17 of 18 people found the following review helpful
Very clever, very readable,
This review is from: Godel, Escher, Bach: An Eternal Golden Braid (Penguin philosophy) (Paperback)
‘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.