JUDITH RICH HARRIS calls “No Two Alike” a “scientific detective story.” The mystery is why people — even identical twins who grow up in the same home with the same genes — end up with different personalities. The detective is Harris herself, a crotchety amateur, housebound because of an illness, who takes on the academic establishment armed only with a sharp mind and an Internet connection. Does home environment — parenting style, marital harmony, the use or rejection of day care — shape a child’s personality, making her more agreeable, less aggressive or more extroverted? Nope. Research shows that twins don’t turn out more alike if they’re raised together than if they’re raised apart.