"To oversimplify quite a bit, I would say Niels Bohr had a very humanistic interpretation. He thought that physics was about describing human knowledge of the world whereas Einstein thought more at the level of God’s knowledge. He often talked that way. Very majestic. Humans are just observers of this preexisting harmony, and they should be awestruck and humble.
So one of the conflicts was, is light a particle or wave? And, in fact, it is both. Sometimes it’s useful to think of it one way. Sometimes it’s useful to think of it another way. And both can be informative in different circumstances. But it’s very difficult, in fact, impossible, to apply them both at once.
And I think that’s the essence of complementarity. You have to view the world in different ways to do it justice, and the different ways can each be very rich, can each be internally consistent, can each have its own language and rules, but they may be mutually incompatible, and to do full justice to reality, you have to take both of them into account.
When people ask me what my religion is, I say I’m a complementarian.
I believe that it’s really interesting and really fun and really informative, and the right thing to do to be able to look at things in different ways, and appreciate there are different ways of looking at things that each have their own validity. And they may conflict if you try to apply them both at once, but, okay, that’s fine. You apply one at a time and try to appreciate both."