Gödel, Escher, Bach: An Eternal Golden Braid

This book is brilliant. You will have intellectual insights in every single chapter. It's not an easy read - you will reread paragraphs, stop and think about what the author is trying to say. It's important to keep "wrestling" with the book, and to not give up. It talks about math, music, painting, information, biology, brains, Zen Buddhism, among other subjects - and the book itself is written as a self-reference. I recommend it very highly.

This book has a preface by the author. After twenty (20) or so pages, I was thinking, "Can I understand what he wrote about in the rest of this book?" but I persevered and read the whole book. This book is intense, like any philosophical book. His motive is to "suggest ways of reconciling the software of the mind with the hardware of brain" and that is quite an endeavor he succeeds at, sort of. No wonder he won the Pulitzer prize for this book. He talks of how he came to write and develop the book, and then, upon preparing for republication, he decides to not redo the book: it is what it is, from back then, any addition or correction would create a new book, and it can been seen every so often he imagines some stuff that we use daily, like spell correction, that were just not available back then. If he was to do that, he might as well write a whole new book, and that was not in the cards, nor was it the purpose of the new edition. Gödel goosed him to realize the notions he writes about, but Escher and Bach represent examples of what Gödel was writing and he is thinking about. As you read the introduction you realize this is one educated and well rounded fellow. He describes the development of Bach's preludes and fugues like a music teacher (I realized that I have a recording of Wanda Landowsky playing "The Well-Tempered Clavier" Book 1, preludes and fugues, but that did not help me understand as you will see). Bach worked up various themes and notions through his music and than then did some fancy finagling and out came some thing wild and crazy wonderful. I listened to the recording I have to no avail. This is something you get to know by playing and playing the tunes, a lot, for yourself, but Mr. Hofstadter's exposition explains what is what for you. Escher is easier (visual experiences are more important or easier to comprehend than aural experiences). The pictures are presented as examples of repetition or growth from one thing into another. The idea of repeating or self-reference is important: it is one thing that computers do not do. We can do imagining things as well, but at a more basic level we self-reference creating a hump of ability that computers have to accomplish if they are to get to be self aware or intelligent. As he said, he wants to understand the hardware of the brain, but in comparison, computers are simpler, but getting more complicated. He is working from the bottom up with computers: machine language, assembly, programing languages, etc. Fro our brains he is working from the top down, trying to see how the thoughts (software) we think get from one point to another. It is difficult because we do not have access to the basic growth of each thought (neurons firing). Logic tries, yet, as that one guy two (2) or three (3) thousand years ago said, "All I know is that I do not know anything." Mr. Hofstadter just comes to that thought in another roundabout way. I kept thinking of sex deviants doing what they do and that if we could look into their heads, we would be hard pressed to see where the impetus for their deviant behavior comes from, how it develops or why they do it. It is somewhere in there, but the thoughts (software) are so complicated that we can not see how it develops into what is expressed. I also think of how we all speak. We talk without thinking (something I am accused of constantly and embarrassingly), but in reality we just do not follow the thought process from what we hear and see, etc., to what we think of it, to what we will say, to saying it. Another thought is what is happening in the brains of mediators, you know, those Zen folks who quiet the mind, what is happening in there then? The mind is just amazing in what it does. Throughout this book Mr. Hofstadter writes of the mind and the brain like a psychologist, how it works and what it does. He also delves into genetics. His forte is math and all its intricacies. He develops a couple of different math models to illustrate Gödel's incompleteness theorem. The logic starts out straight forward enough, then veers off into some esoteric realm where the notion of paradox lives, and this is where we have to develop our math notions. We can study the properties of prime numbers or infinities, but we always must end up knowing we do not know everything, because our logic can not encompass paradoxes, and they will be somewhere in all we do, or something like that. As you can see, I was not able to understand his math models, but I think I got the jist of it. This book reminds me of another book published in 1978, "The Seven Mysteries of Life" by Guy Murchie. It is amazing that they talk of the same things in the same way and for the same reasons. Though this is a treatise on computers and artificial intelligence, and the other is a religious book, sort of, about the awesomeness of life. As for the artificial intelligence aspect, I like his development towards that goal, but, and I find no fault in the imagining of it, I am disappointed that computers will just be like us. It will not create a Spock like machine, or what science fiction has led us to hope for (see Isaac Asimov, "I, Robot" etc.). I did like his notion of combining genotypes to create new genes, but I am a guy and I like that sort of stuff. I find that I agree with someone who said, "There are much more fun ways to create intelligence, and it is not artificial." If artificial intelligence is not going to be all that great, it is only good to try to develop it for the exercise and the experience it will give us, but otherwise, eh, no big deal.

