What is computation? Does computation = causation It is actually incredibly difficult to define "computer" in such a way that just our digital and mechanical computers, or things like brains, are computers, but the Earth's atmosphere or a quasar is not,without appealing to subjective semantic meaning or arbitrary criteria not grounded in the physics of those systems. — Count Timothy von Icarus
The question of "what is computation" and "what is a computer" are different. The latter seems straightforward: a computer is a Turing machine, or something that can emulate one. What is wrong with that.
What distinguishes a computer from other physical systems is not that they have states that evolve, but that they can be set up to compute anything computable. You won't find this in any physical systems other than brains and computers.
The mistake I mean to point out is that we generally take 10÷2 to be the same thing as 5. Even adamant mathematical Platonists seem to be nominalists about computation. An algorithm that specifies a given object, say a number, "is just a name for that number." — Count Timothy von Icarus
If not a name, 10/2 is certainly another form of 5. And transforming numbers from one form to another, like the transformation of all information, requires work. This work of transforming information from one form to another is called "computation". Does that sound reasonable?
If the state of a computer C2 follows from a prior state C1, what do we call the process by which C1 becomes C2? Computation. Abstractly, this is also what we call the process of turning something like 10 ÷ 2 into 5.
What do we call the phenomena where by a physical system in state S1 becomes S2 due to physical interactions defined by the laws of physics and their entailments? Causation. — Count Timothy von Icarus
This doesn't seem quite right. In the ordinary sense of the word, a broken computer doesn't "compute" anything. And yet it has C2s that follow from C1s. What is special about computers is not that its states evolve, but that it can be set up to implement ad hoc rules that proceed completely independently of their underlying physical implementation.
This is seen already with assembly language. It doesn't matter how an assembly language is implemented, only that it is implemented faithfully to its specification. A steam computer would work the same as a silicon computer that both implement the same assembly language. And on top of these abstract rules, more rules can be implemented, that don't resemble even the assembly language. This tower of increasing abstraction can be incredibly tall, and culminates in distributed systems like the web and cryptocurrencies.
What makes computers special is that they are not bound by physical, causal reality. It is as if, in them, the informational component of reality broke free of the physical component. Brains are especially impressive, in that they are not just computers, but computers which which managed to create computers.