a separate projection of the author’s original ideas, along a different vector than the original English version. The approach therefore illustrates the main point of the book, similarly to its cover. Very meta. :)
Is it also valid to draw a comparison to Gravity's Rainbow, or parts 2 and 3 of The Divine Comedy? I ask, because those were on a tier of their own for being impenetrable (to me); I'm worried this will go the same way, but am otherwise intrigued.
Unrelated: Does anyone know of how to get an epub etc of this? Unavailable through Amazon etc.
I would suggest against an epub. I tried finding one too, only to realize the formatting of the book is ill-suited for anything but its original printed format (it’s far too particular for the epub format). Maybe give your local library a try?
Hell is just inherently more interesting to the human mind than paradise or purgatory. I read Ulysses with a book group and a leader that had read it in grad school and a number of books that exist to explain Ulysses. I read GEB as a fourteen year old with no internet access and it changed my life, but the ending isn’t that important. The proof of how the incompleteness theorem works and the stuff on Koans is I think most of the meat.
It is funny that you bring Ulysses into it. I’ve tried reading both GEB and Ulysses multiple times and had to concede defeat every time somewhere between the 100 and 200 page mark. The same goes for the satanic verses. I suppose my mind just wants a book to get to the point more than it wants to get to the end.
Ha I tried reading I Am a Strange Loop and found that meandering and verbose too. Didn’t finish it. He really labors the “greater than sum of parts” point for example. Ugh
I wonder if anyone on the Pulitzer Prize committee for GEB understood this was the idea he was attempting to communicate.
There seems to be a large market for books that make dumb people feel smart.
I have not read Ulysses but I have read other works from Joyce and cannot imagine comparing him to Hofstadter. I put GEB in the same mental box as Sophie's World or the Mr. Tompkins books, where story is used as a means to the end of teaching something to an audience that would otherwise find the material unpalatable.
I found this book dull, uninteresting and pretentious. Whatever it tried to say in what 1000 pages could have been said in 200. People will probably recommend it highly in this thread, but here is a vote to just leave it alone. It's just not good if you like pop sci but don't like pretentious fluff around it. It's the least inspiring and mind-blowing book I ever read. This could be related to having read a lot on the topics in the past so the subject matter was familiar, and having zero tolerance for the type of writing in it.
That's the "problem" right there. It wasn't a pop sci book. TBH while Gödel's incompleteness theorem might be seen as "science" subject, it is actually squarely in the realm of meta-mathematics, a branch of philosophy.
The "writing style" is what most would call "literature", which includes prose, poetry, stories, etc. It's not for everyone, for sure, but some people do enjoy it (I occasionally do, but I lose patience.) Calling it "pretentious fluff" sounds a bit extreme.
> This could be related to having read a lot on the topics in the past so the subject matter was familiar
I think you've hit the nail on the head. For many people, this book is their first encounter with much of this material (as it was for me, so long ago.)
For you, it's like reading a tour guide of your home city. You're not the intended audience.
If you're not a reading-for-pleasure person, or GEB's topics just aren't your thing, you're not going to like the book. It's not a technical volume; it's not something you read for skills acquisition.
That's the usual refrain around hyper-preventious navel gazer books. The moment you criticize, your intellect is up for question, because "you didn't understand it".
This form of logical fallacy is the worst in economics and philosophy.
> stuntkite on July 5, 2018 | flag| favorite | next [–]
> I'd owned this book for many years and had a similar experience to OP. But one day someone gave me I am a Strange Loop, which I started reading and enjoyed way more. After getting in a little bit Hofstadter makes some apologies for GEB saying it was the sum of work of a very young person. I think he was 24? I think it's pretty incredible considering his age. The things that lead him to thinking critically about consciousness because of his disabled sister I found to be something that changed not only how I interacted with people that were differently abled, but also changed how I saw my own disabilities. Sure it's more than a bit full of itself, but I can't for the life of me think how I would edit it any differently. It's honest from the place he was standing. With a lot of thought, a desire to share, and a perspective that no one else could just stumble on. IMO, it really does kind of have to be what it is.
> So, I decided to put down IAASL and try to really get through GEB first.. like for real this time... and found an Open Courseware[0] on the book to follow hoping that would help me really cut through it. It did! The trick that did it for me was the prof's suggestion that you just skip the first 300 or so pages and he picked up from there.
> I'd thumbed through it and much like op had "looked" at every page, but once I skipped the first 300 and followed along with the course, it was like butter. There is something funny about all the intro dialogs that can fatigue by the time you get to the meat.
> That said, I really enjoyed his reflection on GEB in IAASL and enjoyed the read of IAASL a lot more. Regardless of what you think about what Hofstadter proposes, I think his contribution to critical exploration of the consciousness is artful and invaluable. I think it's fun, compassionate, and beautiful, and it really changed how I see myself and my environment.
> It sticks with me and I think about it a lot and it makes me happy to share it with people.
I've made a stab at GEB numerous times in my life, in very different stages of my life. I'm close to 60 now so I've HAD a few different stages. I haven't been able to get through it; maybe not even the first 300 pages.
I may try the "skip that bit" trick and tilt at this windmill once more.
(NB: I hated "The Three Body Problem" when so many seem to love it. I wonder if there's any correlation there.)
I got this book when I was at the first semester of IT. Back in my university town, most students of IT or physics had this book, or lented it from a friend. And we discussed a lot about what was inside.
So I wasn't a seasoned academic, but the new-kid-on-the-block. And my goal while reading was never to understand Gödel. Or to like Bach's music (I actually dislike most of his music). Or to get into arts -- but hey, Escher I like.
My goal was to train my mind. To get into thinking models new to me, because they aren't taught in normal school.
Also, for me this book was an extension. Even while still in normal school, I went to the university library to read "Spektrum der Wissenschaft" (the german version of "Scientific American", but without the nationalism in the title). Many articles were over my top ... but the "Metamagicum" articles I deeply enjoyed. So when this book come out I expected some extension of these articles ... and I was not disappointed.
> I found this book dull, uninteresting and pretentious.
Yup, exactly my thoughts. But for some reason, the HN crowd keeps recommending it. Its gotten previously-- 5-10 years ago, it would be recommended in almost every book recommendation post
Not OP, but as someone who found GEB pretentious, I think the most mind-blowing books I have read were probably Kurt Vonnegut. Mother Night and Timequake probably at the top.
Well, part of the plot is about humanity’s slow and inexorable evolution through the passage of space and time, so the meditative slowness sets the pace quite appropriately.
GED (in my humble opinion etc), doesn’t really need some of the fluff. It’s a large book that’s easy to spot on the shelf, and it’s hard to avoid thinking that the publisher (and some readers) like it that way.
> 2001: A Space Odyssey could easily be trimmed to 25 minutes or less if all you care about is the plot. But should it?
Yes. Tell me that you just sat there watching it without being distracted by your thoughts at all. Being able to handle torture doesn't make torture good.
Did you make it to the part about the tortoise and hare problem where he suggests that the book may actually be finished at that point? With the rest of the book as noise that looks suspiciously coherent despite adding nothing new conceptually? At that point I had to read the second half to check LOL
I enjoyed the first part of it, but then ground to a halt about two-thirds of the way through. It became just so much recursive navel-gazing, and I lost interest. Wasn't worth the effort.
I feel exactly the same. It was like 1000 pages of patting himself on the back for being clever. I certainly didn't learn anything and there was very little art to his writing.
same sentiments. i was on 10th page and i was chuckling because i still got no idea what these geeks are talking about. definitely the day i realized im not that smart, too. haha.
Yep. It's like a conspiracy theory cult. I quit after 50 pages and found it to be a pseudoscientific, dilettante intellectual circle jerk ad nauseum desperate for hidden meaning. I'd sooner spend time reading articles from [Big City] Review of [Each Others'] Books.
Yeah, I don't think it is for me either. I tried a few times but always found that the style of writing is so strange: if this is a science book, I expect succinct style. Instead, I found the dialogs of Achilles and the turtle are just abominable. What the heck are the intention of the author? Just write it like a science text book and I will probably get it. Also, as a big fan of Bach this book has less than 5% content about Bach.
