Whichever hemisphere of the brain is used for dreaming, it must be the one repsonsible for brilliance, because I just woke up from a dream where I was shopping for music by a band called Ikkkea. I saw an episode of Batman: The Animated Series once where Batman was trapped in a dream that he thought was reality. He awoke when he realized that all the written words in his dream were garbled, or maybe spelled out backwards, a sign that only the hemisphere of his brain used for dreaming was engaged. According to Batman, that hemisphere is the creative, but illogical one, and thus bad with grammar and syntax.

There's a picture in this great book about the creation of Batman: The Animated Series that contains all the things they weren't allowed to put in the show; in it were a cross (religion), somebody getting shot and stabbed, and I think somebody using drugs, among other things. The writers and animators used it as a reference.