"Dream Worlds: Modern Japanese Prints and Paintings From the Robert O. Muller Collection," which opens today at the Smithsonian's Arthur M. Sackler Gallery on the Mall, can't be beat for sharpness. This is about as sharp as art gets.

There are 160 woodblock prints at the Sackler, and the block-cutters, the knife men, who carved them are so accurate that they make the best in the West -- Albrecht Durer's, say, or Winslow Homer's -- look like bumblers. What you see on the walls is ink and paper. But the main material of this art is really honed steel. It is shared all through the culture, that allegiance to the edge.

There is a mystery in sharpness. You can sense it in this show. A thousand sharpened chisels, gouges, saws and wood planes gleam beyond this art.

There's a poignant piece of film footage well known in Japan that shows a blade by a 15th-century smith called Kanemoto II striking a machine gun barrel, slicing it in two. The "Dream Worlds" show is as implausible, and as sad.

The message of the movie -- that the old way of the samurai, with its unquestioning obedience, its moon-viewing pavilions and its prohibition of mistakes, will overcome machinery -- is, of course, a fantasy. Machinery will win every time, and the Japanese knew it. The brushmakers and publishers and sharpeners of knives who made these pictures could hear the humming of the printing presses and the clicking of the shutters and guess what was coming. Much as they admired Kanemoto II, the Japanese imperialists didn't stop making guns.

Both the barrel-slicing movie and the pictures at the Sackler give out a sort of sob for very old and beautiful and fabulous technologies too precious to abandon, yet fading now, and dying, and past their time.

These prints were made the old way. No shortcuts were considered. The wood, from a certain wild cherry tree from the Izu peninsula, was seasoned by professionals. The inkers' horsehair brushes were evened, as they always had been, by being abraded on stretched sharkskin. The paper, once placed against the block, was still rubbed with the baren, a hard disk wrapped in a bamboo leaf. In "Dream Worlds" the technologies are old, but the pictures aren't.

That's what's odd about them. Mostly their subjects are traditional -- a temple gate, the moon, a woman partly dressed, a heron in the snow -- but some of what they show is not traditional at all. An automobile, a train, a string of electric lights. One supposes these are there as emblems of modernity. They feel more like symbols of sorrow.

In Tokyo, before photography, cheap, disposable wood-block images known as ukiyo-e, as "pictures of the floating world," were as common as magazines. Like most magazines they specialized in showing what most people like to see: show business celebrities, good-looking women, animals, heroes, ghosts. The prints at the Sackler are different. They aren't ephemera. And they weren't aimed at the local market. Most of them were published as collectible commodities, as high-toned works of art specially designed to meet the guessed-at taste of foreign buyers shopping in galleries abroad.

The old ukiyo-e were so cheap that they supposedly reached Europe crinkled around porcelain teacups, as padding. However they arrived, they gave Western art a shove when they got there. The bold curves, eye-poking graphics and flat colors amazed Whistler and Degas and Gilbert and Sullivan. Vincent van Gogh collected Hiroshige and Hokusai. The fashionable West in the 19th century fell hard for japonisme, and, of course, the flow of thought went the other way as well.

The Gibson Girl. The cocktail. The French impressionist painting, ads of many kinds, and movies by Walt Disney poured deep into Japan. You see them in this art.

The woman depicted in a 1930 print called "Tipsy" by Kobayakawa Kiyoshi (1897-1948) has the white skin of a geisha, but isn't a geisha. Her polka-dotted blouse is sleeveless. She's got a spit-curl and a wristwatch and is sipping a martini. If you recognize her pose it's because you've seen it before in paintings by Toulouse-Lautrec that show solitary women drinking absinthe in Montmartre.

I thought I recognized the too-perfect clouds in "Tega Marsh" by Kawase Hasui (1883-1957) and eventually figured out why. They're a lot like the clouds in a Maxfield Parrish.

