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Gödel, Escher, Bach: An Eternal Golden Braid Paperback – February 5, 1999
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Twenty years after it topped the bestseller charts, Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid is still something of a marvel. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel. It also looks at the prospects for computers and artificial intelligence (AI) for mimicking human thought. For the general reader and the computer techie alike, this book still sets a standard for thinking about the future of computers and their relation to the way we think.
Hofstadter's great achievement in Gödel, Escher, Bach was making abstruse mathematical topics (like undecidability, recursion, and 'strange loops') accessible and remarkably entertaining. Borrowing a page from Lewis Carroll (who might well have been a fan of this book), each chapter presents dialogue between the Tortoise and Achilles, as well as other characters who dramatize concepts discussed later in more detail. Allusions to Bach's music (centering on his Musical Offering) and Escher's continually paradoxical artwork are plentiful here. This more approachable material lets the author delve into serious number theory (concentrating on the ramifications of Gödel's Theorem of Incompleteness) while stopping along the way to ponder the work of a host of other mathematicians, artists, and thinkers.
The world has moved on since 1979, of course. The book predicted that computers probably won't ever beat humans in chess, though Deep Blue beat Garry Kasparov in 1997. And the vinyl record, which serves for some of Hofstadter's best analogies, is now left to collectors. Sections on recursion and the graphs of certain functions from physics look tantalizing, like the fractals of recent chaos theory. And AI has moved on, of course, with mixed results. Yet Gödel, Escher, Bach remains a remarkable achievement. Its intellectual range and ability to let us visualize difficult mathematical concepts help make it one of this century's best for anyone who's interested in computers and their potential for real intelligence. --Richard Dragan
Topics Covered: J.S. Bach, M.C. Escher, Kurt Gödel: biographical information and work, artificial intelligence (AI) history and theories, strange loops and tangled hierarchies, formal and informal systems, number theory, form in mathematics, figure and ground, consistency, completeness, Euclidean and non-Euclidean geometry, recursive structures, theories of meaning, propositional calculus, typographical number theory, Zen and mathematics, levels of description and computers; theory of mind: neurons, minds and thoughts; undecidability; self-reference and self-representation; Turing test for machine intelligence.
From the Inside Flap
e Pulitzer Prize, this book applies Godel's seminal contribution to modern mathematics to the study of the human mind and the development of artificial intelligence. --This text refers to an out of print or unavailable edition of this title.
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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. Mathematics about mathematics. Thinking about thinking. Mathematics about thinking. 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 with this book.
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? The task of reducing mind to math, of connecting the nature of consciousness to an idea in formal systems, is such a lofty goal, that even if true, the author could never rigorously prove this thesis, only approach it from every conceivable direction. This matters less than you might think, because the value of GEB is less about its conclusion and more about the journey getting there, much like The Emperor's New Mind. Whether it convinces you or not, it will give you a lot to think about by trying.
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.
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.