The strings pulled out from the tight stripes of the serape are reembroidered on nails in the wall. Sean Gall

When you go to the international biennial art exhibitions in Venice and Istanbul and you come back and someone asks you how it was, the question really means: What is the state of the world according to art?

According to the Venice Biennale, it's the same it's been for decades. The Venice Biennale presents a fantasy of nationalism, the fantasy that borders are stable: The campus has one building per participating country, as if countries had walls around them, ceilings over them, lines to get in, a door. Also, some countries don't exist. But Venice itself doesn't give that impression. It's a watery city, reflections upon reflections, built for tourists—a postcard of itself, as Mary McCarthy described it—everything borrowed or stolen from somewhere else, a city-as-mercenary, a wildly ahistorical mishmash. Wake up, look out your window across the square, and there are arches from the Ottoman Empire. Venice is a portal to other places. Most of all, it takes you—it took me, at least—to Istanbul, the gateway to the Muslim world, a portal itself.

I had been to the Venice Biennale once before but never to Istanbul or its Biennial, a few decades old, much younger than Venice's—and I needed to go to Istanbul. When Tahrir Square filled up with people, I got a Roku box to watch Al Jazeera on TV, like a lot of Americans trying to go around their cable companies to see a different perspective. Going to the Venice Biennale isn't really like traveling, because you come out into the same art world, the same perspective, but going to Istanbul has the potential to be a different channel. Politics was the intended theme of this Istanbul Biennial, and more artists were chosen from Latin America and the Middle East than anywhere else. Power magazine Artforum reported that the show did not please "the professionals" in the art world. I considered that encouraging. It would be nice if an international art experience were a reflection of an actual international experience.

There is a big international group show at Venice that always tries to make an argument but always ends up being a broad survey, the argument unclear. The flipside is the ridiculous level of clarity you find this year at the United States Pavilion, where a pair of artists named Jennifer Allora and Guillermo Calzadilla flipped a military tank on its back like a bug, suspended a treadmill just above the tank's treads, got the treadmill and the treads rumbling, and hired American Olympic track-and-field athletes to take shifts jogging on the treadmill. "Just keep my focus, is all they told me," one explained when I asked.

One critic called this American artwork political correctness triumphing over political engagement—yup. Inside the pavilion, by the same artists, is a dumb replica of the lady-liberty statue from the top of the US Capitol dome, laid in a tanning bed—wah-wah; a pipe organ that plays when you put your ATM card in it—well, clever; and two sets of replicas of airplane seats performed on by gymnasts—I missed their performances. But the embarrassing display of national might can also be seen as a loud reminder that the United States is a real nation with real borders and weapons, not a melting pot or a salad or anything as fictional/conceptual/light as all that.

The other national pavilion that's horribly heavy, but which implants disgust in you much more deeply, is the Swiss Pavilion by Thomas Hirschhorn, a maze you can't get out of, full of consumer goods multiplying and connecting to each other—mannequins and camping stoves and plastic chairs and fat televisions, their surfaces covered in proliferating crystals and Q-tips and packing tape and soda cans and images of violent deaths and celebrities. It is a planet of shit. It still gives me the heebie-jeebies.

The last time I was in Venice for the Biennale, in 2007, I was wide-eyed. This time I could see my own desires. I was drawn either to total political engagement (direct examination of systems) or its opposite, extreme subjectivity (almost pre-linguistic experience). Take the Roma Pavilion—a series of videos regarding the situation of the Roma people, Europe's most horribly mistreated minority—and contrast it with the installation of pastel-colored and soap-smelling restorative powders and eye shadows applied to papers and turned into sculptures by Scotland's Karla Black. Black's redolent procession was something like being in the UK-based bath-and-body store Lush—if there were no salespeople, if drawings hung in midair and the soaps and powders extended down onto the floor and streaked across plastic sheeting hung in drooping sheets, if dirt lined the floors, and if there were Venetian palace architecture, all implanting vivid, soft memories. You lose yourself in Black's art, but you get very specifically located in the Roma Pavilion, or in, say, the Iraqi Pavilion, where one video described the simple problem of photographers trying to make work in the war zone of contemporary Iraq. I remember them saying simply, We just want to make photography.

These juxtapositions were the meat of the experience, the doubling that came at every turn. Exiting the Museo Fortuny, the palace where shrunken heads are displayed along with glowing fields of light by the contemporary American Quaker artist James Turrell—these fields of light trick you into believing they are projections onto walls, but they are nothing but colored air—my fiancé and I found ourselves in a funny spot. We were sitting between the palace and a row of African men eating pizza out of boxes at the edge of the canal, preparing to take their night shifts as the illegal merchant class of Venice, selling purses and rolly bags after all the shops and the art venues closed and sending money back to their families. Later, trying to place ourselves, we would ask one about his wife and kids in Senegal. My fiancé's family emigrated from Ethiopia only 20 years ago; he was seeing his own doubles.

