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Gödel, Escher, Bach: An Eternal Golden…
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Gödel, Escher, Bach: An Eternal Golden Braid (original 1979; edition 1999)

by Douglas R. Hofstadter

MembersReviewsPopularityAverage ratingConversations / Mentions
11,30599382 (4.34)2 / 218
Douglas Hofstadter's book is concerned directly with the nature of "maps' or links between formal systems. However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.… (more)
Member:Apollo11
Title:Gödel, Escher, Bach: An Eternal Golden Braid
Authors:Douglas R. Hofstadter
Info:Basic Books (1999), Edition: 20 Anv, Paperback, 832 pages
Collections:Your library
Rating:*****
Tags:None

Work details

Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter (1979)

  1. 101
    Cryptonomicon by Neal Stephenson (Zaklog)
    Zaklog: Cryptonomicon strikes me as the kind of book that Hofstadter would write if he wrote fiction. Both books are complex, with discursive passages on mathematics and a positively weird sense of humor. If you enjoyed (rather than endured) the explanatory sections on cryptography and the charts of Waterhouse's love life (among other, rarely charted things) you should really like this book.… (more)
  2. 60
    Logicomix: An Epic Search for Truth by Apostolos Doxiadis (tomduck, EerierIdyllMeme)
    EerierIdyllMeme: An obvious suggestion (surprised it's not here already). Both are creative and fictional riffing off of formal logic and incompleteness.
  3. 50
    Metamagical Themas: Questing for the Essence of Mind and Pattern by Douglas R. Hofstadter (JFDR)
  4. 40
    Incompleteness: The Proof and Paradox of Kurt Gödel by Rebecca Goldstein (michaeljohn)
  5. 20
    A Mathematician Reads the Newspaper by John Allen Paulos (heidialice)
    heidialice: GEB is a thousand times as intense, but if you enjoyed the parts about self-referentiality it's worth a skim. Conversely, if GEB is just too much, Paulos' concise introduction to the theme is very accessible.
  6. 00
    Things to Make and Do in the Fourth Dimension: A Mathematician's Journey Through Narcissistic Numbers, Optimal Dating Algorithms, at Least Two Kinds of Infinity, and More by Matt Parker (Lorem)
    Lorem: Things in 4D I consider a more accessible version of GEB in its breadth and how it does get to complex topics. If you enjoyed the more complicated parts of 4D, definitely look at GEB and if GEB was a little too much, 4D might remind you why math(s) are never boring… (more)
  7. 00
    The Gold Bug Variations by Richard Powers (hippietrail)
  8. 33
    A New Kind of Science by Stephen Wolfram (Anonymous user)
  9. 01
    Dirk Gently's Holistic Detective Agency by Douglas Adams (EerierIdyllMeme)
    EerierIdyllMeme: A few similar themes (Bach, human cognition) come up in similar ways.
  10. 03
    The Flanders Panel by Arturo Pérez-Reverte (P_S_Patrick)
    P_S_Patrick: Arturo Perez-Reverte has recieved inspiration for his excellent mystery thriller from Hofstadter's Godel Escher Bach, even without some of the chapter introduciton quotes, that much is clear. He uses the bewildering Escherian theme of worlds within a world, Godels incompleteness theorum is alluded to in the monologue of one character, and Bach is discussed in relevance to the mystery too, along with a few miscellaneous paradoxes which are also slipped in, in a similar spirit in which they permeate the more complex non-fictional work. Non-fiction readers who have enjoyed GEB should be amused by the Flanders panel, and I think they should enjoy it even if they do not often dip into fiction. It would be harder to recommend GEB to fans of the Flanders Panel, due to its sheer length, but if you were intrigued by the themes in the story then it should at least be worth finding GEB in a library and dipping into it.… (more)
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English (93)  Hebrew (1)  Spanish (1)  Danish (1)  Swedish (1)  All languages (97)
Showing 1-5 of 93 (next | show all)
It's beginning to show its age, and the dialogs are less charming than I remember, but still it's quite combination of ideas skillfully blended. ( )
  le.vert.galant | Nov 19, 2019 |
いや,かれの御手は広く開かれて,御心のままに,惜し・なく与えられる​
  AAAO | Nov 14, 2019 |
Never mind the Escher and Bach stuff; that’s just window dressing. This book is about Godel’s Theorem. And wow, what a book.

Imagine a glorious future in which, by means of magic and genetic engineering, the human species is transformed into a better, smarter, faster, more beautiful, more creative, more moral, stronger, happier species, a more alive species. We make Elysium, then we live in the Elysium we’ve created.

In this Arcadia, this Heaven, this Eden, this Platonic Form of the world animated and electrified by benevolent intelligence, you walk across grassy fields and you see the whole thing, The Dream:

Everyone is wearing flowing white robes. (Why? Just because.)

Over there athletic people engage in athletic contests, their good-natured competition embodying grace, fluidity, and the confidence of a well-disciplined, healthy body.

Over here, mathematicians use sticks to draw in the dirt on a river bank, proving astoundingly beautiful and useful new theorems.

In another direction a young man or woman lounges, back against a tree, releasing sweet strains of melody into the air by means of some sort of elegant string instrument.

Are you with me?

Okay.

In that universe, every non-fiction book is this good.

What’s it about?

