Greentext

That’s still nowhere near unexplainable enough to be impossible to study. You’ve described the god’s behaviour as “sometimes alters reality when prayed to by a devout follower” - if it’s consistent enough for this statement to make sense, that’s already a lot to study.

It might be technically studiable in the way you describe, but there's no requirement for consistency of any kind. My statement was extra-universal, so you can't assume that it's discoverable intra-universally. If the result of your study is "this is behaving in completely inconsistent and random ways", you have technically studied it, but you haven't measured or analyzed it in any way.

You can just apply your approach to our universe. People have spent centuries attempting to measure and analyze miracles. Would you say that we have analyzed and studied the magic system by which the christian god works?

Eh. It’s sometimes fun to read stories like that (one better have fun, since most stories are like that!), but they’re… stories about worlds where there isn’t a single human with common sense or intelligence. Not just in the story itself, but in the world’s entire history, because the author didn’t realise that “people trying to seriously explore the laws of their world” is a thing that necessarily happens in realistic worlds, much like it happens in ours.

You're still making assumptions about the magic system. Take for example the Solphons from "The Dark Forest" - super-smart subatomic machines that change the laws of physics to prevent advances in fundamental physics. Now imagine that they weren't designed by an alien race, but instead by an extra-universal god, and there was no way to ever arrive at this knowledge (since no instruments for measuring etc. can ever be developed).

Suddenly you have a magic system that is fundamentally unstudiable, no matter the amount of humans with "common sense or intelligence". No matter what idea you come up with to study the system, I'll be able to come up with a way to make it fundamentally unstudiable. That's what's great about fiction - we're not limited by the assumptions we have to make in real science.