Godel, Escher, Bach: An Eternal Golden Braid (20th anniversary edition with a new preface by the author) [Paperback]

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.

‘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.

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.