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This is a series on the book Gödel, Escher, Bach: An eternal golden braid by Douglas Hofstadter.  

Earlier diaries are here

Today, we will look at Prelude ,   p. 275 - 284.

From the Overview:

This dialogue attaches to the next one.  They are based on preludes and fugues from Bach's Well Tempered Clavier . Achilles and the Tortoise bring a present to the Crab, who has a guest: The Anteater.  The present turns out to be a recording of the WTC; it is immediately put on.  
As they listen to a prelude, they discuss the structure of preludes and fugues, which leads Achilles to ask how to hear a fugue, as a whole, or as a sum of parts? This is the debate between holism and reductionism, which is taken up in the Ant Fugue

Some questions and comments to get the ball rolling:
p. 277 - bottom - all integers appear somewhere in the decimal expansion of pi.

p. 278 - bottom - Achilles' last statement on this page seems dubious.

p. 279 - top - the 'calculations involving the motions of all the molecules' is done in by two things: First, no computer is big enough; second, quantum mechanics.

   - the Tortoise's statement just after the formula is an isomorphism to Fermat's notation in the margin.

  - middle - Achilles statement about EITHER working  - well, if either works why continue?

p 282 - top - a fugue is an isomorphism to an anthill

Originally posted to plf515 on Sun Mar 29, 2009 at 03:34 AM PDT.

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