The conviction that the world, pace certain "intrinsic" limits of the information-theoretic or quantum-mechanical nature, is understandable is a singularly powerful one. It's something lots of people think they believe, but it took me (anecdotally) until I was 9 or 10 to internalise it. The belief that the X-ray vision you speak of exists is enough in many cases for one to "get" it.
I do not mean to start a tangential flamewar, but the ability to accept and be comfortable with not knowing, while at the same time believing that the unknown is not unknowable, is something a certain kind of religious worldview precludes. This is one thing which I realised quite early on that my parents didn't share my beliefs on: for them, there's some underlying agent that chooses what happens in situations that we call random or do not understand:
"I don't know why this happens, but there's no reason why we never should/it's not computable/etc."
"Ah, child, it's time to accept things as they are. When I do not understand, I say God's causing it to happen."
It's a confusing mixture of the different positions one can take on determinism coupled with a sort of complacence I find remarkable.