papalex on Nostr: Let me add another metaphor which is somewhat the same as Anger Issues 's just in ...

Let me add another metaphor which is somewhat the same as Anger Issues (npub1p89…vv2h) 's just in different clothing: Often the physics thinking works on the very basic level while the maths thinking is on a more complex level, which comes with heavier machinery than necessary. But the heavy machinery has its value in something else than bare necessity: It is the precision tool to assure the statements are understood exactly right (=non-ambiguous) in a most economic (=few words) way.

I want to make a maths analogy which I hope does fit (and I am aware that some here are lightyears more experienced than me in this topic, please be gentle):
one can do a surprising lot of things in maths without the heavy machinery of category theory but using fairly simple stuff, just constructively. For example, to define real numbers via Dedekind cuts one does not need the category theory notion of limits and to extend functions from finite stages to the full reals one does not need Kan extensions, comma categories etc to formulate and proof any of these things (of course one implicitly uses them, but "trivially" so).
But: the category theory language can be very useful for precision in the written text (i.e. if its not written as Agda program), and it is a very economic way of transporting the information content human to human (conditioned on the CT understanding). But this is at a price which may be precisely the price of (non_ambiguity)+(economy).