I'm going to try and explain why it made a difference in my life as briefly as I can.
I read it in the early 90s as a teenager at a community college in the suburbs, along with the Richard Dawkins' The Selfish Gene, at a point in my life when I was struggling with having a lot of doubt about Catholicism, and the _one_ thing that was keeping me from just giving up on religion entirely was that I just couldn't understand how the experience of _being_ could be anything but a spiritual soul, and those two books gave me the intellectual tools to basically completely rebuild my entire conception of what and who I was -- which is to say that I could finally see consciousness as the an emergent property of ordinary matter, and the relationship between consciousness and computation.
It's an experience you can only have if you read the right books at the right time in your life. You can only be exposed to any particular idea for the first time once in your life, and if they ideas in those books are not new to you, I'm sure you'll find GEB pretentious and ponderous or whatever, but for me it was like fireworks going off on every page. I read it and reread it and took notes on it and used it as a launching point for more reading for years afterwards.
edit with some extra thoughts: Keep in mind this book was written in 1979, when vanishingly few people had access to computers, let alone the internet. There was no wikipedia you could go to to scratch an itch about some topic. GEB is encyclopedic in scope and meandering because it _had to be_, he couldn't expect an audience who were familiar with _computers_ let alone artificial intelligence and set theory. It's really extraordinary that it's accessible as it is, given the breadth that it covered.
Today, given the advances in all the things he was talking about, I would think it's mostly interesting to read for historical reasons.
Funny, I did pretty much the same journey when I was young. As I grew older, I became disenchanted and eventually journeyed all the way back.
There are questions about conscience, the origin of the universe, the ultimate nature of reality, etc. that we haven't answered yet and perhaps never will. We have theories and we have models. We don't know which theories are correct yet and, if we eventually find a model that seems to work, we might not even be sure if it reflects reality or simply predicts it (like Newton's equations).
Furthermore, not all questions can be answered in this way. Every ethics system is grounded on metaphysics in one way or another: on concepts which are completely human-made, culturally-dependent, non-observable. Even the most Darwinian doctrines do this: genes don't actually "want" to be preserved and passed on, any more than rocks "want" to fall. Religions are simply more explicit about this than other belief systems.
Finally, it certainly doesn't help Dawkins and his followers that, despite claiming to be on the side of reason and truth, systematically let their judgements be influenced by their prejudices and preconceived notions. A more informed and grounded view of history would understand that a notion of the transcendent and the divine was the foundation for much of the progress of humanity.
So true. In the end, any truth is anchored in a beliefs system and you have to chose yours (or ignore that you've chosen one). Better chose one that helps you live a good and happy life...
I find Penrose's argument uncompelling: he doesn't see how ordinary physics could result in the sensation of beingness and experience, and we don't really understand quantum mechanics, therefore quantum mechanics is responsible for consciousness. (obviously, his book works on it for 500 pages so my summary is a parody, but that was the gist as far as I can remember)
Or one could speculate that consciousness arises from as-yet-undiscovered noncomputable laws of quantum gravity operating within brain structures called microtubules, as Sir Roger Penrose did in his 1994 book *Shadows of the Mind*
Heh yeah doesn’t seem great. I think it’s you nailed it. This is from one of the reviews posted above
The Lucas-Penrose argument is not generally accepted among philosophers. Of course, that doesn't necessarily mean it fails - truth isn't a popularity contest - but it does indicate there are some subtleties at play here; it's not so obvious Emperor of the Mind/Shadows of the Mind succeeds in its argument.
Speaking of Scott Aaronson he has more recently (2013) wrote a much longer exposition about consciousness and (quantum) computation, and has a chapter specifically for Penrose: https://www.scottaaronson.com/papers/giqtm3.pdf
I can't recommend The Selfish Gene enough. I wish it was mandatory reading in school or something. Contrary to GEB it is very accessible and a phenomenal introduction to the theory of evolution. It gets a point across, school books don't.
However, Richard Dawkins has become a very detestable person, cringeworthy culture warrior, rage beneficiary. So, make what you want with that info. Maybe consider a library or pirate the audio book.
I found the book a little depressing eg. the quote on the cover of some editions “We are survival machines – robot vehicles blindly programmed to preserve the selfish molecules known as genes. This is a truth which still fills me with astonishment.”
He got a bit more upbeat in later books. I'm not sure Dawkins is detestable but he's a bit humorless at times. The Telegraph has quite a good article on his culture war stuff https://archive.ph/kNJXN
> robot vehicles blindly programmed to preserve the selfish molecules known as genes
I think, his proposed theoretical framework about genes as the sole target of selective pressure, seems to be widely rejected by evolutionary scientists, these days. Anyway, the way he argues and illustrates evolution on the "atomic" level, that's what I consider extremely valuable. He inspires an intuition for evolutionary processes transcending "living matter". At least in me.
> The Telegraph has quite a good article on his culture war stuff
In what way do you think this is a good article? Do you think it's a very sincere and thorough representation of the extent of his activism?
This is a culture war piece itself, white-washing Dawkins as someone who is "just concerned" about debate and free speech, when in fact he seeks the legal abolition of transgender people, all the way up to the UN's declaration of human rights [1]. Not quite the neutral portrait, full of journalistic integrity, you linked there.
Now, I don't want to get into that argument.
However, should be no matter your political opinion on the issue, if someone in a position of power uses his influence to kick down massively at basic legal protections of a tiny, tiny, tiny and weak minority, without need, just to stay relevant ... that should classify as detestable in my books.
The Declaration on Women's Sex-Based Rights is exactly what it says. That you're framing it as abolishing some other group of people is quite simply incorrect.
Please actually read it yourself rather than biased articles from others complaining about it:
They don't straight up call for the extermination. Lol. The whole text is about abolishing protections granted by gender identity in a law and practice. It is based on the presumption there no such thing as gender identity, as recognized by the UN, most of the medical and psychology community, and advocates for manifestation of their own ideology - therefore implicitly abolishing transgender people legally, and effectively by restricting medical care and access existential resources.
But you know all that. Made an account just to spread some doubt. I wonder, if it's all that harmless and good, why not use your primary account?
No, it's about protecting women's sex-based rights. Having every point in the declaration enacted in law and policy would abolish no-one.
Men could still claim to be women and present themselves in a feminine manner if they so desire. There's nothing to prevent their freedom of belief and freedom of expression. The difference is that this wouldn't entitle them to access female spaces, and indeed would not grant them any special privileges under the law.
This isn't abolition, just like separation of church and state doesn't abolish religious folks, with them being free to practice their beliefs within their own communities of like-minded people. Same principle should apply to 'gender identity' beliefs.
If you disagree, please cite those parts of the declaration that you believe shows otherwise.
Sorry, I wasn't clear: Dawkins signed and promoted it [1].
Side note: A move, by an outspoken and activist atheist, celebrated by various christian think tank outlets. Can't make this up.
Then again, WDI founders themselves collaborated with United Families International, The Heritage Foundation and similar before [2]. All natural allies... lol. But hey, guess that 0.5% of the population, disproportionately affected by precarious living situations and suicide risk, certainly poses the greatest threat to civilization right now, so women's bodily autonomy has to take the L. Totally organic outrage Dawkins is participating in...
> However, Richard Dawkins has become a very detestable person, cringeworthy culture warrior, rage beneficiary.
Yeah.. My personal introduction to Dawkins was actually some TV documentary he made that covered about the same topics as the God Delusion, then I read the book itself. Only after that I read the Selfish Gene, which IMHO philosophically was a much more interesting book.
I did sort-of follow the "new atheism" movement for a time, the "four horsemen" and all that [1]. But it seemed to pretty quickly spiral into the cringy culture war thing you mention, so I stopped.
[1] I don't agree with many of the things Christopher Hitchens said, but damn he was a good orator and public debater.
It's sad really. I mean it. I adored him, his thorough, a bit arrogant style of argumentation. If he had stayed with biology and science education, he could have had a legacy of greatness. Now, he will die as just another edgelord, who thought they've become experts on everything; a content creator for the suck.
