Below is a “teacher’s reference guide” for the ideas found within The Latticework’s Mathematics discipline.
The idea is to help keep these valuable ideas top of mind so that they can hopefully become second nature. It’s also a great exercise to distill some of these rather complex ideas into as simple (but no simpler!) a form factor as possible, getting to its true essence.
Douglas Hofstadter sets out to show that if life can evolve out of simple chemicals and cells and consciousness out of neurons, it is not a far cry to believe that computers will some day gain human intelligence. He explores an amazing array of topics including self-recursion and reduction; all within the structure of the works of Gödel, Escher and Bach. The book follows a unique layout in that he creates a dialogue between fictitious characters which is meant to set the stage for the lesson he is discussing the the following chapter.
I cannot do this book justice in trying to summarize and distill the lessons throughout. I know when I am out of my league and implore you to watch the following videos taught at MIT around GEB. Also found here, on YouTube if you want to watch at double speed.
What I got out of it:
An absolutely fascinating and thought-provoking book. Hofstadter discusses so many topics which were new to me and out of my general area of knowledge and comfort zone. It is refreshing to read about an area that I knew so little about and it gave me a much deeper insight into the beauty of mathematics, art and music than I had ever understood.
Interested in seeing some of M.C. Escher’s amazing works? Artsy is a beautiful website which aims to make the world’s art accessible to everyone. They have hundreds of pieces from some of the world’s most renowned artists. Definitely check them out