Jürgen Schmidhuber distinguishes two fundamental aspects of aesthetic enjoyment: beauty, and interestingness.
In essence, he describes beauty as a subjective property of things that you can describe with very little information. But as we are not infinitely intelligent agents, it might take time for us to unravel the simple algorithm behind a piece of art, and we are in this case constantly refining our mental model of it. Schmidhuber thus describes interestingness as the first derivative of beauty with respect to time; or a measure of how much our representation of the thing at hand is getting more and more simple.
There are a few nuances that I would like to point out in this theory. I’m not sure if Schmidhuber is aware of them, and I would certainly not want to strawman his ideas, but they are usually not pointed out in the summaries I have read.
First, that complexity is subjective. It’s easy for humans to model other humans, and it’s therefore easy for humans to compress information about how other humans are acting. This would explain why plots, which would incredibly complicated to explain in mathematical detail, and the result of which would certainly not be simple, feel very straightforward to us. Indeed, in a children’s tale with a small number of characters, you would have to explain how human perception works, how emotions work and evolve over time, how humans relate to other humans, etc. (assuming that you’re not just modeling the characters’ whole brains!) Other things that are easy to model for humans include the physical motions of objects, and an approximate euclidean algorithm on the frequency of sine tones (more on that later!).
Subtle considerations of human perception and human-compressibility will be necessary for a good aesthetic theory. While a grand abstract theory of beauty that might apply to any intelligent agent is certainly interesting, my goal is to develop something that would be artistically useful. I will expand on this in a subsequent post.
Secondly, some art mediums are not static. Art that is sequential or time-dependent, such as movies, music and literature, reveal their information in a steady stream, and may even have varying objective complexity. The definition of interestingness as the derivative of beauty falls apart here, as you might have a piece of music that has a roughly constant beauty yet also has a roughly constant interestingness. I would rather define interestingness as the amont of cognitive work one has to do to minimize our representation’s complexity.
As an example, you might consider a plot to be interesting if it is surprising, as in it constantly defies what your model of it expects, but “it all makes sense in the end”. This seems somewhat more difficult to achieve: you want to control the flow of information so that the information given thus far always fits in some simple pattern, but each time new information is acquired, the pattern is shown to be wrong. But wait! It was actually part of another beautifully simple pattern! And so on.
Fortunately, this might be easier to achieve than it seems, as there are maybe three bottlenecks to consider: the information output of the artwork, the perceptual input of the audience, and the cognitive treatment of the information. Thus you might give out the information in chunks (such as song sections), and let the chunk stay for a while (make the song section loop a couple times), until the humans have extracted all the information they can.
Thirdly, that there is a difference your system-1 and your system-2’s idea of complexity. One might work cognitively hard to unravel the structure of a serialist piece, and see that there is indeed great beauty in the construction… while still finding it intuitively unappealing, because your brain is simply not good at discerning absolute vs relative pitch, and it’s also bad at recognizing common serialist techniques such as retrograde transformations (playing a sequence of notes backwards). On the other hand, you might feel goosebumps at the climax of a Romantic symphony, without exactly knowing why, except that the whole thing felt like an epic story of some kind.
And now, let’s talk about the title of this post. The following are personal realizations, and I will be muddying the distinction between the beauty exposed above, and beauty as in the general feeling of “wow, this is beautiful!”.
It has come to my attention that, specifically in music, beauty and interestingness do not and should not always go hand in hand!
There is such a thing as being too interesting. Most people listen to music while doing other things, and the last thing they want in this case is to be distracted by it. This is perhaps the great insight of minimalist and ambient composers. Brian Eno is credited as the inventor of modern ambient music, with his album Ambient 1: Music for Airports, and wrote in its liner notes:
Ambient Music must be able to accomodate many levels of listening attention without enforcing one in particular; it must be as ignorable as it is interesting.
And thus I realize that I have dedicated far too little attention to making beautiful things, as opposed to interesting things. Yes, I might have often grumbled about how academic composers focus too much on complexity as a generator of interestingness, but what have I done about it myself?
For one, I don’t think my idea of beauty was much more valid. I have made music that was easy to perceive: contrapuntally clear music, clear sections, clear melodies, etc; while I still placed the beauty of the music in its structure. In other words, I did not try to make the music easy to make sense of, or easily human-compressible.
What I did think about was system-2 interestingness. I expect this to be a common failure mode in composers, as this is what is most easily consciously recognizable. What makes Bach’s music awesome? Why, it’s the amazing complexity of his counterpoint, of course! And not the way he manages to keep our emotional attention… One wonders if the thing that actually made counterpoint so pleasing was that each voice is cognitively interpreted as a different person, who is expressing their personal feelings, with the brain taking great delight in this multitude of interlocking emotions.
Yea, the fact that it’s so easy and natural to model other humans, despite how complicated a task this is, makes a formalization of true aesthetic principles almost impossible. But this in itself is a very useful realization: knowing that empathy is a primary factor in aesthetic pleasure, we can keep this in mind and… well, trust our intuitions.
From here on out, I want to focus on my system-1’s appreciation of beauty. This will take the form of long, boring, but beautiful, loop-based music, where the focus will be on making it immediately pleasing. Making boring music is more difficult than it seems: as the composer, I will be listening to it countless times, and I have to not get bored by it!
footnote: I will be using this blog both as a personal journal to keep my thoughts in a crystallized form, and as a way to let other people into my brain, as I believe my ideas on the specific subject of musical aesthetics might become unique and interesting enough.
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