Alejandro González Iñárritu: This is the jigsaw of our lives

'Amores Perros' put Mexican director Alejandro González Iñárritu on the map. Can '21 Grams' keep him there, asks Jonathan Romney

Four years ago, Alejandro González Iñárritu's debut feature Amores Perros gave Mexico a greater prominence on the world cinema map than it had had for years. With the success of Alfonso Cuarón's Y tu mamá también a year later, pundits forecast a Mexican renaissance to sweep the world. It hasn't quite happened yet, although Cuarón - already an old Hollywood hand - has directed the next Harry Potter film. Iñárritu, meanwhile, has confounded admirers by making his second film 21 Grams in the US, in English and with a cast of Hollywood names - Sean Penn, Naomi Watts and Benicio del Toro. One thing remains the same, however - as in Amores Perros, Iñárritu and screenwriter Guillermo Arriaga have made a film about three people whose lives are dramatically affected by a car crash.

But 21 Grams definitely does not tread old ground, insists Iñárritu, a former radio DJ and a remarkably genial sort for someone who has made such an uncompromisingly harrowing film. "Even if it sounds familiar, this story is completely different. All Amores Perros and this one have in common is that there are people with eyes and a nose and mouths and ears. I feel this film will affect people in a deeper way than Amores Perros. The fact is, I think Amores Perros is more exotic. This film is more intimate, and the characters are closer to everyone's life."

He continues: "Anybody can lose their health any day or lose a family member, or lose our dreams or faith - that makes a film sometimes very uncomfortable for people." What makes 21 Grams truly uncomfortable - and truly fascinating - is its uncompromisingly challenging structure. Amores Perros was already a formidable feat of intricate construction, with its three interlocking storylines, but it looks almost simplistic alongside 21 Grams - a narrative jigsaw of episodes arranged in an order that at first sight appears entirely random. This shape, says Iñárritu, was inspired partly by Michael Haneke's similarly film-in-fragments Code Unknown, partly by novelist Arriaga's long-standing devotion to William Faulkner.

Making sense of 21 Grams is by no means easy, but nowhere near as difficult as it initially looks, Iñárritu insists. "It's an experimental structure which in the end is a very simple one. Once people get the code, everything comes together and there's no problem if I jump from here to here, because people understand the rules. Sometimes people tell me, 'I was completely lost in the first 25 minutes, but then the reward was so big.'"

It's hard to resist searching for hidden patterns in the film, especially given the scene in which Penn - as a mathematician reprieved from a fatal heart condition - gives an impromptu lecture on the hidden beauty of numbers. You wonder whether Iñárritu and Arriaga had their laptops running algorithms on the script. In fact, says Iñárritu, the jumps from sequence to sequence were dictated purely by emotional logic. Nevertheless, he says, there is a mathematical - or at least, philosophical - premise behind the film.

"Before we shot it, I read an article in The New York Times in which a mathematician was interviewed about coincidence - about how much a coincidence really is a coincidence, not just a possibility that's in the air but we don't see it. Coincidence is more normal than we think. Supposedly we are all seven people from everybody. The person that will affect your life forever is now living and is coming in your direction. You don't have a TV switch to see what she's doing, but when you're making films, you have that ability to see the connections."

Amores Perros was widely considered a flagship for a new confident, muscular Mexican cinema that could make its presence felt worldwide. Understandably, Iñárritu has had to defend himself against criticism for making a non-Mexican follow-up (in fact, several compatriots from the Amores Perros crew, notably cinematographer Rodrigo Prieto, are still on board in 21 Grams). Indeed, the film was originally written in Spanish and set in Mexico, but when it received US funding, the setting was changed to Memphis for convenience. This grittily mundane locale certainly gives the film a distinctive look: "It's a real city. It's not a movie set. It's not this fancy trendy global city of the US - all of them look exactly the same now."

There's nothing specifically Mexican about the film, Iñárritu says, or North American either for that matter. "There will always be people who try to reduce art to a local cheap patriotism thing. This film could be shot in England, or Paris or Tokyo. There's nothing local - the themes are so basic, they're all universal characters." In any case, he says, he expects to return to Mexico next, where he and Arriaga intend to complete "a triptych of triptychs". One reason Iñárritu was happy to make the film in the US, he says, was that it allowed him access to the best possible actors, as widely sourced as possible. The international cast includes Eddie Marsan, a stalwart British plug-ugly whose face you'll know, if not his name, and (more awkwardly) French actress Charlotte Gainsbourg, sounding bizarrely like her mother Jane Birkin, as Penn's English wife. Given that the film could have pushed its melodramatic themes - life, love, loss, redemption - to hair-tearing extremes, what is remarkable about the acting is how underplayed it is, most surprisingly from the often overheated Penn.

Iñárritu looked for understatement and implied emotion: he cast del Toro, he says, because "through his eyes you can see a lot of things going on in him - he's so complex, just by doing nothing." He also prides himself on spotting Naomi Watts early on, not in her breakthrough film Mulholland Drive, but in a short playing a struggling actress. "As a director, the one thing I feel comfortable with is that I can immediately recognise the honesty in somebody. I'm a good liar-detector, so I know she's always very honest."

21 Grams could easily sound like a global pudding cooked to Hollywood specifications, if it weren't such a challenging piece of work - an unapologetic art film that looks rougher, grubbier and moodier than any comparable Hollywood production, and that flaunts its metaphysical preoccupations too. Besides, 21 Grams demands far more input from the viewer than mainstream narratives generally do, and emotionally and intellectually, it pays off - Iñárritu is confident of that. "People have to make an investment. You have to go to the bank and put in £1,000, and in two years you receive £10,000. Even though you can't touch it for the first two years, there's a reward."

'21 Grams' (15) is released on 5 March