Godel, Escher, Bach
Gips, James
Imbued with the mysteries GODEL, ESCHER, BACH: AN ETERNAL GOLDEN BRAID Douglas R. Hofstadter Basic Books, $18.50 777 pp. Jones Gips Godel, Escher, Bach is a wondrous book that unites and...
...People are potentially understandable at many levels (psychological, biological, biochemical...
...The principal characters of the dialogues are Achilles and a Tortoise, the protagonists of Zeno's fifth century B.C...
...we truly understand some process (seeing, understanding English, diagnosing medical problems, creating works of art) that requires intelligence, then we can write a computer program that embodies that process...
...Finally I realized that to me...
...Commonweal: 26...
...The idea is this: If...
...Some dialogues have the structure of particular Bach compositions...
...This sequence is a fascinating exercise in the relationship of figure and ground...
...They introduce in rather fanciful ways the ideas presented in the succeeding chapters...
...Along the way there are excursions into Zen, DNA, particle physics, and ant colonies...
...Godel, Escher, Bach is imbued with the mysteries...
...The structure of the dialogue "Little Harmonic Labyrinth" explains the critical idea of recursion as well as any English description could...
...I tried to reconstruct the central object, and came up with this book" (p...
...Strange Loops result from what Hofstadter calls "Tangled Hierarchies," from mixing the levels of understanding...
...then is the same as "What are the limits of rational thought...
...Besides the word HE itself...
...Can a mind (or computer program) fully understand itself...
...Godel and Escher and Bach were only shadows cast in different directions by some central solid essence...
...The question "What are the theoretical limits of Artificial Intelligence...
...To switch to a stronger metaphor of Hofstadter's, each of the ideas is seen to be a choice in a fugue, containing variations of the same themes, all forming a harmonious whole...
...Succeeding chapters explain and relate important ideas from the mathematics, logic, philosophy, and computer science in a playful, entertaining, insightful, and understandable way...
...In a way, this book is a statement of my religion" the author writes at the begihning of the book...
...Jones Gips Godel, Escher, Bach is a wondrous book that unites and explains, in a very entertaining way, many of the important ideas of recent intellectual history...
...Hofstadter begins the book with discussions of the three men whose names form the title...
...The dialogues, and the chapters of the book, are full of word play, musical puns, and logical puzzles...
...Throughout the book we are treated to drawings by Escher, by Magritte, and by the author, and to compositions by Bach and to the marvelous dialogues...
...Not only do the dialogues present the ideas, they embody the ideas as well...
...The content of the book effectively traces a major line of thought in the twentieth century...
...While the levels of people and computers do not precisely correspond, Hofstadter emphasizes that just understanding the interactions between the levels of a computer can help us understand ourselves and the world around us...
...Like any religion it has its faith and its mysteries...
...Though, I am reminded of the famous two-word dictionary definition of recursion: SEE RECURSION...
...Hofstadter develops novel insights and interconnections...
...Artificial Intelligence is the field in which people design computer programs that enable computers to perform tasks that we normally consider to require intelligence...
...All Cretans are liars' said Epimenides the Cretan" is an ancient example of a Strange Loop...
...In the second half of the century, I at least believe, 18 January 1980: 25 there has been an important shift of focus to computers and Artificial Intelligence...
...All consistent axiomatic formulations of number theory include undecidable propositions" is Hofstadter's paraphrase of Godel's Incompleteness Theorem, the proof of which contains a crucial Strange Loop...
...Computers too are understandable at many levels...
...The second part of the book concentrates on ideas from these fields...
...is a contemporary Strange Loop...
...Preceding each of the chapters of ¦Godel, Escher, Bach is a dialogue...
...Further, by attempting to write these programs we enhance our understanding of the processes themselves...
...There are many books Commonweal: 24 that are imbued with the faith of this religion...
...Indeed, this idea of a hierarchy of levels of understanding is crucial to Hofstadter's investigation of Strange Loops...
...A set that contains itself figures in Russell's Strange Loop...
...A central mystery is what Hofstadter calls "Strange Loops...
...It is a "religion" thai I and many other people share with him...
...These dialogues are immensely entertaining...
...A religion based on a faith in rational thought" certainly has the seeds of a Strange Loop, especially if a central mystery of the religion is that of the Strange Loop itself...
...Other characters enter the "dialogues," including a crab, Zeno, Charles Babbage (the 19th century English inventor of the computer), and "a brilliant young computer program" named SHRDLU...
...What English word begins with HE and ends with HE...
...Or, are the chapters merely footnotes to the dialogues...
...Thereupon the characters and the author discuss various aspects of the book...
...What is the rule for the sequence 1,3,7,12,18,26,35,45,56...
...To illustrate this point, Hofstadter himself enters the final dialogue and shows a copy of the book to the characters...
...Godel, Escher, Bach begins with a weaving of three strands—the works of Godel, Escher and Bach...
...paradox...
...Central to the faith is belief in logic, in mathematics, in computers, in rational thought...
...By the end of the book the author skillfully was woven many strands into a fabric containing an important portion of modern thought...
...The first part is concerned largely with ideas developed in logic, mathematics, and formal systems during the first half of the century...
...Godel's theorems and proofs, Escher's drawings, and Bach's compositions contain Strange Loops but are seen to be connected even more strongly...
Vol. 107 • January 1980 • No. 1
