When aging ladies’ man Don Johnston (Bill Murray) gets an anonymous letter informing him that his 19-year-old son, whom Johnston didn’t know existed, is on his way to find him, it doesn’t affect him much. Nothing does. His driven neighbor Winston (Jeffrey Wright), an amateur detective and family man whose full life emphasizes the void in which Johnston lives, convinces him to track down the mother. Armed with a list of four possibilities, an itinerary provided by Winston, and his deep, quiet sadness, Johnston hits the road.

The road-trip portion gets started on what feels like a bad note, with Laura (Sharon Stone) and her nubile daughter Lolita (Alexis Dziena) providing a few too many easy laughs. That’s just to lull you into thinking you know what’s going to happen; the sequence with Dora (Frances Conroy of TV’s "Six Feet Under") takes another easy situation and turns it on its head, as a dinner scene featuring her husband (Christopher McDonald, one of the most underrated character actors working today) turns unexpectedly uncomfortable and poignant. Nobody does silent, odd discomfort like Jim Jarmusch, and this scene ranks up with his most painfully funny—you don’t know whether to laugh or to cover your eyes, so you do a bit of both.

Carmen (Jessica Lange) is an animal communicator whose cat understands Johnston’s motives better than he does, and Penny (Tilda Swinton) lives in Alexander Payne territory in a remote shack with violent, toothless men. By this time—indeed, ever since the painful dinner—it’s unclear why Don is going through with it; perhaps it’s inertia pushing him forward once he starts moving, or perhaps being on the road is a way of avoiding the potential knock on the door from his long-lost son.

Does Johnston find the mother, a solution to the mystery? That’s up to each viewer to decide. Credits-watchers might find a “solution” in the cast list, but the answer there feels like a red herring. The real search in the film is not the search for the mysterious writer, but Johnston’s search for who he was in the past and how he ended up where he is at the beginning of the film, watching The Private Life of Don Juan on his big-screen TV as his latest girlfriend (Julie Delpy) leaves him because he won’t commit to her, or to anything. Murray, with his sad face and far too understated performance, so understated that it borders on the inert, doesn’t let us in until the end, and only partly so there. It’s about questions, not easy answers, and its refusal to provide them might frustrate some viewers unaccustomed to Jarmusch’s elliptical style.

It's a strangely flat movie. There's a line somewhere between reserve and inexpressiveness, and the film spends too much time on the wrong side of that line. Murray's clownish face is asked to carry too much of the burden, and whereas this performance might look like a carbon copy of his turns in The Life Aquatic with Steve Zissou and Lost in Translation, there's substantially less to it. I hope it's the last entry in his stone-faced period, because he has so much more to offer as an actor.