Godel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter Summary and Reviews
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Book Reviews of Godel, Escher, Bach: An Eternal Golden Braid
Book Review: Brilliant!
Summary: 5 Stars
Scientists seem to love quoting Alice in wonderland, as it seems applicable in so many fields. This book is a grown up version of Alice, an invaluable reference for anyone interested in the universe around them.Book Review: It is big and it is clever
Summary: 4 Stars
This enormous book is a hymn to the "strange loop", a term coined by the author. Loosely, a strange loop occurs when, after moving up a level in a conceptual hierachy, one is brought strangely back to where one started. It's closely related to those paradoxes of self-reference which can occur when form and content become intertwined.
An example is the old joke about the park keeper angry that his park has been littered with leaflets entitled "Keep Britain Tidy". Another is building one computer system to test another computer system, and then needing a third system to test the one you've just built. Yet another is the Wikipedia entry of Douglas Hofstadter which, at the time of writing, contains a quote from Hofstadter stating that his Wikipedia entry is full of inaccuracies. (So, do you trust the entry enough to believe this quote claiming it's unreliable?) You get the idea.
Hofstadter sees these strange loops everywhere: in the music of Bach, the art of Escher and, most significantly, G?del's incompleteness theorem, in which an algebraic system is used to prove a result about itself (rather than about numbers). After he's presented the various variations on these ideas, he then moves on to Artificial Intelligence, examining the "state of the art" as he sees it and discussing the implications of the earlier material for this subject.
Along the way he delves into various other diverse subjects such as the structure of the human brain or the challenges of translating a novel into different (human) languages. Much of this is fascinating stuff and if you are mathematically inclined, there is plenty to love about this book.
Given all the above, why not give the man 5 stars - what more could one possibly ask for?! Well, personally I have a number of objections to this work which I'll mention briefly before the crowd throws rotten fruit at me. Firstly, I am not sure that *all* Hofstadter's examples are on the ball. For example, the loop in Bach's "endlessly rising" canon is simply a consequence of there being 12 semitones in an octave, rather than any subtle paradox of self-reference. Similarly, the main theme from Bach's Musical Offering is not "Babbage" backwards, however you push it! In short, I suspect the author's obsessions can cause him to see patterns in the world around him which aren't really there.
Secondly, his would-be humorous writing style, quirky and lively though it is, will not be to everyone's taste ("Why, you don't say, Mr T!"). Thirdly, some readers will wish he had been more honest up-front about the book really being about AI (and something of a polemic, as evidenced by his almost mean-spirited attack on the philosopher John Lucas in several places): personally, it's not a subject close to my heart and I would have been rather more interested in delving into, say, what makes Bach's music beautiful and spiritual, as the cover suggests we will be doing. And fourthly, and most seriously, I am not convinced that Hofstadter is that great a pedagogue: the facetious style and inordinate length of the book can serve to obscure, rather than illuminate, his meaning.
These niggles notwithstanding, this book really is a fine achievement and, if you have the time and inclination (you'll need both in spades), likely to be a very rewarding read.
Book Review: Do buy this edition!
Summary: 5 Stars
A wonderful book well worth reading.
I feel obliged to note that, contrary to a previous review, the book supplied to me had not lost '...the aesthetic appeal the previous editions had'. In fact, the paper quality was not '...really bad', but rather good, and the pages were certainly not '...almost transparent'. The book's size is very similar to a previous edition I have encountered and the margins are not smaller than they should be. I really cannot find fault with this edition of the book and strongly recommend that you buy a copy.
Book Review: A great intro to some profound mathematics
Summary: 5 Stars
I read this when it was published back in '79 and it helped inspire me to more fully understand the massive achievments of Kurt Godel and his quite astonishing incompletness theorem.
For the casual reader, this is a wonderful book that will inspire you and give you a glimpse into the unsettling world of axiomatic set theory and it's uncany relationship to the music of Bach and the artistry of Esher.
Book Review: Engaging and mind bending
Summary: 5 Stars
Even though it is old, it still holds all its qualities intact. To me it is the bible of everything that begins with "meta". It hovers elegantly around so many subjects and still ties them together into self-reference and I doubt anyone can help but be charmed. The challenges are put forward in such a playful manner that only the crankiest stick in the stickiest mud could not help but swaying their way. But be warned - it does take an effort - and all other books will feel both easy, shallow and... well... literally light by comparison.