One of my favorite books is the astonishingly imaginative Gödel, Escher, Bach: An Eternal Golden Braid, by Douglas R. Hofstadter. This Pulitzer-Prize-winning book, published in 1979, is an extended meditation upon the underlying connections between the work of the three men mentioned in the title – Johann Sebastian Bach (who needs no introduction), the Dutch graphic artist M.C. Escher, and mathematician Kurt Gödel. Hofstadter, who inherited the prestigious editorship of Scientific American’s Mathematical Games column from the incomparable Martin Gardner, has described his inspiration for the project:
“I realized that to me, Gödel and Escher and Bach were only shadows cast in different directions by some central solid essence. I tried to reconstruct the central object, and came up with this book.”
It is hard to describe the tone and content of the book – it is at times witty and playful (much of the book takes the form of imaginary dialogues, a la Lewis Carrol, between Achilles and the Tortoise, and there is a great deal of word play and hidden puzzles), at times dense and didactic, but always unflaggingly, utterly brilliant. Really, and I mean this, GEB is so startlingly clever and original that at times it quite literally – and I do not ever misuse the word “literally” – took my breath away.
It is hard to say in a few words what the book is about. It is about about recursion, logic, music, art, fractals, DNA, number theory, formal systems, computer science, artificial intelligence, and much, much more, but all with one overarching theme, as described by the author:
“GEB is a very personal attempt to say how it is that animate beings can come out of inanimate matter. What is a self, and how can a self come out of stuff that is as selfless as a stone or a puddle?”
Here is a tiny tidbit, from the chapter Figure and Ground, which is about recursively enumerable systems, and positive vs. negative definitions of sets. Can you characterize the following set of integers?
1 3 7 12 18 26 35 45 56 69 …
If you have not read this book, your life and mind are the poorer.