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Sonata for Unaccompanied Achilles

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Overview Edit

A Dialogue which imitates the Bach Sonatas for unaccompanied violin. In particular, Achilles is the only speaker, since it is a transcript of one end of a telephone call, at the far end of which is the Tortoise. Their conversation concerns the concepts of "figure" and "ground" in various contexts—e.g., Escher's art. The Dialogue itself forms an example of the distinction, since Achilles' lines form a "figure", and the Tortoise's lines—implicit in Achilles' lines—form a "ground".

While you read Edit

Questions Edit

  1. What was the tortoise doing that caused Achilles to twist his neck?
  2. What was the tortoise's ingenious but degenerate solution to the HE puzzle?
  3. What was the tortoise's second solution to the HE puzzle?
  4. What is the solution to the ADAC puzzle?

Music Edit

Bach - Sonata no08:59

Bach - Sonata no. 1 for solo violin (Arthur Grumiaux)

The first few movements of BWV 1001, one of the Sonatas for Unaccompanied Violin.

Hofstadter's particular inspiration was Bach's sonatas for unaccompanied violin (BWV 1001-1006). I also recommend the sonatas for unaccompanied cello (BWV 1007-1012), especially in Yo-Yo Ma's famous performance.

Bach - Cello Suite No09:28

Bach - Cello Suite No. 1 in G Major BWV 1007

The first three movements of BWV 1007, Sonata No. 1 for Unaccompanied Cello, performed by Yo-Yo Ma.

All of these pieces of music have the property that you hear only the "figure", a melody performed on a single string instrument, but based on your familiarity with Western music, you can hear the "ground" of harmonies that go with this melody. You hear occasional bits of the harmony from chords played on multiple strings, but most of it is left implied.

As Achilles and the unheard Tortoise discuss at the end of the dialogue, you could imagine a perfectly nice-sounding harpsichord part supplying the harmony, and the result would still sound like Bach. But you don't need it.

Easter eggs Edit

The Tortoise's responses may be non-obvious around where Achilles is asking what instrument he plays. They get filled in for you when the same snippet of conversation happens later in the Crab Canon:

Achilles: Say, don't you play the guitar?
Tortoise: Fiddle. It makes a big difference, you know.
Achilles: Oh, well, it's all the same to me.
Tortoise: To be precise, one has no frets.

This appears at the bottom of p. 200. Because of the structure of the Crab Canon, these lines have double meanings -- they also appear in the opposite order, forming a different conversation, at the top of the page.

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