Gödel, Escher, Bach: An Eternal Golden Braid (book)

Wow, this one was a mental workout. The book is very enjoyable, but light reading it ain't. It's amazing how many meanings/interpretations he can give to a single word/symbol of his own book. In a way, of course, that's what this book is about, how words mean instead of what they mean. One effective way to get that across is to reinterpret a single symbol multiple times.

Hofstadter deftly combines heavy speculation on the nature of intelligence with a bizarre sort of humor that will have you convulsing with laughter from its sheer unexpectedness. This book's greatest virtue also makes it difficult to do justice in review. It's so tightly woven together that you can't draw out a single thread to illustrate its quality.

I read this book in a seminar earlier this year. I was fortunate, because I'm not sure I'd have been brave enough to read this book on my own. GEB is an incredibly cerebral creation, and not for the faint of heart. It's without a doubt the most challenging thing I've ever read, but also the msot rewarding.

The core of the book is to explicate the complex mathematical theorem of the incompleteness of formal systems in mathematics, something which a lot of math majors don't even understand. I don't really get it either, but even if Godel's Theorem surpasses you, the other concepts presented in this book make it well worth the read. It changes your brain, and the concepts I learned while reading it are ones I find I encounter again and again. It's not just about mathematics; on the contrary, the book is written in such a way that non-mathematicians can understand. It's kind of like core concepts of life through a mathematical lens.

If you're willing to put in the time and effort, you won't be disappointed with this book. Even if it does have you bashing your head against the wall sometimes.

Overall, the book looks at the author's views on how consciousness and a sense of self can arise from what is nothing more than the mind, a collection of neurons that follow fairly precise rules at a granular enough level. How can something as complex as a symphony be produced by what is nothing more than a collection of cells?

What made the book such an enjoyable read was the author's ability to meld these three individuals' lives (Godel's, Escher's, and Bach's) and work together into a seemingly finely interwoven mosaic. In virtually every chapter there's multiple works by Escher that, upon seeing them within the context of the chapter's topic, makes you think Escher created that work for Hofstadter's book. Similarly, I learned a lot about music structure and the little games and slieghts of hand Bach's works contain.

One unique thing about this book was the structure. Between each chapter the author included a dialog between, typically, Achilles and the Tortoise. These two chums would have discourses on topics that played into the material presented in the following chapter. These dialogs are worth the price of admission alone. In particular the Crab Canon is a piece where a new character, the crab, is introduced, and he has one line right smack dab in the middle of the dialog. The first half and second half of the dialog, however, are identical in words, but shifted in meaning. For example, the dialog starts with Achilles saying, "Good day!" as a greeting, and ends with the Tortoise saying "Good day!" as a goodbye. It's amazing how well it all works together. (You can read this particular dialog in its entirety here - http://www.barryland.com/canon.html) In music, a crab canon is a kind of canon in which one line is reversed in time from the other (e.g. FABACEAE <=> EAECABAF).

Hofstadter explores these ideas in part by looking at Goedel's incompleteness theorem, which states that given a complex enough of a formal system (such as number theory), there are theorems in the system that are true but cannot be expressed in the system. In other words, interesting formal systems are incomplete. The canonical example used to illustrate Goedel's theorem is the statement, "This sentence is false." Goedel's theorem is founded in number theory, not English, but the point is that given a complex enough system, there are things that are "beyond" the system.

The chapters I enjoyed included:

* The one on Zen Buddhism, which I knew little to nothing about beforehand, but like the explanation that the author provided. Sounds like a very interesting philosophy. (How honest/complete an overview the author gave, I don't know, not being familiar with the philosophy myself.)

* The chapters describing the basics of the cell, how cell's replicate and how DNA, RNA, mRNA, and ribosomes work together to create the proteins used by the cell.

* The final chapter, as it posed many open-ended questions about "strange loops and tangled hierarchies" (a concept discussed throughout the book) in everyday life.


Overall, I would highly recommend this book to those who are interested in a discussion on what might constitute consciousness, thought, the soul, and existence, and how these concepts can be materialized from lower-level mechanical processes. Furthermore, the author examines how he views things like true artificial intelligence - a computer with a soul, with a sense of self - would have to be accomplished. Understand that the author does not get to these concepts right off; rather, he spends significant time building up the base of understanding to have a discussion on these topics, and the topics are not fluff ones. At times it can take several minutes just to get through a single page (at least for me).

But if you put the time in, I think you'll reap the reward by the book's end. Personally I liked every chapter except for the few close to the end that detailed the "progress" in AI research. (I use "progress" in quotes because this book was written back in 1979.)

I first read the 1979 edition of this book in 1988, and have been dipping into it periodically for insight and edification ever since. Its richness and depth defy adequate description in a short review.

Hofstadter uses the music, mathematics, and art of the three title figures, as well as examples, concepts, and metaphors from diverse domains such as physics, genetics, computing, language, propositional calculus, Zen Buddhism, artificial intelligence, formal systems theory, and a whole lot more, in order to elucidate such notions as meaning and form, pattern, theoremhood, self-reference, and strange loops. It's a roller-coaster-ride of astuteness and wisdom, and some of the insights such as "Isomorphisms Induce Meaning" simply blew my mind when I first grasped their impact.

What makes the book even more special is that it is written with humour, and employs storytelling in the form of dialogues between Archilles, the Tortoise, and the Crab. I recommend it without reservation. For me it was more than a learning experience, it was a formative one.

You might have been recommended this by a friend, or come across web recommendations. Almost everyone gives it more than 5 stars! But...
you can think of many reasons why you do NOT want to read this. There is lots of maths (it is a book about maths!?), it is loved by geeks, and it seems to cover too many things (consciousness, intelligence, reductionism, holism, recursion, self and soul!)...

You don't know if you want to start on an epic 700 page book about abstruse stuff right now. Perhaps later.

Hold it! You can enjoy this book just because of the brilliant writing, the puzzles and wordplay that make it a dream of Renaissance-style writing. The Rule of Four, Hypnerotomachia, Name of the Rose etc can't match this brilliance.

I suggest a really easy way to start this book: Read a dialogue. Each chapter has an opening dialogue: Tortoise and Achilles and a few others spar; their verbal wizardry opens up new worlds; each is set to music, imitating the style of a Bach piece so closely you can almsot hear the music while you read. The main chapters discuss the serious stuff seriously. A typical dialogue is less than 5 pages; so give it a quick try NOW.... see if you enjoy the heady mix of literature, puzzles and deep stuff!

My favourite is Crab Canon.. this was the first bit written, the whole book was written around it. Crabs (supposedly) walk backwards; see the illustrations (Escher's art, Bach's score, both called Carb Canon) upside down, and then .. read the dialogue backwards.
Here it is: http://www.barryland.com/canon.html

Or try "Sonata by Unaccompanied Achilles": this has a couple of lovely little puzzles.
http://www.rdegraaf.nl/index.asp?sND_ID=141084

Or, ... oh! there's so many little gems to recommend.

And if you like the first dialogue you read, get the book. Then read the preface, and then read the dialogues - in order - and skip the chapters .. till later.
That makes it a great fun read.. and a short book in itself!

Then having enjoyed yourself, read from the beginning and enjoy the whole thing afresh... at yor own pace. I read the dialogues quickly, and absorbed the book over a year, solving word and logic puzzles, tripping over imagery and more ...

So, have fun with this great book. It might change your life, as it did mine.