Reading Godel, Escher, Bach is like joining a club. People who see you reading it will open spontaneous conversations and often gift you with unexpected insights. (I had a fascinating conversation with a total stranger about Godel's theorem.)
Wish I could give more than five stars.
As the book introduces the reader to cognitive science, the author draws heavily from the world of art to illustrate the finer points of mathematics. The works of M.C. Escher and J.S. Bach are discussed as well as other works in the world of art and music. Topics presented range from mathematics and meta-mathematics to programming, recursion, formal systems, multilevel systems, self-reference, self-representation and others.
Lest you think Gödel, Escher, Bach: An Eternal Golden Braid, to be a dry and boring book on a dry and boring topic, think again. Before each of the book's twenty chapters, Hofstadter has included a witty dialogue, in which Achilles, the Tortoise, and friends discuss various aspects that will later be examined by Hofstadter in the chapter to follow.
In writing these wonderful dialogues, Hofstadter created and entirely new form of art in which concepts are presented on two different levels simultaneously: form and content. The more obvious level of content presents each idea directly through the views of Achilles, Tortoise and company. Their views are sometimes right, often wrong, but always hilariously funny. The true beauty of this book, however, lies in the way Hofstadter interweaves these very ideas into the physical form of the dialogue. The form deals with the same mathematical concepts discussed by the characters, and is more than vaguely reminiscent of the musical pieces of Bach and printed works of Escher that the characters mention directly in their always-witty and sometimes hilarious, discussions.
One example is the "Crab Canon," that precedes Chapter Eight. This is a short but highly amusing piece that can be read, like the musical notes in Bach's Crab Canon, in either direction--from start to finish or from finish to start, resulting in the very same text. Although fiendishly difficult to write, the artistic beauty of that dialogue equals Bach's music or Escher's drawing of the same name.
As good as all this is (and it really is wonderful), it is only the beginning. Other topics include self-reference and self-representation (really quite different). The examples given can, and often do, lead to hilarious and paradoxical results.
In playfully presenting these concepts in a highly amusing manner, Hofstadter slowly and gently introduces the reader to more advanced mathematical ideas, like formal systems, the Church-Turing Thesis, Turing's Halting Problem and Gödel's Incompleteness Theorem.
Gödel, Escher, Bach: An Eternal Golden Braid, does discuss some very serious topics and it can, at times, be a daunting book to handle and absorb. But it is always immensely enjoyable to read. The sheer joy of discovering the puns and playful gems hidden in the text are a part of what makes this book so very special. Anecdotes, word plays and Zen koans are additional aspects that help make this book an experience that many readers will come to feel to be a turning point in their lives.
Like every other book written by Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid, has an index and a bibliography that must be noted as exceptionally well done.
Although filled with English wordplay, this book is in no way tied to the American origin of its author. For years, it was thought that Gödel, Escher, Bach: An Eternal Golden Braid, would be impossible to translate, but so far, it has successfully been translated into French, German, Spanish, Chinese, Swedish, Dutch and Russian.
A profound and beautiful meditation on human thought and creativity, this book is indescribably gorgeous and definitely one of a kind.