This seems to imply that brains work in "background" to some extent.

YES! and I think the lesson to be learned is that forcing it is detrimental...

It is so easy to force your thought process into a rut... In my example from last week I had a scope trace reminding me constantly of a possible solution of my problem... I had immense pressure to solve the problem and I started to move to the wrong solution based on the visible data and the pressure- I recognized what was happening and knew it was time to take a few minutes to ignore the problem.

I took a break, even though the time pressure was intense. I went outside and looked at the view from the summit, after about 5 minutes my thoughts returned to the problem- I started considering ALL the data I had taken to diagnose the problem- once I was out of the mental rut I could see some of my measurements that I had taken revealed the true cause of the problem... IT WAS OBVIOUS! If I had kept pounding away at the problem without taking a break I would have accomplished nothing for hours or even days. But 10 minutes 'goofing off' allowed me to come up with a solution that took 15 minutes to implement.

I dont think my mind was working on the problem sub-conciously, I do think that my mind was working itself into a rut, and getting out of that rut was the key.

As for Larry's post... I have only had one revalation while I was sleeping- I was trying to understand a concept in special relativity, I dreamed that I was working on a homework problem that required understanding that concept, in my dream I solved it easily, and gained the insight I was missing - It actually was very creepy....