Dawkins is an old, old man, his days are counted. I hope with time The Selfish Gene will get a life of its own, with the person Dawkins becoming nothing more than a short side note, on a great educator falling victim to his ego. This book will endure, his Tweets won't.
Every book about the nature of consciousness has problems. It's not a solved problem. For me it wasn't the details but just laying out the landscape and I could see how to get there from here, if that makes sense.
Beautifully put! I recommend “Kants System of Perspectives” by Palmquist, it’s free online, short/skimmable, and explains in detail how Kant (200y ago!) was trying to do exactly this; acknowledge the unknowable parts of the problem, and instead focus on reasoning out the “landscape” or structure of it
What an unexpected connection: Stephen Palmquist used to run the Hong Kong Philosophy Café, until he left the city recently, possibly in the wake of the political changes.
Judging by the description on Skeptics I’d expect strongly Kantian views to not be very well received (they don’t particularly align with physicalism, and I find when people mention “science” they typically mean physicalism/materialistic monism), but who knows!
It's untestable. You cannot experimentally measure qualia, so there is no real way to differentiate between these theories. But any one of them fully explain the phenomenon, without resorting to nonsensical quantum woo.
I'm not arguing about the nature of consciousness. I'm just pointing out it's not the same as qualia. I am 100 percent sure animals experience the sensation of qualia. I don't know if they are conscious. Same with newborns. It's unclear. Qualia has nothing to do with awareness of oneself. It's different altogether.
If Hofstadter's book were right, it explains only consciousness. To put it another way.. he may really truly be a strange loop but what is the feeling of being a strange loop?
GEB is crucial reading in that if you want to appear intellectually superior all you have to do is sprinkle “Ho ho! Much like the eternal golden braid I must say!” into conversation and no one will call you out on it or ask you to extrapolate (or if in the off chance that they do, you can say anything and still get away with it)
The best response to someone bringing up GEB in casual conversation is to look them dead in the eye and simply say “I have also read that book.”
This will instantly create palatable tension and a change of topic
When someone enthusiastically mentions something they liked and wanted to talk about and you immediately take a shit on it, it's not really a surprise that this creates "palatable tension" and a change of subject (and likely a longer-term wariness to share when talking to you). If you really dislike discussing related topics, there are surely less condescending ways of expressing that.
They’re implying that many people use it as a way to take some moral high ground in a conversation, not knowing that others might also have acquired this ‘intellectual power’.
My experience is that when faced with what seems at first like pseudo-intellectual nonsense, it's usually more productive to either explicitly say I don't feel like discussing the topic, or else try to get someone into a serious conversation about the details, instead of trying to insult or shame the other person. Sometimes people are just bad at smalltalk / earnestly oblivious to the impression they leave / trying hard to impress for whatever reason, and aren't really trying to be pretentious even if they initially come across that way. YMMV.
I took the book with me on holiday and I couldn't put it down, almost literally reading right up until lights out each night. I was surprised and somewhat disappointed to be done in short time. The literary writing combined with the deep mathematical/philosophical meanings is entrancing.
I don't often get to meet people IRL who have read the book and wish I had more opportunities to discuss it. One (of the many things) that stuck out to me was the idea of foreground and background. Prime numbers to me is background that remains when you construct all the composite numbers, so technically they're 'non-composite' lacking the property of being a product of distinct numbers.
> GEB is crucial reading in that if you want to appear intellectually superior... This will instantly create palatable tension and a change of topic
Ouch... Why would you assume that the other party's goal is to appear "superior", and not that they are legitimately passionate about something? Do you dislike when people are passionate about topics that don't interest you? Or do you just believe that it is fair to assume that everyone who outwardly likes this book is secretly doing so because they want to seem smart or something? Or something else?
This is my impression as well. Kinda similar in its "bragging rights" to The Art of Computer Programming.
GEB was a frustrating read. I mean, it's interesting in places, but it's just all over the place, jumping between many different topics. The central theme is meant to be the strange loops, but it's IMHO not very interesting concept and his application on the cognition is just author's personal conjecture.
It's utterly unlike TAOCP. One is a comprehensive algorithms reference full of (hard) technical problems. The other is an extended personal essay. (Neither one is worth "bragging" about reading in my opinion.)
"Reading" all of TAOCP would take literally years of intense effort even if you set aside all other activity. There are a lot of great problems inside, and plenty of dry humor, and I would recommend people try to at least skim sections of TAOCP which seem interesting or relevant to their work, but very few people are going to even nominally work through the whole thing, and the people who might are professional scholars of the topic.
Reading GEB can be done leisurely over the course of a few days or maybe weeks, depending on how much time someone spends reading every day. It's not quite as easy a read as a pulp novel or comic book, but it also doesn't take any inordinate amount of work to make basic sense of, or require any special skills or background understanding to start on. It's a fun book to hand to a ~13–16 year old.
You are absolutely right. It was a great book to hand to a 21 year old me.
I've often read the hate on this site for this book. At least for me, I find the discussions and analogies to help me in thinking about, and eventually understanding the material. I contrast it with a graduate intro to Recursion Theory which can leave a reader feeling that they followed all the precise arguments but still somehow missed a lot.
I compared the two in the sense how it's fashionable to have them on your bookshelf, but IMHO few people actually enjoy them and understand them beyond the surface level.
This discussion is evidence that some people really liked GEB and other people found it boring or too unfocused. It can't be that many people who bought it just to look cool on a shelf. The people who found it boring should perhaps try to appreciate that sometimes other people can genuinely like things they don't like (and vice versa I guess).
Again, if you do any work with computer algorithms, it's worth checking out TAOCP at the library and skimming the sections relevant to your work. If you might need it as a reference, it's not a bad source to have at hand; I look things up in there maybe a few times a year for the past decade. Some parts are now a bit outdated in this fast-moving field, but it's still the best available survey source about some topics, and there are some nice explanations and a lot of great problems in there. Knuth is a pretty funny writer if you enjoy dry humor.
This is very different from my experience. Whenever someone I was in a conversation with brought up GEB, it was always a great pleasure of mine. I'd get the chance to discuss the main ideas of the book, and the way I assimilated them. I tend to not even engage in conversations with people who do it mostly to show off the extent of their knowledge. I believe this second point is the important one. GEB is completely orthogonal to the problem you describe.
Your response to somebody appearing to be intellectually superior because they bring up GEB is to act even more intellectually superior? It sounds like you feel you're so far beyond them, you won't even engage in a discussion about it.
Or you can read it and not tell anyone. This comment is a pretty pathetic attempt at shaming anyone who displays even a modicum of discourse higher than the baser level. Congratulations.
This is funny but GEB is also good so you wouldn't want it to go much further than this. Congratulations for getting there, now it would be great if you could focus that same energy on shooting down people trying to build upon or me-too this snark.
It is a good book, but it is a shame that so many pitch it as being a portal into a new and transcendent plane of understanding. Especially with it being a rather difficult read it leads to people trying to get more out of it than was in it to begin with.
To quote one of my professors from back in the day: “Life is short and you don’t have to read it if you don’t want to”
There is also the issue that it takes longer to read than you expect it to, even when taking into account that it will take longer to read than expected... ;)
I loved this book when I was young. Like 16 years old or so. I am still very interested in things like formal systems and automated theorem proving and that started with this book. However, when I now look at the main idea of the book I find it quite cringeworthy, because, besides when he is speaking about real mathematics and science, much of it is very speculative and probably just false. At best it can be thought provoking, but I think it is just not very nice to immediately answer the some very real questions with highly speculative answers. It snared up the admiration of my 16-year-old self pretty effectively, though.
I loved GEB, I read it twice and found it mind-blowing.
That said, I don't think it was life-changing in the sense that it gave me any interesting perspective on life in any way. I didn't find any of the philosophies to be useful in that sense.
However, what the book does do, is manage to explain an incredibly complex, deep mathematical theorem while using almost no mathematical notation. It does it all mostly through similes and wordplay and art, which is quite brilliant.
One of the great things about the book is that even if you give up on the math, you can still appreciate each chapter as clever writing in its own right.
