Oh, wow...I read maybe a third of it in bits & peices!(and I 'almost' understood self-referential loops)...but, have you seen Hofstadter's 2nd book, "Metamagical Themas: Questing for the Essence of Mind and Pattern"? .a collection of essays on topics like 'how we tell what is true, relevant and meaningful'.... that man do go on!

(as a kid, I went to a barbershop with mirrors on both walls and was facinated by the infinite reflections! Maybe that explains something?)