If you open up the "20th Anniversary Edition" of GEB, you'll see that the first thing Douglas Hofstadter does in the introduction - the very first thing - is grouse that nobody seems to understand what his book is about. At its heart, this book is about whether you can start with simple parts and from them, build a system which is so complicated that it becomes more than the sum of its parts in a significant sort of way. The answer Hofstadter likes is that the brain operates on many different interacting levels, and that conscious thought is a product of the complex interaction between all these levels. So in order to understand something you're reading, you depend on individual neurons operating in basically deterministic ways to move signals around your brain, but you also depend on groups of neurons in your vision centers to recognize text, as well as other groups of neurons on other levels to understand that text, and other groups of neurons on other levels to fit that new understanding into the context of the previous sentence, and so on. Overall, this approach is very good at getting you to understand the complicated ideas Hofstadter is getting at. He loves it so much that he tries to infect you with his own personal sense of wonder and whimsy at how complex and beautiful art and life and science are. Also, those forced injections of wonder and whimsy start to take on the flavor of little plugs for the personal fantasticness of Douglas Hofstadter. If you think you'd be interested in the subject matter AND you wouldn't mind playing simple word or math games in the service of understanding it AND the inner workings of a computer scientist's marvelous brain seem interesting to you, then definitely read this book. But if you read this review and you get the feeling you probably won't like this book, you're probably right.
There's a lot of other fun stuff as well, but it's the Gödel proof that's the core of the book, and if that doesn't turn you on then you aren't really going to think GEB is worth the effort. PS I remember, not long after GEB came out, leafing through an interview with Sylvester Stallone.
As I work my way through this dense book, I am reminded of the Zen tale of 4 blind men and an elephant. Gödel, Escher and Bach The heart of this book is these Strange Loops that represent the activities inside our brains that turn into consciousness. GEB uses art and music, in combination with math and computing, to illustrate these self-referential loops. The mechanic of the loops is represented by the works of the mathematician Kurt Gödel, the artist M.C. Escher, and the musician J.S. Bach. Eschers visual endless loops, Gödels incomplete self-referential theorem, and Bachs canons and fugues in varying levels help to illustrate the characteristics of consciousness. The purpose of the Dialogue is to present an idea intuitively before it is formally illustrated in the following Chapter. GEB presents varying ways of explaining about systems and levels that create these self-referential infinite loops. To stop endlessly generating strings requires the second type of theorem in which we analyze the system itself. GEB gives a detailed account of how enzymes work on the strands, with typographical manipulations creating new strands. GEB gives further details on the complex process of chemicals and codes, but this is the basic idea. This pattern recognition occurs countless times as part of our intelligence process such that we dont even notice it. The lower level isomorphisms are so simple, that we only see explicit meanings. From our experiences, we all have lower level explicit isomorphisms from which we deduce new patterns. When we see new patterns, we create higher level isomorphisms until the system is consistent to us. If you are familiar with building structures, you would start off identifying the lower or established isomorphisms, the staircases, the people, etc. From the lower isomorphisms, you create higher level isomorphisms with the new bizarre patterns that defy the physical laws. Perhaps that person would only see geometric shapes and nothing else, since there are no lower level isomorphisms of building structures, etc. The chapter Figure and Ground starts with a set of rules for typographical operations which were used in the MU-puzzle and the pq-system, which is the mechanical process of the Turing machine, the parent of what we now know as computer intelligence. This process of generating theorems is reliant on the sifting out of nontheorems. A recursive set is one in which figure and ground holds equal importance. However, GEB showed that there exists formal systems in which the figure and ground are not recursive, do not carry the same weight, and are not complementary. A typographical decision procedure sifts out nontheorems from theorems by performing tests that use the logic of the figure/ground. Recursion is the process of building up from a block of structure. The process is explained in GEB as push, pop and stack of Artificial Intelligence. We use the push, pop and stack process especially in our usage of language.
Number theory requires no great resource of mathematical knowledge - just an extremely agile and open mind. Godel shows us that (I paraphrase drastically) that all logical systems allow statements about natural numbers that are true but unprovable within the system.
It would be like recommending large doses of LSD to everyone: some small minority will find the experience invaluably enlightening, but for most people it's just going to melt their brain. If you really like math, then this is going to be one of the best books you've ever read. But if you really like math, then you've almost certainly already read it.
I'm as likely to read this as a book on string theory. Please don't tell me I have read a book on string theory, I'm trying to forget the whole sordid story.) But. I hope you like this. He did it on a wing and a prayer, he was a young teaching academic who couldn't find in print the old literary books he wanted to use as texts and so he set about publishing them. Some years later he was in NY lunching with the boss of Basic Books, a US academic publisher.
