Eskimo artist Paul Tiulana cherishes the 'old ways'

''I weigh the two worlds I live in,'' says Paul Tiulana, an Inupiaq Eskimo from tiny King Island, 35 miles off the coast of Alaska and 50 miles south of the Bering Strait.

''My way of life is better - we don't have no divorce, no state trooper, child abuse, alcoholism, no lawyers,'' continues Mr. Tiulana, a carver, singer, dancer, and one of 17 National Heritage fellows appointed this year by the National Endowment for the Arts.

But Anchorage, Alaska, where he now lives, is glutted with all of the above.

''I don't like it,'' he says without pause, ''but I know how to handle it; I know the problem areas. And it was better for our children,'' he adds, pointing with considerable pride to his two daughters, both of whom have university degrees.

As he talked, Mr. Tiulana carved away on a wooden walrus mask for the Smithsonian Institution's 1984 Festival of American Folklife. Later in the week, he donned the mask to perform a powerful and energetic walrus dance, imitating the motions and sounds of this two-ton beast, to the delight of festival-goers.

Using wood or ivory, Mr. Tiulana usually carves replicas of the animals he hunts. In fact, he had just returned from his annual jaunt to King Island to kill walrus before he came to the festival.

The Eskimos use every part of the animals they kill. They eat the meat and blubber, use the hide to cover their boats, and burn the bones for heat and light.

Speaking of the traditional ways of life brings a special, warm smile to this man's face. ''My grandson kill his first seal last year,'' he says, ''and I was the proudest grandfather in probably all Alaska.'' A hunter's first kill is traditionally given to the elders of the community, he explains, as part of a system of ''respect'' with which the community is governed. ''Then we hold a special potlatch (gift-giving party) and do many dances,'' he says.

Dancing, now held chiefly for the entertainment of tourists, says his wife, Clara, was once the Eskimo entertainment. ''We didn't have no TV,'' says Mr. Tiulana. The smile bubbles up again: ''We even have a TV dance. One Eskimo from Little Diomed went on 'This Is Your Life' and made up a TV dance,'' he explains.

But many of the dances have a spiritual significance, showing respect for the animals who feed the Eskimo people. ''I did a Wolf Dance a few years ago; there were only three elders left who knew the dance,'' he relates, ''me, and two others.''

In one part of the traditional dance, a dancer dressed as a hunter shoots another ''hunter'' with a real arrow as he ''mistakes'' him for a caribou; the dancer is expected to sacrifice his life for the dance. ''We decided to leave out that part,'' Mr. Tiulana says, smiling.

It took them nearly three months to prepare for the dance, practicing the steps and making the costumes. ''And you know how long it took to do? Thirty minutes.'' He beams again. ''Now it's all on videotape; the young people only have to watch to find out how to do it.'' The dance, along with other efforts he makes to teach the young their traditions, earned Mr. Tiulana the 1983 Alaska Native Citizen of the Year Award.

Communication between the generations of Eskimos has broken down considerably , Mr. Tiulana says. ''They go to grade school, high school, university, and learn different things. We're losing our connections,'' he says, referring to the complex channels of communication that kept the small groups of people hospitable toward one another in a difficult land.

''There are some kinds of cousins who can only say kind words to each other, so if they have a quarrel with each other,'' he explains, ''they have to find someone from another kind of cousin to go and speak for them. It's very complicated; even the anthropologists don't understand it all.'' He pauses, and smiles. ''Even I get confused, trying to explain it.''

Some of the connections, however, seem very familiar to nearly all cultures. Take his mother's reaction on the day Mr. Tiulana killed his first polar bear:

''My father was a very brave hunter, killed 35 polar bears in his lifetime. He didn't come back from hunting one day when I was 9. My mother wanted all my life for me to be like him, to hunt like him,'' Mr. Tiulana relates.

One day he went out hunting with his nephew and saw three bears. ''They were from here to that building,'' he says, pointing to the Department of Agriculture headquarters 200 yards away, ''and my nephew say, 'Uncle, why don't we shoot?' He was scared, but I tell him, not yet.''

As they got closer (''from here to that tent'') he said, ''Go ahead, shoot. And we got all three. I was very brave that day,'' he says.

''My mother had tears of joy in her eyes, she was so proud. Then she was satisfied,'' he says, and stopped urging him continually to go out hunting polar bears.

Obeying the elders in this way ''protects the community,'' Mr. Tiulana believes. Newly elected to his village corporate board (Alaska is divided into several native corporations that administer mineral rights, and each village belongs to a corporation), Mr. Tiulana hopes to imbue his village with a renewed sense of respect for the old ways as they learn to walk in the new.

His wife, meanwhile - a shy, pretty woman, also at the Folklife Festival to demonstrate skin sewing - thinks the new ways are ''better for women. We have washing machines, dishwashers, TV. It's easier for the women; not as much work.''

She uses her teeth to crimp the leather that is later used around the toes on her mukluks. ''I learned this from my mom,'' she says, ''asking her so many questions I drove her crazy. The girls today aren't as interested.''