It’s about, principally, Godel’s Theorem. The other stuff, at least in the first part (Escher, Bach, etc.), is just add-ons. Godel’s Theorem is often mis-characterized as “disproving all of mathematics!” or some similar nonsense. No. It says something about formal mathematical systems, systems of clearly stated axioms with clearly stated rules of inference for deriving implications of the axioms. The theorem essentially says that any formal system sophisticated enough to be used for number theory - reasoning about integers - either has internal inconsistencies or is unable to prove every truth in number theory.

This does not “Undercut all of mathematics” or whatever. It simply means that a consistent formalistic approach to mathematics can never derive all mathematical truths. There are some truths that can only be proven in other ways. Indeed, Godel shows how to prove some of those truths by reasoning outside formal systems!

To prove it, Godel had the profound insight that any formal system can be re-interpreted as a set of numbers and arithmetical operations on them, so formal number theory talks about itself! This is so cool.

E.g., suppose your formal system has the symbol string x#@^&?G-!y. (This might mean, say, “x is the largest number in the prime factorization of y.”) We also have a rule that allows us to derive x<=y (x is not greater than y) from the first string. But we also can interpret x as 5, # as 0, @ as 2, and so on, so the initial symbol string can be interpreted as a number. And so the second string is a number that we can derive from the first. So the rules of inference in this interpretation are arithmetic operations on numbers. Thus we can apply mathematical reasoning to the system and derive conclusions about the symbol strings it will generate and those that it won’t generate.

A simplified analogy: Suppose that we can prove - by reasoning outside the formal system - that the system will never produce a string whose number is prime. What Godel proved, in this analogy, was there is always a symbol string that asserts “N is a prime number” (in the first interpretation) whose number was N (in the second interpretation). Thus, if the statement is true, the formal system will never prove it!

(It is possible to verify that a well-designed system will never "prove" a false statement, so you can avoid that problem.)

In fact, no only do such true-but-formally-unprovable statements exist, in any formal system complex enough to be useful, but an infinity of them exists!

It was the idea of reinterpreting the symbols as numbers that was Godel’s real stroke of freakin’ genius. The theorem is based on that.

Anyway: The next time someone tells you, “Godel’s Theorem proves that all mathematics is invalid,” or whatever, just give them a wedgie and move on. All it proves is that a certain approach to mathematics cannot prove everything. Which, unless you had unrealistic ambitions for it in the first place, is not that surprising. ( )
1 vote TFleet | Jun 17, 2019 |
Notes whilst reading it.
The first part on logic is a bit tough going in places. Take home message for me was: is order innate (normal) or depending on one's perspective? i.e. will supposed other worlds be able to make sense of a the record man sent into space. Will Bach be order for them too, or will they see order in Cage's creations?
A bit dated as the author uses examples of records and jukeboxes to illustrate his stories. I get it; does a teenager?
  robeik | May 10, 2019 |
This is certainly the greatest book of popular science I've encountered or heard of yet--it's accessible, engaging, playful, but also very deep and original in its analysis. It gives brief intellectual history where necessary, and repeats the same arguments in many surprisingly different ways for comprehension.

But its ultimate ignorance/dismissal of the social world, assertion of objective meaning, and computational theory of mind force me to give it a lower rating. ( )
1 vote alexanme | Dec 9, 2018 |
Showing 1-5 of 93 (next | show all)
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» Add other authors (23 possible)

Author nameRoleType of authorWork?Status
Hofstadter, Douglas R.primary authorall editionsconfirmed
尚紀, 柳瀬Translatorsecondary authorsome editionsconfirmed
Feuersee, HermannTranslatorsecondary authorsome editionsconfirmed
Jonkers, RonaldTranslatorsecondary authorsome editionsconfirmed
Wahlén, JanTranslatorsecondary authorsome editionsconfirmed
Wolff-Windegg, PhilipTranslatorsecondary authorsome editionsconfirmed
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Frederick the Great, King of Prussia, came to power in 1740.
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In its absolute barest form, Gödel's discovery involves the translation of an ancient paradox in philosophy into mathematical terms. That paradox is the so-called Epimenides paradox, or liar paradox. Epimenides was a Cretan who made one immortal statement: “All Cretans are liars.”
Whereas the Epimenides statement creates a paradox since it is neither true nor false, the Gödel sentence G is unprovable (inside P.M.) but true. The grand conclusion? That the system of Principia Mathematica is “incomplete”—there are true statements of number theory which its methods of proof are too weak to demonstrate.
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Il libro che ha svelato a una immensa quantità di lettori, in tutto il mondo, gli incanti e le trappole di un’Eterna Ghirlanda Brillante i cui fili si chiamano intelligenza artificiale, macchina di Turing, teorema di Gödel. Una «fuga metaforica» nel variegato mondo che si dispiega fra la mente, il cervello e i computer.

«Ogni due o tre decenni un autore ignoto produce un libro di tale profondità, chiarezza, vastità, acume, bellezza e originalità che subito esso viene riconosciuto come un avvenimento di prima importanza: Gödel, Escher, Bach è un’opera di tal genere… La struttura di questo libro è satura di complicato contrappunto non meno di una composizione di Bach o dell’Ulisse di Joyce»

MARTIN GARDNER, «Scientific American»
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