Little Harmonic Labyrinth

Overview

This is based on the Bach organ piece of the same name. It is a playful introduction to the notion of recursive—i.e., nested—structures. It contains stories within stories. The frame story, instead of finishing as expected, is left open, so the reader is left dangling without resolution. One nested story concerns modulation in music—particularly an organ piece which ends in the wrong key, leaving the listener dangling without resolution. (p. ix)

While you read

Questions

Some questions are adapted from Curry and Kelleher's lecture notes on this chapter.

1. On the first page the Tortoise says “This is my favorite ride. One seems to move so far, and yet in reality one gets nowhere.” What other aspects of GEB is he referring to?
2. When Hexachlorophene J. Goodfortune introduces himself, there are a lot of Random Capitalizations. Can you detect any patterns?
3. What would it be like to live in a perfectly consistent world? How about an inconsistent one? What is our world like?
4. What do you think happened to the Weasel (p. 106) who took the popping-potion in our reality? Why did Hofstadter choose a weasel? What connotations does the weasel have?
5. What is the “Tunnel of Love” (p. 108)? Why is it sinister?
6. Why does the lamp have an “L” on it? What role does it end up serving in the story?
7. Relate what happens with wishes and the genies to pushing and popping stacks in a computer program.
8. How does the dialogue illustrate the object-language/meta-language divide?
9. Why does each Meta-Genie perform its task “twice as quickly” as the Genie before it?

Music

J.S.Bach (1685-1750)-Little Harmonic Labyrinth in C Major (Robert Köbler)

Unfortunately for GEB, we now believe that Bach did not write the organ piece called "Little Harmonic Labyrinth" (formerly BWV 591). It doesn't sound very much like Bach, and it's more likely one of the many pieces from that era that was misattributed to Bach. It might be by ➟ Johann David Heinichen.

Amusingly, the one recording on YouTube that attributes it to Heinichen also cuts off the ending, possibly tricking you like the Majotaur tricks Achilles. Except you're probably not tricked. It doesn't sound much like an ending at all, so it seems Achilles is a bit musically gullible.

Topics

Other nested works of fiction

This idea of "pushing" and "popping" into an alternate reality is of course not unique to GEB:

• The idea that you can "pop" out of what we think of as reality into a more real one is the central idea of ➟ The Matrix.
  • Justin Curry asked this question in his notes that may not have an answer: "Both in the Matrix and the Little Harmonic Labyrinth, blue and red are used as archetypal colors for chemical escapism. What is the deal?"

• ➟ Inception, of course, is a film known for having nested levels of story, dreams within dreams, that interact with each other -- so much that it has become an idiom to refer to nested levels of X as "X-ception", for any X.
  • But then, Inception didn't originate that story structure either -- some have noted that the same structure appears in the Donald Duck comic ➟ The Dream of a Lifetime.

Commentary

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• Billy Joel provides an alternate soundtrack:

  I've always been a bit disappointed that the piece Little Harmonic Labyrinth doesn't sound that much like the dialogue describes. However, I came across some music that does fit the dialogue, in what is probably an astonishing coincidence.

  Billy Joel wrote an album of classical piano pieces. Yes, that Billy Joel. It's honestly not bad. His Waltz #1 (Nunley's Carousel) has a structure that actually does push and pop a stack of themes, modulating to different keys, with a free-form part in the middle that revisits some themes out of order. If you were to draw a diagram of the music, it would look something like p. 126. And as it pops the second-to-last theme off the stack, it actually has a fake ending!

  This can't really anything to do with GEB -- unless Billy Joel is a secret fan -- but I recommend listening to this piece if you actually want to have the Majotaur experience. --rspeer

• I took some questions from Curry's notes that I don't actually know the answer to. For example, what is the deal with the Random Capitalizations? --rspeer