"The Dice Man" by Luke Reinhart. In my teens it didn't hurt that it had some pretty intense pornographic sex scenes, but the real takeaway - the idea that there is no "singular you", just a swirling multitudes who bob to the surface for attention depending on the context ... yeah, that changed my perspective on life.
Too bad about the misogyny. Might even have been racist, but I don't remember that.
> there is no "singular you", just a swirling multitudes who bob to the surface for attention depending on the context
Sounds a little like “One, No One and One Hundred Thousand” have you read that one?
Also,
> In my teens it didn't hurt that it had some pretty intense pornographic sex scenes
For me, that book is Lockpick Pornography - it’s a fairy horny story, but the main character struggling to figure out what to do about gender and sexuality, and the way that struggle starts out seeming like it’s about systemic oppression and heteronormativity but quickly spirals into the character just having a series of self destructive meltdowns is so so compelling. It even manages to have a bit of a happy non-ending.
When I was working on m Masters degree in Electrical Engineering way back in 1978, when dinosaurs roamed the Earth :) I had a prof who was really amazing, he was a Comp Sci prof and he gave me a copy of GEB and it changed my life. OK, I'm probably overstating a bit, but that first edition copy, it's one of my prized possessions. Even to this day, every once in a while I pull it out and re-read a chapter.
Same. It has the exact same junior high-school giddiness of excitement as The Martian, another book that I just couldn't tonally work my way through.
I don't mind books that explain concepts in fun ways, but I do find it jarring if I'm being treated like a child with an overbearing parent, telling me why I should be excited about something instead of just telling the story and letting me feel how I want to feel about it.
I wanted to love this book. I understood the concepts and found them legitimately thought provoking - I just disliked the writing style. He uses elaborate metaphors, strained socratic dialogue, peppered with cultural references and visual cues... and relatively few paragraphs actually articulating the core ideas. I only understood Godel's incompleteness theorem when I looked it up elsewhere. It's like he focused entirely on the mystical "look how deep all this stuff is..." story and forgot to actually explain the subject at hand.
I share your experience and I've tried it three times. Couldn't get through any of his Metamagical Themas articles in Scientific American, either. I thought he was in love with writing, not communicating, and didn't want to remove a word once he'd put it down.
I'm also struggling with it despite having it on my bookshelf for a while. Not an easy read. It's cited and referred to all over the place, so maybe it's worth getting through it.
I would say give yourself license to skip some stuff, the parable stuff (for instance) is either super fun or a chore, depending on the mood you are in. A lot of the Achilles stuff is more akin to poetry instead of an illuminating guide.
There's a point in the middle where he's building a foundation of formal systems that's a real slog. If you push through that, it gets progressively more interesting.
This book played an important role in pushing me into a career in software. During the recession in 2009, I lost my industrial design job. And GEB started me down a rabbit hole learning more and more about software and learning to code. That turned into a great software career. I've also read hacker news just about every day since.
The most valuable thing about GEB for me was how self-indulgent it is. The book is entirely Hofstadter having fun: all those tricky dialogues, acrostics, puns where the setup and payoff are hundreds of pages apart, the marrying of form and content, just the overall tone of excited sharing…. Hofstadter has put a lot of himself into it—it's a deeply personal book—and it was revealing to me to see that one's emotions don't have to be set aside when writing, nor is it necessary for the kinds of feelings that mathematics evokes to be “translated” into more familiar ones.
(Edit: As an aside, Hofstadter's translation of Pushkin's Eugene Onegin is similarly self-indulgent, and a joy to read. Of course one ought to read a couple of other translations first and keep them nearby, to become familiar with the content, but in terms of sheer wordplay and outrageous rhymes, it tops anything.)
(Edit 2: Ha, a search reveals I posted a similar comment a little over a year ago: https://news.ycombinator.com/item?id=32830008https://news.ycombinator.com/item?id=32878471)
The book itself is challenging and at times even cryptic. I watched the lecture after reading it, but in hindsight would have followed the course or read after.
Maybe the book went over my head but it didn't live up to my expectations. The book's thesis seemed to boil down to "isn't recursion cool, maybe it has something to do with consciousness". I did enjoy some of the digressions though.
I thought it was going to be first something like "isn't recursion cool" (like, look at these fractals in sea shells!!!!), until GEB actually tried to explain, in detail, how Godel's proof works. tbh, that's kind of what makes the book cool, it just assumes anybody with a passing interest in compsci would also love to dive deep into fundamental theorems of mathematics. Those sort of bold assumptions, and the author just doubling down on them (e.g. you're going love these dialogues!). Crazy that it won a Pulitzer too, a real bestseller.
GEB is my personal bible. It looks like I'll need to write a post just like this when I have a chance as it impacted me for all of those reasons, but my most significant take-aways(abstraction, the significance of analogies, and the meaning-of-meaning) are not even on OP's list.
I've not read the book so am looking at the comments here for reasons why I should. The majority seem to be something like "I read it when younger and it was like a powerful transformational psychedelic experience at a one day festival".
It is meaningful, reading it is something that is shared with others, but it is an event in time and is unrepeatable, and it's somehow unable to be fully communicated about to others who were not there.
For some it seems foundational because it was encountered at a certain time in their life without really elucidating how their life actually changed
(it's understandable because if it was done at their start of their life.)
That may well be some people's experience. It wasn't mine.
Not because I didn't like it: I enjoyed it a lot, I learned things from it, it was one of my favourite books, etc. I still think it's an impressive piece of work. But there was nothing particularly ineffable about it.
So let me try to summarize some of the perfectly effable things that people who like GEB tend to like about it, which might (or might not!) make it worth reading for you.
1. It's a playful book. Hofstadter is having a lot of fun as he writes. (I think this is one of the things that people who don't like the book tend to really dislike: if you don't happen to enjoy the same things Hofstadter does, it can just feel self-indulgent.)
Here's a fairly typical example of the sort of thing he does: the book alternates between ordinary chapters, where Hofstadter might explain some bit of mathematics or talk about an incident in the life of J S Bach or whatever, and dialogues between some imaginary characters. Each of those dialogues is named after a particular piece of music by J S Bach. For instance, one of them is called "Crab Canon", after one of the little pieces in Bach's "Musical Offering" which has the amusing property that it's the same forwards as backwards. So Hofstadter's dialogue is also the same forwards as backwards, and he's constructed it so that the conversation makes a reasonable amount of sense both ways around.
That's a fairly superficial sort of play -- it doesn't have much to do with the deeper underlying ideas Hofstadter is trying to explore, it's just a bit of fun. But he does play around with the deeper ideas too.
2. It brings a bunch of apparently different ideas together and relates them to one another. The "psychedelic" aspects may come from this -- there's something of the "wow, I never realised before, but everything is, like, one thing" to it. And this is another thing that you might either really like -- he's made a bunch of unobvious connections between things you mightn't have seen links between, and connecting things better enriches your mind -- or really dislike, if you feel that the connections he's claiming to make are bogus.
For instance, Hofstadter is very keen on what he calls "strange loops", in which category he includes (1) indirect self-reference, as in the machinery of Goedel's incompleteness theorem or "quining" (copy this down, first without the quotes and then again, after a colon, with them: "copy this down, first without the quotes and then again, after a colon, with them") and (2) what happens when a person thinks about their self and (3) Escher pictures like "Print Gallery" or "Drawing Hands" that somehow show something containing or creating a representation of itself and (4) the way in which DNA codes for proteins which make cells with machinery for converting DNA into proteins which etc. and (5) rather more tendentiously, one of Bach's canons which ends a tone higher than it starts so that if you kept on playing it the key would keep rising and rising. The common theme is something about traversing levels of a hierarchy and somehow coming back to where you started. If you agree with Hofstadter that this is an interesting and important general phenomenon (he thinks it's essential to how conscious minds work) and that all these diverse things are cases of it, then you'll find this enlightening, maybe even exciting. If you think he's just grouped together a bunch of things with little in common and convinced himself they're all the same thing, then not.
