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