I feel like this is on to something. I remember earlier in my career whenever I hit a really, really hard problem I'd have an instinct to try to stare of into the far distance (especially if there's like a distant skyline) and sort of zone-out. It was like shower-thinking or almost sleeping, and then come back with a deeper understanding of the problem.

Psychology research backs this up -- I think there are studies that show students who have a break between two classes before better in both classes (it's called interference).

Anyways it felt weird to me that our work never accommodated this, I think peak performance requires tuning the environment to the human biology, not management optics.