“It is in the inevitable self-mirroring that arises, however impartial or imperfect it may be, that the strange loops of consciousness start to swirl.” Somewhere in this wonderland adventure through strange loops in math, music, and art (also genetics, metaphysics, and quantum mechanics), a path of liberation is revealed. You may find, after a sufficiently assiduous reading, that you have awoken from a dream. ”An “I” comes about…via a kind of vortex whereby patterns in a brain mirror the brain’s mirroring of the world, and eventually mirror themselves, whereupon the vortex of “I” becomes a real, causal entity.” A strange loop is a level-crossing feedback loop in a hierarchical system. After many clever demonstrations from mathematics, biology, and art, a pattern emerges, much like deducing the shape on the book’s cover from its various shadows. It’s everywhere. Everything we know is a part of it. Isomorphisms of strange loops abound because all of nature, including us, is made of them, and therefore the paradoxical nature of strange loops is built into us, too. But what can we say of truth, and reality, when everything we know seems to be paradoxical at its base and its apex? To this question Hofstadter answers: “Mu”. He teaches us the path of “Ism”, of “No-mind”, and the art of un-asking. ”Zen is holism, carried to its logical extreme. If holism claims that things can only be understood as wholes, not sums of their parts, Zen goes one further, in maintaining that the world cannot be broken into parts at all. To divide the world into parts is to be deluded, and to miss enlightenment… an enlightened state is one where the borderlines between the self and the rest of the universe are dissolved.” My own thoughts on this: When your context of self-reference extends to the horizons, all becomes one, and that One is you. I think it’s a journey of ultimate self acceptance, and also ultimate surrender of self. Somehow the truth is always couched in paradox. The greater our sense of "I", the more inclusive we become, as those "others" become part of "me", and as the division vanishes, so does the original self. The more we see ourselves in the world around us, the more conscious we become, and the more of life’s infinite wonders we will witness—both without and within. A dualistic division between self and other (this or that) is necessary to form human thoughts and language. When the divisions dissolve, we accept ourselves and others as ripples of a much vaster ocean of Self. The prize, I believe, is peace in the mind and love in the heart. The freedom to enjoy life regardless of context, although that will still, paradoxically, involve suffering (we level-hopping strange loops can contain both at once). Spoiler: The ‘e’ ‘n’ ‘d’ is indicated by exclusion on the “file not found” page amidst a conversation about ultimate contextuality of numerical properties, referencing Cantor’s infinity of infinities. I might guess he meant us to form conclusions about the oneness of reality and its incomprehensible vastness, but, like any great artist, Hofstadter leaves interpretation to the reader. This book is a masterpiece of great cleverness and depth, but it is not for the fainthearted. It will challenge you. It was written for math lovers, but even those hopeless at math (like me) can struggle through with a bit of determination. It’s an older book, and the bits about AI should probably be completely rewritten in the light of our current understanding. All told, I’m not sure who I’d recommend this to except those seeking the roots of consciousness. For us, it is a jewel.

Incredible book, very deep conceptually but worth the read

This really is an amazing book. And an extraordinarily difficult book to comprehend, for this bear-of-little-brain. There's a lot going on herein, including the author's ingenious interweaving of the mathematical theories of Godel (especially his Incompleteness Theorem), the artwork of Escher, and the music (especially the fugues) of Bach. On top of all that, he manages an ongoing conversation between Achilles, a tortoise, and their friends, inspired--as the book's subtitle would suggest by Lewis Carroll. There's a lot going on, here. It's both magnificent and overwhelming. I confess to having skimmed major portions of the time's 742 pages, as Hofstadter demands more of the reader than my philosophically challenged peabrain was able to offer. In essence, he's driving through the course of the book to tackle the problem of consciousness. Are our brains analogous to a computer, as they seem to be, and if so, what explains the vast differences between human and computer intelligence? And what do the answers to these questions portend for the future of artificial intelligence? I'd give the book five stars for the author's brilliance in making extremely complex topics accessible, and three stars for my ultimate interest, which was related to my inability or unwillingness to seek the depth of comprehension the book required. Buyer beware. What you're getting yourself into, that is.

