Laurie Anderson's multimedia blitz

Laurie Anderson wants to wake us up, shake us up, catch us off guard - and while she's at it, do the same services for herself. How else to explain her artistic odyssey over the past dozen years? A recognized visual artist, she has taught art history and published several books of poetry and prose. A trained classical violinist, she has released a rock album - ''Big Science,'' on the Warner Bros. label - and recorded a single called ''O Superman'' that hit the top of the British pop charts.

And she has turned her attention to less familiar paths as well, composing ambitious mixed-media collages of music, words, gestures, and filmed images. These have been performed throughout the United States and Europe, building Miss Anderson's reputation as an aesthetic pioneer.

The culmination of all this activity will take place Feb. 3 when she presents the world premiere of ''United States,'' a four-part multimedia extravaganza that has been developing in bits and pieces since 1979, at the Brooklyn Academy of Music. It will run about six hours and require two complete evenings of watching and listening, and will continue through Feb. 10. Miss Anderson will be the star as well as the creator, assisted by more than a dozen colleagues, ranging from backstage technicians to onstage ''talkers.''

To find out more about ''United States,'' I phoned Miss Anderson - a fitting idea, since the telephone is one of her favorite props - at her lower Manhattan home. To begin, I asked how she would describe this massive enterprise.

''Visual songs,'' she replied. ''My main intention is to make a portrait of a country. At first I thought it was just the United States, but it's not turning out to be that way. It's a portrait of any highly technological society.''

Like such a society, ''United States'' is complicated, full of interlocking pieces. ''As I work on it,'' the artist said, ''I realize that it's made of many small, movable parts. I'm experimenting with different positions for them, figuring out how they'll fit together best. And I'm finding that each little segment means something different, depending on how you fit it in, and how it relates to all the other parts.''

Among the elements of ''United States'' will be plenty of music - from keyboards to bagpipes - and lots of film, which has a clarity that Miss Anderson prefers to the more flexible but less visually striking images available from video techniques. Also expect electronically altered voices, and sounds from the ''tape bow violin,'' an Anderson invention that replaces the strings of a violin with an ''audio head'' and substitutes recording tape for the usual horsehair of the bow.

Though the epical ''United States'' will make its debut before a New York audience - at the innovative ''Next Wave'' series hosted by the Brooklyn Academy - Miss Anderson is anything but parochial in her performance habits, often ranging far from her home city. About half her work is done in Europe, where (like many other innovators) she finds audiences much more patient and willing to try new experiences. ''I think 'United States' might be better understood in Amsterdam or Berlin than in, say, Tennessee,'' she opines.

Yet she has an abiding respect for American audiences, including those not usually exposed to unconventional art events. In fact, during recent American tours she has made a point of appearing in places quite removed from the usual art-world venues, bringing her wares to fresh and unjaded spectators. ''I've been reaching out more, recently,'' she told me. ''At first I didn't know how people would take my work, but it's turned out very well. Audiences are smarter than I thought,'' she concluded with a quick laugh.

Miss Anderson is controversial, to be sure. Some critics - including a few who are normally sympathetic to new explorations - have attacked her work as facile and trendy, or dismissed her versatility as dilettantism. And some caveats are certainly in order: It's true, for example, that her brief ''O Superman'' makes a better case for her musical ingenuity than the album-length ''Big Science,'' and that her public personality sometimes seems more likable than substantial.

But even the casual observer of recent Anderson work can sense an energy, a drive, and a sense of purpose to it - a sense of purpose so strong that it's about to weld the whole Anderson career (so far) into a single monolithic experience that takes two nights to see and is named after a whole country. It promises to be the definitive occasion for summing up and evaluating the contributions of a most unpredictable artist.