Sunday, November 8, 2009

sounds like bach - douglas hofstadter and formalism in classical music

Douglas Hofstadter, author of Gödel, Escher, Bach: An Eternal Golden Braid, in an article titled "Sounds Like Bach" on computer programed classical music:
In my lectures, I usually have a second musical interlude, this time involving mazurkas -- one by Chopin and one by EMI [Experiments in Musical Intelligence]. One time, when I gave this lecture at the world-famous Eastman School of Music in Rochester, New York, nearly all the composition and music-theory faculty was fooled by the EMI mazurka, taking it for genuine Chopin (and the genuine Chopin piece, by contrast, for a computer-manufactured ditty). An Eastman music student, Kala Pierson, wrote me an email about this event in which she said, 'I voted real-Chopin for the second piece, as did most of my friends. When you announced that the first was Chopin and the second was EMI, there was a collective gasp and an aftermath of what I can only describe as delighted horror. I've never seen so many theorists and their composers shocked out of their smug complacency in one fell swoop (myself included)! It was truly a thing of beauty.'
Much, much more here

Marvin Minsky, called the "father of AI", takes up the same topic but a little earlier than Hofstadter. His argument is more theoretical so he's making a slightly different point from Hofstadter: basically, that the formalistic models of classical music are incomplete but that does not mean we have to give up on the project:
Minsky: In a computation-based treatment of musical expression you
would expect to see attempts to describe and explain such sorts of
structure. Yet the most "respectable" present-day analyses -- e.g., the
well-known Lerdahl & Jackendoff work on generative grammars for
tonal music -- seem to me insufficiently concerned with such
relationships. The so-called "generative" approach purports to describe
all choices open to a speaker or composer -- but it also tries to abstract
away the actual procedure, the temporal evolution of the compositional
process. Consequently, it cannot even begin to describe the choices
composers must actually face -- and we can understand that only by
making models of the cognitive constraints that motivate an author or
composer. I suspect that when we learn how to do that, many
regularities that today are regarded as grammatical will be seen as
results of how the composer's motivations interact with the
knowledge-representation mechanisms shared by the composer and the
listener. In any case it seems to me that, both in music and language,
one must understand the semantics of tension-producing elements -- at
least in the forms that resemble narrative. Each initial discord, be it
melodic, rhythmic, harmonic, or whatever, can be seen as a problem to
be later resolved. A lot of what a composer does is setting up
expectations, and then figuring out how to frustrate them. That gives
the composer some problems to solve. The problems and their
solutions are then like elements of a plot, and composition becomes a
kind of story telling.

Otto Laske: To look at composing as a variety of story-telling, and at music as
a pseudo-story, wouldn't that help us to arrive at a theory of musical
Just a few paragraphs down we come to what I find to be the most interesting aspect, the (partial) answer to the above:
OL: So, then, for you to apply AI to music, if one can say apply...

MM: ... would be making composers, or at least listeners...

OL: By "making," do you mean to produce a robot-like creature that
does certain things like, observably composing?

MM: Yes, indeed. And in the case of listening it would have to know
when to say "oh, this is exciting," or "how very tender," and the like. I
haven't seen much of that.

OL: In Japan, one has built a robot that is capable of reading music,
and play it on the piano.

MM: Yes, that fellow at Mazda.

OL: Is that something you have in mind here?

MM: Not at all. Because I'm more concerned about what happens at
larger scales of phrase and plot. Our listening machine would have to
understand the music well enough to recognize from each moment to
the next which problems have been solved, and which remain open.

OL: How would that understanding have to become manifest?

MM: Well, for example, an understanding listener can hear a piano
concerto and appropriately say things like "that was a good idea here in
the cadenza, but he didn't carry it through." I'd want the robot to make
similar analyses.

OL: To do that, the robot must be able to recognize solutions, good or
bad. But then how would it communicate this to others?

MM: One way might be to have it write the sorts of sentences that
critics write. Or to have work more in the musical realm by performing
as a teacher does, explaining differences by demonstration -- "Look how
much better it would be to delay a little these notes here, and make
those near the end more staccato, like this, and this." And of course if
our machine turned out to able to produce interesting enough
interpretations, then we might be satisfied by that alone -- if many
listeners were to agree that "really, that performer has a lot of good ideas
about this music, and brings out stuff that I didn't realize was there."
Here is the lengthy conversation. All emphases my own. See about halfway down for the quoted passages. To defend him, he does consider the possibility of alternative logics (even mentioning Hegel), but "the idea is not carried through." :)

See this comment thread which took place on Joe Rebello's blog back in August where we have a spirited discussion of formalism(s) in economics which directly relates to Minsky's discussion of alternative formalisms in the article.


  1. Music is well beyond my comfort zone, but from what I can tell from the full interview his point is not simple that we should not give up on formalism, but that this is not giving up involves supplementing it with "qualitative data." In other words, he does not seem to be saying that the solution to one formalist approach is just more formalism:

    "It's mostly the same in AI. Most hope to understand language by using compact theory-tricks, like formal grammars. But that simply
    can't do enough by itself. You need some sort of data base, of experience. A few little stories about each word. And the same for music. Surely you can't react "properly" unless you possess some "stories" about each chord sequence, or melodic turn, or rhythmic variation."

    So the formalism in social science I was criticizing appears much different than Minksy's point, in that in the former the solution to incompleteness is just (1) more formalism or (2) strictly quantitative data. In this popular formalism "stories" are bullshit at best. I believe we have been taught that economics is strictly about causality and has nothing to do with interpretation by a number of our teachers.

    As before I think our point of disagreement is where you worry about people giving up on formalism and I worry about why someone would worry about the dominant methodology in the dominant social science.

  2. Joe,

    You make a good point. I was reading what I wanted to get out of it (i.e., this idea of other formalisms)and therefore I did not consider qualitative aspects, but certainly Minsky is looking for a way to incorporate these story elements into a model of Artificial Intelligence (which, of course, can include quantitative and qualitative dimensions).