Gödel, Escher, Bach

Rob Speer

This is the course page for the discussion-based seminar, SP.258: Gödel, Escher, Bach. The course is taught in ESG, by Rob Speer.

Class meetings: WF 2-3pm
Location: 24-622 (ESG Bio Room)

Relatively small link to this page: http://torg.media.mit.edu/rob/index.php/GEB

Contents

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Further reading

Here are my recommendations for further reading, in books by Hofstadter or by others.

If you want more recreational math
  • Metamagical Themas, by Hofstadter. A hodgepodge of all things Hofstadter, collected mostly from his Scientific American columns. Includes the group theory of Rubik's Cubes, an attempt to explain LISP to a general audience, a theory of fonts, and the beginning of his "letter spirit" analogy puzzles.
  • The Last Recreations, by Martin Gardner
  • Just about anything by John Conway, but try The Book of Numbers.
If you want more about languages
  • Le Ton beau de Marot, by Hofstadter. This book is about translation and the endless creativity involved in using natural languages. It's a lot of fun, even though Hofstadter's poetry sucks.
  • The Unfolding of Language by Guy Deutscher. The clearest, most interesting overview I have ever seen of how and why languages change, all done without unnecessarily assuming untested theories like Universal Grammar.
If you want more philosophy
  • The Mind's I, edited by Douglas Hofstadter and Daniel Dennett. A whirlwind overview of modern philosophy built out of many essays and short stories, with Hofstadter's commentary added after each chapter.
  • Infinity and the Mind by Rudy Rucker. Okay, I haven't read this, only skimmed it in a bookstore so far, but Rudy Rucker seems to have a freewheeling writing style reminiscent of Hofstadter.
If you want more AI
  • Fluid Concepts and Creative Analogies by Hofstadter and his students. This is the most "academic" of Hofstadter's books, and you probably won't get anything out of it unless you are specifically interested in analogy-based AI.
  • The Society of Mind by Marvin Minsky. Minsky presents his ideas on the structure of the mind in a unique format -- one chapter per page, with copious references between chapters.
  • The Age of Spiritual Machines, by Ray Kurzweil. Dated by its 90's optimism, but still an interesting read (and also built around dialogues).

I don't recommend reading Hofstadter's new book, I Am A Strange Loop, after GEB, because it duplicates too much of its content.

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Links

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Readings and music

These are the chapters from the book and the music I chose to accompany them. I've included the BWV numbers so you can find your own darn recording. If you're at MIT, you can download the music files directly, either by clicking on the links or by getting the contents of this directory.

