I’ve been thinking in terms of “composition of transformations” lately, an idea inspired from Category Theory.
I won’t talk about math, however. The best example of this is how Piccasso thought about painting. It’s tempting to think that a painting has a “done” state, but according to Picasso, that is not true.
He worked through a system of “Metamorphosis”. Every single state of the canvas was a valid painting, each stroke would just transform the painting into a new - just as valid - one. He would continuously transform the canvas until he was satisfied, not until it was finished.
This has some psychological advantages, as well as theoretical ones.
The eternal artist’s dilemma lies in finishing. When is the project done? It will never be perfect, obviously. However, in practice, we often forget that perfection is impossible, so we hack ourselves in circles chasing completion. A philosophy of metamorphosis can help mitigate this.
Every time I commit a code change, for example, I make sure that the code is “valid” in the sense of Picasso. If I never pick this up again, does it work? This forces small chunks of metamorphosis. I implement one, full feature at a time, and never leave a project broken.
This is easier said than done in the moment, because it's easy to get frustrated and walk away, but with practice I am finding the usable nuggets and focusing on those as I go. It leads to a much less stressful experience.
I am attempting the same thing in my writing. Whenever I write, even a journal entry, I try to make one self-contained idea at a time. This has the practical advantages of not leaving dangling threads, but is theoretically important as well.
A self contained argument can be COMPOSED in the sense of category theory. The idea can be folded into another argument as a building block. When I rewrite it later, or use the same idea in another train of thought, it is a metamorphosis on an already valid idea.
I am not necessarily constructing an explicit library of ideas, I think productive thought is too messy for such a system. This is simply a model of mental organization which (I hypothesize) will allow for much more elegant thinking.
This principle is manifest in this article. My mind is currently itching to continue the train of thought in open-ended elaboration, but I can’t indulge. I will look back upon what I’ve written and massage it into a composable idea - a standalone thing that can be applied to a large class of unforeseen arguments without a fundamental modification.
-Adrian