I had the opposite reaction: I lost faith in the book's analytical process only ten pages in, when Hofstadter claimed that Bach's canon was a "strange loop" simply because it modulates to a higher key. Sure, if you keep doing this you can get to the same key, an octave higher, but that's only because pitch itself is periodic, repeating the same notes every octave. There's nothing unique or mysterious about Bach's canon in this regard; anything that modulates up a step has the same property (for example, the chorus to "Mandy" by Barry Manilow).

I think the far more interesting observation is that octaves in music work this way, where we as humans somehow perceive frequencies in a 2:1 ratio as "the same, but different." A 440 and A 880 aren't the same pitch, and we can clearly perceive the difference between them, and yet the seem "the same" to the point that we give them the same letter and think of them as the same. I find that very interesting and slightly mysterious.

Anyway, since music is my area of expertise (as opposed to the other things described in the book) I lost faith that his explanations of the other subject material wouldn't have similarly sloppy thinking. The impression I got was that, in an effort to weave an interesting and engaging narrative, he was too quick to see things as instances of these fanciful concepts like "strange loops."

He's discussing our perception of the tones, you might want to check out this entry on wikpedia to understand what he's referring to:

http://en.wikipedia.org/wiki/Shepard_tone

This is a common concept in music synthesis, as you can create an endlessly rising 'melody' by repeating only 1 octave of some properly constructed timbres. This is the 'strange loop' he's referring to.

Bach's canon is not a Shepard tone. A Shepard tone would have been a more credible example of a "strange loop" than Bach's canon. But "Godel, Escher, Shepard" doesn't have the same ring to it.

He actually does discuss Shepard Tones and the Shepard Scale in the book, and explains how he thinks they are related to Bach's compositions.

Near the end of chapter 20, there is an example of a harmony that, when looped, creates the illusion of an endlessly rising melody.

In this harmony, the loudness of each note in the melodies rises and falls so that the lower melodies feed into the the higher melodies and ultimately fade out. In our brains, we hear this as an endlessly rising melody.

Interesting! Reminds me of the criticism leveled against Freakonomics, and it's genuinely the first time I've heard it applied to GEB. What you're saying is obvious and makes perfect sense, I wonder if we're both missing something, or if Hofstader was playing a little too merrily outside his domain of expertise.

Edit: first time until I got lower down this thread, wow!

The Bach metaphor is really bad. I believe Hofstadter referees to the canon by which Bach inscribed "Ascendenteque Modulatione ascendat Gloria Regis" ("As the keys ascend so may the glory of the king also ascend"). Bach did not mean that after going up an octave the king's glory would have returned to it's starting point.

disclaimer: I did not read the book.

I agree - I think the Bach and Escher examples throughout the book are frequently a stretch. There's plenty of value outside of these areas, however. I think that without being an expert in each of the fields, we can use our critically thinking to see through the fanciful aspects and get to the core.

I think you might be right. The most valuable thing for me from the book was the explanation of Godel's theorem, and I really enjoyed all the language play. After that, I grew really uncomfortable with the comparisons to "this could be how the brain works."

I have the firm belief that figuring out how the brain works will not be accomplished through pure mathematics, but through scientific inquiry.

"I still think I'm missing something with breaking the record players, but based on my understanding it's a metaphor for incompleteness."

The record player is a Turing Machine interpreter. The "blowing up" is going into an infinite loop, or stopping the record incorrectly when it would have in fact terminated. The record player doesn't blow up if it A: runs a terminating program or B: correctly stops the record by determining the program will never halt. The differing record players represent the fact that you can write interpreters that will detect certain cases of infinite looping, but the halting problem prevents you from catching all cases. The repeated sequence in the book is:

1. A new "guaranteed safe!" record player is produced 2. A record is produced which breaks it (a program that loops but gets past the player is produced) 3. Goto 1.

At least, IIRC, it's been a few years since I read it.

Have you ever seen Hofstadter try to summarize the idea conveyed in the book? He really is not able to, and so I think the book pretty much boils down to "hey here's a bunch of weird/cool stuff." Which is not such a bad thing. But for me, there was a point where I had to stop reading, I think when he tries to independently derive propositional logic or something like that? (It has been a while.) I just remember finding it to be a tedious retread of something everyone already took for granted.

He's pretty explicit that the idea is: consciousnesses is a strange loop, and since it's sometimes impossible to understand a system from within that system, we may never be able to understand the human mind because we are trapped within human minds.

See also: "The Emperor's New Mind" - 'Consciousness is a quantum phenomenon since they're both really weird".

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Thank you!