But this all breaks down when we go to the very large or the very small, where we can’t make intuitions. All we have are mathematical descriptions based on subtle experiments. If we go over the math and the experiments repeatedly, we can get a kind of intuition, but it’s really a mathematical intuition.
I think there’s a similar intuition with programming, but it’s possibly even harder to explain. Some people “get” it, others don’t. It doesn’t have anything to do with intelligence, but it’s hard to teach.