Wednesday, March 10, 2010

This statement is false

Last night I picked up the book, Gödel, Escher, Bach: an Eternal Golden Braid (A Metaphorical fugue on minds and machines in the spirit of Lewis Carroll) by Douglas R. Hofstadter. I had recently watched a documentary on the study of infinity and one of the four mathematicians featured was Kurt Gödel. I love the work of M.C. Escher, Bach, and Lewis Carroll (aka Charles Lutwidge Dodgson), so when I saw all four of these names mentioned within a single title I was fascinated. The book is quite a tome, and I've only read the first chapter thus far, but it is very insightful, and I'm looking forward to reading the rest! Hofstadter's aim is look into the nature of infinity and contradiction. Within the universe there exist 'strange loops' that defy our understanding. Simple statements such as 'this statement is false' or 'The following sentence is false. The preceding sentence is true.' can be eerily complex.

Here are some works by M.C. Escher that play along this theme. There are plenty of places you can read about the man and his works, so I'm not going to attempt to put it all here, but you can read about him on plenty of places on the net. There's a good article on Squidoo.

Escher did a number of pieces displaying the Moebius effect. In 1858, two German mathematicians, August Ferdinand Möbius and Johann Benedict Listing, independently discovered what is popularly known as the Möbius strip. The characteristic feature of Möbius strip is that it is a surface with single side. In its most simplest form a Moebius strip can be constructed out a a strip of paper which is twisted halfway and the ends joined together. If one were to start tracing a surface, by the time they complete one trace they find that they are tracing the opposite side of the paper than the one from which they started. Go another round and you come back to the same side.

All of this strangely reminds me of the ancient symbol of the Ouroboros, the snake swallowing it's own tail.

Anyway, the third person that Hofstadter focuses on is Bach because he had a way of showing the infinite within music. Here is one piece that is referred to in the book, from Bach's A Musical Offering.

The fourth person (who is mentioned in the subtitle) is Lewis Carroll. I love Carroll (or should I say Dodgson), and I am very much looking forward to the new Alice in Wonderland movie that is coming out soon (all the more so because Johnny Depp is my favorite actor of all time).

I had just put the following quote on my facebook status the other day and I think it very much sums up the book I am about to delve into:

“If I had a world of my own, everything would be nonsense. Nothing would be what it is, because everything would be what it isn’t. And contrary wise, what is, it wouldn’t be. And what it wouldn’t be, it would. You see?”–Alice, Alice in Wonderland.

1 comment:

Dionne said...

These infinity puzzles amaze me. I love trying to work out where they start and where they end, which is impossible!


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