on 7 May 2007
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, Gödel'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.
on 13 October 2008
I have to admit that this book was sitting on my bookshelf for a while before I started reading it. In fact, I think it was about three years (I hadn't heard of the book's reputation, and so wasn't aware that I shouldn't have been intimidated). Once I got going, however, it was immensely enjoyable. The book covers a wide range of topics (number theory, art, consciousness and so on...), all of which are beautifully intertwined, as the title suggests. Some of the maths is pretty heavy going, I can't claim to have fully understood it on a single read, and I didn't do as the book suggested and worked through some of the examples (which would undoubtedly have made later ideas easier to understand), but even so, there is so much else in the book that it really doesn't matter. Different chapters tend to deal with different themes, so maths doesn't enter them all, and all are preceded by a dialogue which sets up the theme and keeps the mood light. These are beautifully crafted, with many hidden meanings, and, once again, probably require several reads to spot all the layers of meaning (however, a single read will illuminate several of these). The dialogues are so well-written, in fact, that they really kept me reading, as I was determined to plow through some of the heavier stuff to get to the next one.
Overall, I thoroughly enjoyed reading this book and look forward to coming back to it at some point in the future to see what else I can get out of it.
on 28 June 2000
This is a brilliant book. Back when I was in school, I used to borrow this book from the library during summer vacation, read it throughout the summer and return it in the autumn. For every year, I understood more and more :-) Mind, I was around 15-16 years old, so this was all new and exciting stuff. Now, several years later, I find that bits and pieces crop up in ordinary discussions - recursion, DNA/RNA mechanisms, fractals on a musical level, Zen philosophy,Number theory, AI and mind discussions - that I have long since gotten a sort-of grasp of, due to this book. This is also the book that led me to read "Zen and the art of motorcycle maintenance" (another necessary book). Nowadays, 10 years later, I keep two copies of GEB on my shelf, one in english and one in swedish. Everybody need at least one...but you won't get mine!
I guess I should comment on the way tha hofstadter manages to mae the most complicated subjects understandable, how he manages to find links and analogies in very interesting places, how one can read the book again and again and still find new things to ponder...But I won't. You need this book. Your brain need this book. If you haven't read it yet, Do.
on 4 February 2006
‘GEB’ is a hodge-podge of maths, philosophy, music, art and computer science, centred around a single idea that was captured mathematically in the early 20th century. known as Gödel’s theorem. It is difficult to describe briefly (indeed it takes a few hundred pages for it to become clear in the book) but it is, basically, an idea which states that it is impossible to have a complicated system governed by formal rules in which everything which is supposed to be in the system is described by those rules, and those rules alone are sufficient. Although Gödel’s theorem refers to number theory specifically, he realised that it would also apply to anything which could be described in number theory which, as Hofstadter demonstrates, is pretty much everything. Thus, things that we like to think of as being governed by formal rules (up to and including our own thought) actually can’t be. This expansion of Gödel’s theorem is mind-blowing.
Although ‘GEB’ follows the development of a mathematical idea, the book doesn’t require the reader to have a great maths brain. Hofstadter approaches Gödel’s theorem obliquely from all angles (particularly maths, music and art), partly because it has implications for all of these, but partly because it is so difficult to think about it directly that indirectly thinking about its implications is the easiest way of understanding it. (Hofstadter draws an informative analogy with Zen Buddhism, in that it is very Un-Zen to study Zen directly). He builds up a huge array of analogous systems with which to think about the problem, but builds them up so skilfully that you start to see the relationships between them easily, and flipping between music, art and maths becomes conceptually simple. I am not a mathematician, but had no problem understanding the importance of Gödel’s theorem.
As well as been very scholarly, ‘GEB’ is also very entertaining. The chapters are separated by dialogues featuring Achilles and the Tortoise, and other characters. In the dialogues, the characters discuss Bach’s music, Gödel’s maths and Escher’s art. The subject of the dialogue helps to illustrate the following chapter, but each also has many layers of meaning, with the structure mirroring a Bach fugue or Escher drawing. This helps to draw the apparently disparate strands underpinning the book together. These dialogues were very entertaining, and helped break up what would otherwise have been a slightly heavy read.
Overall, ‘GEB’ is clever, entertaining and informative. It illustrates an extremely difficult, but astoundingly important, idea very well, and its application to thought as a whole was mind-blowing, and felt like a revelation to me. It does get difficult in places, but never discouragingly so. Some of the latter chapters (after I had got the point) did drag on a little. Nevertheless, this is a brilliant book, and I would recommend it to anyone prepared to challenge their world view.
on 17 September 2000
I first read this book as a budding software engineer. It inspired me to a lifelong interest in logic, AI and cognitive science, twenty years later I am still on that road and on my third copy having worn out two previously - maybe I should get a hardback edition! Be warned this book may change your life, certainly it was an intellectual watershed for me. Read it.
on 21 February 2004
There is some really serious mathematics at one point in this book. I read that chapter 10 times and made myself believe that I understood it. I'd have to read it again because I can't hold it for long.
