Stephen Wolfram, among others, points out that we used to treat computing problems as separate things. Sorting a list, taking a square root, and checking whether a phrase is a palindrome looked like three different tasks. Since Kurt Gödel and Alan Turing we know they are the same kind of problem. They are all cases of universal computation. I find that shift in view still worth pausing on.
One tempting conclusion is that we can compute anything with the newest models and enough machines. Wolfram’s computational irreducibility says that is wrong. For much complex behavior there is no shortcut theory. You cannot predict the result. The program must still be run to get an answer.
I wonder how much of that was already implied by complexity theory, by Gödel’s incompleteness theorems, and by the halting problem. Those ideas are almost a century old.
Caring about computation matters because it leads to big shifts in how we see things. Copernicus moving us away from the center of the universe is the famous example. Before and after him, computing planet positions with Ptolemy’s epicycles worked well enough for most uses. It was only less accurate. More accuracy in our understanding is what such a shift buys.