Wednesday, February 6, 2013

Gödel, Escher, Bach: Introduction

I have to start out this installment with a comic from xkcd, found by a guy in our Facebook reading group:



Yep, nailed it. Our group discussion wandered through self-referential words and the difference between a fugue and a canon, and landed on Gödel's Incompleteness Theorem, which no one really claimed to fully understand, but lots of us wrestled with. Here are some resources and links we found helpful, and my thoughts on the three sections:

Bach:

I really loved the Bach section -- it was so interesting to learn about how these musical compositions really begin with math problems, and how composers would set challenges for each other that could be solved mathematically. The anecdote about Bach sitting down to extemporaneously compose such a complicated canon for the King of Prussia was almost unbelievable, but I'm willing to swallow it. Then again I was a Lance Armstrong supporter for years. Maybe I'll believe anything of someone I want to be brilliant.

Here's a recording of that six part fugue, RICERCAR:



Here's a video of Bach's never ending canon, which rises in a "strange loop," mentioned on page 10:



Escher

I found the concept of "strange loop" easiest to understand visually, in Escher's work. Here is a link to a large image of Escher's "Waterfall" and also a video of Metamorphose, by Escher, hanging in a post office:



Gödel

I fell off the book backward at the Incompleteness Theorem, I'll admit. I was helped by several different ways of looking at it, including this post. Here's an interesting discussion of Gödel, by Stephen Hawking, called "Gödel and the End of the Universe."

I loved the stuff about Ada Lovelace and early computers. Was intrigued by predictably intrigued by L'Homme Machine, enough to buy a used copy in the French. The strange loops elude me at this point, but I think all of us in the group are hoping to understand the mathematics parts more fully as we go along. Comforted by the fact that "This is only the introduction!" we persevere.

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