“Nymphomaniac” plays Saturday night (“Part I” at 7 p.m, “Part II” at 9:30 p.m.) at the Union South Marquee Theatre, 1308 W. Dayton St. as part of the UW-Cinematheque summer series. Not rated, 4 hours 2 minutes, three stars out of four. FREE!

You know how cartoon characters like Elmer Fudd will have a little Elmer Fudd angel on one shoulder and a little Elmer Fudd devil on the other? Lars Von Trier has that. Only he has a devil on one shoulder and another devil on the other.

One devil is the pitch-black moralist, who sees the human condition as an unending exercise in misery, much of it self-inflicted. But the other devil is a naughty schoolboy, the one who can chuckle nastily at this misery, pushing his characters and his audience so far through the wringer that it becomes almost funny.

Both devils are in fine form in Von Trier’s notorious new film “Nymphomaniac,” presented in two two-hour segments. Von Trier wants to titillate and unsettle us with a barrage of graphic nudity and sex. But underneath the raunch is a much sadder story.

The film opens with Joe (Charlotte Gainsbourg, who should get medals for what Von Trier puts her through) lying beaten and bleeding in an alleyway, an uncomfortably lovely snowfall covering her broken body. She is taken in by Seligman (Stellan Skarsgard), a kindly intellectual who gives her tea and fresh clothes, and a sympathetic ear.

Joe begins to tell the story of her sexual life in a series of chapters, starting with 12-year-old Joe grappling with the new sensations flooding her body. Then, for the rest of Part I, we meet teenage Joe (Stacy Martin), and follow her picaresque bed-hopping adventures from one man’s bed to the next. Then, in Part II, we’re with adult Joe, whose quest for fulfillment takes her into much darker places — the chapter called “The Dangerous Men,” with boyish Jamie Bell as a polite sadist, is a hard one to take.

The four hours fly by — “Nymphomaniac” is by turns sad, brutal, philosophical and, yes, sexy, and Von Trier seems incapable of composing an uninteresting shot or pulling a less-than-compelling performance out of an actor. And, startlingly, it’s even funny, at least in “Part I.” Seligman keeps hilariously interrupting Joe’s tales of sexual abandon to relate it to something high-minded, like a Bach piece, or architecture, or even fly fishing. He’s sort of like the grandson in “The Princess Bride,” although instead of wanting to skip the “mushy stuff,” he wants to annotate it.

Even some of the roughest moments of the film contain some humor; Uma Thurman is fantastic in a scene as the wronged wife of Joe’s married lover who brings their three small children over to confront her. “Would you mind if the children see the whoring bed?” she asks politely, which drew a huge laugh from me, even as I recognized the genuine agony behind the laugh line. Another sequence, in which Joe sits by the bedside of her dying father (Christian Slater) is more punishing, Von Trier rubbing our faces in the fears of every child with an aging parent. You don’t see that in a lot in films on sale at Red Letter News.

That’s sort of the rhythm of the film, to lure us in with Joe’s salacious tales over and over, only to suddenly yank us back to reality with a moment of tragedy, or act of violence, or one of Seligman’s digressions. It’s either one of the worst pornos ever made or one of Von Trier’s best films, a look at the danger of either denying one’s sexual self or embracing it too deeply. Love it or loathe it, no one else could have made this film.