The boy has grown up under the care of his imperious grandmother, who takes one martini at 6 p.m. daily and maintains certain expectations about Jay's behavior. At the Guggenheim Museum (built by one "Frank Lord Right"), she orders him to run up the spiral ramp while she sails ceiling-ward on the elevator. "Frank Lord Right was not building Calvary, she said, did not mean us to trudge upward to our crucifixion." Questions about Jay's radical parents, whom the boy barely knew, haunt this finely portrayed cocoon of Park Avenue privilege.

At its best, this curious novel is a study of disorientation, of knowing neither where nor who one is; the unmapped Australian wilderness provides a strange and lovely analog to Jay's mysterious parentage. (In one of the many stunning phrases that stud His Illegal Self, Jay imagines his bearded father possessing a "secret itchy life enclosed in hair.") His urge to understand his past grants the book a powerful emotional anchor.

Dial, herself a former radical, struggles with her own complex identity. Unfortunately, we grapple with it, too. Her believability as a character suffers a blow when she improbably attacks an acquaintance with a plank of wood. Jay's behavior, likewise, occasionally seems unlikely for someone so young (as when he says, "You can't imagine me"). By the end, we feel a bit unsure of who Carey's characters really are—making it fitting, if not satisfying, that they bear so many names.