3. It talks about some really quite exciting mathematics (at least, for those who are able to be excited by mathematics): Goedel's incompleteness theorems. If you just want to learn about how Goedel's stuff works, you can get that more efficiently and probably more clearly in other places. But Hofstadter's explanation isn't so bad, and he intertwines it with all those other things he's interested in, and once again you might like it or hate it. In any case, for many people GEB was their first exposure to the idea that some statements that are just about the properties of the positive integers might be provably neither provable nor disprovable, and to the neat techniques Goedel cooked up by which, in some sense, statements about properties of positive integers can "really" be "talking about" mathematical statements and proofs and whatnot, and these are (again, for some subset of the population) exciting ideas.
4. Escher made some really cool pictures. Bach made some really cool music. If you happen not to be familiar with them before reading GEB, then being introduced to this cool stuff is a pretty valuable service GEB can do you.
5. Chunks of GEB are about artificial intelligence. The world of AI has changed a lot since GEB, of course, and today's AI systems don't have at all the sort of structure I think Hofstadter expected them to have. (It may be that they have some of that structure "hidden inside" -- artificial neural networks are mysterious and inscrutable in something like the same way as brains are -- but I think Hofstadter was expecting that structure to be in the code.) I haven't read GEB in a while and won't try to pronounce on how much value his thoughts-from-way-back-then have today. But I think one thing some people have found exciting about GEB, especially when reading it early in life, is that it was the first thing they read that took seriously the possibility that computers might be able to think in something like the same way as humans, and tried to think about how that might work. The ideas of AI are much more "in the water supply" these days; I doubt anyone will first hear about them from reading GEB any more.
6. (Same theme as 3, 4, 5.) There are just lots of interesting things in GEB. Zen koans. Fractals. Winograd's "SHRDLU" AI system. Bacteriophages. Non-euclidean geometry. Srinivasa Ramanujan. Etc. You won't learn much about any of these things from GEB, but encountering them at all is delightful if one happens not to have seen them before. So the experience of reading the book, if one happens not already to know everything, is one where at any moment you may suddenly encounter some fascinating new thing.
I am not claiming that you should read GEB. It's pretty long. All the individual things you could learn from it, you could learn another way. If you're a generally-well-informed adult, you probably already know a lot of the things some people first encounter in GEB. You might not share Hofstadter's taste in wordplay and the like. But it definitely has merits that can be described.
Wow, this is a great explainer. I think you captured most of it. The other things others have highlighted is that when it came out in 1979, and many fans read it, there was no internet to speak of, definitely no WWW or YouTube, and these ideas were not as easily accessible as they're now. So for many this book might well have been the first encounter with many of the themes, thus mind-blowing.
> "I read it when younger and it was like a powerful transformational psychedelic experience at a one day festival"
I never had a psychedelic experience but I wouldn't object to this way of framing my experience with the book.
I would say there's something more "profound" than what you'd get from reductionistically learning the concepts introduced in the book one by one. It feels as if the author had a powerful transformational psychedelic experience and afterwards he wrote the book to share what he learned about consciousness and its relationships with self-referential computation.
While it seems the crowd here is focused on the "Gödel" part, the book actually dives deep into a lot of auxiliary topics, for example (from memory having read it 20 years ago) - ideas about Zen, tensions between reductionism and holism, how DNA replicates itself, contrapuntal music etc. And while GEB isn't necessarily a great introduction to these topics, the concepts are indeed related in some way towards the philosophical question of consciousness, and IMHO the reader benefits from having been introduced these concepts in such a context.
So if you're just trying to understand Gödel's theorem there are better books. And the mismatch in expectation is probably much of the frustration by those who didn't like the book that much.
All that said, just try reading a couple chapters and see if you like it. The "psychedelic experience" isn't for everyone, so just try it and see for yourself if it vibes with you.
Why not just read it? You can always give up halfway through if you get bored.
I quite enjoyed it, but there's something of the Young Adult Reader about it that sat ill with me. One of those books where (once I'd read it) I found myself slightly wary of anybody that would bring it up. Same goes for Atlas Shrugged, and Zen and the Art of Motorcycle Maintenance.
The dice man book is played too clearly for laughs IMO, but perhaps that one as well.
> Same goes for Atlas Shrugged, and Zen and the Art of Motorcycle Maintenance.
I've got all three of these on my bookshelf behind me. Seems like we have similar taste! Any other recommendations? One I'd add to the list would be Unsong(can find it free online).
Do you also have a full printed out copy of Harry Potter and the Methods of Rationality on that bookshelf? I'm not sure you understood your parent comment's point.
the comment you refer to was just attempting to displace the discussion we have been having about interesting ideas with chimpanzee dominance games and ingroup-outgroup dynamics, and it should have been flagged. the comment you were replying to was refusing to play the chimpanzee dominance game and returning the discussion to the topic of interesting ideas. your comment is again attempting to return the discussion to chimpanzee status displays and ingroup-outgroup dynamics and should also be flagged
no, it's mostly that it's 700 pages long (about half the length of the christian bible) and very wide-ranging (also like the christian bible), so you can't put it into a comment on the orange website
howard anton's textbook calculus was foundational for me because it was the textbook i learned the integral and differential calculus from. reading an introductory calculus textbook for me today would not be the same kind of transformational experience because i'd be brushing up on particular integration techniques and theorems rather than encountering a wholly new way of understanding the world for the first time, then struggling to assimilate it into my worldview and skillset. want to know how it changed my worldview? well, if you don't know calculus, i could fully communicate it to you if you make enough effort, but communicating it to you would involve teaching you calculus, and either writing a calculus textbook or persuading you to work through an existing one. you aren't going to understand what i'm talking about after reading a comment on here
and geb is the same way. it was my introduction to the following ideas: formal axiom systems, baroque music theory, symbolic ai, gödel's incompleteness theorem, the foundations of mathematics in general, the formalist conception of mathematics in particular, hilbert's program and the entscheidungprobleme, mathematical isomorphisms, the art of magritte, the music of john cage, the central dogma of molecular biology, the concept of holism, the artistic difficulty of linguistic translation, non-turing-complete programming languages, lucas's flawed argument against the possibility of ai, tarski, quines, and shrdlu. there are probably numerous others i've forgotten. some of these he carefully explains in detail; others he just touches on. about a third of these topics have formed significant parts of my intellectual life in the ensuing decades
quite aside from thus broadening my intellectual horizons enormously, it was a pure delight. the author's enthusiasm for playing in these fields of thought was contagious, perhaps because i was not yet the bitter, jaded cynic i am today. the aesthetic experience of being led through this gallery of wonders is of course not communicable, any more than the experience of listening to bach (or cage, or king crimson, or icp, or system of a down, or myrath, or the beatles) or watching the sun rise on a partly cloudy day
probably if i hadn't run across geb at puberty i would have eventually encountered most of those ideas anyway, and probably encountering it later wouldn't have been nearly so delightful, because explanations of ideas one already understands are rarely as exciting as explanations of utterly novel mind-expanding ideas
so in that sense it's true that 'it is an event in time and is unrepeatable', in the same way as learning anything is unrepeatable. it's true that 'it's somehow unable to be fully communicated about to others [who haven't learned it]', in the sense that you can't fully communicate concepts within any given field of knowledge to people who aren't familiar with its basics. if you don't know what a derivative is, nobody is going to be able to communicate stokes' theorem to you. if you don't know what money is, nobody is going to be able to communicate why microsoft europe is headquartered in ireland to you. and, in the same way, if you don't have any idea what string rewriting systems have to do with mathematical provability, gödel's theorem will sound like crazy moon language to you, though of course geb isn't the only way to become acquainted with those notions
i think the major difference from psychedelic revelations is that many of the things you'll learn from geb are actually true, in an objective, scientific sense, though not some of the 01970s conventional wisdom about how artificial intelligence could be built
hopefully that helps to clarify things for you a bit
After 742 pages and even after having written the paragraphs above, I still struggle with a simple answer to the question: “What is this book about?” The best I can come up with is that GEB equips you with mental models to contemplate philosophy.
