What Makes Music, Math, and Art a Must-Read for IMO Gold Medalists?

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SUMMARY

The book "Gödel, Escher, Bach: An Eternal Golden Braid" (GEB) is highly regarded by International Mathematical Olympiad (IMO) Gold Medalists for its dense and entertaining exploration of complex concepts such as infinity, self-reference, and strange loops. The author, Douglas Hofstadter, uses creative examples, including Escher's artwork and Bach's music, to illustrate these ideas. Readers are encouraged to approach the book slowly, digesting each chapter to fully grasp the intricate dialogues and the underlying structure of the arguments presented. GEB serves as a model for understanding cognitive processes and is essential for anyone interested in the intersection of music, mathematics, and art.

PREREQUISITES
  • Familiarity with basic concepts of infinity and recursion
  • Understanding of self-referential statements
  • Knowledge of Escher's artwork and Bach's musical compositions
  • Interest in cognitive science and philosophy of mind
NEXT STEPS
  • Read "Gödel, Escher, Bach: An Eternal Golden Braid" by Douglas Hofstadter
  • Explore the concept of strange loops in cognitive science
  • Investigate Gödel's incompleteness theorems and their implications
  • Analyze the relationship between art and mathematics through Escher's works
USEFUL FOR

This discussion is beneficial for mathematicians, cognitive scientists, philosophers, and anyone interested in the interplay between music, mathematics, and art, particularly those seeking to deepen their understanding of complex intellectual concepts.

PrudensOptimus
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Why was this book among the favorite books of IMO Gold Medalists?
 
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I am currently working on a re-read of GEB, first time was ~20yrs ago. It is a challenging read, it is very information dense, but also very intertaining.

Take a deep breath and dive in.
 
So why do IMO guys like this book again? I'm on like page 22, so far I have understood that it's about infinity works of Escher and Bach and Godel.

Escher's paintings are amazing, that waterfull, bach's whatever music piece i didn't understand, and Godel's weird proposal...
 
Who or what is IMO? I can't tell you why they like it, I can only tell you why I like it.

It remains my best model of how the brain works, he explains this by using an anthill as an example.

Then there is the palindrome dialog called Crab Canon, 2 pages of dialog which reads the same forwards and BACKWARDS.

This book is full of information presented in a very creative fashion. I Would recommend reading it slowly, digesting each chapter before starting the next. If you have interest in strange loops, this book is required reading.
 
It is a challenging intellectual exercise to read GEB. Some of his points are very interesting, and it presents Godel's theorem so that it is relatively easy to understand the proof as opposed to just the theorem.

Sometimes the diagogues between tortoise and achilles seem a bit pointless, but then something clicks and you can see the structure and the point the author is making.
 
It is fascinating how the concepts of the strange loop as presented in Music, Math and Art are blended together in a work which becomes an example of the strange loop in litureature. This is all about self referential statements in many different forms.

It is a challenging read, but worth the effort.
 

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