One of the most influential figures in European modern culture never set foot in Europe. Katsushika Hokusai, like all subjects in self-isolated Edo Japan, could not have left the archipelago if he wanted to, and his publishers could not export his prints of Kabuki actors, flowers and Mount Fuji. But a few years after his death in 1849, when the “black ships” of Commodore Matthew Perry sailed into what’s now Tokyo Bay, Japan’s markets were forcibly opened, and Hokusai’s woodblocks started to flutter over the ocean. In France, in Britain, and soon in America, a whole new kind of art would emerge: born in Tokyo, spanning the whole world.

In “Hokusai: Inspiration and Influence,” an exhibition of Japanese woodblocks and global contemporary art at the Museum of Fine Arts, Boston, one of the greatest of all printmakers appears at the nucleus of a worldwide cultural transformation, in which art became more urbane and more fleeting, and the observed world got flattened out into signs and symbols. Beautiful and bloated by turns (but well worth the trip), it makes ample use of the MFA’s unparalleled collection of Japanese art. (In fact, the MFA organized the very first American Hokusai retrospective, back in 1892.)

Here you will see more than 100 of Hokusai’s prints, paintings and manga — literally “whimsical sketches” of bathers and courtesans and birds and beasts, which Hokusai published in 15 best-selling volumes. There are 11 ice-crisp sheets from his most famous series, “Thirty-Six Views of Mount Fuji,” including those two coffee-mug icons: “Fine Wind, Clear Weather,” which distills the august mountain to a clay-red cone, and “Under the Wave Off Kanagawa,” known familiarly as the “Great Wave,” in which the snow-capped Fuji nearly disappears beneath a tentacular blue breaker.

As the title signals, “Inspiration and Influence” is a show of two halves. A first section, fixed in 18th- and 19th-century Japan, charts Hokusai’s education, apprenticeship, independent career and instruction of younger makers of the prints called “pictures of the floating world.” He shares these initial galleries with his master teacher, Katsukawa Shunsho; his greatest rival, Utagawa Hiroshige; as well as several female artists, including his talented daughter, Katsushika Oi, represented by a handsome scroll painting of an all-women musical trio.

Then comes a more global second half, which skips across chronology, media and tone to highlight the worldwide migration and metabolization of Hokusai’s vivid compositions and bourgeois themes. Prints by Gauguin and Whistler imbibe Hokusai’s blocky colors and flattened spaces. There are Japan-mimicking decorative arts from the Steuben Glass Works or Boucheron jewelers, and snatches of Debussy’s “La Mer,” whose published score has Hokusai’s wave on the cover. New art, of greater or (often) lesser importance and subtlety, hangs with contemporary manga.

Hokusai himself worked in commercial domains (the Western distinction between fine and popular art was hardly bright in the Edo period), so it’s perfectly fine that this show skitters from paintings to comic books. By now he has penetrated popular culture so thoroughly to have become the only artist with his very own emoji: the cresting blue wave [🌊], denuded of the half-drowned fishermen in the original woodblock.

But a lot of the contemporary work here is chintzy or schematic, and in going for quantity over quality, the show’s second half feels a bit like … a tide crashing over you. The MFA’s best impression of Hokusai’s wave appears here not in contemplative isolation but crowded among imitations, parodies and tribute acts. We find “Great Wave” copies by Andy Warhol and Yoshitomo Nara; some Mexican waveform bracelets and some trompe-l’oeil surfer-dude furniture; and even a promotional image of the willowy Olympic champion figure skater Yuzuru Hanyu, swanning in a blue-and-white costume and arcing his right arm like the Kanagawa surf. Roy Lichtenstein’s “Drowning Girl” — lent by the Museum of Modern Art and picturing a blue-haired woman vanishing beneath silvery waves — is facing, embarrassing to say, a replica of Hokusai’s big kahuna made from blue and white Lego blocks.

Hokusai was born in 1760, as Japan was coming out of a long depression and returning to prosperity. He was adopted by his uncle, who served the shogun as a maker of mirrors, and at age 19 he entered the studio of Shunsho, who specialized in imagery of actors and women. In a handsome side-by-side display of two scroll paintings by master and student, we see Shunsho distilling a dancer’s motions into ripples of floral patterns, and Hokusai later using the same lines for the bunched fabric of a woman carrying firewood. The aristocratic and spiritual dimensions of painting were giving way to something more fashionable, more mondaine. The stage, the street, the bathhouse, the brothel: These would become, as much as the Japanese landscape, Hokusai’s inspirations and obsessions.

Critically, his scenes of pleasure were more cosmopolitan than Westerners, who idolized the supposedly untainted beauty of “closed Japan,” would later acknowledge. Hokusai and his students and rivals made use of Chinese and also Dutch antecedents to flatten the world into color and line, and sometimes used foreign pigments imported (or smuggled) through the trading post off Nagasaki.

