Stephen Wolfram, amongst others, mentions that we used to compartamentalized computational problems. For instance, we used to think that sorting a list of words, or computing square roots, or determining if a particular phrase is palindromic were three different things. However, since Kurt Gödel and Alan Turing we now know that they are computationally the same problems, universal computation.
One interesting implication from this revelation is that technically we can compute anything, once we have the newest and greatest models and the most powerlful enough machinery. Wolfram uses the term computational irreducibility to say this is perhaps mistaken. Maybe there is no easy theory for any behavior that seems complex. You cannot predict the outcome beforehand, and the program must still be run, for us to get an answer. However, isn’t all this a predicate of complexity theory, and also related implications of Gödel’s incompleteness theorems, especially regarding the halting problem, ideas which are almost 100 years old?
By the way, caring about computation is essential because it leads us to paradigm shifts. One of the most famous example was Copernicus’s notion that we’re not at the center of the universe. Before and after Copernicus, computing planetary positions with Ptolemy’s epicycles was and is adequate for most situations, albeit not as accurate. So, we care about paradigm shifts because they usually bring forth more accuracy to our understanding.