Godel, Escher, Bach by Douglas R. Hofstadter

Frankly, Achilles, being rather conservative and orthodox myself, I was a bit concerned about that very point on first receiving the letter. In fact, I suspected at first that here was an out-and-out fraud. But on second thought, it occurred to me that not many types of people could manufacture such strange-sounding and complex results purely from their imagination. In fact, what it boiled down to was this question: “Which is the more likely: a charlatan of such extraordinary ingenuity, or a mathematician of great genius?” And before long, I realized that the probabilities clearly favored the former.

So says “Crab” in one of the many “Dialogues” that Hofstadter put in-between the chapters of this long and difficult book. And just as Crab speculates on the intentions of a fictional letter-writer, I came to find myself making the same speculations about Hofstadter himself. A charlatan of extraordinary ingenuity? Or a mathematician of great genius? Perhaps more than a morsel of both.

Truth be told, I have found books on quantum mechanics to be clearer and easier to understand. The author is not so much dealing with math, but with the underlying structure that makes math work. For a while this is fun - a little like brain teasers. Like trying to do math in Base8 instead of Base10. But soon it gets too complicated (at least for me), and then you realize you have 500 more pages to go.

The fatal flaw is that Hofstadter assumes that the underlying structure of math IS the underlying structure of reality -- and that’s where all his comparisons between Godel, Escher, and Bach begin to stretch beyond my patience. In Hofstadter’s world math equals computer science equals the human brain equals objective reality, and those are leaps that I’m not willing to make, no matter how many creative word games he can weave around them.

It’s not until he starts talking about how the human brain interprets art that he once and only captured my attention.

There is a strange duality about the meaning of a piece of music: on the one hand, it seems to be spread around, by virtue of its relation to many other things in the world -- and yet, on the other hand, the meaning of a piece of music is obviously derived from the music itself, so it must be localized somewhere inside the music.

The resolution of this dilemma comes from thinking about the interpreter -- the mechanism which does the pulling-out of meaning. (By “interpreter” in this context, I mean not the performer of the piece, but the mental mechanism in the listener which derives meaning when the piece is played.) The interpreter may discover many important aspects of a piece’s meaning while hearing it for the first time; this seems to confirm the notion that the meaning is housed in the piece itself, and is simply being read off. But that is only part of the story. The music interpreter works by setting up a multidimensional cognitive structure -- a mental representation of the piece -- which it tries to integrate with pre-existent information by finding links to other multidimensional mental structures which encode previous experiences. As this process takes place, the full meaning gradually unfolds. In fact, years may pass before someone comes to feel that he had penetrated to the core meaning of the piece. This seems to support the opposite view: that musical meaning is spread around, the interpreter’s role being to assemble it gradually.

Yes. It is like I’ve been saying for years. Art does not happen on the canvas. It happens in the mind of the observer.

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This post first appeared on Eric Lanke's blog, an association executive and author. You can follow him on Twitter @ericlanke or contact him at eric.lanke@gmail.com.