Or has it become dated and irrelevant?
Not in the least. I’m about two thirds of a way through it, and everything he writes about computer science is very much relevant to this day. The only portions which feel dated are his discussions about artificial intelligence and its importance to computing, which time have shown to be by far overestimated. Of course, all the discussions on art, literature and music are timeless.
Honestly though, I don’t think I’d get a tenth of what he’s talking without having a masters degree in computer science myself 
Thanks, Kombatminipig, that’s what I needed to know. If it’s too difficult I might give it up, but I didn’t want to start at all if it was too out of date.
Anything he says about specific technologies is horribly dated, but there’s very little of that. The rest of the discussion is as good as it ever was.
To be fair, Hofstadter would say the same thing.
Gödel, Escher, Bach is a great book, but it is very dense and complex. Don’t think that you are just going to skim through it lightly and get anything useful out of it. It is the kind of book you need to pick up, read a chapter or two, put down, do some research and contemplation, and then reread the same chapters again. The reviewers that complain that the book is a themeless, scattered mishmash of ideas have failed to comprehend the often subtle connections between the chapters. You may want to read Hofstadter’s I Am A Strange Loop first, as it seeks to explain many of the connections in GEB.
Stranger
I’ve never read it but I’ve heard that one of the important aspects is Godel’s completeness theorems. In quantificational logic we were taught that you could derive any conclusion from a contradiction. I think one of the theorems states that no axiomatic system can ever be complete (allow you to deduce all true conclusions). That has always implied to me that any complete system must necessarily include contradictory axioms - which of course would be worthless.
However I sometimes wonder if the natural world isn’t a bit more laid back about things we would consider contradictions. There are plenty of apparent contradictions in quantum mechanics for example.
So Bob, where exactly is this electron right now.
Well Tom, it’s technically anywhere that it’s wave function permits it to be.
So you mean it’s everywhere and nowhere at the same time.
Well, sort of . . .
You’re conflating two different concepts here (complexity and completeness of quantum mechanics in the framework of a macroscale world). It is true that any sufficiently complex system of axioms–to wit: any system involving the set of natural numbers–will allow you to state a theorem which can be neither proved nor disproved (hence, it is incomplete), and hence, it is possible to create a system of apparently contradictory theorems or statements without positive resolution. That doesn’t mean that the axioms themselves are contradictory, and in fact, if you can demonstrate a contradiction between axioms, you’ve demonstrated that you have an inconsistent, and therefore not logically useful system.
The apparent contradictions in quantum mechanics come from an attempt to impart a particular interpretation or classical analogue onto the behavior of objects on a quantum scale. The “particle/wave duality”, for instance, comes from a desire to classify fundamental quantum objects as either particles (because they operate as a discrete act at a locus), or waves (because they demonstrate wave-like interference behavior with other objects and themselves). If you accept that a quantum object doesn’t exist as either a discrete particle or a distributed disturbance in some media, and just accept that the observed behavior is a limitation of how we’re able to model and observe it from our mathematical tools and everyday experience, there is no contradiction, at least in quantum electrodynamics, and while QED cannot be described as a formally axiomatically consistent theory it is a relatively consistent set of rules that are functionally complete (at least, stochastically) within a restricted set of boundary and initial conditions.
Quantum mechanics should be regarded in terms of Plato’s allegory of cave; we see shadows on the wall that give us clues to the whole form, but never the whole thing at once, nor enough that we can construct a complete understanding of the model.
Stranger
I was just making an observation and you definitely misinterpreted what I was trying to say. That may have been my fault but at the time I though what I had written was fairly clear.
I understand that completeness applies to deductive systems and QM is about as empirical as you can get (leaving aside predictions by the std model). My point was more metaphysical. Also, from the point of view of our daily experience, there are many phenomena in QM which would be considered “contradictions” or simply be labeled impossible were it not for the fact that they happen to be true. If you don’t like the wave function example, then there is always the example of a particle traveling all paths simultaneously en route to a destination - or, the apparent contradiction of entangled particles communicating instantaneously over vast distances. I’m sure I can come up with more if pressed.
The point is that our reason has limits that falls infinitely short of what reality has to offer and only by transcending labels can you hope to have any true understanding.
The point is that nothing in quantum mechanics is contradictory, so the fact that a contradiction implies everything simply doesn’t apply.
As for wave-particle duality, my favorite analogy is uncle-brother duality. Am I an uncle or a brother? Well, if you ask my sister, I’m a brother, but if you ask my nieces, I’m an uncle. There is no one person to whom I’m both an uncle and a brother: To any given person, I’m at most one or the other, or possibly neither. But there are people to whom I am definitely an uncle, and people to whom I am definitely a brother. Likewise, there are some experiments to which a photon is a particle, and some to which it’s a wave, but no experiment to which it’s both.
