"There are different stages when you fly," he explained. "The first stage is the dollhouse effect, seeing everything on Earth like it's a model. Suddenly all of your concerns seem very small."

"The second stage at 400 to 600 feet is when it looks like the Earth curves in the wrong direction, curving up to the horizon. Then around 50,000 feet, you see the curvature of the Earth in the right direction."

You can experience that second stage by standing on the cinder covering the rim of the crater, which reaches about 600 feet above ground level. Look at the land below and it seems to curl up gently at the edges of your field of vision, like a sticker losing its adhesive.

Then, climb down into the bowl of the crater and you can experience "celestial vaulting" — a term Turrell borrowed from art history. Lay down on one of four limestone benches that he has precisely positioned and angled around the eye of the crater. Look up at the sky, and it no longer appears as a flat expanse stretching above you but "vaulted": It seems to curve over you, while the Earth below curves up to meet the sky, almost as if you were caught inside a snow globe.

While his scale is epic, his goal is intimate: to heighten our sensory connection to the cosmos. "I want this universe that we are in to become part of our personal space, part of our lived-in territory," Turrell said. "I'm looking for a grandeur that does not belittle you."

Inside the volcano, different chambers offer different experiences that vary with the time of day and weather conditions. Many of the chambers are dark, so our pupils open. "We weren't made for this daylight," he said. "It's in twilight, in the light of the caves, where we see the best."

One of the most dramatic experiences is the 854-foot-long darkened tunnel, which leads to a room with a hole in the ceiling affording a glimpse of sky. Stop midway through the tunnel and crank a large lens into place, and the entire tunnel becomes a telescope, sending the image of that patch of sky ahead of you onto a large white marble disc behind you that serves as a screen.

The crater is a "pointing sculpture," he said. "So it's not like Stonehenge but more like Abu Simbel [in Egypt] and Newgrange in Ireland," he said, naming prehistoric monuments known for their astronomical precision. "When alignment [with celestial bodies] occurs, the light enters and there's an event in the space."

Then, if you continue walking through the tunnel toward the patch of sky up above around sunset, the color, texture, size and volume of that patch will magically morph before your eyes. The blue deepens to inky black. The perfect circle of sky elongates into an ellipse, bulging like an egg before receding and ultimately becoming a flat expanse, so that the sky appears to be stretched across the opening above like a painting.

This particular construction, a precisely cut and lighted aperture in a ceiling designed to deliver the sky to the viewer, is known in Turrell territory as a skyspace, and he has perfected it over the years in projects outside the crater. Since his first, installed in the home of legendary collector Giuseppe Panza in 1974, he has designed 80 more in different forms for clients from Argentina to Australia.

Selling skyspaces to wealthy collectors at costs up to seven figures has become one means of funding Turrell's work on the crater. Another is cattle ranching, which he famously started on the advice of his local bank. It was 1986, and he was trying to assume ownership of more than 600 acres of land from the Dia Art Foundation, which had been sponsoring his crater project.

"The bank wouldn't give me a loan to make art, but they would give me an agricultural loan if we put three properties together as a ranch. So we went ahead and did it," he said. Today he breeds Angus cattle to sell mainly to the restaurant trade and talks about the beautiful marbling of the beef.

He also has received private funding on and off throughout the years, most notably from the Dia and Lannan foundations.

After withdrawing support, Dia resumed its involvement nearly a decade ago under the leadership of Michael Govan, now LACMA's director. Govan was struck on his first trip to the crater by Turrell's persistence of vision: "It's this bold individualism we saw in the '60s, this very American idea that anything is possible: an individual can change the world, not by force and running armies but through the power of ideas."

Govan soon learned to fly a single-engine plane, which comes in handy for making trips there and talking engines ("is that gas or turboprop?") with Turrell. He has also become a Skystone board member (one of three) and co-curated the new museum retrospective. As for LACMA, Govan says the museum is "not officially involved in Roden Crater fundraising yet."

"I am looking at the idea of putting together a consortium of museums" to ensure the crater's longevity, Govan said. "Our culture doesn't have pharaohs, kings or presidents who support art in this way or over this time span. We have to develop new mechanisms to think about these things." The next step, he said, is a financial projection. Neither he nor Turrell would state the project's cost so far.

He also described the Skystone foundation's long-term plans for guest lodges (one done, three to go) and hosting visitors to help support the crater's maintenance. Some patrons would pay "the real price" for staying the night, while artists or students could stay for free.

In the meantime, the LACMA show promises to draw more attention to Turrell's work at the crater and beyond. It features 10 sizable light projections or installations as well as smaller works.

The showstopper just might be Turrell's newest "ganzfeld" installation — a term psychologists use for a uniform field of light with no point of focus or depth. He has made few in the U.S. since 1980, when a Whitney Museum visitor mistook one of his ganzfelds for a wall she could lean against, fell, broke her wrist and sued. (At LACMA, there will be guides.)

Turrell talks about this series rather mystically, describing a world without horizons that he sees as characteristic of the 21st century. He spoke of the space age as well as the Internet age, with disembodied and distributed fields of data.

"I think we're moving to a new landscape without a horizon. It's like flying in a fog or skiing in whiteout conditions," he said.

If it sounds like a dangerous art form, Turrell says not to worry. "It's not deeply disorienting," he said. "When you create these experiences in small increments, it can be exhilarating. I think many people will experience that."