GEB: EGB is basically an exploration of the idea of intelligence, artificial and otherwise. Hofstader's goal is to shed some light on how intelligence / consciousness / self-awareness happens. I would call him a materialist, in the sense that he believes that there is a physical basis for thoughts, feelings and emotions. He is dismissive of "soulists," who believe that there is some sort of inexplicable metaphysical aspect to consciousness. The question, in Hofstader's mind, is, "If the human brain is made of essentially the same stuff as a kitchen table or a pocket calculator or a tree, why does the first have a sense of of self -- of being an 'I' -- whereas the others do not? Hofstader explores how physical activity in the brain, which seems completely mechanistic and completely unlike the process of thought that we experience, can in fact give rise to a qualitatively different sort of activity occurring at the "higher levels" of the brain. He gives several examples of such systems, such as an ant colony: the individual ants are stupid, acting in response to basic stimula, but the colony as a whole is much smarter. This kind of qualitative difference between the different levels of a system is key to Hofstader's thesis that critics of the possibility of artificial intelligence have misinterpreted the implications of such limitative notions as Godel's theorem. Godel's theorem states, in essence, that any sufficiently powerful system will contain truths that are not provable within the system. The problem with computers, these critics charge, is that they are stuck within a particular system -- there is no way to program them to realize that there is no solution to a particular problem within the system, even though such a fact would be perfectly obvious to an intelligent person who can "jump out of the system." So the computer is stuck trying to solve the problem with a method that is doomed to fail. Hofstader argues, on the other hand, that there is nothing magical about being able to jump out of the system and reflect on whether it is the appropriate system to be using. In fact, in doing this one is still "in" a system -- it's just a bigger system, one that has the ability to think about lower level systems. And one can jump out of that top level system and reflect on it as well -- but then of course one has entered a new system again. There's always another system, at a higher level, no matter how high up you go. At a certain point these levels blur together, because they are recursive -- meaning they reflect back on themselves. Hofstader uses the works of Escher and Bach to illustrate the concept of recursivity. For example, there is Escher's stairway that goes up and up until you are back where you started, or the two hands, each of which is drawing the other. Hofstader believes that self-awareness -- the "I" -- arises from this kind of recursivity. To put it very simply, at the highest levels the brain is a system that deals with symbols, and the "I" is the symbol for the system itself. There is much, much more to this book. There are lengthy tangents into mathematics, philosophy, biology (the section about the recursion that takes place in the copying of DNA is particularly fascination), etc. Thankfully the book is organized into sections that alternate between straight exposition of some concept and a fictional dialogue that illustrates the concept. Still, it's not light reading, and I did wish at points that there was a Reader's Digest version that would just give me the main points without going off on a tangent for 30 pages about wasps or something. Godel, Escher, Bach made me rethink a lot of my preconceptions about consciousness and artificial intelligence, and is well worth reading the next time you have three months to spare.

GEB is a singularity of very cool ideas. Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything. The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done. This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways. Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful. In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course. Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm. In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet. It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.

When you read, please pace yourself. Don't try to digest all @ once it all examines how self-referencial systems create emergent complexity, creativity, and meaning, offering deep insight into consiousness and inteligence. Using examples from mathematics, art, music, and biology, Hofstadter shows that simple recursive rules, such as those in DNA or Gödel’s incompleteness theorum, can lead to surprising complexity, similar to the emergent properties of the human mind. He argues that paradoxes, like the liar paradox or those found in Gödel’s theorem, are natural features of self-referencial systems, reflecting the ambiguites of human thought. The universality of self-reference, visible in diverse areas like Escher’s Drawing Hands or Bach’s recursive musical canons, emphasizes its importance in both natural and artificial systems, including consciousness itself. Hofstadter introduces the idea of "strange loops," where self-referencial processes seem to rise to higher levels but eventually circle back, proposing that human consciousness itself works this way, observing and defining itself in a loop. Moreover, he stresses that meaning in self-referencial systems, like quines in computing or DNA in biology, comes from their interaction with their surroundings, much like how human consiousness interacts with symbols and reality. Hofstadter ties these concepts together to show how self-referencial systems not only expose the limits of formal logic but also explain the emergence of meaning, intelligence, and creativity, bridging formal systems with human experiance.

A good book

Il faut avoir un bon sens de mathématiques et de l'anglais pour apprécier les phrases super-bien construites. Si c'est le cas ce livre est un bijou sans comparaison. Les paradoxes mathématiques inhérent dans la langue même dont on décrit la mathématique est clairement mis en avant. Et les liens avec l'art, que ça soit les dessins paradoxaux d'Escher ou la musique auto-référente de Bach, sont captivants.

It's amazing how much one can get out of this book. It covers pretty much everything... like all things. While I don't agree with everything in there, it's very fascinating and a fun read. It's one of those books where you can flip to any page and find a fantastic little gem. In saying that though you will want to read it cover to cover, as you can lose a bit of context jumping around. It's a book that tends to be recommended a lot to programmers, but I bought it for my wife when she was studying psychology and she loved it!

While reading this book , many times I stopped and smiled with joy from all its ingenuity

This book will guaranteed rewrite your brain chemistry. Good if you like math, logic, art, music, programming and computer science concepts, or any intersection of the previous subjects and more.