abstraction layers

Abstract vs general vs category hierarchy vs abstraction layer

Concrete → Abstract: Which? → What kind?
Specific → General: Narrow kind→ Broad kind

Specific → General operates within the space of categories.
Intension … defining properties of a category (what it is)
Extension … the set of things that fall under that category
Shrinking the intension → expanding the extension (and vice versa)

	Specific	General
Abstract	Int	Num
Concrete	42 :: Int a ⇒ a	42 :: Num a ⇒ a

Category hierarchy: A is-a B is-a C … requires only shared properties (e.g.: tabby $\subset$ cat $\subset$ mammal)
Abstraction layer: hides a mechanism, exposes an interface … requires near-decomposability (e.g.: the structure of reality)

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To understand the universe at a particular level, you don't necessarily need to go all the way down.

You might just go one level lower and start modelling things there, at the cost of some approximation errors, but if you do things well enough / ask the right questions, you’ll see emergence of the higher-level phenomena you’re interested in and build on top of it, layer after layer, as this emergence appears to be constant across scales.

Different layers are recognizable by the kind of goals they’re trying to solve… for which (N)CAs appear to be a reasonable model for many differnet layers in this architecture.

What’s Life?

As systems grow complex, they form abstraction layers - atoms form molecules, molecules form cells, cells form organs. Each layer interprets the one below, like software running on hardware running on physics.
In biological systems, each layer can adapt, unlike the rigid stacks of computers.

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abstraction