Resistance, the enemy of our brain

We all had the experience of working hard on a project, trying to force our way through a stubborn problem.
We look at the watch hanging on the wall, it's already two in the morning, and we haven't advanced an inch.
We shuffle our tired feet to the bed, feeling uneasy, helpless and frustrated.
The next day, after waking up, and while brushing our teeth, a clear solution to our problem comes to us, dancing before our eyes in front of the fogged up bathroom mirror.
Our brain, during our sleep, unencumbered by our conscious, tremulous thinking, came up with a solution.
During our sleep, we are unconscious, unable to interrupt the workings of our brain with our mindless mental thrashings. The solution it presents to us is simple, elegant, and it fits exactly the issue we were grappling with.
Serendipity is the perfect example of the idea conveyed here. It describes the accidental discovery of a solution to a specific issue, while being engaged in something completely unrelated.
"Esprit de l'escalier" is another example of what the brain could do for us, if we just give it instructions, then mentally "slumber".
By doing this, we leave it unshackled, and give it full power to handle the issue without our meddling.
"Esprit de l'escalier" describes a situation where, for example, during a heated conversation with someone, we freeze, unable to respond or defend ourselves against the slew of biting remarks hurled at us.
We walk away in shame, downtrodden with our head bowed down,we accept "our defeat", and we start to calm down.
As we collect our thoughts and quiet down, our brain relaxes and manages to come up with the perfect retort that would have sent our bellicose interlocutor into a numbing daze.