Broken Flowers (15)

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For two-and-a-half decades, Jim Jarmusch has been the exemplar of cool in American cinema - and I mean "cool" as it was defined decades before the the word became a Starbucks-era shibboleth. I mean "cool" as in a few degrees above glacial, as in cool jazz - the art of placing the fewest notes in the perfect places with sublime diffidence. In acting, the current paragon of such a stance is Bill Murray, and the idea of him and Jarmusch collaborating might suggest prospects of a stillness way beyond zen. Yet Broken Flowers is not only a work of crystalline simplicity, it's also Jarmusch's most entertaining film in years and by far his warmest. That's in spite of its deep-rooted melancholy; but imagine something like Sideways in a less convivial minor key, or a road comedy as Ozu might have made one, and you get a sense of Jarmusch's take on the male middle-age blues.

The build-up is languidly assured: a woman posts a pink envelope, and to the woozy crawl of a Sixties-ish pop ballad, we watch its progress through the US postal system. It arrives at the door of Don Johnston (Murray), just as his younger girlfriend (Julie Delpy) is leaving him, tired of living with "an over-the-hill Don Juan". Left alone mooching on the sofa to Fauré and Marvin Gaye, Don opens the letter: it's unsigned, from a lover of 20 years earlier, announcing that Don has had a child with her, a son who's now grown up. Don's Ethiopian neighbour Winston (Jeffrey Wright), an internet sleuth, badgers him into visiting his girlfriends from that era, to identify the mystery woman: the suspects are played by Sharon Stone, Frances Conroy, Jessica Lange and Tilda Swinton, barely recognisable as a backwoods biker.

Broken Flowers is only nominally a detective story: there's a mystery, but no real intrigue. The real riddle is less about the letter than about the past and where it went: who Don and his girlfriends were, and who they've become. Lawyer Carmen (Lange) has become a beatifically composed "animal communicator", a converser with cats and iguanas; stiff suburban Dora (Conroy) is revealed in an old photo to have once been a wafting-in-the-wind flower child.

The coda has Don delivering a philosophical payoff of sorts, but it's so general as to mean almost nothing: the past is past, the future hasn't happened, all we have is the present. This is virtually a parody of road-movie wisdom, but what's fascinating is how Jarmusch dramatises it visually. Repeated shots of Don's wing-mirror show the road receding behind him, as he drives into an uncertain autumnal future.

The general rule of such American pilgrimages is that the protagonists should be seriously changed by the end: in fact, Don starts out battered emotionally, and returns battered more visibly, bruised by his investigations just as Philip Marlowe used to be. Just how he's changed is left for us to divine: Jarmusch declines to reveal too much. There are some wonderful moments when you think you know exactly what you're seeing, and yet you couldn't easily spell it out. What's Don thinking when he watches two young girls on a bus giggling about a handsome young man? What's going through his mind when he glances at, but seems to shy away from, a leggy flight attendant? Or when he's confronted by Stone's teenage daughter (Alexis Dziena), prancing before him in all her pink precocity? The infinitely interpretable nature of Murray's low-register reactions is what makes his performance so rich; it's also what enables him to crack you up just by spearing a forkful of sliced carrot, or exchanging stares with an equally inscrutable tabby cat.

Even though the external signs are much the same, Murray here conveys an entirely different world-weariness to the one he exuded in Lost in Translation. A limited range can sometimes make for the greatest screen acting, and Murray is limited in the way that Bogart was, or Mitchum: instead of widening his repertoire, he's extended inwards, developing the most telling possible range of finely modulated nuance.

Jarmusch shares this taste for the muted, in every sense. Listen to the background silence in Dora's sepulchral show home, where a doorbell seems to chime from a continent away; and watch how the Carmen sequence ends with a tiny, almost throwaway gesture between Jessica Lange and Chloë Sevigny, sketching in the characters' back story in the cinematic equivalent of invisible ink.

It's all so low-key that when Jarmusch does seem to press a point - as in the repeated references to Don Juan, or Laura's daughter actually being called Lolita - it comes across as a tight-lipped joke about other films' tendency to overstatement. The felicities are endless: Sharon Stone, genially flirty, at last chalking up another performance to match her turn in Casino; the poignant, sober perfection of Don's visit to a dead girlfriend's grave and his quiet, solemn "Hello, beautiful"; and on the soundtrack, the sinuous horns of Ethiopian jazz artist Mulatu Astatke. Broken Flowers is a beautiful film, the smartest, saddest American comedy in ages, and incidentally, a pretty compelling argument for the value of letters over emails.