Perhaps the strangest loop in this book that hinges on that very concept is that GEB contains, more or less as a thesis, an indictment of its own genre. The thesis - and Hofstadter may protest "people don't understand my book" all he wants, but this is one thesis among the many that this sprawling tome contains - is that when we jump levels, when we summarize information, we sacrifice precision in an effort to attain understandability and/or utility. In other words, in contructing analogies and systems that we can understand, we invariably lose details of the system beneath. But this is precisely what the genre of popular science engages in: translating ostensibly real, complex and inscrutable science into simpler, overarching concepts that the lay person can penetrate and, hopefully, understand. On the one hand, there is nothing wrong with this: Hofstadter insistently pushes across the idea that this is just a fundamental aspect of comprehension, because although systems may be built of their components, it is impossible to comprehend them purely on that level. Words cannot be understood as merely the details of their letters, melodies cannot be understood at the level of their notes, computer programs can't be understood on the level of their bits and, central to the text, minds / brains can't be understood at the level of neurons. On the other hand, though, this loss of detail renders readings metaphoric and not isomorphic, as he continually insists. This book, and others in the pop science genre, destroy some aspect of their truth in those acts of simplification.
In many pop science works, that's a forgivable sin; as problematic as it is, we can't be renaissance men anymore in this hyperspecialized world. So some reduction is necessary if ideas are ever to be communicated. Clearly, though, that reduction needs to be tempered in an effort to preserve essence and meaning; authors need to be wary of dropping too much. But beyond that, authors need to not abuse the act of simplification, and they need to not extend the negative space of missing information in an effort to be mystical, whimsical, or to speculate well beyond what the original details permit.
All of this probably sounds like the beginning of a negative review, and I would like to reject that notion from the outset. A book this sprawling, while somewhat simplifying the topics it engages, defies meta-simplification as a "good" or "bad" book. A quick review of the reviews at Amazon will demonstrate a nagging tendency to do just that. "Brilliant," "Life-changing," and "Masterpiece" get tossed about with the opposing "confused," "boring" and "pointless" takes with equal fervor. Reviewers are, predictably, obsessed with slamming this into a treasure/trash dichotomy, demanding to know whether Hofstadter is right or wrong. While I think that you can pick this work apart and discuss whether different aspects of it represent wise / unwise choices, going with its central theme, the different aspects of the book being good / bad does not equate to the book as a whole as worthwhile or not. I could make these kinds of "sum of its parts" jokes forever - like Hofstadter did - so I will try not to, but suffice it to say that a rendered opinion of good / bad is going to be so based on the reader's subjectivity and/or what specific aspect of the book they are actually focusing on as to be rendered not meaningless, but very narrowly meaningful. Stepping back to a wider social / academic level, any *thing* that challenges thought and initiates a deeper attempt at understanding is good in that respect, so the book's existence as a popular phenomenon should be called, for lack of a better term (ha!), a good thing.
One thing that permeates throughout these reviews is how apparently difficult to read it is, largely attributable to its math / formal systems focus early on in the book. It is difficult to formulate this without coming off as an elitist jackass, but this book simply is not difficult in that respect. Allow me to clarify: *this book* is not difficult, number theory and formal systems are. Much of this book deals with outlining Gödel's Theorem, and in order to do that, the author had to outline formal systems. If you have encountered these things before - if you have taken logic classes and read Gödel's paper itself, or a more technical interpretation of Gödel's Theorem, then it becomes quite apparent what an excellent job Hofstadter has done of teaching these concepts within the context of the book. This has two effects: one, even though he did a good job of teaching them, the concepts are in themselves complex and not beach-reading fare, so it's going to take more effort than typical for a reader to understand them. Everything is there, though, so i feel comfortable in calling out any complaints of "incomprehensible" as being a fault of the effort of the reader and not that of the writer. The other effect, though, is that if you already understand these concepts, if you've already put int eh leg work, you see the shortcuts and simplifications that have been taken, and you can quickly get annoyed at the omissions and the window-dressings that obscure them. This book, then, is aimed at a middle ground reader, one who is willing to put in the effort to at base understand something as difficult at Gödel's proof, but one who hasn't already done so. I personally did not sit in this middle ground, and while I still found some of this book very insightful and good fodder for my thinking, a lot of it struck me in a dismissive Ringo Starr sense of "it's been done."
(Incidentally, I suspect that a number of the negative reviews of this book come from people who sit outside that target range: those who say "I don't get it, this is boring and inpenetrable and pointless" and those who ask "why is this such a big deal? I covered this in philosophy of mind 101!" The first approach grates; "if the author can't state his ideas clearly in seven hundred pages, then the ideas aren't worth hearing" is a pathetic approach to the world of ideas, truth, and information. Some things don't fit into a 30 sec commercial divided into 2 second edits, unfortunately, and Gödel's proof is one of them. On the other side, it's a pretty common phenomenon: smart people sometimes forget that they, too, were students once. It's surprising that they don't evaluate the book for what it is, pop science, and recognize that these tough concepts have been spooned out pretty cleanly. I suppose that's why we need more and better teachers, eh?).
It would behoove me at this point to commit the aforementioned sin and simplify this unsimplifiable book. Essentially, this is an exploration of Gödel's Theorem and its implications for artificial intelligence. So what is Gödel's Theorem? Super-simplified version: Gödel proved that there is a way to translate sentences about numbers into numbers themselves. And then he proved that there is a way to make a number (called 'G') that "says" "I am not a proveable theorem." This is a twist on the old "this sentence is a lie" trick, only this time there is no linguistic confusion about things; it is almost like it is a number that says "I am not a number." The clear problem with this is that either G is false, in which case it's true because false things are not theorems, or it is true, in which case G is a true idea that we cannot prove. All of this demonstrates that any system either is going to have inherent contradictions (G and not G) or it's going to be incapable of proving every true thing out there.