That is the only off-putting part. You can scan the chapter or skip read it and you won't lose out.
The rest is wonderfully entertaining, thought provoking and carries real insight into the way we view ourselves and our world.
Patterns are important, life needs repetition and replication to anchor itself and provide the secure basis for going forward.
Life, the mind, the ghost in the machine is mystical and can't be explained but this book carries you along paths towards an explanation. Perhaps the truth is that the explanation lies outside our plane of existence but where might those planes be?
Is the ant colony more alive than the ant? Is the "life" in a human being the same "life" that exists in a blood cell, or a sperm or an egg?
If you want to tease your brain or find something stimulating or entertaining to read then this book will reward the effort. You don't have to read it end to end, there is progression in each chapter but I suppose you could read the chapters in reverse order.
In fact one chapter can be read backwards. A wonderful feat when you see it in all its ingenuity. Read it forwards, read it backwards, like Bach, Escher and Godel and all causality, which way does it go?
on 2 November 2012
This book uses the Goedel Incompleteness Theorem as a starting point to define what the author calls "strange loops". The idea of a "strange loop" is explained using analogies from other disciplines, hence the title. Although the topics dealt with are very varied, in some sense they are unified by the general picture which is : looking for the essence of mind and pattern. Through seemingly random examples and paradoxes, Hofsdtadter attempts to cast some light on the process that transforms a series of sounds into an emotion-inducing melody, or a series of electronical functions and instructions into intelligence, or a series of genetic instructions into something alive and thinking.
The book exposes interesting trivia or fun facts about random disciplines such as Maths, Zen Buddhism, Biology, Psychology, A.I., Music, Physics and Painting (graphic art). It organizes all these little facts in a train of thought that progresses towards the general aim of the book: a reflexion about what is "self" or "intelligence" and how something like this can originate from inanimate matter. In other words, how is it possible to generate A.I. from an inanimate mechanical/electronical object that is a computer.
This book is like a puzzle made of many pieces, where the puzzle is interesting as a whole but the individual pieces are even more dazzling. The variety of subject covered makes it very interesting. In each chapter, the author gets you thinking about a little detail and then leads you to place this detail into the bigger picture of the puzzle. Each chapter begins with a fun fictious dialogue between two protagonists, that illustrates the point in many layers of understanding. The author subtly points out these details but never explicitly, so that the reader does not feel patronized and it is up to him to figure them all out if he finds the subject interesting enough. Then the serious talk begins, in which one can learn about meaning and form in mathematics, consistency, completeness and decidability, number theory, recursivity and A.I.
Goedel, Escher, Bach won the 1980 Pulitzer Prize for General Non-Fiction.
on 9 November 2001
This book is excellent at making you think about how a mind works, be it artificial or real. There are lots of interesting ideas put forward and some of the links and parallels between fields is astonishing. It is however quite self-indulgent and depending whether you choose to 'buy into' the experience you might find it a bit slow moving in parts.
I must admit I went through phases of boredom followed by phases of intense interest but this could be due to the author labouring over areas that twenty years down the line I am already familiar with - so perhaps I am a little unfair here. However, you do need to keep your wits about you if you are to truly understand all of the concepts, and for 700+ pages it is asking a bit much to keep up the enthusiasm. This is not to say that the book isn't highly entertaining in parts and one marvels at the ingenuity behind some of the dialogues which simultaneously represent several complex concepts. Reading this book you may feel that you are reading parables of science open to interpretation, and ultimately there is no real conclusion. I do however feel I have learned much and it has affected the way I look at things.
I enjoyed the ride but I'm so glad It's finished.
I originally had one of the editions from the 1980s and I found the book engrossing as a student then, when I had the time and frame of mind to immerse myself into reading about and understanding complex ideas. Then life went on and I lost the book between travel and various moves. I saw this latest edition on Amazon whilst looking to acquire again. I added it to my wish list and a kind friend gave it to me this Christmas.
I like the new preface by the author which gives an insight particularly useful if you've read the book (even if not in entirety) before. I like that he tells us what he wanted it to be about and I like the context he gives to where the work now sits in relation to his other publications.
The only thing stopping me giving 5 stars to this edition is the size of the pages vs text and the binding. They've attempted to make the paperback a bit more compact (tough job given the size of the book) and with the binding it's quite difficult to view each page in full without seriously bending the spine back. The text runs very close to the bound edge of each page. But if you have never read it then despite the physical appearance of the volume, this has to be the version you first read because even with minor updates to the text, the author has approached the revisions with 20 years more insight and maturity under his belt!
on 20 December 2001
Don't buy *this* edition of this wonderful book.
The paper quality is really bad (the paper is very thin, almost transparent), the whole book has shrunk in size, the text looks really cramped, the margins are smaller than they should be (I guess to save paper!) and to cut a long story short the aesthetic appeal the previous editions had is completely lost.
My recommendation: Try to find a copy of one of the previous editions if possible, and buy this edition if an only if you fail!