Successful leaders process information differently, says Roger Martin, dean of the University of Toronto Business School.

“They have the predisposition and the capacity to hold in their head two opposing ideas at once, and creatively resolve the tension between those two ideas by generating a new one that contains elements of the others but is superior to both.”

He asked several how they recharge their brains when the ideas stop flowing. For example, right before he falls asleep, the inventor Ray Kurzweil “reviews the specifics of a problem — the background, options context — until they become embedded in his dreams, a state where taboos relax and the rules of logic evaporate.