abstraction

All categories are an imperfect depiction of reality. The truth always lies in the concrete.

Create abstractions from the concrete, to the degree they are useful for the task at hand.

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Abstract vs general

	Specific	General
Abstract	interface Stack<T> { push; pop } — hides the implementation of a stack only.	interface Monoid<T> { empty; combine } — a very high-level pattern many types fit (strings, numbers, sets…).
Concrete	class IntArrayStack — fixed array stack for int.	function sort<T>(xs: T[], cmp) — works for any T, but it’s concretely “arrays + a particular algorithm.”

https://fhur.me/posts/2024/thats-not-an-abstraction

Do perfect abstractions exist?

I think there are perfect abstractions when considering a specific problem from a specific perspective. Like those that allow you to actually solve the problem (most) efficiently/robustly/whatever you have in mind. So in that sense abstractions/representations are highly subjective.

And from a philosophical perspective, I don’t think that there are ideal forms or essences of things that are ontologically prior (“treating the map as the territory”); inhabitants of a separate ideal realm. Ideas are historically produced abstractions and a result of material interactions.

That’s why I find it hard to grapple with some aspects of what levin argues.
Specifically that he argues that these patterns “ingress” from some realm of ideas, independently causing the physical. Yes, there are objective, lawlike structures (symmetries, attractors, …) and we can and should map and experimentally verify those. The “necessitation” we feel from mathematics is a feature of how well our abstractions capture the immanent constraints of matter in motion. Like if a system has certain material constraints, then any realization of those constraints will exhibit the same pattern, which we can then abstract. Saying the math causes the physical world has it backwards, it’s just compressing what those constraints entail (that’s also why it’s obviously important to anchor in empirical reality).

Minds, embryos, and algorithms realize and exploit these (and we should too – I think that’s his main point)
Explanations run upward (composition) and downward (constraint) (picture) but all causation is materially implemented.
Like, when levin says abstract properties from maths / geometry are true no matter the laws of physics … well, but we pick the axioms and rules of our mathematical language based on what helps us model the physical world.