What does video art look like? Sometimes it can be a sculpture

Until recently, ''video art'' - the art of the television tube - was a minor offshoot of the avant-garde. A medium for tinkerers and experimenters, it was so new that nobody had quite figured out how it worked, much less what to do with it.

In the past couple of years, though, video art has done a lot of growing up. The novelty has faded, the grammar has been worked out, and significant work has emerged.

The dominant figure of this activity has been Nam June Paik, a Korean-born composer, artist, and performer who switched from music to video in 1963 and hasn't looked back since. His current exhibition at the Whitney Museum of American Art--perhaps the most prestigious American showcase for major video work--makes a compelling case for this new, blossoming form.

What does video art look like? Generally speaking, nothing like ''Mork and Mindy'' or ''Life on Earth,'' or even the video games that have sprouted like weeds lately. Most video artists--including Paik--work in a poetic vein, expressing ideas and feelings in a personal and subjective way. Image and structure tend to be more important than story or character. Visual imagination is the highest priority.

The results may be videotapes that look like TV poems. Or video may be used as a plastic form, like painting or sculpture, in works nicely suited to galleries and museums. As this trend continues, video is gaining recognition as a versatile and malleable medium. After all, as long as the electricity stays on , a video work is as permanent as any other. And despite its complicated circuits, it's no more heterogeneous than the mixed media of, say, a Joseph Cornell collage or a Robert Rauschenberg ''combine painting.''

Paik's exhibition focuses on video as a sculptural element. In some cases, the video tube contains the work of art like a picture frame. Good examples are the ''Magnet TV'' pieces, with images bent into shape by simple magnets placed on television consoles. In other cases, the video tube becomes part of a larger construction. The most striking case is ''Video Fish,'' in which tropical-fish aquariums are lined up in front of 15 TV monitors jumping with kinetic pictures of blue skies, zooming airplanes, imposing buildings, and yes, more tropical fish.

Isolated in its own dark corridor, such a work isn't just a sculpture, it's an environment. The same goes for ''Fish Flies on Sky,'' which invites viewers to lie on the floor and watch TV monitors dangling from the ceiling. ''Laser Video'' fills a wall with bright green images of Merce Cunningham, the dancer (in a superb videotape by Charles Atlas), punctuated with frantic beams of pure red light.

Other environmental works build a quieter atmosphere. The dazzling ''TV Clock'' presents an array of slanted lines on a gently curving string of 23 monitors. ''Moon Is the Oldest TV'' displays the lunar phases. A less impressive piece called ''Imagine There Are More Stars on the Sky Than Chinese on the Earth'' projects round, blurry images onto otherwise bare walls and ceiling.

Imposing works, every one. Yet there's a sense of whimsy lurking here--after all, the dominant motif is tropical fish! As it happens, Paik is a joker as well as a thinker, and he was a dadaist before he became a technologist. A sly sense of humor shines through much of his activity: There's a photograph of him in his music-student days, slumped over a keyboard in solemn slumber. There's his ''TV Chair,'' a gloriously impractical invention. There's the ''Violin With String,'' a bedraggled instrument to be dragged along the ground, and the ''TV Cello,'' built of working picture tubes.

Then too, Paik is not entirely a rampaging modernist. Tradition threads through his work, along with a wry nostalgia for nature. The fabulous ''TV Garden'' surrounds upended monitors with a lush roomful of green plants. Another work features a video image projected on a huge glass egg--giving a touch of the farmyard and a hint of three-dimensional television. The meditative ''TV Buddha'' is a stone statue contemplating its own ''live'' image on a monitor buried in dirt, while nearby a small copy of Rodin's ''The Thinker'' gazes at a tiny Sony screen. ''Real Fish/Live Fish'' juxtaposes more of those ubiquitous tropical fish with their own televised ghosts, in a punning comment on the word ''live.''

More radically yet, the wonderful ''Candle TV'' dispenses with electronics completely, replacing the picture tube with a lonely candle burning brightly in an empty console. Another piece contrasts a traditional sculpture with a fire-damaged TV set. Even a static work like ''Life Ring 66''--a beat-up old electromagnet--reflects a healthy demystification of technology.

It seems clear that Paik is steeped in science, art, and nature, all at the same time. Some of his most expansive works are intimately tied to the computer age, from his friendly-looking robot (named K-456) to his babbling tower of TV tubes, the ''V-rymid.'' Yet touches of sea, sky, and earth are never absent for long. It's this balance of the timeless and the timely that puts Paik at the forefront of the burgeoning video-art movement. Firmly rooted in the real world, and swarming with tropical fish to prove it, his antic technologizing has a great deal to tell us.

The exhibition of works by Nam June Paik will continue at the Whitney through June 27. In conjunction with it, a selection of Paik videotapes will be shown on Channel 13 in New York each Sunday evening through June 20. The museum will sponsor a panel discussion of Paik's art on May 21, and performances by Paik and cellist Charlotte Moorman will take place on June 2 and 3.

After closing at the Whitney, the exhibition is tentatively scheduled for the Museum of Contemporary Art in Chicago, the National Gallery in West Berlin, and the Museum Moderner Kunst in Vienna.