Gödel, Escher, Bach
Douglas Hofstadter wrote Gödel, Escher, Bach nearly 50-years ago, and it won a Pulitzer Prize, the National Book Award, and got featured in the popular press. It’s been on lots of college reading lists, from 2007 online coursework for high school students was available from MIT. The FBI concluded that the 2001 anthrax scare was in-part inspired by elements of the book, which was found in the attacker’s trash. Anyone who’s wanted to engage with the theories and philosophy surrounding artificial intelligence has had plenty of materials that get fairly in-depth asking and exploring these same…
Douglas Hofstadter's work provides several examples. * Gödel, Escher, Bach: an Eternal Golden Braid (GEB) * Metamagical Themas * I Am A Strange Loop (IAASL) GEB and IAASL are thematically similar, and both are worth a read if you're interested in both Gödel's theorems (plus related work eg Church-Turing) and Hofstadter's philosophy of mind. GEB is a lot more creative and fun; IAASL does a better job of communicating the key technical ideas like incompleteness. Metamagical Themas is a collection of shorter work, generally technical and fun. Although Hofstadter was the first to come to my…
As it might be quite common among the HN crowd, Douglas is my hero - I have read three of his books. First of all, hats off to him for his extraordinary display of humility in this interview. People rarely change their minds publicly, let alone hint that they no longer believe in their own past work. However, I'm genuinely surprised that he, of all people, does sees intelligence in GPT-4 output. I think humans are just very eager to ascribe intelligence, or personality, to a bunch of text. A text may say "I feel " and that text can easily manage to permeate through our subconsciousness.…
One line in the article piqued my interest, as it echoes something I read somewhere else. Seeing as it comes from someone who is an absolute expert on the subject makes it even more interesting. > "In both books, dense narrative tensions are never fully resolved..." It has been noted that this type of recursion/layering is something that we can't help but be intrigued by. This subject is explored in great detail, and unparalleled depth, in the book Gödel, Escher, Bach[0] by Douglas Hofstadter. He notes that this doesn't only happen in stories and is a common theme in music as well and may…
My apologies, the actual book had a better format. Although not quite a summary, here's what it's about: "The content that most interested me was Hofstadter’s insistence that self-awareness and consciousness arise directly from what he calls “strange loops”, i.e. self-referential structures in formal systems, of which human minds are just one example (what else could they be?). It’s a very difficult subject to think about in a reasonable way. We all have that sensation of the homunculus inside our heads, somehow driving us from a seat just behind our eyes, and we naturally ascribe the same…
We each find different things delightful. What I like, you may not. And vice versa. But it is easy to present deep ideas from constructivism, without mentioning the word constructivism. Or even acknowledging that the philosophy exists. For example the second half of https://math.stackexchange.com/questions/5074503/can-pa-prov... is an important constructivist thing. It shows why everything that a constructivist could ever be interested in mathematically, can be embedded in the natural numbers. With all of the constructions needing nothing more than the Peano Axioms. (Proving the results may…
I tried and failed to get ChatGPT to tell me the title of the Stanislaw Lem story about the stubborn computer that insisted that 1+1=3 (or some such formula) and got violent when contradicted and destroyed a town -- do any humans remember that story? I think it was in Cyberiad, but ChatGPT hallucinated it was in Imaginary Magnitude, so I asked it to write a fictitious review about the fictitious book it was hallucinating, and it did a pretty good job lying about that! It did at least come up with (or plagiarize) an excellent mathematical Latin pun: "I think, therefore I sum" "Cogito, ergo…
IMHO if you understand the history it makes sense why the theorem is both important and confusing. In 1921, Hilbert had this idea, that mathematicians could create an algorithm that would automatically prove every true statement and disprove every false statement. Wouldn't that be neat? It's important that this idea predates computers. When Hilbert was thinking about an algorithm, it wasn't an algorithm as we would think about it in computer science today, because the modern idea of a computer hadn't been formalized. In 1931, Godel proved that it was impossible for an algorithm to…
I was afraid somebody would ask that question. I don't have a simple answer to that question. As best as I can explain it, GEB provides an intentional stance that makes it much easier to exist in a chaotic world that we know little about. The lynchpin around which that stance revolves is Goedel's proof that classical reasoning systems are necessarily incomplete. In short, that there are true things we can never prove to be true, and false things that we can never prove to be false, and an entire category of statements that are neither true nor false. Coming to terms with the provable fact…
I would never call it my "all-time favorite" (no paper qualifies for that title in my book), but Satoshi Nakamoto's paper, "Bitcoin: A Peer-to-Peer Electronic Cash System" deserves a mention here, because it proposed the first-known solution to the double-spending problem in a masterless peer-to-peer network, with Byzantine fault tolerance (i.e., in a manner resistant to fraudulent nodes attempting to game the rules), via a clever application of proof-of-work: https://bitcoin.org/bitcoin.pdf Others in this thread have already mentioned papers or opinionated essays that quickly came to mind,…