QM and the limits of intuition and "common-sense"

I have a confession to make. I don’t understand Quantum Mechanics.
Now there’s no shame in that; Richard Feynman famously said “I think it is safe to say that no one understands Quantum Mechanics.” But the reason I mention this is that I’m pretty sure that I don’t understand it less than I used to. This is progress.
I’ve always known that I didn’t understand QM, because my common-sense interpretation of the words that physicists used to describe QM violated … well, common-sense. So I thought to myself, “Which is more likely? (a) My understanding is correct, and it’s OK that it seems absurd, because it’s supposed to seem absurd. Or (b) my understanding is wrong, and the real explanation is quite different. (And still possibly absurd from a common-sense point of view.)” Obviously(?!) (b) seems much more likely, so I put QM aside and tried to make sense of scientific discourse without looking too closely at it.
People are quite good at faking stuff like that – almost as good as they are at holding mutually contradictory beliefs without their heads exploding.
Recently I read The Grand Design by Stephen Hawking and Leonard Mlodinow. In general, I quite liked it, although I thought it a bit repetitious, and less well organized than it could have been. However in one chapter the authors take a crack at explaining the basics of QM, and it was a revelation to me. Specifically, I realized how my common-sense interpretation of the language of QM had led me to the particularly absurd conclusion which I’d correctly rejected. And I understood how the authors’ explanations of the ideas of QM made sense – though not common-sense.
I’m not going to try to reproduce my understanding here – at least, not yet. I’ve taken QM off the shelf, so to speak, and I’m looking forward to reading (and hopefully understanding) more, without those earlier misunderstandings getting in the way. I know that to really make progress I’m going to have to understand at least some of the mathematics, which will be a challenge. I think it will be a worthwhile one.
However the most important thing about this episode for me was that it reinforced something I believe very strongly, and wish that others did too. It’s simply this: common-sense, intuition, instinct, call it what you will, is a function of our evolved human brains. It was selected for, along with other skills that were adaptive for our survival. It applies to the world we experience, and interact with, at our scale: medium size objects, medium sized environment, medium periods of time. It works pretty well for rocks, and foodstuffs, and small groups of people and other animals, and actions like running, catching and throwing. But outside that range, there’s no reason to expect it to be reliable – and it isn’t.
From 1mm to 1km, 1 second to 60 years, 1 gram to 1 tonne, 1 kph to 100 kph, and -20C to 100C, we’re pretty good. But the subatomic world doesn’t behave the same as the rocks or the trees, any more than the larger universe does. The regularity, and even causality, that we build our common-sense view of the world on simply don’t work at radically different sizes or times. And this isn’t simply a matter of faith: we can measure it, and we’ve learned to rely upon what we measure. Every time you use your computer, or consult a sat-nav, or take a modern drug, you are relying on the fact that a bunch of scientists and engineers looked at the data, did the math, created explanatory models, tested them, and relied upon the evidence rather than “common-sense”.
I could add a couple of paragraphs about the relationship between this big idea and religion, particularly the arguments that are offered for the existence of god, but if you’re smart you’ll already understand them, and if not you’ve probably given up by now.