So what did you do at school today?
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To all appearances, Gus Van Sant's Elephant - last year's Palme d'Or winner in Cannes - is about, or at least is inspired by, the Columbine high school massacre. Perhaps it's more accurate to say that Elephant is about the events leading up to a similar massacre - except that would imply some simple causality, which isn't the case here. Strictly speaking, the film tracks events during a day at an American high school in Van Sant's own home town of Portland, Oregon - a day which happens to end with two boys slaughtering many of their fellow students. But saying that events end in catastrophe is not the same as saying that they lead directly to it: that would suggest that they explain it. Nothing actually "leads to" the killing here: simply, the killing is the point at which the film's various narrative paths converge, at the end of what seems a haphazard drift.

Acted by real-life Portland students improvising their dialogue (plus three professional adult actors), Elephant depicts a single day which is no less ordinary for the fact that it comes to an extraordinary ending. The film seems interested less in the cataclysm than in the mundane goings-on that precede it: three girls bicker over lunch, a boy takes photos, another reports to the principal's office. And two more admire their new gun and plan a military assault on the school. Some of the students are living through personal crises - family trouble, exclusion, possible pregnancy - of the sort that would make for verbose, tear-stained melodrama if this were a mainstream high-school melodrama or an episode of Dawson's Creek.

Elephant, however, only allows us the briefest glimpses of inner lives beneath the ebb and flow of quotidian event. We get a strictly external view of things: Harris Savides' Steadicam drifts along behind the students as they cross lawns, walk up corridors, dawdle in lunch queues, allowing us to know them only briefly before they merge into the crowd. As the teenagers interact, the film barely sketches out their relationships with each other or with the school. Everyone is either lost in his or her own world, or is in relationships that seem as much to do with conventional role playing as with emotional connection - such as handsome sweethearts Nathan and Carrie, and a trio of bulimic teen princesses who are the only figures here approaching caricature.

Throughout the day, scenes overlap as the characters cross paths at moments that, inconsequential as they are, help map out the course of events. The repeated moment when one boy photographs another provides a recognisable landmark in time. But it also functions like a still photo - a moment detached from the continuum. It's a moment that is given a particular charge of significance of the sort that ordinary moments retrospectively receive when they precede catastrophe.

When the film leaves the school, it enters riskier territory. Showing us the two young killers at home, the film practically dares us to jump to conclusions. There's a documentary about Hitler on TV; they play a violent computer game. Obviously this explains everything. But one of the boys, Alex Frost, also plays the "Moonlight Sonata" and the drawings on his wall suggest he's a skilled artist: does this explain everything too? Or rather, is Van Sant taunting us into looking for facile logics where there simply aren't any on offer? The most debated moment in the film occurs before the killings, as the two boys share a kiss in the shower: again, is Van Sant, one of America's most prominent gay directors, provoking us into making blithe assumptions about gay teenage Nazis? Or he is highlighting our desperation to grasp at easy answers, to reduce all these people to ready-made labels: gay Nazi, jock, nerd, prom queen?

One of the points made by Elephant seems to be that the American high-school universe doesn't offer its youth many options for complex, nuanced identities. We think it's easy to understand who people are, and what their actions mean, but Elephant disproves this by keeping us at a distance from events and from characters' experience - much of the time literally, as the camera drifts several paces behind them. The teenagers' faces - often beautiful, placid, opaque - reveal nothing.

Yet the film sometimes allows us to reach a more acute awareness of these teenagers' situations, by virtue of what isn't revealed. Michelle (Kristen Hicks), an awkward, middle-aged-looking girl, sits hunched in the changing room: we hear girls talking behind her, out of shot, and though we can't make out a word they're saying, we sense they're discussing her, because we sense she's sensing it. It's as if the film takes us into Michelle's head by keeping out of it. Sure enough, the scene ends just as we make out the word "loser". Elephant also plays with our assumptions about narrative: a completely new character, a muscular black kid (Bennie Dixon), strides into the chaos at the eleventh hour, but his role proves to be nothing like it would be if this were a conventional Hollywood treatment of the Columbine story: Van Sant may rigorously plot out the course of this fateful day, but the intent is not to create a coherent storyline. This is not a story, just a collection of events. The reality depicted here is abstract, arbitrary: people get killed for no apparent reason.

Elephant is not a shocking film although it deals with a shocking incident. Instead, it covers events in a style that is disarmingly detached, incongruously cool. Van Sant has been accused by some critics of turning slaughter into an aesthetic experience, although that's just what Hollywood routinely does every week and no one turns a hair. This is not the case with Elephant. It may be beautiful, even poetic, in its apparent detachment, but it is above all a film about detachment, about people drifting through events they don't comprehend in a world they don't comprehend.

Perhaps the most striking shot shows Alex ploughing down teenagers who happen to be in the wrong place at the wrong time. But we barely see the effects of his action, just a medium close-up of his face, the camera hanging over his shoulder as his gun goes off: it's as if he's observing the killing in a trance, as if he weren't a part of it. It's clear too that when the boys plan their action, heralded in brief flashes-forward, they use a ready-made language of guerrilla war that allows them to play at being adults: "We should be able to pick off kids as we traverse the East Wing." That stilted "traverse" says it all: they aren't even present in their own language.

Elephant shares its name, and its tactic of confronting hard reality with formal abstraction, with the 1989 drama by British film-maker Alan Clarke about sectarian killings in Northern Ireland. In fact, Van Sant says he used the name by way of allusion to the story of the blind men who each describe a different part of the animal without discerning the shape of the whole. This is similarly a film of fragments, hints, intuitions, a film that refuses to paint us a reassuringly coherent big picture. This is not Columbine as Hollywood, or even Michael Moore, might explain it to us, but something much more troubling and resonant.