Natori Shunsen's 1926 likeness of a Kabuki actor called Jitsukawa Enjaku II shows him made up for the tough-guy role of Danshichi, a down-and-out warrior like the ones played by Toshiro Mifune. Weirdly, Shunsen's print looks a lot like a Hollywood glossy. The spirit in these prints is uneasy. They're part new and part old.

Much modern Japanese art is like that. It can't quite make up its mind. It suggests two different Japans. One is the old land of the cherry blossom and the teahouse and the paper wall, and the other is the realm of the Honda and the bullet train, of westernized technology enthusiastically embraced. Lots of Robert Muller's prints feel racked between those poles.

For instance: Zojoji in Tokyo was the favored temple of the Tokugawa shoguns. Its entrance, in falling snow, appears in muted colors in a 1936 print by Hasui, but under the old temple's familiar red gate he's parked a shiny black sedan.

That's what western buyers wanted? Isn't it?

Look carefully. The colors have been perfectly registered. The inked ridges of the woodblock can be as thin as hairs. How do you ink a block of wood so that a passage of soft color drifts off like a puff of smoke, or gradually dissolves? Today one cannot quite believe that craftsmen sitting cross-legged produced these things by hand.

When the late Robert O. Muller first fell for them in 1931, he wasn't a collector, but a "tieless and unkempt" undergraduate at Harvard.

"It was a casual glance toward a window display on West 57th Street in Manhattan," he wrote, "that lured me to the world of the Japanese print."

His money came from Pfizer, his enthusiasm from who knows where. The month after his wedding in February 1940, the collector and his bride sailed to Japan where, in the next five months, he spent $9,000 (the equivalent today of $120,000) on tens of thousands of prints.

The 3,800 that he bought from Takemura Hideo, the Yokohama publisher, cost 17 cents each.

They're worth a lot more now. Their rarity was much increased when tens of thousands of impressions were lost in the Tokyo earthquake of 1923. Many more were burnt in the fires of the war.

Most of Muller's prints were bought for resale, but some he purchased for himself. Over the next half-century, while running galleries in Manhattan and New Haven, Conn., he gradually and steadily improved his core collection. In the 1990s he considered selling it, but changed his mind.

When he died at 91 in April 2003, Muller left 4,500 woodblock prints to the museum on the Mall. At his death his big collection may have been the strongest still in private hands.

Its light effects are wonderful. In a series of seascapes by Yoshida Hiroshi (1876-1950) -- all pulled from the same blocks -- the sailboats are seen at night, and in the early morning, in the daylight of the afternoon, or swathed in gray mist.

The show's curator, James T. Ulak, the deputy director of both the Sackler and the Freer Gallery of Art, has arranged it in four chapters: "Beauty Personified," "Creatures Real and Imagined," "Stage Presences" and "The Quality of Light." He also has included some thrilling smoke-filled battle scenes, made as propaganda, of fearless modern warriors storming the castle wall for honor and the emperor like the samurai of old.

But these prints are exceptions. Most depict a world much softer. Its cherry blossoms drift as they have for centuries, the women do not age, the stainless snows fall softly, the moon shines through the trees. What one most remembers from the "Dream Worlds" exhibition is its sense of loss.

Dream Worlds: Modern Japanese Prints and Paintings From the Robert O. Muller Collection, at the Smithsonian's Arthur M. Sackler Gallery, on the Mall at 1050 Independence Ave. SW, through Jan. 2. The Sackler is open daily from 10 a.m. to 5:30 p.m. Admission is free.

In "The Great Gate, Shiba," Kawase Hasui parks a symbol of modern times in the middle of a traditional subject of Japanese prints.Above, a 1926 likeness of a Kabuki actor resembles a Hollywood glossy. "Tipsy," below, mimics a pose in paintings by Toulouse-Lautrec.In Kobayashi Kiyochika's "Taro Inari Shrine at the Asakusa Ricefields," top, and "View of Takanawa Ushimachi, Under a Shrouded Moon," above, an old technique is used to capture both traditional and modern subjects.