- Paperback: 800 pages
- Publisher: Penguin Books Ltd; New edition edition (20 Nov 1980)
- Language English
- ISBN-10: 0140055797
- ISBN-13: 978-0140055795
- Product Dimensions: 23 x 15.4 x 4 cm
- Average Customer Review: 5.0 out of 5 stars See all reviews (3 customer reviews)
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Amazon Bestsellers Rank:
79,029 in Books (See Top 100 in Books)
- #27 in Books > Science & Nature > Mathematics > Mathematical Foundations
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Product Description
Product Description
Originally published by Penguin in 1980, when it was winner of the Pulitzer Prize for General Non-fiction, an anniversary edition of an illustrated examination of the nature of human thought processes.
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Customer Reviews
Most Helpful Customer Reviews
8 of 8 people found the following review helpful
Format: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.
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.
7 of 9 people found the following review helpful
Format:Paperback
This book is probably the best book I have ever read. And I love books. In style it's like the writings of Lewis Carroll, but with more maths, better pictures, and stuff on classical music, computers and art and science and AI and gazillions more- with loads of stories including tortoise and hares.
On the other hand, this book isn't a totally easy to read. Hofstadter covers Goedel theorem and there's only so much you can do to simplify complex ideas like that one. Still, Hofstadter uses every trick. And even if you don't finish it, you can buy it and leave it lying around- the Escher pictures are amazing. I lent my copy to my sister. She isn't talking to me since I took it back.
Finally the price. Over a decade ago it cost more than twice as much. And it was still worth it. It was literally cheap at twice the price, and it's now half the price!
This book is:
epic, amazing, mathematical, musical, self referential, about computers, poseur material, a fun read
it isn't:
a quick read, an easy read, a boring read, lightweight
4 of 6 people found the following review helpful
Format:Paperback
GEB is one of those books you can't believe noone wrote before. it is absolutely brilliant. the ideas are not simple but DRH explains them in such a way thateven a layman can grasp. Godel Bach and Escher 3 distinct shadows of one entity looked upon from various points of view.
It has it all : math, logic, art , AI.
this is a book that you will make you go "wow" each page you get by.
do yourselves a favor and read it, a few words can not convey the entire idea which is being develped as you march through the 700 odd pages.
Not a dull moment.
A must.
Gal.
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