GÖDEL, ESCHER, BACH: An Eternal Golden Braid
Douglas R. Hofstadter writes in his own updated preface of the 20th anniversary edition, how surprised he is over the interpretations of his now famous tome. I would not dare to comment on what he is up to, I will share some thoughts that occurred to me from reading the introduction.
It seems the key theme is strange loops and how they show up every time someone tries to express conscious thought. The three models that Hofstadter chose to include in this book, provide the reader with specific examples of strange loops in action.
J.S. Bach wrote Canons and Fugues that were based on expanding or contracting musical tones that eventually returned the listener to the original key. M.C. Escher created visual equivalents to Bachs fugues, whereby the viewer was led on an impossible journey between what seemed to be reality and fantasy, only to be returned to the beginning at the end.
Kurt Gödel was a mathematician that dispelled the authors Bertrand Russell and Alfred North Whiteheads intent to try and remove ambiguity in the language of math in their book Principa Mathematica. (P.M.) Gödels famous argument that all Cretans are liars was a paradox that Russell and Whitehead could not shake loose from. The source of the paradox is that no one can refute the statement. In the case of P.M., Gödel said that there are true statements of number theory which its methods of proof are too weak to demonstrate.(G.E.D. Hofstadter. Pg.18) Metamathematics became the new term for studying math because the very awareness of studying it was accepted as a hybrid of actually doing it, similar to the revolutionary ideas posited in relativity and quantum mechanics. The idea that we as observers forever change the subject from our observation, is another example of strange loops. Shrödingers Cat comes to mind as the Physics paradox of the century.
I look forward to the many constructs that Hofstadter has created like theTortoise and Achilles to demonstrate his thesis in the coming chapters.