Subconscious Processing Of Chess Positions

It is said that when playing chess both sides of the mind are engaged simultaneously (analytical & creative).

I have noticed when I leave the board in the middle of the game (usually this seems to be to answer "nature's call") I am able to mentally process positions in my head and sometimes I am able to "see" things that I missed when infront of the board.  I've read about a certain GM who when it was his turn to move would turn away from the board; he stated something to the effect that this was so he could "really see the position".

I have also noticed that the longer I look at a position, the deeper my understanding of it becomes; games where I have taken extra time and effort to look deeply into the positions are always the ones where I make the strongest moves.

There is something profound here that I have not quite grasped but may be close to discovering...