This happens to me now and then. I find the "clarity" of which you speak is the common thread. I almost seem like I'm at peace. Instead of attacking the problem in my usual manner, the solution just comes to me in some sort of divine fashion like I've been "in this place" all along. It doesn't seem to involve any high level of skill......in fact, the solution is simple but was always hidden from me before. Perhaps at these times, I'm not under the spell of BP after all. My mind is clear and calm.