Godel, Escher, Bach: Un Eterno y Gracil Bucle (Spanish Edition) (Paperback)

by Douglas R. Hofstadter (Author)

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Product Description
¿Puede un sistema comprenderse a sí mismo ? Si esta pregunta se refiere a la mente humana, entonces nos encontramos ante una cuestión clave del pensamiento científico. Y de la filosofía. Y del arte. Investigar este misterio es una aventura que recorre la matemática, la física, la biología, la psicología y, muy especialmente, el lenguaje. Douglas R. Hofstadter, joven y ya célebre científico, nos abre la puerta del enigma con la belleza y la alegría creadora de su estilo. Sorprendentes paralelismos ocultos entre los grabados de Escher y la música de Bach nos remiten a las paradojas clásicas de los antiguos griegos y a un teorema de la lógica matemática moderna que ha estremecido el pensamiento del siglo XX : el de Kurt Gödel. Todo lenguaje, todo sistema formal, todo programa de ordenador, todo proceso de pensamiento, llegan, tarde o temprano, a la situación límite de la autorreferencia : de querer expresarse sobre sí mismos. Surge entonces la emoción del infinito, como dos espejos enfrentados y obligados a reflejarse mutua e indefinidamente. Gödel, Escher, Bach: un Eterno y Grácil Bucle, es una obra de arte escrita por un sabio. Versa sobre los misterios del pensamiento e incluye, ella misma, sus propios misterios. / Winner of the Pulitzer Prize, this book applies Godel's seminal contribution to modern Twenty years after it topped the bestseller charts, Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid is still something of a marvel. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel.mathematics to the study of the human mind and the development of artificial intelligence.

Product Details

• Paperback: 882 pages
• Publisher: Tusquets; Spanish edition (October 2007)
• Language: Spanish
• ISBN-10: 8483830248
• ISBN-13: 978-8483830246
• Product Dimensions: 8.1 x 5.6 x 1.9 inches
• Shipping Weight: 1.8 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars See all reviews (4 customer reviews)
• Amazon.com Sales Rank: #547,462 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

8 of 9 people found the following review helpful:

5.0 out of 5 stars Must for Math Majors and Enlightened Individuals, March 7, 2003

By	Randy Given (Manchester, CT USA) - See all my reviews (TOP 500 REVIEWER)    (REAL NAME)

This review is from: Gödel, Escher, Bach (Spanish Edition) (Paperback)

This book is a must for math majors (as well as many logic and philosophy majors). Anyone else in the hard sciences should also read this book, at least to be enlightened. Initially, it is easy reading, then becomes slightly foggy, but pushing through is rewarding. Of the three, my favorite is Godel and I always mention his Incompleteness Theorem whenever his name comes up. It his probably actually best mentioned by Rudy Rucker in his book "Infinity and the Mind". I think it is significant enough to mention here:

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The proof of Gödel's Incompleteness Theorem is so simple, and so sneaky, that it is almost embarassing to relate. His basic procedure is as follows:

1. Someone introduces Gödel to a UTM, a machine that is supposed to be a Universal Truth Machine, capable of correctly answering any question at all.

2. Gödel asks for the program and the circuit design of the UTM. The program may be complicated, but it can only be finitely long. Call the program P(UTM) for Program of the Universal Truth Machine.

3. Smiling a little, Gödel writes out the following sentence: "The machine constructed on the basis of the program P(UTM) will never say that this sentence is true." Call this sentence G for Gödel. Note that G is equivalent to: "UTM will never say G is true."

4. Now Gödel laughs his high laugh and asks UTM whether G is true or not.

5. If UTM says G is true, then "UTM will never say G is true" is false. If "UTM will never say G is true" is false, then G is false (since G = "UTM will never say G is true"). So if UTM says G is true, then G is in fact false, and UTM has made a false statement. So UTM will never say that G is true, since UTM makes only true statements.

6. We have established that UTM will never say G is true. So "UTM will never say G is true" is in fact a true statement. So G is true (since G = "UTM will never say G is true").

7. "I know a truth that UTM can never utter," Gödel says. "I know that G is true. UTM is not truly universal."

Think about it - it grows on you ...

With his great mathematical and logical genius, Gödel was able to find a way (for any given P(UTM)) actually to write down a complicated polynomial equation that has a solution if and only if G is true. So G is not at all some vague or non-mathematical sentence. G is a specific mathematical problem that we know the answer to, even though UTM does not! So UTM does not, and cannot, embody a best and final theory of mathematics ...

Although this theorem can be stated and proved in a rigorously mathematical way, what it seems to say is that rational thought can never penetrate to the final ultimate truth ... But, paradoxically, to understand Gödel's proof is to find a sort of liberation. For many logic students, the final breakthrough to full understanding of the Incompleteness Theorem is practically a conversion experience. This is partly a by-product of the potent mystique Gödel's name carries. But, more profoundly, to understand the essentially labyrinthine nature of the castle is, somehow, to be free of it.
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This is the kind of mental freedom you will gain by reading this book. Highly recommended.

1 of 1 people found the following review helpful:

5.0 out of 5 stars Computer Science, September 26, 2008

By	Carlos Jorge (Lisboa, Portugal) - See all my reviews

Godel, Escher and Bach, written by Douglas Hofstadter, while the title would suggest it is discussion of a mathematician, an artist, and a composer, is a complex examination of how human beings develop perception and meaning. More specifically, the book explores, through a series of dialogues and narrations, how symbols, thought and language are all intertwined and how reality is essentially a composition of overlapping meanings and perceptions. The book challenges the reader to observe the system of symbolic meanings around him or her objectively.

5.0 out of 5 stars we should never forget, June 26, 2009

By	Erik Jan Paul Moller "Vikingbass" (Marbella, Spain) - See all my reviews (REAL NAME)

Obviously time has passed since this book appeared the first time and after some years we are facing new theories and new points of views, but this book is to me a type of "need to read" if you wish to experience were our thinking can go and how important it is to consider were you focus from. I consider this book a real masterpiece in content, form and exposition method. And it is really addictive.