YOU'VE HEARD about Arizonans. They want you to visit, but please don't stay. If people keep moving to Arizona, some of the major reasons to make to move - the wide open spaces, the fresh air - will vanish. It's a familiar dilemma, but it's one that not many admirers of Arizona fun-and-sun pause to consider.

Well, if you're planning a spring jaunt to Phoenix (and that's the best time - when the desert foothills to the north and east are in bloom and the sun is still fun), pause and consider. This place is Horizontal City, U.S.A. It goes on and on. Those foothills I just mentioned are being turned into residential neighborhoods. One-story structures advance farther and farther into the desert. It would resemble a flood if only there were a few drops of excess water. There aren't. Then there's the smog generated by all the cars used to travel all those distances. When I visited the erstwhile Valley of the Sun recently, there was very little sun and-the smog was vintage Los Angeles. Phoenicians who always mentioned Los Angeles as the dreaded prototype to the West knew what they were talking about.

In short, this city is in trouble. A suggestion to travelers in Phoenix: After you've taken your dip in an extravagantly wet swimming pool or hiked through the already overused desert, take a day to examine some alternatives to the traditional (i.e., post-World War II) way of life in Phoenix. Think vertical.

I'm not talking about the fledgling Phoenix skyline. It looks like any other city's skyline, and it hasn't slowed the horizontal growth. Begin instead with a visit to Cosanti, the home and studio and headquarters of the visionary artist Paolo Soleri.

Soleri came to Arizona from Italy in 1947, equipped with a doctorate in architecture, to study with Frank Lloyd Wright at Wright's Taliesen West in the desert outside Scottsdale. But the elaborate individual projects designed at Taliesen West did not interest him as much as the idea of designing fabulous new cities for the future. Citing the dangers of urban sprawl that now seem so obvious, and Phoenix is a case in point, Soleri proposed building cities up into the sky. He drew plans for fantastic structures that would house thousands of people and greenhouses and markets and offices and industry and leisure facilities under one roof, leaving the great outdoors relatively untouched, used only for light agriculture and recreation.

Drawings and models of these proposed "arcologies" are on display at Cosanti, and they are fascinating, but by themselves they don't justify a trip to Cosanti. They also are available in Soleri's books and in his traveling exhibitions, one of which drew large crowds at the Corcoran Gallery here in 1970.

No, Cosanti is an interesting tourist stop for reasons of its own. There (at 6433 Doubletree Rd. in the posh suburb of Paradise Valley) Soleri built down rather than up, scooping out mounds of earth from under concrete shells, creating a cool, serene, half-subterranean oasis. Soleri-designed bell assemblages, which help pay for Soleri's experiments, are on display and tinkle in the desert winds. Unless you're with a large group, there are no tours; but literature is available, questions can be asked, and wandering is encouraged except in Soleri's living quarters and the actual workshop spaces.

Cosanti is even more interesting as a preparatory course for the living embodiment of all those plans, Arcosanti.

To get to Arcosanti, you go about 60 miles on Interstate 17 north from Phoenix, ascending through the desert hills to a splendidly barren mesa top. At a little hole in the road called Cordes Junction, you leave the freeway and all that it represents, drive a few miles northeast down a dirt road, and arrive at Arcosanti, Soleri's vision of things to come.

When I was there on the day before the New Year, the air seemed fresher than any I had ever breathed. The human mood at Arcosanti did not quite match the air. The place has been under construction since 1970, and there's a long, long way to go. Funds are few, and most of the labor comes from the hundreds of students who have paid Soleri for the chance to work on the project with him at summer workshops (most get academic credit out of it). Except for the tours (held at 9, 11, 2 and 4 each day), there wasn't much visible activity on Saturday, Dec. 31. The student who conducted my tour was obviously a Soleri disciple, but she wasn't naive about it. She knew that the completion of Arcosanti was not right around the corner.

Even so, Arcosanti is a beguiling reason to leave the freeway. Perched on the northern edge of a little canyon that juts into the mesa, Arcosanti currently consists of seven buildings of various audacious shapes and sizes, connected by twisting paths that will eventually cluster around the base of a 25-story structure designed to house 5,000 people. Nearly everywhere is a nifty view, particulary from the natural-foods cafe atop the highest building. Ceilings are tall enough to ward away any potential claustrophobia. Curves abound. All this will be solarpowered, or so they say.

A tiny settlement can be seen in the distance, on the banks of the Agua Fria River. That's where the students who do the work are housed, though a few of them - and one family - are already living on the site. Across the little canyon is an amphitheater where an arts festival is held every October. Last year's attracted Jackson Browne, McCoy Tyner, the Paul Winter Consort, the Ririe Woodbury Dance Company, composer John LaMontaine, Betty Friedan, several local native American and mariachi groups and 10,000 spectators. As at Cosanti, Soleri's bell assemblages chime at the slightest breeze.

Everything is astonishingly peaceful for an institution that wants to be known as the wave of the future. Or maybe it just seemed that way in comparison to the monster Phoenix shopping mall - complete with five huge department stores, dozens of smaller shops and stills more businesses sprouting out of a mammoth parking lot - that I had visited shortly before my trip to Arcosanti.

Of course, it's difficult to imagine how the more grandiose hopes for the future of Arcosanti will ever be fulfilled. Americans enjoy spreading out so much that it would take a lot of persuasion to induce most of us to leave our flat, isolated spaces and move up to townhouses in the sky. However, the physical growth of Arcosanti is not nearly as important as its mental stimulation. It raises so many questions about our future that it serves as a veritable gymnasium for a vacation-dulled mind.

Arcosanti is not alone. As long as you've seen a posthistoric cliff dwelling, you might as well check out one of the prehistoric variety. Go 25 miles further up Interstate 17 and you'll come to the turnoff to one of the best, Montezuma Castle National Monument.

Montezuma Castle was a five-story apartment hose built around 1250 A.D. by a group of Sinagua Indians who "were probably forced out of the Flagstaff area (50 miles to the north) by overpopulation," according to a National Park Service brochure. Sounds familiar. In fact, it sounds much like the saga of Arcosanti. Montezuma Castle was designed for fewer people, but the land can be saved for agriculture, hunting and weekend outings.

Tourists have damaged the castle so much that no longer can you climb the ladders to the interior and peer into the nooks and crannies. However, Montezuma Castle isn't alone, either. You can get closer to Sinagua ruins at Walnut Canyon National Monument, near Flagstaff. Or, slightly northwest of Montezuma Castle, you can climb a mound to the ruins at Tuzigoot National Monument, which relates to Montezume Castle rather like Cosanti relates to Arcosanti.

Juxtaposed next to horizontal Phoenix, these examples of vertical living may not seem very practical. There are too many of us to fit into the cliffs, and there are probably too many of us to fit into the sky. However, Phoenix is spreading itself too thin and too far. Arcosanti and Montezuma Castle remind us there are other ways of looking at the world.