One night this spring, Amanda Burden went to see the new Broadway musical “If/Then.” She had recently returned from a “psychic healing” retreat in Arizona, having spent twelve years as Mayor Bloomberg’s director of city planning. One of Bloomberg’s aides had recommended “If/Then,” which stars Idina Menzel (you have heard her sing “Let It Go”) as an urban planner named Elizabeth. After a chance moment in a park, her life takes two divergent paths: In one, she calls herself Liz, marries an Army reservist, and has two kids. In the other, she’s Beth, a career woman who becomes New York City’s chief planner. Burden trembled in her seat. “Oh, my God,” she recalled thinking. “I think that’s me!”