I apologize if I misconstrued your post, but you seemed to be relating Gödel’s incompleteness theorems–which are proved statements about the incompleteness of constructed systems with self-consistent axioms–to the semantic paradoxes of our conception of the behavior of the natural world in general, and (some) interpretations of quantum mechanics specifically. In the case of the former, the incompleteness is an inherent artifact any system of axioms expansive enough to be useful in describing anything complex. The latter is isn’t really a contradiction, but just a lack of having the words or concepts to appropriately describe behavior of the world. It would be like only having words for the colors “red”, "blue, and “green”, and having to describe purple as being “both red and blue and not either.”
To borrow your examples, the supposed contradiction of “a particle traveling all paths simultaneously en route to a destination - or…entangled particles communicating instantaneously over vast distances,” are only contradictions if you hold unproved axioms (that quantum particles are single valued in their loci, or that instantaneous communication between two non-local points is impossible). Since those are assumptions, albeit dearly held ones, they can’t be regarded as inherent contradictions in either the formal or informal sense, but rather, preconceptions that are invalidated by experiment and therefore not a necessary feature in workable quantum theories. In fact, there is nothing in QM that makes it “impossible” to connect two non-local points, although many interpretations specifically forbid it in order to justify another rationale (like transactionalism). In actually studying quantum theory, rather than noodling about it, students are instructed to “Shut up and calculate,” as there is no expectation that any interpretation of quantum mechanics will ever map onto our everyday concept of the world.
I would not describe quantum mechanics (or at least, not quantum electrodynamics) as empirical in the epistemological sense, insofar as the theory is mathematically formalized from a set of basic postulates from which all other behavior is derived. The formalistic rigor of renormalization in quantum field theories may a point of contention, but the procedure results in an exact result, independent of any experimental evidence, and the predictions of QED, particularly of the Lamb shift, are the most precise in all of physics. It is true that actual states of quantum systems can only be known a posteriori (and even then only in conjunction with the systems observing or measuring the quantum system, which themselves are fundamentally quantum systems) but that is an implicit feature of quantum mechanics, not some kind of experimental error.
Getting back to something adjacent to the o.p., it is Hofstadter’s central thesis the inability to synthesize complex systems or behavior like cognition with a model that is significantly less complex than the system (i.e. a logic map or computer program of human thought processes) isn’t a lack of current ability or vocabulary, but an inherent quality of complexity; in essence, that you can’t differentiate out the individual variables and then reintegrate them back into an abstracted model. I believe Hofstadter would say something to the effect of that we’ll never be able to make a conventional architecture computer “think” like a person regardless of how sophisticated the software is, because the software still has to break down “ideas” into discrete binary logic statements for the hardware to process, and our brains just don’t function that way. In order to make a computer that has cognitive abilities similar to a human, we’ll have to build a computer that that is fundamentally like a human brain in many salient ways (i.e. the “software” and “hardware” are all an inherent part of the self-modifying “wetware”). Hofstadter wrote this back in 1979, and research on both the abstract side (artificial intelligence) and the empirical side (cognitive neuroscience) have increasingly converged on this answer. That alone argues the continued relevance of GEB. That any specific technically he talks about in regard to synthetic intelligence may be obsolete is only a minor anachronism in an otherwise fundamentally topical book. I’d still recommend Strange Loop as a good precursor (as it will help address some of the questions you may come up with when reading GEB). To understand the “hardware” side of our current understanding of neuroscience I’d recommend pairing it up with Ian Glynn’s An Anatomy of Thought or, if you want something less technical and more conversational, Eric Kandel’s In Search of Memory. This isn’t necessary, as Hofstadter is dealing with abstractions with complexity, but this does provide a sort of grounding for why cognition is so complex.
Stranger
I read it mainly for the maths portions of it. I agree with what most other people said: some bits have been surpassed, but most of it is as interesting and true and funny as it ever was[1].
And, yes, you get much more out of it if you’re willing to follow along and do the exercises, though many bits are entertaining/informative even if you don’t.
The one caveat I give people is that it’s full of interesting stuff Hofstadter thought, but that (a) just because it’s interesting doesn’t mean it has the status of unassailable truth and (b) it may help to explain Godel’s incompleteness theorem, but it’s possible to prove it in a much much shorter and concise book, so if that’s what you’re interested in, it may be worth reading a more concise version at some point, and then going back and dwelling on Hofstadter’s extended version.
[1] One of the advantages of maths
It’s not completely rigorous either, but Nagel and Newman can still be recommended as the terser classic popular explanation of the proof. That current edition - which I haven’t read - is edited and revised by Hofstadter.
I’ve actually read Nagel and Newman’s book, which I enjoyed. I think I will follow Stranger’s advice and read I am a Strange Loop first, though I usually like to read an author’s books in order.
EtA: Thanks for the link to that interview, Stranger. Some of the comments were pretty acerbic.
Just to add to this (and I’m immensely fascinated by this whole exchange), Hofstadter’s dialogue on ant hills was in my opinion a fascinating discourse on this. Naturally he doesn’t claim to be explaining either the mechanics of an ant hill nor of the human brain, but he gives a possible theory to the workings of sentience based on what was then known about neuroscience (though I’m not sure how much that has changed since). That chapter is worth reading on its own.