To find a sound she wanted, Björk played Justin Timberlake, then Stockhausen: “It’s very simple. A little Justin, a little Karlheinz.” Photograph by Richard Avedon / © The Richard Avedon Foundation

I first met Björk in the lobby of the Hotel Borg, a funky Art Deco place in the center of the Icelandic capital of Reykjavík. The Borg opened in 1930, the dream project of a famous wrestler who liked to host swank parties for American military officers and the odd movie star. Eventually, the wrestler died and the hotel fell on hard times. In the early nineteen-eighties, it became the gathering spot for a group of aggressively bohemian teen-agers, who theorized punk-rock anarchy at the hotel bar. One of the gang was Björk Gudmundsdóttir, the daughter of an electrician and a feminist activist. She sang in a band called Kukl, which means “black magic,” and she outraged older Icelanders with her antics. Parents shuddered when the singer bared her midriff on television while visibly pregnant. Now she is thirty-eight, but she still looks as though she could fall in with a group of fashionable delinquents. She walked through the door of the Borg wearing a ladybug cap and white shoes with red pompoms on the toes.

It was a pale, mild morning in early January. The day before, an ice storm had rendered the city impassable, but some shift in the Gulf Stream had warmed the air overnight. We took a taxi into the suburbs, where Björk was working on a new album. She held in her hands a program for the play “The Master and Margarita,” which she had seen the night before. She read Mikhail Bulgakov’s novel, on which the play was based, when she was a teen-ager, and it remains one of her favorite books. “The book is very popular with Icelanders,” she said. “It has a very Nordic feeling to it, even though it is Russian. It ridicules bureaucracy, it has black magic and Arctic magic realism. You could say it is ‘Alice in Wonderland’ for the Arctic grownup.” I nodded, and glanced significantly at a snowcapped mountain ridge in the distance. “Of course,” she added, looking at me carefully, “you have to watch for the Nordic cliché. ‘Hello! I am a Viking! My name is Björk!’ A friend of mine says that when record-company executives come to Iceland they ask the bands if they believe in elves, and whoever says yes gets signed up.”

Björk is probably the most famous Icelander since Leif Eriksson, who discovered America a thousand years ago. Vigdís Finnbogadóttir, who served as the country’s President from 1980 to 1996, once compared her to the strong women of the national sagas, like Brynhild and Aud the Deep-Minded. Björk has spent much time abroad in part to escape this monumentalizing attention, which makes her uneasy. Instead, she has ended up with a global sort of fame: as the creator of seven solo albums, involving English, American, Indian, Iranian, Brazilian, Danish, Turkish, and Inuit musicians; as a sometime actress, who in 2000 won the best-actress prize in Cannes for her performance in “Dancer in the Dark”; and, more recently, as a denizen of the New York art-world circles frequented by her partner, Matthew Barney. Her appearance, last week, at the opening ceremonies of the Athens Olympics, singing an ornate new song called “Oceania,” confirmed her status as the ultimate musical cosmopolitan, acquainted with both Karlheinz Stockhausen and the Wu-Tang Clan. Though she now spends much of her time in New York, she keeps coming back to Iceland, where she lives for several months of the year. The relative simplicity of the place is reassuring to her. Once, she translated a local news headline for my benefit: “tire tracks in football field.” A look of pleasure crossed her face as she studied photographic evidence of the catastrophe. “This is so Iceland,” she said.

In my talks with Björk, which began in Reykjavík and continued in New York, London, and Salvador, Brazil, she returned often to the “Nordic idea,” although she never said anything too specific about it. I think she simply wanted me to keep it in mind. Some sort of Nordic idea is plainly at the heart of her new album, “Medúlla,” which Elektra/ Atlantic will release at the end of the month. The moment you try to put this idea into words, however, the glacier of cliché begins to advance. Ásmundur Jónsson, the visionary manager of the Icelandic record label Bad Taste, once said that her earliest solo recordings evoked for him a solitary figure standing in an open space; but there is nothing inherently northern in that. Whatever is Nordic in Björk’s music is filtered through her own creative personality, which is all-devouring by nature, taking in dance music, avant-garde electronic music, twentieth-century composition, contemporary R. & B., jazz, hip-hop, and almost everything else under the winter sun. Björk has traits both elemental and eclectic: she wants to get to the core of her world, but she also wants to melt it down.

When it becomes known that you have met Björk, people tend to ask, with an insinuating grin, “What’s she like?” She is expected to be a cyclone of elfin zaniness; she is, after all, the woman who showed up at the 2001 Academy Awards with what looked to be a swan carcass draped around her body. She does have her zany moments—I won’t soon forget the image of her dancing down a street in Salvador shouting “Bring the noise!”—but it is not the first word that comes to mind. She is warm, watchful, sharp-witted, restless, often serious, seldom solemn, innocent but never naïve, honest and direct in a way that invites confidences, shockingly easy to talk to on almost any subject but herself. Teresa Stratas once said that Lotte Lenya was “an earth sprite, a Lulu, at once vulnerable and strong, soft and hard-edged, child-like and world-weary.” Much the same could be said of Björk, except that she is rather nicer than Lulu—and far from being weary of the world.

Early work on “Medúlla,” whose name describes the inner part of an animal or plant structure and, more appositely, the lower part of the human brain, was done at Greenhouse Studios, which belong to the producer Valgeir Sigurdsson. Valgeir is a mellow, soft-spoken guy in his early thirties; he has worked with Björk since 1998, when the two collaborated on the soundtrack for “Dancer in the Dark.” The studio is at the end of a cul-de-sac in the suburbs of Reykjavík. From the outside, it looks like an ordinary home, which it partly is: Valgeir lives with his family on one side. The main recording console is in a long room with cathedral-style windows and gleaming beech floors. Downstairs is a small performance space, with an adjoining kitchenette. The place is cool, spare, and eerily neat, Valgeir’s T-shirt-and-torn-jeans style notwithstanding. By the time we went upstairs, the midwinter day was already ending. An hour later, a full moon was hanging uncomfortably close. The white-capped mountains glowed in the distance.

Björk sat down to listen to sketches and partly finished versions of the songs that she wanted to put on the album. She had written some of them at the end of last year, during a trip to La Gomera, in the Canary Islands. “I am at the point where I can let it out for other people, hear them through other people’s ears,” she said. “There is a point where you are very secretive, but then you become confident enough that you can hear criticism, and not become discouraged.” I nodded sympathetically, as if I, too, were an Icelandic pop star who has erased boundaries between genres. Björk often uses the second person to close the distance between herself and others.