And that is a GROSS oversimplification. But the idea, when considered in full, has vast implications. The primary one that Hofstadter focuses on is that there at first appears to be something that humans can figure out is true but that a formal system (read: a computer) cannot. (He goes on to refute this by pointing out that even if we can figure this version out, that this concept can quickly spiral up into systems that are so complex that we can't comprehend / keep track of things any more. So the reality is that neither people nor computers can represent all truths, not that computers inherently lack something that we don't). He also goes on to demonstrate that the key to this complexity is the concept of multiple levels, and that specifically in this case, they are levels that become entangled in their ability to reference one another and ultimately tangle into self-references. And then he attempts to tie this concept into something resembling a theory of mind, consciousness, and intelligence (artificial and otherwise) by citing examples from art, music, poetry, etc.
Enter Bach and Escher. And biomolecules. And Lewis Carroll. And computer programming languages. And zen koans. And brains and minds. And... well, and all of the complexity, problems, beauty, brilliance and annoyance of the work. The thing that some find fascinating, others find nauseating, and at least one other (I!) identify as a jumbled exercise that is apt to produce a variety of reactions (according to taste) is that the book itself attempts to instantiate itself as a self-referencing series of loops. The basic structure is culled from Lewis Carroll in that the book alternates between dialogs by cartoonish characters and more traditional pop-sci prose. It is in the dialogs that Hofstadter permits things to get wacky. Characters discuss Escher pictures, notorious for their playing with frame of reference, while themselves playing with frame of reference and jumping in and out of pictures; characters discuss fugues and the characters enter the scene one by one with the same theme... just like a fugue! One section discusses a "crab cannon" a Bach work where instruments enter and play the same line in reverse order against each other; in the section, the characters' conversation contain the same lines spoken in reverse order to one another, resulting in a coherent narrative (largely pulled off via puns and open-ended greeting/farewell, like "Good Day, Sir"). So it's example after example of content referencing form and vice versa, and then the book itself ends with a reference to the author writing his work and thrusting the characters back into the introduction, somewhat insinuating that this work needs to be read on a repeated, looped basis to be totally understood.
Is this clever? Is this brilliant? This aspect of the book reminded me simultaneously of novelty music and virtuoso guitar. Don't get me wrong; I love me some Weird Al Yankovic, and Joe Satriani is a stud. But listening to novelty music or shredding solos for hours on end would drive me insane. Holfstadter's punning and wordplay had this effect on me, bringing all the cheesiest Dr. Demento tunes instantly to mind. I like puns, too, but these were unsubtle sledgehammers. The virtuoso guitar aspect came in w/r/t Hofstadter's structure: sure, 32nd notes are amazing, and it takes a whole lot of work to master that level of play, but after a while, the onstentatious nature of such a display invites questions of "So What?" The superstructure and metareferences were certainly complex and I'm sure took a great deal of effort to design, but their blatant nature - and Hofstadter's constant need to say "hey look what I did there" - defeated their purpose. A prime example of clever for clever's sake, the structure of the book is largely divisive and, to me, detracted with distraction a lot more than it added to the book by providing examples. Again, this is largely a matter of taste, and I can't emphasize that enough. If you dig Zappa, you might fall in love with these dialogues and related lines of self-conscious wizardry; Bach and Escher (at least in some respects) seem to fall squarely in this category, too. If you don't, those dialogs reek of onanism, and you are unlikely to get any nerd-giddy benefit from them.
If that is my structural complaint, then to get back to the intro of this long-winded review, my content complaint is Hofstadter's abuse of his "pop-science" format. He exercises little to no rigor in defining terms, he appeals to self-declared assertions as infallible and does little to differentiate his speculation from his research. Again, this is all par for the course for pop-science writing, but I do feel that Hofstadter - in playing fast and loose with terms like "isomorphism" and in drawing inexact analogies between, for example, formal systems and protein synthesis - abuses the negative space of his text like a behind-curtain wizard. His attempt to draw parallels between such a wide range of topics and his simultaneous effort to keep things simple result in a book fraught with inexact oversimplifications. Not to belabor that single term, but Hofstadter repeatedly invokes the idea of isomorphisms when actually citing analogies. The details omitted, if not fatal to his claims, certainly would prompt questions that he seems unwilling to acknowledge.
I also found his derogatory attitude toward (his label) soulists to contradict his overall thesis; in fact, if as he asserts that there may be a level of meaning which we as humans do not have access to, then the soul may be a better approximation of that level than any substantial model that materialism has put forward. In other words, he seems to be refuting a theory from a level which he all but states we currently do not have access to. That may not be bad materialistic science, but it's pretty poor metaphysics.
I would say that this is not the golden tome that people claim it is. It's a great introduction to many of these topics, and as such deserves its exalted place in the pop science canon. But that canon is something entirely different from the canon of transcendent works. GEB's lack of rigor and sometimes facetious structure keep it well out of that particular canon. I don't doubt that this presentation is heartfelt and a good representation of Hofstadter's belief system. That belief system, though, betrays its authors infatuation with unsubtle literary fireworks that will either excite or annoy readers - and maybe betrays a more problematic tendency to leave terms ill-defined. I'll leave this with an analogy that maybe only I will understand: "In It For the Money" is a great Zappa album, but that doesn't necessarily make it a great album. So it goes with GEB.
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