The idea presented there is To suggest ways of reconciling the software of mind with the hardware of brain is a main goal of this book. As far as I can tell, the book is really about intelligence, both human and artificial. That doesn't mean that you won't understand many of the book's salient points if you can't successfully answer his questions. The idea of nested hierarchies is central to the understanding of what makes human intelligence different from machine intelligence. The issue is that the layers interceding between neural electrical firings and human thought are tangled. You see, Hofstadter never convincingly shows those transitional layers between neural activity and thought, though he claims they must be there. The concept here is that human thoughts can deal in a larger possibility space (my words) than machine intelligence. Hofstadter comments: Now poor Professor Frank is dead; and clearly it is nonsense to suggest that someone could read books written after his death. This is just one case portraying the difficulty inherent in trying to define and understand intelligence and the connection between brain hardware and mind-thought. I'm not convinced that Hofstadter was fully convinced that there will ever be a machine so intelligent as to completely mirror human thought. Besides, Hofstadter gives an implicit warning when quoting Marvin Minsky, who said: When intelligent machines are constructed, we should not be surprised to find them as confused and as stubborn as men in their convictions about mind-matter, consciousness, free will, and the like. In other words, if we do somehow construct true Artificial Intelligence, with the same capacity for thought and feeling as human beings, whose to say the person we create isn't going to turn out to be a real douchebag?
Gödels incompleteness theorem, which states that all consistent axiomatic formulations of number theory include undecidable propositions, is certainly a large part of what made the book so fascinating and addictive. Here is a brief summary of the Gödel in the book: The above image knocked my socks off when I first saw it, and Im still running around barefoot. My personal favorite part, math-wise (other than Gödels insanity of course), was Cantors Diagonal Argument. Just think of the all the real numbers contained between 0 and 1, for instance: there is an infinite universe contained therein. The field of real numbers is just so badass and beautiful. Overall, however, no matter how annoying the authors too-clever cleverness could be, the fact remains that the book explored some genuinely fascinating, complex conceptual realms, and did so in quite a bit of detail. Ill leave you with two philosophical nuggets from the book (the second is clearly humorous in tone, but fun to think about nonetheless): From the balance between self-knowledge and self-ignorance comes the feeling of free will. I am just reminded of Gödels second Theorem, which implies that the only versions of formal number theory which assert their own consistency are inconsistent
The reading of a book and its interpretation are determined in part by the cytoplasmic soup in which it is taken up. This is how I read Hofstadters book: as a crab canon. I reversed Hofstadters organization of the book, reading the dialogues as the primary portion and treating the chapters as their mere explication. So but, what is made clear, if the prospect of AI is not, is that metafiction is not just a bunch of intellectual masturbation but is a fictioning which takes real things, ie, metamathematical structures, and uses them in structuring a story or fixing them into narrative metaphors. He writes about his fascination with the coast-line measurement problem and the prospect of structuring his fiction upon principles similar to such things as fractals, Mandelbrot and all that. Form and content have always mutually determined each other in any fiction worth reading. So, shall we say that the form and content of our beloved metafiction of the past half century is in part derived from discoveries in mathematics and metamathematics (Gödels contribution)? Metaphiction is about a real thing, our experience of self-consciousness and what it makes us do. I believe that this wicked name calling in regard to smart fiction is due to a defense formation against the trauma of being the kind of thing we are and the kind of world we make for ourselves, compulsively.
Hofstadter (Original Review, 1980-09-24) Before we ask "Are dolphins intelligent?" we must ask "What is intelligence?" Doug Hofstadter, in his book "Gödel, Escher, Bach: The Eternal Golden Braid", presents a way of looking at intelligence that is not as restrictive as most current definitions.
Hofstadter is College of Arts and Sciences Distinguished Professor of Cognitive Science at Indiana University in Bloomington, where he directs the Center for Research on Concepts and Cognition which consists of himself and his graduate students, forming the "Fluid Analogies Research Group" (FARG). He was initially appointed to the Indiana University's Computer Science Department faculty in 1977, and at that time he launched his research program in computer modeling of mental processes (which at that time he called "artificial intelligence research", a label that he has since dropped in favor of "cognitive science research"). At the University of Michigan and Indiana University, he co-authored, with Melanie Mitchell, a computational model of "high-level perception" Copycat and several other models of analogy-making and cognition. Hofstadter collects and studies cognitive errors (largely, but not solely, speech errors), "bon mots" (spontaneous humorous quips), and analogies of all sorts, and his long-time observation of these diverse products of cognition, and his theories about the mechanisms that underlie them, have exerted a powerful influence on the architectures of the computational models developed by himself and FARG members.