A good book on this is A Whole New Mind by Daniel H. Pink, and a good article on the science of this is “A Wandering Mind Heads Straight Toward Insight” by Robert Lee Hotz from The Wall Street Journal. While many parts of the brain come in two halves, it’s only the more recently developed cortex, which accounts for three-quarters of the brain, that has been shown to have functional differences between the right and left sides.