Who hasn't heard that people are either left-brained or right-brained—either analytical and logical or artistic and intuitive, based on the relative "strengths" of the brain's two hemispheres? How often do we hear someone remark about thinking with one side or the other?

A flourishing industry of books, videos and self-help programs has been built on this dichotomy. You can purportedly "diagnose" your brain, "motivate" one or both sides, indulge in "essence therapy" to "restore...