In an older post, I talked a bit about my model of brains and music: what makes music beautiful, what makes it interesting.
This time, I’m interested in how making music works. How is it that we can make music that can consistently surprise and please ourselves? After all, we can’t tickle ourselves, nor will rubbing our bellies cure our hunger.
To summarise the previous post, you have to picture a listener as someone who’s trying to figure out what notes or sounds will come next, given all they’ve heard of the song so far. You could picture it as someone who’s trying to figure out the rules that are generating the sounds, or just as a probability distribution over all possible future sounds telling you which ones are the most likely. As you receive more notes, you gradually prune the possible rules, or you gradually get a narrower distribution, reducing prediction error.
This is entropy. When many different rules are possible, when the distribution is wide, the entropy is high. When few rules are possible, when the distribution is narrow, the entropy is low.
Remember, as I pointed out last time, that entropy here is a very subjective phenomenon. What is objectively easiest to compress might not be what is easiest to compress for humans. We are designed to be very good at modeling other people, at doing language, and at motor skills, which can all be mathematically very subtle; and yet we have no trouble interpreting musical parts as different “characters”, and at feeling the movement inherent in a percussive hit or in the gush of wind of a string section crescendo. Somewhat more personally, I’ve always interpreted melodies as abstractly discursive, as if it were speech.
The fundamental thing here that distinguishes the music situation from general machine learning and pattern recognition is that the rules might very well change over time! The process generating the music is itself dynamic. Maybe each section has a different groove, or maybe you’ve got different parts coming in, or perhaps everything is in flux. In any case, going “haha you think you figured out how this worked? psych!” is, I think, pretty fundamental in how we appreciate music; although you could definitely formulate the resulting song as one meta-rule.
There are, of course, plenty of other psychological and sociological reasons for which we enjoy music, such as how musical aesthetics help reinforce a sense of tribalism, or how music allows you to express yourself without getting into arguments, and of course all the emotional stuff, but we’re going to focus on the information-theoretic parts.
According to Karl Friston’s free energy principle (FEP), the whole point of life itself is to minimize prediction error. It’s a cute theory. I think it’s clear that humans are constantly learning, and that we take pleasure in learning. Who doesn’t love it when you finally understand how a bunch of different things fit together? When what seemed to be different rules suddenly reveal themselves to be facets of the same master pattern?
Rule #1: Aesthetic pleasure is proportional to the decrease in subjective entropy.
And yet, simply knowing the high level rules governing a piece of music is not enough. Take, for example, Steve Reich’s Piano Phase.
In Piano Phase, Reich uses a very simple rule to produce a whole 6 minute piece of music which, in my opinion, stays interesting throughout (and real performances last up to 20 minutes!). How can this be?
Friston’s theory doesn’t only apply to learning. In line with predictive processing ideas, it could also explain how and why we even do anything.
Suppose that I expect there to be an apple in my hand. Suppose also that there is not in fact an apple in my hand.
We’ve got some prediction error going on!
Call it entropy, call it cognitive dissonance, or free energy, whatever: it’s not a nice state to be in.
Now, there are two ways to rectify the situation. I could simply update in favor of not expecting there to be an apple in my hand. But I might be hungry, in which case getting hold of that damn apple might be a good thing, and besides the hunger itself might be an expectation of eating something, which is not rectified. The other way is to change the world to fit my beliefs: I can just pick up the apple that was lying there, and that would resolve this brain-world dissonance.
The mental model I have of this whole scenario is that of the brain as a sort of thermodynamical system, in which energy/heat represents beliefs. The system reaches equilibrium when your beliefs perfectly match the world, or rather, your perceptions thereof. But hey, heat exchange goes both ways! Which represents the two possibilities above.
The general strategy, then, in order to make yourself do something, is to expect really really hard that it will happen. This creates a large heat differential, a bunch of potential energy, and you can then just let thermodynamics do its heat exchange and reach equilibrium, and voilà! You’ve done the thing. Or you’ve stopped believing in it.
Rule #2: Expectation spurs action, it is self-fulfilling.
You see this pretty clearly in near-autonomous actions, like, you know, grabbing an apple, or walking. You don’t really consciously control your limbs, you just sort of expect yourself to move to some place, and your body executes it. You also see this in action, though at a higher level, when you sleep on a problem and wake up with the solution magically in mind. My guess is that considering a problem is creating cognitive dissonance, which might be prediction differentials between different parts of your brain. These conflicts might require some pretty traumatic neural restructuring, during which you’d experience nonsensical thoughts, hence why you need to either focus your attention elsewhere, or go to sleep, during which the nonsense sometimes rises up in the form of dreams…
Friston holds that FEP is true not only of brains, but of life at all levels, from individual cells to societies; so long as they are sensibly causally distinct. So I feel no remorse in considering the prediction errors of different brain parts, maybe even of different limbs (the classical framework we have for this is the system 1-system 2 thing).
I have been pondering, lately, how it is that we can even write any new music at all. Or do anything creative.
Think about it. How is it that I can write a piece of music that I myself can enjoy listening to? If I’ve made it, then shouldn’t I know it well enough that everything will be predictable? I ask this with a very practical goal in mind, which is that of getting off my ass and writing music, and doing so efficiently to boot.
The fundamental observation here is that we can listen to a piece of music many times, and still find it satisfying, even if we know its global structure. I know very well how Piano Phase works, but I still find it interesting.