This show includes two magnificent six-panel folding screens that Shunsho painted around 1790, in which well-dressed women lie along parallel diagonal lines at the same scale — so-called axonometric perspective, a pillar of Chinese painting. Hanging right alongside is a lavish print series by Hokusai made 20 years later. It depicts a house of pleasures in Edo — but now, the ladies up front are drawn bigger than the ladies in the rear.

One-point perspective, so revolutionary for the European Renaissance, became familiar to Japanese artists as early as the 1740s — and they weren’t that impressed. If a few, notably the printmaker Utagawa Toyoharu, made cunning use of the European technique, most saw it as little more than a party trick. Or so it was until Hokusai began integrating Asian and European methods of spatial delineation into a new, hybrid image of the modern world. My all-time favorite Hokusai is one of the “Thirty-Six Views of Mount Fuji” (and FYI, for your next art history pub quiz, there are actually 46 views: his publisher asked for some sequels), depicting travelers blown off a twisting road by a sudden gust of wind. The figures on the right-hand side are placed along a diagonal in the Chinese manner, but on the left, the figures shrink and recede upward, European-style. As for Fuji, the most majestic site in the country, it’s nothing but three quick strokes: a swoop to the top, a bobble for the summit, a long glide back to the ground.

Europeans had, by Hokusai’s day, been drawing from Chinese, Persian and Indian examples in the creation of the decorative arts. But when Japanese prints finally began to circulate in Western Europe after his death — especially in 1870s Paris, defeated in war and transforming at full tilt into a metropolis — they appeared as both aesthetic gems and spiritual life rafts. In Hokusai and his rivals, young Parisians losing their roots found a liberation from worn visual vocabularies, and Japonisme, as the fashion was called, stretched from the painting salon to the dinner table. Fuji-themed inkstands. Velvet curtains bedecked with lotus blossoms. Transferware with fish and fowl copied from manga. “Japonisme was in the process of revolutionizing the vision of the European peoples,” wrote the diarist Edmond de Goncourt. The pottery, the lacquerware, and above all the woodblocks “brought to Europe a new sense of color, a new decorative system, and, if you prefer, a poetic imagination.”

That these artists, composers and designers did not take a scientific interest in Japanese culture hardly needs spelling out, any more than Japanese printmakers did when they depicted the “exotic” West. But the French fashion for things Japanese offers one of the richest examples ever of the productive capacity of misunderstanding foreign things — above all for the artists who would become the Impressionists and Post-Impressionists, whose soft colors, flat expanses and neglect of shading would never have emerged without their Japanese forerunners. It wasn’t just the pictorial grammar; it was also Hokusai’s bourgeois sensibility, his attention to theater and fashion and women of the night. That taste for city life convinced Monet, Degas and their peers that their fleeting impressions of modern French life could be the stuff of high art. And even as they indulged stereotypes of Japanese delicacy or purity — when they fell into the “battery of desires, repressions, investments, and projections” that Edward Said called Orientalism — these Europeans were changed all the same by Japan, and irrevocably.

The MFA show is too pell-mell in its second half to chart properly how Hokusai’s example took global flight in the 20th century. The contemporary selections in particular have the feel of search-engine curating, and that Lego “Great Wave” should have stayed by the gift shop. What I’d really wished for, rather than all those literal waves and mountains, was more of the eclecticism that characterized Japonisme and that also animated the exchanges between Asia and the West in the 2009 Guggenheim exhibition “The Third Mind: American Artists Contemplate Asia, 1860—1989.” A notable miss is the art of Yasumasa Morimura, who fed European artists’ misapplications of Japan back into his own alienated self-portraits.

It would really have helped — because a few years ago, America went through a painfully simplistic debate about how artists from one place should or should not depict images and objects from another. New shibboleths arose, phrases like “lived experience” and “power imbalance,” to adjudicate who had the right to what pictures, what materials, what forms, what words. (The MFA crashed on these shoals; in 2015, it drew protests and counter-protests for inviting visitors to try on a kimono in front of a Japoniste portrait by Monet.) But what Hokusai and his successors affirm over and over is that there’s no such thing as a pure “culture” divisible from others — not even the culture of a shogunate whose subjects couldn’t leave on pain of death. Culture is always an ebb and flow of fragmentations and recombinations, of encounters both violent and peaceful. You cannot stay separate; everything floats; your job is to ride the wave.

Hokusai: Inspiration and Influence

Through July 16, Museum of Fine Arts, Boston, 465 Huntington Avenue, Boston; 617-267-9300; mfa.org.

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