A strip of land running along the Atlantic edge of Spain, Portugal was a maritime culture. Already, in the 15th century, its merchant-sailors were feeling their way down the west coast of Africa, keeping an eye out for gold, slaves, potential Christian converts and information about places, things and people they didn’t know.  There was a lot that the Portuguese, and other Europeans, didn’t know. The world maps that open the exhibition inspire a mild sense of vertigo, so disorienting are their distortions and omissions. In a hand-drawn “world map” from around 1489, Europe is more or less center stage; Africa is a slug-shaped mass, Asia a big, bland lump. There are no Americas and no Australia. They didn’t exist yet.  But maps changed fast. They had to. In 1488, as the finishing touches were probably being applied to this one, Bartolomeu Dias, an ambitious Portuguese seaman, rounded the tip of Africa and looked on the Indian Ocean. A decade later another adventurer, Vasco da Gama, followed his lead and made it to India.  Soon afterward, Portugal engineered a destiny-shaping commercial coup when it took control of the international spice trade, centered in Indonesia. It also established a store-minding colonial outpost in Goa, India, from which new art emerged, part Indian, part European and entirely something else. In an ivory sculpture of a Krishna-like Jesus, and in a translucent tortoise-shell bowl that seems to burn like an open fire, you can see that something else.  China was next on the itinerary, as always a tough nut to crack. Then came Japan, where the insistent religious evangelism that loomed large in Portugal’s export package really paid off, spiritually and aesthetically, inspiring a wave of Japanese conversions that in turn sparked an industry in a home-grown devotional art.  But the mood wasn’t pure brotherly love. Many Japanese regarded the Western “barbarians” with disdain, and this, too, found an outlet in art. If a missal stand covered with gold-leaf flowers and shell-inlay birds is one of the show’s prettiest objects, a lacquer food box with images of clownish, snorkel-nose Europeans is one of the funniest.  Meanwhile, on the other side of the globe, another go-getter, Pedro Álvares Cabral, had reached Brazil, though this was an accident; he was shooting for India. Anyway, he made the best of his error by starting a lucrative trade in a local hardwood. And simply by being where he was when he was, he entered history as a founding father of the only substantial land-based colony that Portugal ever had.  The Portuguese, unlike the Spanish, weren’t of a settling-down disposition. They liked to do business on the move. Typically, they would sail into a port, make some lasting contacts, sell, buy and move on, repeating the same routine later. This isn’t to say that Portugal had no empire. It did have one, and for a while it was vast. But it was also, in a sense, virtual, taking the form of disposable property rather than real estate.  Brazil was the primary exception. The Portuguese occupied it, worked its land and people hard, and imported slaves from Africa for good measure. Here, too, a hybrid culture grew, but one more intense and lasting than elsewhere. In Brazil, Roman Catholic church art entered a beyond-Baroque, laceratingly emotive phase; a small room of devotional sculpture in the show is as steamy as a pressure cooker. Simultaneously, grass-roots religions developed, as Brazil’s native and African people took a foreign faith they had been handed, radically customized it and through its new form reclaimed power.  Many Brazilian slaves came from parts of Africa — the kingdoms of Benin and Kongo, and present-day Sierra Leone — that had long been under Portuguese supervision. And artists from these areas regularly produced art, specifically ivory carvings, for the European market. The work ranged from elaborate prestige commissions to modest, delicate animal-head spoons. Fancy or not, this art was always inventively conceived and exquisitely made.  The selection of it at the National Museum of African Art was the high point of the show for me. I had to pull myself away. Did the carvers who made these sculptures consider their work as a kind of tourist art, tailored to European expectations, and perhaps subtly pricking European pretensions and adding African content like a secret signature? If so, this is some of the greatest tourist art ever made, souvenir items of humbling magnificence.  Europeans fully recognized the beauty of this art, its fineness and preciousness. That’s why so much of it has been preserved in Kunstkammer, or treasure room, collections, set among other objects considered wondrous but strange. What was often forgotten was that these ivories were carved by Africans. For many Europeans, the words African and art did not compute.  Over all, “Encompassing the Globe” represents a European sensibility, and a one-directional one. In a 17th-century painting of an Indian woman done in Brazil by the Dutch artist Albert Eckhout, the nude subject strikes a conventional portrait pose against a bucolic landscape. We’re in both Brazil and Europe, an interesting idea. Then we notice that the woman is holding a severed human hand; a human foot protrudes from the basket on her back. Suddenly, she’s a cannibal, a savage. That’s how Eckhout sees her. That is his connection to her.  But in reality connections are mutual, psychologically interactive; they flow both ways, as they often do in the art chosen for this show, which is what makes it more than a treasury. We can never know what the woman in Eckhout’s painting might have thought of him, this peculiar white man making marks with a wet stick. But we do have examples of other outside perspectives on the West to balance the ones we know so well.  Again, there are the Japanese artists responding in paintings to alien Europeans centuries ago. They see blundering creatures barging in from nowhere, wearing silly clothes and acting as if they owned the world. But they also see people who came with a very interesting religion that valued humility and charity above all else.  Mughal art communicates similarly conflicted attitudes. One 16th-century miniature, as vivid as a news clip, depicts a mob of Portuguese sailors attacking and killing the sultan of Gujarat. And we get a pretty good idea of where the artist’s sympathies lie. But what to make of another painting, this one of a European gent with a hankie in one hand, a sword in the other, and a two-tone cloak over one shoulder? An admiring portrait? An ethnographic study? A sendup? A little of each?  Like most art, this little picture gives out and picks up signals, suggests ideas, hints at opinions and invites responses, all at once. Many of the objects at the Sackler do the same, glinting and flickering through the galleries like nodes on a switchboard. All the lines are active, and one message keeps coming through: that everything is connected, always has been. The version of the Internet invented in Portugal centuries ago was also being invented in Delhi, and Nagasaki, and Benin, and Bahia. It was all one network. In Washington we start to see the links.  An art review in Weekend on Friday about “Encompassing the Globe: Portugal and the World in the 16th and 17th Centuries,” at the Arthur M. Sackler Gallery in Washington, misidentified the nationality of the 17th-century artist Albert Eckhout, whose painting of an Indian woman in Brazil is in the exhibition. He was Dutch, not Danish.  “Encompassing the Globe: Portugal and the World in the 16th and 17th Centuries” continues through Sept. 16 at the Arthur M. Sackler Gallery, (202) 633-4880, and the National Museum of African Art, Smithsonian Institution, (202) 633-4600, in Washington.  A version of this review appears in print on , on Page E31 of the New York edition with the headline: Portugal, Conquering And Also Conquered. Order Reprints| Today's Paper|Subscribe
The Arthur M. Sackler Gallery’s show glows like a treasury, radiates like a compass and seems as rich with potential information as the World Wide Web.