No thanks. I'm not reading a book that even its fans can't adequately explain.
if there was a simple answer to the question, hofstadter either wouldn't have needed 742 pages to answer it, or needing to do so would show that he was a terrible writer, but in fact he's a great writer and he did need them
GEB is like Git. Git is fundamentally a DAG, that’s it. It’s beautiful. But it’s expressed via a bunch of tortured confusing words like refspecs, detached heads, tree-ish’s, and on and on.
GEB is a love letter to some beautiful elegant ideas, but it’s expressed via a confusing assortment of record players, tortoises, and puns. One StackOverflow answer made the incompleteness theorem more clear to me than this whole book.
> I had a secondary goal in the back of my head... if you have a copy of GEB on your shelf collecting dust and you've never read more than a chapter or two, dust it off and see how it goes this time.
Dusted it off and after only a few pages, it's already a completely different read to when I read (a fraction of) it a decade or so ago.
GEB is one of the books that as an adult I have learned to not care about anymore. I've unsuccessfully tried reading it a few times (once made it a couple of hundred pages in) and came to the (personal) conclusion that if I want an intellectual challenge I'll just directly do maths instead of reading a semi-literary essay about maths.
Just like (some of) Joyce's work, GEB seems to me a puzzle who's main prize is the satisfaction of having understood it - obfuscation and abstruseness for their own sake.
For actually understanding Godel's work I would recommend Gödel's Proof (Nagel, Newman, somewhat ironically, prefaced by Hofstadter) or Philosophies of Mathematics (George, Velleman).
> That’s a lovely fantasy, but Gödel shows that there are fundamental epistemic limits to the universe, things that no genius will help us to know, no alien race could teach us, no machine could be built to solve, and no new kinds of mathematics will uncover.
That's not quite true. As an example, take differential calculus. It is hard to see how that would have been an idea to arrive at automatically by an algorithm, but a few geniuses (Newton/Leibniz) got there anyway. Similarly, even when a theorem doesn't follow from the usual axioms (and neither does its negation), maybe another genius comes along with an axiom that is quite obvious, and allows us to prove the theorem (just like peano axioms are axioms we would just accept as being obvious).
So it is not that we cannot know everything, it's just that there is no guarantee and no obvious way of doing so.
But, that's not what Gödel proved. Not that things are hard, or non-obvious. But, that there are actual limits we won't be able to get past regardless of how much time and cleverness we apply to them. The limits might be very large. Might be unlimited for practical purposes. But, they are there waiting for us.
I don't understand his theorems well enough to pretend to explain them to this audience. But, this is my understanding of them.
> But, that there are actual limits we won't be able to get past regardless of how much time and cleverness we apply to them.
Nope, all he proved is that there is no automatic and purely formal way of arriving at truth. Doesn't mean that for any particular truth we cannot stumble upon a way to understand it anyway.
For example, we cannot write a program (= automatic and purely formal way) to determine in general if an input program halts. But for a particular input program, we might be able to understand whether it halts anyway. There is just no a-priori guarantee that we will.
I really don't think that this is the case. Godel proved that some truths cannot be proven. That seems pretty fundamental, and I think that's what made him so impactful, e.g. much more than e.g. the halting problem, which is about computation solely.
What Godel also showed was that we can expand our a prioris, e.g. add another truth that "feels" intuitive to the axioms, and then we can understand some theorem or truth (ie. look under the hood, understand its mechanics). But that means expanding the system by some sort of oracle, some sort of "genius intuition". Fair enough, mathematicians will agree by consensus if it's the right think to do, but it's also infinitely regressive. So I'd agree with corysama here "we won't be able to get past regardless of how much time and cleverness we apply to them".
If by proof you mean using a fixed formal axiom system, then yes, you are right. But let's look at one particular such thing that cannot be proven formally within itself: The consistency of Peano arithmetic. But, I don't need a formal proof for that: It's obviously consistent, because the natural numbers form a model for Peano arithmetic. So I just gave you a proof, but it is not a formal one. Yet, I don't see how anyone of sound mind can reject this proof.
So Peano arithmetic is obviously something we can assume when proving other, more complicated truths. And nobody can say, not even Gödel, that we will not keep finding similarly obvious truths for the more complicated truth we otherwise care about, but which might not be provable from the currently established axioms. Given that Gödel is a Platonist, he would probably agree with me on that.
I'm not sure you're responding to the same point by the GP. GP claims some truths cannot be proven. You took one claim that could be proven ( https://en.wikipedia.org/wiki/Gentzen%27s_consistency_proof ) and tried to proclaim its truth without referring to the proof.
Even the GP's claim is problematic. The Gödel's theorems don't prove that some truths cannot be proven. It only proves either ZF is inconsistent, or some truths in it cannot be proven.
Ironically GP's implicit assumption that ZF is indeed consistent mirrors your response in which you claim Peanno is consistent... :D
That said, if you somehow proved that "some truths cannot be proven within a fixed formal axiom system (that is sufficiently powerful)", and then you also take into account the Church-Turing thesis, i.e. that Turing machines can fully model our thoughts, then the proof of the claim about "some truths cannot be proven" is more or less complete.
Of course you can always posit the existence of some "unknown unknowns" that are outside of our wildest imaginations and thus invalidating whatever we thought we have known. But that's outside of our current ability to reason.
I could go on and talk about what I understand about divine inspiration and knowledge, but I suppose those topics are a bit too speculative for the crowd here...
> I could go on and talk about what I understand about divine inspiration and knowledge, but I suppose those topics are a bit too speculative for the crowd here...
you're appealing to common sense to demonstrate the consistency of peano arithmetic. this has two main problems:
1. it's subjective and culturally dependent. most people intuitively reject peano arithmetic in their childhood; until they have been repeatedly told otherwise, they intuitively believe that there must be some biggest number. often in english-speaking countries they think that number is called 'infinity'
2. common sense is also what tells us that the earth is flat, the sun goes around the earth, it's impossible to create a vacuum, things only keep moving as long as there's some force impelling their continued motion, people can't fly, if a vacuum did exist rockets wouldn't work in it, and so on
it turns out that once people stopped relying on common sense so much and started using formal axiom systems, they were able to learn a lot of things in only a few centuries that not even their smartest ancestors had ever been able to figure out during thousands of centuries
This I learned from GEB too I think, the aha moment around 200 years ago when people understood formal axiom system can be arbitrary, and even counterintuitive. Rather than creating a crisis of confidence, and the collapse of the field, it was the start of a whole new era for mathematics (and eventually physics, e.g. it's hard to imagine something like, I don't know, relativity, if math/physics had remained rooted in "common sense").
note that this isn't the first time; you can see it clearly in eudoxus, euclid, archimedes, and the antikythera mechanism, and lucio russo's book tells the story of how science was rapidly developing until the roman conquest brought it to a crashing halt
So you are saying Kepler and Galileo used formal axiom systems? Give me a break.
1. needs a citation. I never believed such a nonsense.
Common sense with respect to the physical world is different to common sense with respect to the world of mathematical objects.
In fact I don't like the word "common sense" when applied to mathematics, I prefer the expression "mathematical reasoning". In fact we model the physical world by representing it via mathematical objects, because mathematical reasoning is so much more reliable than common sense with respect to the physical world. In fact the advantage of such a mathematical model which we can subject to mathematical reasoning are so big that we are OK with the fact that the model might only be approximating physical reality.
In the mathematical world formal logic is a great tool for mathematical reasoning. Mathematical reasoning tells us that if we can represent our reasoning via formal logic, then we can be sure that it is correct. But formal logic has its limits, and in the end mathematical reasoning is the final arbiter, not formal logic: The peano axioms are consistent, because the natural numbers exist. Which is obvious and doesn't require a formal proof (which does not exist, by the way, and will never exist; but that we can know this, is a testament to the power of mathematical reasoning).
no, kepler and galileo didn't understand formal axiom systems; even today you can read galileo's mystified remarks upon encountering that manner of thought in the surviving fragments of eudoxos
when you say 'because the natural numbers exist' what you are really saying is 'because i am a platonist'. while that is a perfectly reasonable reason for you to believe things, it's not going to convince anyone else, in many cases not even other platonists. i reserve the term 'mathematical reasoning' for things that do, and i think that's a more widespread definition than the one you are using
Well, show me a mathematician who does not believe in the natural numbers. And yes, I am a Platonist, just as Gödel is. If you are not a Platonist, your view cannot be defended. It is as simple as that. I don't really care to convince non-Platonists, except for them to become Platonists.
