I re-read the classic from the late 1970s, 'Godel, Escher, Bach' by Douglas Hofstadter. This book won the author his Pulitzer prize when he was quite young. This book inspired a generation of Artificial Intelligence researchers, which 30 years later has evolved to research in 'cognition', i.e. how we perceive the world.
I re-read this book every few years and alternate it with the other book by Hofstadter titled, 'The Mind's I' - which is an anthology of essays from scientists and mathematicians regarding how the sense of self evolves in all of us. The themes range from mathematics to biology to physics to AI.
I am partial to the second book compared to the first. But both combined are a very modern, and deep take on the evolving view of our sense of self.
Every time I read these books, something new pops out for me to consider on its own merit.
In this current reading of Godel, Escher and Bach, Hofstadter's notes on Bach stood out. And in the main, his view of Bach's Crab Cannon. In the 1750s, King Fredrick II gave the visiting Bach a small piece of a tune and asked him to develop them into a multi-level fugue. Bach succeeded in creating a marvelous and complex piece which was later titled, "The Musical Offering'.
A famous piece out of this musical offering is the crab cannon. It is presented akin to a mobius strip. A mobius strip is an infinite loop. An ant crawling on the mobius strip would cover both sides of the strip in an infinite loop. It is the symbol for infinity that we all use in mathematics.
Picture of Mobius Strip below and ants crawling on them:
The following link is an excellent visual/musical illustration of the crab cannon. It is a 3 - 4 minute piece that is worth listening to and shows how Bach combines a tune that goes forward and backward into one fugue. It is clever, it is melodious and in is revelatory.
I have a couple of additional notes should this topic that might be of interest:
Note I. Recursion:
The main theme of Hofstatder's work is 'recursion.' It is a theme in computer science, mathematics and logic. It represents objects that repeat themselves in a self-similar way. An image of you looking into a mirror with a mirror behind you will show an infinite set of images of you looking at yourself. The most complete recursive mathematical set was created by Benoit Mandelbrot. It looks like this:
Note the recursion. Every little loop (even the tiniest) is a FULL repeat of the big picture with no loss of fidelity. The point that Hofstadter makes is that at sufficient levels of symbolic complexity, recursion leads to self-awareness. Bottomline: our sense of 'I' is a recursion.
Note 2. Strange Loops
Hofstadter later wrote an entire book just on the strange loop. Which is the second note here, my earlier review of his book:
Hofstadter later wrote an entire book just on the strange loop. Which is the second note here, my earlier review of his book:
3 comments:
Yes, I liked it very much. As I’ve said, it’s one of those books (in fact, all three sit on my shelf unread) that I know I should read.
Also, I very much liked the very helpful audio/video explanation of that Back fugue as it relates to endlessly recursive loops.
Finally, I’m with you re the ‘pluralistic’ approach to such a seemingly endlessly complex subject like consciousness. As Sandra Mitchell says regarding science today in Unsimple Truths, “It is incumbent on us to develop and refine an understanding of the kinds of explanations that science can provide of the multicomponent, multilevel, evolved, and robust complex systems, and correspondingly turn our decision making and policy strategies to that knowledge. Integrative pluralism is a step on the road to an expanded understanding of our complex world.”
And nothing we know of is more complex than the human brain.
Good stuff. Thanks.
I had all but forgotten the Mobius strip. Thanks for reminding. I cannot remember but when I learnt it in India it was also referenced to a sanskrit or Vedic symbol....just cannot recall - if it appears on the horoscope (" jadagam").
Very interesting and enjoyed reading.
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