Yesterday a friend and I had a conversation about category theory, how it can be a useful pattern description language, but also about how people have unrealistic expectations for it, believing category theory can deliver something for nothing.
Later I ran across the following post from Qiaochu Yuan. It felt as if he had overheard my conversation and summarized it in a tweet:
category theory is just some straightforwardly useful stuff for some purposes in some fields! you can elegantly simplify and streamline some proofs. then there is the mythology of category theory, which is some other thing entirely, mostly wishful thinking and projection afaict
His phrase “the mythology of category theory” gives a name to this idea that category theory can deliver specific outputs without specific inputs. It helps to distinguish CT as a scrapbook of patterns from CT as sorcery.
This clarified something for me, a recovering CT dilettante — it’s not actually about new results, per se, (other than in CT, ofc) but about “pattern description’. Very helpful in its own right, but I kept looking around for results at the level of, say, e.g. the Kalman Filter or Lagrangian/Hamiltonian or perturbation theory or geometric algebra level of goodness to appear.
It’s not like that as far as I (the dilettante, remember) can tell — it’s about describing how things work in general/in abstract.
Maybe with such descriptions we can then find new tools and techniques we missed along the way.