A couple of years ago, I asked 20 friends to imagine they were banished to a desert island. On this journey to nowhere, they would be allowed to take only a single science book. What would it be? And just to make the game interesting, I required that the choice be a volume published in the second half of the 20th century and not an encyclopedia or some other type of general reference volume. My own choice was the book under review, Douglas Hofstadter's Pulitzer prize-winning volume, Gödel, Escher, Bach ( GEB ). What surprised me a bit was that it was also the independent choice of three others. This was quite a testimony to the almost infinite depths of Hofstadter's masterpiece, given that the professional interests of the people I contacted ran the gamut from anthropology to zoology and almost everything in between. One may wonder just what it is exactly about this book that evokes such rapture in the mind of its readers.
Hofstadter himself tries to answer this question in his 21-page introduction to this anniversary edition of the 1979 publication of the book.
According to Hofstadter, GEB is "about how animate being can come out of inanimate matter. What is a self? How can a self come out of stuff that is as selfless as a stone or a puddle?" That is the leitmotiv of GEB , which the book explores in a bewildering array of formats, the most visible being the various dialogues between the Anteater, Achilles, the Tortoise and the Crab. Each of these dialogues introduces in a whimsical way an important theme in the mosaic of ideas that taken together constitute the author's answer to the aforementioned basic question. These themes are worked out in the text using the intricate musical structures of Bach, the phantasmagoric artistic patterns of Escher, and the self-referential loops inherent in Gödel's exploration of the limits of logic. Taking a high-altitude flyover of the entire book, one sees its structure mimicking the very structures it aims to express, namely, the emergence of a unified whole from a collection of individual elements that do not seem to contain within themselves anything approaching an answer to the over-arching question. For many readers, this aspect of the book is probably the most frustrating.
Where is Hofstadter going with this? To those with a system-theoretic bent, this "emergent property" of the book is what gives its lasting charm and attraction. And for me, anyway, it is exactly why this is the one book above all that I would want with me on that proverbial desert island.
While the global structure of GEB provides an answer to how a self arises from inanimate matter, the local structure of the pieces are of considerable interest in their own right. The system-theoretic topic that GEB relentlessly explores is the idea of self-reference together with the notion of a hierarchy. Hofstadter calls this a "tangled loop" - the process by which a system - logical, artistic or musical - turns back on itself to use its symbolic structure to speak about the system from within the system. This "inside-outside" dichotomy is what gives rise to the logical incompleteness discovered by Gödel, as well as the seeming paradoxes in Escher's art and Bach's fugues.
During the course of this 700-plus-page exploration of mind, brain and machine, Hofstadter addresses a bewildering array of sub-topics and themes. Among them, formal logical systems, deduction versus induction, consistency and completeness of formal systems, Gödel's Incompleteness Theorem, recursion, the location of meaning in DNA strands and phonograph records, the propositional calculus, Zen koans, reductionism versus holism, levels of hierarchies, fugues, relation of concepts and neural activity in the brain, computer languages, self-replication, brain activity and computation, truth and proof, the Turing-Church thesis, artificial intelligence and musical canons. Whew! How could one not draw an almost infinite supply of inspiration from such a rich list of intellectually fattening themes?
The only difficulty in reading this book is the very fact that it is chock-full of so many themes, sub-themes, concepts, ideas and speculations that it is difficult keeping them all in mind. Readers who approach the book in the usual serial fashion of most single-theme volumes may well feel overwhelmed, confused, or just plain troubled by the rapid switching from one theme to another and then back again as they make their way through the book. It is a bit like being on an almost endless intellectual roller-coaster ride, wondering if it is ever going to end. Of course, some of us felt a kind of sadness when we came to page 777 and saw that all good things -even GEB - must eventually come to an end. So when I saw that a 20th anniversary edition of the book had been issued, I hoped against hope that it would take up the story of the foregoing themes 20 years later, and that what we would have is a kind of "expanded edition" of GEB . Of course, the book under review is no such thing. And all to its author's credit.
The only addition in this anniversary edition to the 1979 original edition of the book is the 21-page preface. But this material is well worth the price of the book. In it, Hofstadter elaborates on a number of historical issues surrounding the creation, production, publication and reception of the book 20 years ago. Along the way, he also manages to touch on several of the themes in the book, bringing the reader up to date on his thinking about language, self-reference and several other key elements of the book. Personally, I found his stirring account of the difficulties he had in finding a publisher willing to take a chance on an unknown author with a 700-page manuscript that seemed to be all over the intellectual landscape a story to inspire every fledgling author. And this is not to mention his spirit of adventure in personally typesetting the entire volume using the primitive computer typesetting systems available in the late 1970s. Such an undertaking would not be a cinch even with today's systems, and to produce such a magnificent work with that technology boggles the imagination.
At the end of his new preface, Hofstadter takes up the pros and cons of producing a fully revised edition of the book. Arguments in favour of this approach included the emergence of a lot of interesting new material on Gödel and Bach, material arising from the many foreign editions of GEB . In addition, there was the continuing temptation to update some of the claims made in the book, such as the completely wrong prediction about computer chess-playing programs. There was also the idea of making GEB into a multimedia product by producing a CD-Rom version of the book, or even a web-based version complete with hyperlinks. Hofstadter rejects all of these notions with the simple statement that he intended GEB as a book, not a multimedia circus. He concludes his preface by arguing against even a revision of the text by stating that GEB was written in one sitting, so to speak, and was the labour of a particular person at a particular point in time. He is not that person any more; hence, the book should not be touched. Who can really argue with that? This book should not be touched - only savoured and enjoyed.
John L. Casti is professor at the Santa Fe Institute, New Mexico, United States, and the Technical University of Vienna, Austria.
Gödel, Escher, Bach: An Eternal Golden Braid
Author - Douglas Hofstadter
ISBN - 0 14 028 920 8
Publisher - Penguin
Price - £14.99
Pages - 777