Haldeman’s “Counterpoint” appeared in his short story collection Infinite Dreams in 1978. He wrote, in the introduction, that it was “loosely patterned after a Greek myth.”
In the story, two babies are born at the exact same moment, in New York and Louisiana, in 1943. One of them, Michael, is a millionaire’s son, well-raised, handsome and successful at everything he does. Roger, the son of a prostitute, is ugly and neglected from the very earliest days of his life. Michael has everything handed to him on a silver platter; Roger has to work hard for everything.
Both end up as U.S. Army officers in Vietnam, although they never meet. While his base is under enemy attack, Michael calls in an artillery strike from the unit that Roger is serving in. Roger, a math genius and extremely capable artillery officer, orders the barrage that stops the attack but disables Michael.
Michael, brain damaged, lingers in a VA hospital for years and eventually dies at the exact same moment in 1985 as Roger does. Roger had become an academic celebrity for his math skills, finding love, fame and fortune only much later in life.
Turns out the two men are half-brothers. Michael’s father was once a client of Roger’s mother, the prostitute. They have lived parallel lives, with Michael having a very successful early life and an unfortunate later one, while Roger’s was the other way around.
Does that remind you of any Greek myth?