My suspicion about the mechanism is that as you work on a problem, you tend to get stuck in one particular approach. When you step away from the problem, you allow yourself the possibility of approaching it from a new angle. Being so focused on idea X before, could have prevented you from considering alternative ideas Y and Z. So suppose you’re thinking about something else, but your brain then briefly flicks back to the problem. This time, ideas Y and Z popup, and it’s suddenly obvious that if you combine them, that you’ll get the solution. So, it isn’t clear at all that you would need any kind of background processing to occur in order to observe this effect. It wouldn’t surprise me at all if sleep helped here as we know it rearranges memories, but I’ve seen this effect without any sleep at all and I don’t know enough neuroscience to know if there is any brain optimising going on when you’re awake.
My suspicion about the mechanism is that as you work on a problem, you tend to get stuck in one particular approach. When you step away from the problem, you allow yourself the possibility of approaching it from a new angle. Being so focused on idea X before, could have prevented you from considering alternative ideas Y and Z. So suppose you’re thinking about something else, but your brain then briefly flicks back to the problem. This time, ideas Y and Z popup, and it’s suddenly obvious that if you combine them, that you’ll get the solution. So, it isn’t clear at all that you would need any kind of background processing to occur in order to observe this effect. It wouldn’t surprise me at all if sleep helped here as we know it rearranges memories, but I’ve seen this effect without any sleep at all and I don’t know enough neuroscience to know if there is any brain optimising going on when you’re awake.