What is your definition of mathematical reasoning then? If it is just formal logic, we could not even work with natural numbers. Even better, we could not even justify formal logic.
I am a big fan of formal logic, so much that I got myself a PhD in implementing formal logic on a computer. I want to do as much mathematical reasoning using formal logic as I can. But it is clear that formal logic has its limits, but that doesn't mean that mathematical reasoning has the same limits. The natural numbers show us otherwise.
mathematics probably began as platonism, but eudoxos put it on a purely hypothetico-deductive basis before platon's corpse was cold, so this debate has been going on for a while already. however, from the end of the hellenistic age until the 19th century, mathematics was utterly dominated by platonism
the social situation is quite different today. as you and i both know, there are plenty of formalists in mathematics, and quite a few constructivists as well, and none of them are platonists; we might even argue that at this point formalism is more popular than platonism among people working on foundations of mathematics. wildberger, a constructivist, is probably the most notorious living anti-platonist extremist who's still within the mainstream (i.e., he's a real mathematician, not just some bozo like me): https://njwildberger.com/2021/10/07/finite-versus-infinite-r... is a sample of his anti-platonist rhetoric. and, as you are certainly aware, voevodsky's extremely influential hott is fundamentally constructivist. https://en.wikipedia.org/wiki/Ultrafinitism is (or was) full of mathematicians who do (or did) not believe in the natural numbers. and it's easy to find working mathematicians saying things like https://old.reddit.com/r/math/comments/fx6bqv/why_did_brouwe...:
> I don't even know if 7 "exists," let alone pi. Such questions may be interesting, but they're philosophy, not math. Meanwhile, it's useful and mathematically interesting to count to 7, so we do it.
from a sociological perspective, a reasonable definition of 'mathematical reasoning' might be 'whatever arguments platonists can use to convince formalists and constructivists, or vice versa, without resorting to empirical evidence'. (this obviously isn't a logical definition, but i would argue that definitions of commonly used words and phrases are always sociological rather than logical in nature, though we can certainly stipulate a logical definition within the context of a given discussion.) this excludes, for example, which territory rightfully belongs to belgium, whether the earth orbits in an ellipse, or whether the natural numbers exist or not; but it includes the area inside a particular proposed national border for belgium, the properties of ellipses, and the consequences of the peano axioms
i think it is correct that formalists do not believe that formal logic is justified in any fundamental sense, but i haven't actually asked them
Here's the thing: any definition of mathematical reasoning that excludes the natural numbers, isn't a definition of mathematical reasoning.
For example, I cannot convince some constructivists that A or not A is always true when it comes to mathematical reasoning. But it is always true, anything else just doesn't make sense. So a constructivist who doesn't acknowledge that, I cannot take anything serious they say. Note that this is different from coming up with interpretations of ∨ and ¬ such that A ∨ ¬A is not always ⊤, such as Heyting Algebras, for example. And it is different from doing constructive mathematics, which is a very interesting subject.
Voevodsky was not a constructivist. He was looking for a way to do the kind of mathematics he likes on a computer to ensure correctness. He first visited the Isabelle development group to find about that, but simple type theory was not flexible enough for his purposes. So afterwards he fell into the hands of the dependent type theorists, who are all constructivists. He tried to do classical mathematics in their framework, that's where his univalence axiom comes from, but that didn't really work out well so far, and I doubt it ever will (but I don't really understand it, so that's just my opinion).
certainly you have to be able to do mathematical reasoning about natural numbers, but that doesn't necessarily imply determining their ontological status
another useful definition of mathematical reasoning is 'arguments strong enough to convince someone who cannot take seriously anything you are saying and does not trust you at all'
i appreciate the correction about voevodsky; i don't have a phd in the field myself, so that may not be all i got wrong
> certainly you have to be able to do mathematical reasoning about natural numbers, but that doesn't necessarily imply determining their ontological status
That's true, of course you can use something without understanding it, but can you use something, and then deny its existence?
I want to correct what I said earlier about the natural numbers and infinity. Of course you could add infinity to the natural numbers, if you wanted to. This can be done in different ways. It's just that natural numbers without infinity are a simpler starting point.
if i use monopoly dollars to buy the b&o railroad, does that entail that i believe that monopoly dollars exist? surely not in the same platonic sense that you and i believe that 53 exists. monopoly dollars are, i think uncontroversially, merely a socially constructed consensus hallucination, like national borders, google, or adultery; as far as i can tell, formalists claim that 53 is too. for that matter, subjective idealists like berkeley claim that so are physical objects like electrons
i haven't seen a satisfying formalist explanation of why mathematicians of different cultures come to identical conclusions about 53 but vastly different conclusions about national borders and adultery. (borges' tlön, uqbar, and orbis tertius famously makes a similar point satirically about subjective idealism.) but i am forced to admit that the formalists themselves do exist and do make this assertion about 53, and while many working mathematicians are unwilling to wholeheartedly embrace formalism (and even fewer constructivism, though, as you point out, for example in type theory constructivists are ubiquitous), fairly few of them are willing to wholeheartedly reject it and declare certainty about platonic realism, as you are
what i was saying about the natural numbers and infinity is that the "common sense" of many children (though perhaps not your own childhood self) insists to them not that a maximum natural number is logically consistent, which i agree with you that it is, but that it is logically necessary, which of course the peano axioms reject. this, to me, is good evidence that common sense is not a solid enough foundation for reaching mathematical truth
by the way, i want to express gratitude for your willingness to discuss epistemology and ontology without descending into the kinds of vicious personal attacks i generally expect on this website, or more generally when discussing epistemology
A most interesting book in this context is [1]. It has introductory discussions of logicism, intuitionism, and formalism by Carnap, Heyting, and von Neumann, and interestingly, they were not aware yet of Gödel's results at that point which were published in the same year. After that, Heyting's "Dispute" is a nice exposition of the different view points, and I find myself agreeing with much of the intuitionist point of view, namely that mathematical reasoning cannot be reduced to formalism (but I don't agree that intuitionistic reasoning is the only allowed form of mathematical reasoning). I mean, Gödel's incompleteness result is as hard a proof of this as you will ever get! And again, in a later piece by Paul Bernays, "On platonism in mathematics", Bernays states: 'Is it possible to draw an exact boundary between what is evident, and what is only plausible? I believe that one must answer [this question] negatively'. In other words: Common sense is a necessary part of mathematical reasoning. Fundamentally, there is no way around this.
i'm pretty sure lots of greek people know calculus, learning latin isn't that hard, and there are actual calculus textbooks in greek now anyway
if, on the other hand, you mean classical athens (platon and sokrates and all those dudes) then, no, they weren't, archimedes wasn't even born until like 180 years later
I had an ex that went to Bard and she adored this along with the zen motorcycle book, the windup bird book, and pretty much anything by Gladwell and his contemporaries (definitely that pretentious Lehrer guy). The comments in this thread confirm that I was correct to avoid it.
Zen etc. was nearly ruined for me by others holding it up as some sort of philosophical holy book - that part of the writing didn’t appeal much to me ultimately, but the story it tells?
a man struggling with mental health issues, struggling to discover and decide who he actually is and who he actually wants to be - while also being responsible for his kid, and of the kid not understanding what’s happening to his father… that part I loved. The ghost story of Phaedrus.
The scene towards the end when he finally sits down with his kid and tries to explain what’s going on and what’s going to happen next, and his son’s response just gutted me. Never expected to have that emotional of a story from the way the book had been sold to me.
I heard Murakami has some good stuff and I know my wife has some on the bookshelf. But I'm more commenting on the particular milieu, if you will, of a particular pretentious type of literature that I could never really get into. Perhaps if I went to class naked when I was in college I'd understand better.
i've definitely been to hacker hot tub parties on several occasions, so i'd probably enjoy the naked classroom too
i think what these authors have in common is not so much pretension as giving free rein to their very active imagination: caring as much about what could be as about what is. in the case of gladwell and lehrer, they've let it blur the lines between fiction and reporting (to everyone's detriment), but i don't think that's really the case with hofstadter, pirsig, and murakami
Godel did not argue or show "there are fundamental epistemic limits to the universe". The universe is not a formal axiomatic system.