Introduction
Brandenburg Concerto No. 5 (BWV 1050), for no particular reason except that it's a good Bach piece to start things off.
1. Three-Part Invention
The Three-Part Ricercar, from the Musical Offering (BWV 1079), introduces the King's theme (which appears in nearly every piece of the Musical Offering) and the fugue style in general.
2. Two-Part Invention
Two-Part Invention in C major (BWV 772)
3. Sonata for Unaccompanied Achilles
Sonata No. 1 for solo violin: Adagio (BWV 1001). If an accompanied version of this exists somewhere, I don't know where to find it.
4. Contracrostipunctus
Contrapunctus 19 from the Art of Fugue (BWV 1050). This performance abruptly ends in the same place that the score ended due to Bach's death. Bach left his name in the music, as the German notes B-A-C-H, a few measures before the end.
5. Little Harmonic Labyrinth
The Little Harmonic Labyrinth turns out not to be by Bach at all! It was written instead by his much lesser-known contemporary, Johann David Heinichen. Disappointingly, it doesn't even have a fake resolution near the end, as the dialogue implies. Also, it's boring.
A completely unrelated piece, however, does have a clear "pushing and popping" structure to it, and a fake resolution: Waltz #2 by Billy Joel. Yes, that Billy Joel, retired from pop and writing classical music. Allow Achilles and the Tortoise one more anachronism and pretend this is what they're listening to.
6. Canon by Intervallic Augmentation
Bach never multiplied the intervals of a theme by 3 1/3. He did multiply them by -1 in this canon by exact inversion, the Canon Perpetuus from the Musical Offering. An effect of the exact inversion is that the piece has to oscillate constantly between major and minor chords, and technically it can't end.
7. Chromatic Fantasy, and Feud
The title is a pun on the Chromatic Fantasia and Fugue (BWV 903). Hofstadter acknowledges that the dialogue "bears hardly any resemblance, except in title" to the music.
8. Crab Canon
Hofstadter's entire dialogue structure emerged from writing a dialogue based on the Musical Offering's Crab Canon (Canon Cancrizans).
9. A Mu Offering
If I can pick any piece of the Musical Offering I want to listen to, it's the Allegro from the Trio Sonata at its center. It's mostly a free composition, but listen closely for where the King is hiding.
10. Prelude...
11. ...Ant Fugue
The Prelude and Fugue in C Major (BWV 846) open the first book of the Well-Tempered Clavier. "ATTACCA" is notated in between them in the score, meaning you should progress immediately from the prelude to the fugue.
12. English French German Suite
English Suite No. 2 in A Major, Prelude (BWV 807). You won't hear any Jabberwocky here, just a lively Bach keyboard piece.
13. Aria with Diverse Variations
This chapter refers extensively to the Goldberg Variations (BWV 988), an extensive set of variations on an aria. The 30th and final variation is a straightforward statement of the theme called the Quodlibet, after which the variations continue on with a "post-ending ending", the Finale.
In the Glenn Gould recording (which I would post here if DRM were not interfering with education), you can in fact hear him singing along under his breath.
14. Air on G's String
Bach's Air on the G String (BWV 1068) is a soothing string piece, much unlike Gödel's unsettling mathematical string.
15. Birthday Cantatatata...
The characters refer to a cantata Bach wrote for the birthday of the King of Poland. When you track it down (Wikipedia reveals that this person was in fact better known as the King of Saxony), it leads to Cantata 206 (BWV 206), an obscure but wonderfully joyful cantata.
16. Edifying Thoughts of a Tobacco Smoker
The poem really is by Bach, and he even supposedly set it to music, but I would have no idea where to find it.
17. The Magnificrab, Indeed
The title is a pun on the Magnificat in D Major (BWV 243), whose translation begins "My soul doth magnify the Lord". ("My soul! How you magnify the Crab!")
18. SHRDLU, Toy of Man's Designing
A pun on Jesu, Joy of Man's Desiring, a well-known movement from Cantata 147 (BWV 147).
19. Contrafactus
Contrapunctus 12 from the Art of Fugue can be played either in its standard form ("rectus") or inverted on the scale ("inversus"). They are usually performed back-to-back in that order, but clearly they would be performed in the other order if up were down. Or would they?
20. Sloth Canon
This is the name Hofstadter gave to the Canon by Augmentation in the Musical Offering. Like in the dialogue, one part is twice as slow and inverted with respect to another part, while the third part is free.
Ch. 20 itself refers to the Musical Offering's "Endlessly Rising Canon"; you can hear it in fact rise endlessly when performed on the Shepard scale. (This recording is on a synthesized Shepard harpsichord, and performs the canon 12 times so that it cycles around the scale twice.)
21. Six-Part Ricercar
A dialogue full of deep structure and subtle tricks, based on a fugue that could be described the same way: the Six-Part Ricercar that ends the Musical Offering.


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Additional readings from the class

  • Ch. 5 of Le Ton Beau de Marot (between Part 1 and Part 2)
  • Chapters from Metamagical Themas (toward the end of the class): A Coffeehouse Conversation on the Turing Test and Who Shoves Whom Around Inside the Careenium?
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Translation assignment

(due after reading Ch. 5 of Marot and Ch. 12 of GEB)

Pick a section of GEB -- from a chapter or dialogue -- and "translate" it into some constrained language. There should, of course, be some parts of your translation that require the kinds of clever shifts that Hofstadter talks about in Marot.

Some possible constraints:

  • A lipogram: forbid the letter "e" (or possibly even more letters!)
  • The Game of Four: use only words of four letters or less
  • Use only words of one syllable
  • "Ander-Saxon": avoid all words with Latin or Greek roots (tricky)

Here's mine from last year: GB, Part VIII: Typographical Counting Math

An impressive constrained piece of writing, including several constrained translations, is the story "Cadaeic Cadenza".

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Course expectations

This course is graded pass/fail. Getting a "pass" grade is very straightforward:

  • Attend the seminar. You can miss two class sessions and still pass; more than that, and you'll have to make up the missed sessions somehow.
  • Do the reading before each class, and participate in discussions.
  • Complete the assignments that I'll give out at various times (no more than once a week).

The course text is, of course, the book Gödel, Escher, Bach, by Douglas Hofstadter. You may be able to find the book at a local used bookstore, like Rodney's or the Harvard Bookstore; you can also, of course, order it online.

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