I have two non-mutually exclusive hypotheses for why that is. The first, and the more boring one, is that although the large scale structure is simple, the combinations it generates are very chaotic, unpredictable. This is true, but unsatisfying. If I know how the song is made, then I should be able to generate it, and there should not be any surprises. But wait, there’s no reason to think brains have that much deliberate processing power, and they certainly don’t; it is therefore our duty as artists to exploit people’s cognitive limitations.
The other hypothesis is that
Rule #3: there is a part of us which never learns, or barely, or forgets really quickly, and that is the part which music speaks to.
What does it mean for a living part to never learn, if we follow FEP? It means that it’s the action-oriented part, since the only way it has to minimize free energy is to change the world to fit its predictions. It becomes no surprise that music often spurs us to action, literally in the form of dancing, but also when we listen to music while working on stuff.
It’s still weird though. A piece of music is a playground, designed to bring you the pleasure of learning, albeit mostly for your system 1. So when you are writing music, you might a priori expect that applying the FEP principle would end up in you producing what would be the most predictable sensory inputs for yourself, and the piece of music would be boring. Therefore there has to be some mechanism which prevents us from always going with the most obvious choice.
This makes complete sense as an evolutionary strategy. You want to be able to consider unlikely cases! Otherwise you will eventually fall prey to a tiger hiding in the bushes, even though that barely ever happens, or, well, only happens once and then you die.
That’s where aesthetic pleasure comes in. You’ll notice that we don’t feel pleasure when something is predictable, no; we feel pleasure when something that was first unpredictable becomes predictable. We are thus incentivized for exploration: we seek out what we don’t understand in order to understand it.
I believe the right framework is to view the whole thing as your system 1 and system 2 playing games on each other, which would mean that creating music exploits the inferential gaps between the two.
And here’s the thing: that means you can expect to be surprised. That it’s possible to have beliefs about beliefs. I’m not sure if it’s just about things like system-2 expecting system-1 to act a certain way, or if it’s true self-reference, but yeah, it seems like a fundamental creative mechanism.
The metaphor I have is that of designing a maze for yourself. You might know it very well from above, but not from inside it, and so navigating it will still prove to be a challenge.
And yet, as I mentioned in my other post, it is a challenge to write something which has just the right amount of entropy for a new listener, not just for yourself as you write the song and listen to it over and over again. Perhaps the answer is to not listen to it too much as you work on it? Being more improvisational. I know that I haven’t reread this post all that many times!
The first thought is to use the technique of “believing really hard in something and letting thermodynamics solve it,” which might translate to the obvious:
Advice 1: To make music, put yourself in a particular mood and just start writing or playing.
If we were talking about writing text, I would instead advise you to hold the ideas in your mind, and simply let yourself try to explain them. The distinction here is that music seems to speak to the unconscious, the system 1, which is why it must first come from moods and emotions and such.
(Konstantin Stanislavski seems to have had similar ideas, but for theatre)
Yet the pathways that your brain will take to fix the world might not be optimal. If you’ve never written music before, you just won’t know how to start at all, and it will likely make you feel rather discouraged and confused.
That is the role of training. You must work on meaningless sketches, all the time, without the pressure of finalizing them (although finishing something might be good training in itself).
But also, that is where deliberate practice comes in. You must force your brain to look at itself, in order to change itself. You must hold the contradictory phenomena tightly in your attention, you must not let your brain treat them separately. This is essentially the therapy method described in Unlocking the Emotional Brain, and it seems to work, but I think it works much more generally than just for therapy; in anything where you need to fix internal alignment problems between subconscious parts, this method should work.
(I should look into how athletes practice, since they are explicitly training the parts of their nervous systems that, apparently, should not be able to learn. Something something muscle memory?)
When performing, that means focusing on a very short passage, and thinking both of how you expect the passage to sound like, and what it actually sounds like when you play it.
When composing, that means explicitly figuring out why something works, holding your attention on a minute detail, and trying out that pattern in different situations. I think of this as the “hit the TV” method. Disturb your equilibrium in the hopes it will settle on a better one.
It’s also how I study math: most of it consists in recalibrating your intuitions, which is a very meditative endeavor. In my experience, one requires very little intense self-focusing of this sort to see major improvements, but one does require a lot of sleep — although it’s true that I’m a particularly abstract thinker.
The human brain has very little working memory. That is why we must always think of things in chunks: by dividing large things into smaller pieces, or by abstracting smaller pieces into larger things.
This is “compositionality”. It’s the insight behind logic, especially since Euclid (chaining together obvious things to arrive at surprising things), and it’s the core of category theory.
Again, it might seem like very obvious advice, but
Advice #2: focus on parts separately, and at different levels; and the larger the object, the vaguer your view of it.
I realize this is not very actionable advice, but we already see this: from voice leading to chords, to phrases, to sections, to movements… In a way I feel like music of the classical era was when this idea went too far: extremely clear cut sections, separated by mind-numbingly obvious cadences (like that pernicious cadential trill). The urge to remove chaos from the world is strong.
(There’s this interesting FEP-related phenomenon where, yes, the categories were made for man, but by constructing theories, we also tend to conform to them, and so artistic theories can often be self-justifying)
By developing this compositional view of composing, you might be able to effectively focus on all parts of song sufficiently well enough to form it to your liking, while avoiding listening to it in its entirety so often that it becomes boring to you.
Perhaps the gist of what I mean to say is that the actual production of a creative work happens very quickly, although there might be some roadblocks, and the polishing process can also take a while. But the actual work resides in the deliberate practice and sketching done prior to and alongside the true creation. Creating, putting ink to paper, should not feel like all that much work.
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