This repeats an very old, popular pop-philosophy misconception about Godel's theorems and GEB seems to have done nothing to help with this category error.
Whether or not the universe is (or, to split hairs, may be exactly expressed as) a formal axiomatic system, was very much an open question, one which Gödel helped answer conclusively in the negative.
I don't have my copy with me right now, so perhaps I'm misremembering, but I recall Hofstadter explaining in the preface of my copy that the point of his book was how the mind - consciousness - could arise from the brain (or something like that). I myself failed to get past the ~100 page mark (he went in depth explaining topics that I was already familiar with from other sources, which bored me. And I didn't really find the connections to art and music that insightful or interesting - but maybe I'm just too uptight). My understanding from skimming the book and reading some of Hofstadter's other works (including his response to Searle's "Minds, brains and programs" article) is that the book is trying to establish how complexity can emerge in systems with many simple moving parts via recursion (or something like that) in different scenarios, suggesting that this is how consciousness emerges from a complex web of neurons (the brain).
This seems a little wishy-washy to me. I don't see this as a good counterargument against Searle's argument that syntaxx alone is not enough to give rise to semantics. (I find Dennett's argument about intuition pumps a more convincing counterargument.) Maybe my understanding of Hofstadter's argument is too simplistic - I'm happy to be educated (I wasn't able to make it through even half of GEB after all).
And of course, that's not to say that GEB isn't a valuable book - it seems like most readers really enjoy it and learn a lot, even if they don't much care for the ultimate cognitive science/philosophy of mind position Hofstadter is trying to defend.
> it seems like most readers really enjoy it and learn a lot,
I think it's one of those books which most people actually don't enjoy that much, but don't want to admit it, because it has such an intellectual aura around it.
i think it's more that the people who talk about it most are the ones who really did enjoy it that much. (i assure you we exist, even if you prefer hanging out with the people who only pretend to have enjoyed it.) i suspect this is because, unlike hemingway and shakespeare and hegel, it's fairly rare for people to be coerced into reading hofstadter
YES. So, so true. And Hegel in turn was just adapting Kant, despite calling him a “blockhead” in the preface (hilarious, can’t even imagine what 1800s German for “blockhead” is). It’s absolutely Hegelian. To make it more explicit for the HN audience:
Hegel wrote a very famous book called the “The Experience of Mind” (or, in obnoxious philosophy language, “The phenomenology of Spirit”). In it, he details how he thinks the mind is made up of successive levels of distinct programs, each of which builds on what came for it in a very specific way he calls “dialectic synthesis”. In this way he goes through all the perceived capabilities of the mind (the big four in order roughly being sensation, understanding, awareness, and reason) and ties them to specific steps in this synthetic chain.
I hope it’s obvious from that how this argument mimics GEB (which I understand as roughly “the human mind is a collection of looping programs with these characteristics”).
> which I understand as roughly “the human mind is a collection of looping programs with these characteristics”
uh ... the center of Hofstadter's worldview, which he re-enunciated later in "I am a strange loop" is almost precisely the opposite of Hegel's persepective. Hofstadter came to see the idea of "heterarchical systems" as central to creativity and, in his opinion, consciousness. These systems are precisely not what Hegel describes, with "each level building on what came before it", but instead the levels are functionally and physically entangled so that "higher level" ones can intimately and profoundly impact "lower level" ones and vice versa.
I love hacker news - I missed this a few days ago. You’re the first human I’ve talked to about these ideas I’ve been obsessing over for months, so it feels good to get some feedback!
I’ll definitely have to look more into that. I guess my conception of Hegel has room for such “looping” — Kant explicitly says that high-level Reason produces ideas that directly impact the nature of our low-level Understanding, and I sorta assumed Hegel would agree. He’s obviously much more into the Synthesis as a means-onto-itself, not to mention much more dramatic, so it wouldn’t surprise me if the last chapters of PoS made no mention of the lower faculties.
Thanks again, if you ever scroll back through your old comments and see this :). A helpful response indeed
Here is one you won't hear many people say: I met my partner due to GEB.
Some twenty years ago I was operating a muni network and was up at stupid hours due to a maintenance window. The people I normally talk to were all asleep, so I made a script that searched people on live journal that had similar tagged interests and added them to my aim buddy list-- then if they were online I messaged them.
She was awake at an odd hour because someone had pulled a fire alarm in her dorm.
I later went back to see why my program had added her, and there were a number of overlapping tags but it turns out there just weren't many people that listed "douglas hofstadter" as an interest on LiveJournal-- maybe 8 in total at the time-- so it had a lot of weight.
GEB is in my top three as well. But looking back at it and the other important books in my life, it seems that it matters very much when I read them, and where I was at the time. For example, the Lord of the Rings was hugely influential for me, in part because I bought it (in one volume paperback) with the sales of my first program, and read it in school (also during our English lessons, the good teacher let me do that when she saw what I was reading).
I bought this when I was like 19 and going through some "i'm going to be a physicist" mental break and obsessing over michio kaku and wild theories and it made absolutely no sense to me at all. Do I need to try again now that I'm a grown adult?
Do you remember what you were confused about? The book does not assume the reader has any advanced math education (from what I remember) - it tries to teach you the relevant math itself. It is long and windy though, so maybe you read through too quickly or got bored. You'll probably have more success with it now that you're more mature.
Couldn't really make it through GEB. I like literary or maximalist fiction like Pynchon despite not being smart enough to understand most of it, so it wasn't the style, and I like out there scientific speculation like The Bicameral Mind so it wasn't that either.
Most of GEB just has this weird vibe of Hofstadter trying to come off as smart and trying way too hard. It's not that the ideas in the book are bad but they're also not really that interesting or deep or at least weird enough to justify all the flourish around it. It's very similar to Infinite Jest which to me also felt like the "young, overeducated man namedrops everything he knows without saying much" kind of thing.
lol in this thread full of dozens of paragraph-long attacks on this book, yours is by far the most damning. And funny. For those that are unaware like me:
Hofstadter's law is a self-referential adage, coined by Douglas Hofstadter in his book GEB…:
Hofstadter's Law: It always takes longer than you expect, even when you take into account Hofstadter's Law.
**History**
In 1979, Hofstadter introduced the law in connection with a discussion of chess-playing computers, which at the time were continually being beaten by top-level human players, despite outpacing humans in depth of analysis. Hofstadter wrote:
In the early days of computer chess, people used to estimate that it would be ten years until a computer (or program) was world champion. But after ten years had passed, it seemed that the day a computer would become world champion was still more than ten years away... This is just one more piece of evidence for the rather recursive Hofstadter's Law.
It's a long time since I last read the book but I remember that in a sense the book ends at about 50%, that is a meta discussion in the book says it ends now and the rest that's following is a redundant. Will have to re-read it to find that location again...
I loved the dialogues and the poems, with their various translations. The discussio around the "musical offering" is incredible, and helped me learn to appreciate music (not only Bach). This is one of my favourite books!
The math was insufferable, however. And I say that as a mathematician and programmer... I wonder if musicians and poetry translators will find "their" parts correspondingly unbearable?
I gave up at this point: "We might describe the way that planets fly around stars as isomorphic to the way that electrons fly around nuclei."
We might, but we'd be mistaken.
Why bring incredibly complex topics into a general discussion unnecessarily? Why not even bother googling a correct explanation of those topics first? (I could guess why, but I don't want to ruin the article with spoilers.)
I picked up GEB after seeing a post about it here on HN. Although Hofstadter makes a few connections I was unaware of, such as Escher's artwork expressing recursive patterns, it was really underwhelming for the most part. As others have said, it takes 1000 pages to get to a point, that could have been made in significantly less. My only thought is that perhaps Hofstadters' rambling was an attempt at literary recursiveness, but his execution was lackluster.
