Pros: Range of topics, witty, scientific, informative and thought-provoking.
Cons: Quite a bit of scientific and mathematical content.
The Bottom Line: Its one of the most unique books ever written. Hofstadter manages to bring tie together many different topics, and also manages to infuse wit and humor. A must-own!
aaragorn's Full Review: Douglas R. Hofstadter - Godel, Escher, Bach: An Et...
At the core of "Gödel, Escher, Bach: An Eternal Golden Braid" is Douglas Hofstadter's attempt to describe the self, and how self can manifest itself from the underlying inanimate matter. A question that that has been the subject of discussion and research by historians, mathematicians, physicists, biologists, computer scientists, theologists and philosophers and that has been addressed in many papers, theories, research projects and books, is addressed by Hofstadter using Strange Loops and Tangled Hierarchies.
Having said that, GEB is also an insight into a variety of topics including logic, artificial intelligence, computer languages, mathematics, DNA and the genetic code, recursion, reductionism, formal systems, typographical number-theory, Zen Buddhism, musical fugues, cannons, and art. But, the reader has to be aware that while delving into this sometimes very complex and abstruse text, the mathematics, logic and, art and music just serve as a build-up to explain Hofstadter's central theme: the understanding of human consciousness.
What are Strange Loops?
Loosely defined, Strange Loops are observed in hierarchical systems wherein by moving upwards (or to a higher plane) or downwards (to a lower plane), we end up at where we have started. The loop essentially represents a never-ending process in a finite number of steps; the concept of infinity is inherently ingrained in Strange Loops. Formal systems in mathematics (or any other hierarchical systems in general) can be considered as Strange Loops, and such a system can describe itself, talk about itself, perceive itself, and can become "self-aware". In trying to understand and explain formal systems, we can hypothesize that through their Strange Loops, they can acquire a "self" or "consciousness", and an ability to describe themselves and understand themselves.
Why Gödel, Escher and Bach?
Why does Hofstadter use Gödel, Escher and Bach? Where do they fit in?
Kurt Gödel:
An Austrian Mathematician, Gödel is most famous for his "Incompleteness Theorem". He tried to translate the ancient Epimenides paradox "All Cretans are Liars" (Epimenides himself was a Cretan) into mathematical terms. He aimed to use mathematical reasoning in analyzing mathematical reasoning itself, and reasoned that all formal systems are "incomplete" because they are unable to articulate statements that say of themselves that they are unprovable. There is Strange Loop inherent in Gödel's work, to prove the "Incompleteness Theorem", one has to embark upon writing a self-referential Mathematical statement.
Maurits C. Escher:
The Dutch graphic artist, MC Escher's artwork involved spatial illusions, paradox, repeating geometric patterns, and subliminal graphic transitions. Widely popular, Escher's artwork represents a series of Strange Loops; "Drawing Hands", for example, shows a right hand and a left drawing each other and "Metamorphosis" shows the seamless transition from fields to patterns to insects to fish to birds to cities to a chessboard! Stairs that lead to nowhere, walls that seem like floors and waterfalls that are nothing but a loop of water are very common motifs in Escher's work. Many mathematicians were interested in Escher's work and his symmetrical patterns, and they form by far the most amazing visual representation of Strange Loops.
Johann Sebastian Bach:
Bach's musical compositions, particularly his Musical Offering to the king of Prussia have been used to demonstrate Strange Loops in Bach's brilliant work. Not only does the piece contain a six-part fugue (considered almost impossible to compose), but also one of the canons begins in C-Minor, and through a transition almost imperceptible to the human ear, ends in D-Minor. The process can be repeated in the next modulation, and through six such modulations, the original key of C-Minor is restored. Bach, though his phenomenal gift of music does what Escher was to do later using art, demonstrate Strange Loops using music.
Where does this all lead to?
Through an insight into many varied topics, Hofstadter tries to argue if machines can possess originality, and think and rationalize about themselves. He discusses the hiccups that arise when systems turn back on themselves like a self-modifying chess game, or government investigating government and so on. But the most pressing argument he tries to make is the enormous complications involved in how we see "ourselves", the conflicts between the internal and external perceptions of who we are and trying to understand our self and our consciousness. However, there is the futility and the desperation inherent in the fact that our quest towards self-realization and self-actualization will always be "incomplete", there is always a certain unknown and a certain paradox. Although our intelligence and mental faculties would always propel us to seek the "ultimate truth", we should approach this with caution, and might end up, as Hofstadter quotes the Zen master saying "I do not understand myself"
The Book
This is a magnificent work. It cannot be categorized into mathematics, philosophy, science, or entertainment. Although the text contains a lot of abstruse chapters about mathematics, computer science, logic, reasoning, DNA and the like, Hofstadter infuses it with a lot of wit and humor. A high degree of scientific understanding and mathematical background is not needed to understand this book. As long as the reader can follow the idea that Hofstadter is trying to put across, its a great read. It also exposes the layman to some of the theories and concepts that have revolutionized the scientific world. Achilles, the Greek warrior and a Tortoise are the only two characters in this book, and their conversations are witty, humorous and brilliant.
GEB is not an easy book to understand or to write a review about! It’s a must-own book, its one of those books which you can read time and again. And in the end, it makes us ponder about our identity and whether we can ever "understand" and comprehend our “self”.
The textbook, Godel, Escher, Bach : Eternal Golden Braid, by Douglas Hofstadter, available in Paperback. Published by: Perseus Distribution. Editio...More at Textbooks.com
Individual Artists - General Art - Douglas Hofstadter s book is concerned directly with the nature of maps or links between formal systems. However, a...More at Barnes and Noble
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