I’ve been a bit under the weather the past few days, but I don’t want to get behind on this project. So… onward!

Current Assignment: Thursday, September 24 (where is the month of September disappearing to!!??)
Read: Contracrostipunctus and Chapter IV: Consistency, Completeness, and Geometry
Listen: 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.

Summary of Contrastipunctus
This dialogue is central to the book because it contains a set of paraphrases of Gödel’s self-referential construction and of his Incompleteness Theorem. One of the paraphrases of the Theorem says, “For each record player there is a record which cannot play.” The Dialogue’s title is a cross between the word “acrostic” and the word “contrapunctus,” a Latin word which Bach used to denote the many fugues and canons making up his Art of the Fugue. Some explicit references to the Art of the Fugue are made. The Dialogue itself conceals some acrostic tricks.

Escher Relativity

(Brief) Summary of Chapter IV: Consistency, Completeness, and Geometry
The preceding Dialogue is explicated to the extent it is possible at this stage. This leads back to the question of how and when symbols in a formal system acquire meaning. The history of Euclidean and non-Euclidean geometry is given, as an illustration of the elusive notion of “undefined terms.” This leads to ideas about the consistency of different and possibly “rival” geometries. Through this discussion the notion of undefined terms is clarified, and the relation of undefined terms to perception and thought processes is considered.

Discussion Ideas

  1. (for the Dialogue) GEB pp. 81 – For instance, Lewis Carroll often hid words and names in the first letters (or characters) of the successive lines in poems he wrote. Poems which conceal messages that way are called “acrostics”. Might this quote apply to this dialogue?
  2. Why does DRH keep apologizing about his use of the term “isomorphism”?
  3. What’s the problem with interpreting mathematical objects? In the case of the modified pq-system? In the case of Euclidean geometry? What’s wrong with our interpretation of a “straight line”?

(that’s enough to get you started)

Escher Relativity in Legos
Click on the photo to view how this image was created.

Up Next: For Monday, September 28
Read: Little Harmonic Labyrinth and Chapter V: Recursive Structures and Processes
Listen: 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.