Systems and Apparent Complexity

Posted 5 months, 1 week ago | Originally written on 21 Dec 2022

Consider a girl at a piano. The way her fingers move is hard to associate with the beauty of what she produces (if she’s any good; let’s assume she is). Of course, she may convey something of the rhythm of the music by how she moves parts of her body. This is inevitable given that it is by pecking at the keys that her fingers produces the music. But if you asked an untrained observer to reproduce her actions so as to generate beautiful music you will be sorely disappointed.

While her hand movements appear extremely difficult to memorise and replicate the result is magical. In other words, the beauty is the result of remarkable complexity. However, she would disagree. What she is doing is orderly, methodical and structured. She will forget the countless hours she has practiced to get to that level of expertise. Furthermore, if you would spy her at practice you would find it hard to associate the repetitiveness of practice with the transcendence of beautiful playing.

As with most phenomena, I have a growing suspicion that the complexity they portray is the result of what I’ll call ‘system effects'—the emergence of nontrivial outcomes from apparently simple components. The elements of excellence at playing the piano—or any task of economic value—are actually relatively simple and generally unremarkable on their own. It’s in their combination that a synergy of complexity emerges. In my narrow understanding, playing the piano fundamentally (not exhaustively) consists of mastering how to express pitch and rhythm. Thereafter, adding tempo and other dynamics such as volume only serve to expand the expressive and hence the complexity of the result—a complexity sufficient to amuse an intelligent being like our species.

In effect, most of what we refer to as complexity really isn’t—we simply observe the system effects of a small assembly, each of which can have multiple conformations resulting in a horribly large state space that we cannot traverse without practice. Playing piano is easy because little children without any understanding of what they are doing but faithful following their teachers instructing can produce the required complexity.

What matters then is, not an understanding of the system. That’s impossible. Rather, one needs to accept and follow the rules required to carry out the basic content actions through whose interaction may they produced the desired effects.

There is also a surprising corollary to this idea that complexity is for the most part illusory. It doesn’t take many basic components to produce complexity. Even four fundamental components are sufficient to produce such a wide set of systems effects that it would take the patience of an Einstein to disambiguate them. For example, the simple fact that the Earth’s axis of rotation is tilted is sufficient to produce the seasons, which result in such dramatic effects as animal migrations, variations in flora, ocean currents and so on.