The Structuralist Mindset

Epistemic status: False model; looking for feedback in order to improve it. It also needs much more examples. I read Gwern on the hacker mindset: Here I have a system W, which pretends to be made out of a few Xs; however, it is really made out of many Y, which form an entirely different system, Z; I will now proceed to ignore the illusory X and understand how Z works, so I may use the Y to thereby change W however I like. and it made me think of this: Another characteristic of the open cognitive style is a facility for thinking in symbols and abstractions far removed from concrete experience. https://www.personalitytest.net/ I propose a synthesis and an added category:[1] Concrete experience is one pole, but on the other hand we find two things that are quite different. I will speak of atoms to refer to the simplest unit that still belongs to a system. Words are atoms, mathematical concepts are atoms. I will speak of subatoms to refer to units simpler than the atoms, when they exist. Letters are subatoms. Pen strokes on a paper are subatoms. Pixels on the screen forming a letter are subatoms. Enjoyers don't think in abstractions; hackers think in terms of subatoms. Structuralists are interested in structure, which sometimes means thinking about atoms, but not always, and atoms is not always the most interesting part. The atoms of every mathematical objects are its elements in the set-theoretic sense, but thinking about elements isn't particularly interesting. I make the risky move of identifying mathematicians and cultural scientists as having the same attitude, applied to different objects. This is the point I'm least sure about, so I'm very open to better suggestions. Puns The hacker loves puns. The enjoyer can laugh at a couple of them, but doesn't see the point after a while. The structuralist likes homonyms and paraprosdokians[2]. They like some puns. The difference is that the hacker goes down to an underlying layer that is outside of the system (letter), whereas the structuralist enjoys playing with the properties and the structure from inside the system. Words that rhyme are a zone of overlap, and yet in a specific way that, being obvious to every native speaker, actually belong inside the system as well. Games Chess is a game where the simplest elements are inside the system, so hackers and structuralists enjoy it equally. I once met a enjoyer who liked chess, but disliked the stalemate rule, because it stopped them from immersing themselves in battle simulation. Enjoyers enjoy immersing themselves in improv.[3] Structuralists find scenes with a lot of dialogue easier, whereas in more physical ones they are lost. Hackers tend to go meta in every single scene. In between these two extremes there are things like D&D or very complex board games, both of which try to model a scenario (a conquest of the galaxy or taking care of a farm, etc.). The hacker tries to get as many points as possible (they are a munchkin); they would play exactly the same even if the whole "modelling something else was removed". The enjoyer gets into the role and enjoys their simulated role. They would play similarly if the values of the elements were changed a bit. The structuralist is lost. As their knowledge of the game progresses, they see more and more that the two elements (game mechanics vs. theoretically modeled scenario) are distinct and disconnected. They are unable to get in the role (how can they ignore the point of the game?), but unlike the hacker they see no point in optimizing points that don't mean anything. Written at Inscribe. ^ I'm agnostic as to how stable these "attitudes" are, and as to whether one person can swap between them. An enjoyer once told me that they enjoying thinking abstractly, but for 10 minutes a day at max (they were very intelligent, but spent their free time mostly drinking coffee and enjoying the sun). I've also met a Math professor that told me they would have no interest in doing any Math if it was not for the high salary, and also used their (scant) free time to drink coffee and enjoy the sun. Brilliant programmers can be bad at abstract math; brilliant mathematicians can be bad at programming. But some people are good at both. Postrats are a good candidate for someone who is very comfortable in at least two categories. I'm agnostic about these complications and focus on capturing the platonic idea, which I still haven't done to my satisfaction. Claude recommended to have a look at Marr's three levels of analysis (computational, algorithmic, implementational), which I haven't done yet but will at some point. ^ Here is what I suspect is a structuralist describing how much she likes paraprosdokians. ^ Stretching it a bit, possibly the same applies to things like emotional work and things like circling: they come naturally to enjoyers; hackers always go to the meta-level, and structuralists can enjoy them despite being bad at being present in the moment. A language-less versio