So, I've been reading this quantum mechanics for idiots book recently, mainly because I'm a nerd but also because everyone time I've tried to talk with someone In the Know(tm) about QM I get a "don't worry about it" in response. The book I'm reading is Quantum: A Guide for the Perplexed by Jim Al-Khalili and it does a pretty good job of both not descending too far into the mathematics and acknowledging that basically everything is counterintuitive and the natural response is to say "no wai! lies!".
Any rate, my big epiphany was that everything at the atomic level appears to be indeterministic. Which is highly unsettling because all that stuff we learned in high school is based on the assumption that we live in a deterministic universe: that you can know everything about anything and make predictions accordingly. We've used these tools to split the atom, go to the moon, approximate how long ago dinosaurs roamed the earth, hurl data around the globe, and create machines that can peer inside your head and let a doctor see if blood vessels in your brain are healthy or not.
And it's basically all been an approximation.