No wonder art right now is restless and irritated, particularly at the presence of history, although it's still as visceral and beautiful as always. In one room of the big group show was a sculptural installation by Haroon Mirza, the British artist who was named this year's promising young artist at the Venice Biennale. The installation had scattered parts on the floor. It was named Sick. Its wall label said it included nine grams of raw gold nugget, but I couldn't find any gold nugget. I asked the guard. "The gold was stolen," she said. "Twice."

The first morning in Istanbul, we awoke to the sound of two men singing at an ungodly hour under a celadon sky. The voices were loud, coming across on the speakers that pervade Istanbul. How this projection is possible in a city of umpteen million—Istanbul is huge—I don't know. First, only one man sang. Another broke in, another, another. I was lying in the bed we'd rented for two nights, feeling the blanketing weight of religion (I'm not religious), when my fiancé whispered to me, "They're competing." We giggled as they threw their voices on top of each other. They became just men, not imams. They could have been us. Maybe that's all the idea of "globalism" means: You don't have Others under deconstruction, you have doubles under construction.

Recent Istanbul Biennials were staged so you had to travel around the city to see the art, encountering at each venue the historic sites/sights: Turkish baths, mosques, squares, markets. This year, curators kept everything in one location instead, in two identityless warehouses next to the modern museum. If you want to go see the city, go see the city, the curators seemed to say: But here's the art.

The man who rented us our room online told us to check out some "anti-biennial" events in Istanbul, too, but he wasn't there, he was somewhere far off traveling or working, and we found ourselves instead sharing the place with a young couple that lived there, an Italian woman who'd adopted Turkey as her home (her life, doubled) and a man from New Zealand, and neither of them knew what "anti-biennial" meant.

If there is a strain of good old-fashioned resistance in the Istanbul Biennial, it is against good old-fashioned European and American modernism. To this end, the curators chose as patron saint Felix Gonzalez-Torres, the Cuban-born gay American postminimalist who died in 1996. He's a popular patron saint. His installations implanted powerful, ongoing infections into the minimalist cube.

Watching the ritualistic, perpetually unfinished murder of modernism holds a certain perverse pleasure. At the Istanbul Biennial, you can see it in Cuban artist Wilfredo Prieto's watermelon hacked into a wet red gloppy cube on the floor, titled Politically Correct; Lebanese artist Mona Hatoum's grids, mounted and framed, made of human hairs entwined and fixed with hairspray; Brazilian artist Adriana Varejão's canvas that looks torn into by the claws of a beast, which is also a beast itself, bloody viscera bulging forth from its openings—a jacked-up version of the delicately sliced, famed modernist paintings by postwar Italian painter Lucio Fontana. It's possible to go on and on here: There were artworks featuring the Iranian consumer price index as a pristine white embossed print, à la temple decor, and a series of pieces time-lining real historical links between oil companies, the Museum of Modern Art in New York, and war. One of my favorites—by artists Alessandro Balteo Yazbeck and Media Farzin—linked Truman, Churchill, Hirohito, and Marcel Duchamp's female alter ego, Rrose Sélavy, as nodes on a charming Alexander Calder mobile sculpture. (Calder is the Boardroom Favorite; the empty spaces of modernism are now voids where trustees rush in.)

The youngest artist in the Istanbul Biennial is a 24-year-old named Clara Ianni, from São Paulo. She contributed a shovel hanging on the wall—a reference to Duchamp's famous readymade In Advance of the Broken Arm—but her shovel has a square hole cut out of its scoop. This shovel will pick up nothing, accomplish nothing, get no work done. It's an artwork that won't work—the ultimate modernist problem, that art's autonomy from unpleasant concerns like history and politics is its death, that even the dirt required to bury modernism will just fall through that empty square if you try to cover the coffin. And Ianni's shovel is in a room entirely devoted to the zombie of modernism.

So why won't modernism die? Art itself is modernist—its white-cube galleries and its dense texts—so they keep each other alive by definition. But the curators in Istanbul this year invited artists who emphasized that pathetic life-support system repeatedly, sometimes poignantly, as in Palestinian-born Taysir Batniji's juxtaposed photographs of father figures with photographs of watchtowers. The watchtowers reference a series of famous minimalist photographs of charming industrial water towers in Europe and North America by German minimalist photographers Bernd and Hilla Becher. You have water towers, Batniji seems to say—we have watchtowers. But we both have photography, so what are we going to do about it?

Hanging on a hook on a wall near the entrance to the Istanbul Biennial is a serape, a multicolored Mexican blanket. What looks like a very large geometric drawing made in faint colored pencil covers the wall next to the blanket. But it isn't pencil. It's the strings of the blanket, pulled out from the tight stripes and re-embroidered on rows of nails in the wall to create a whole new landscape of pink-and-yellow highways to nowhere and green cubes and brown hourglass shapes—all stretched taut like musical strings waiting to be played. The blanket is doubled, or more than doubled; it, too, is still under construction. It's called Far and Wide, 2011. The artist is Adrian Esparza, from El Paso, Texas, just across the border from Juarez, Mexico.

After leaving Istanbul and arriving back in Venice, the image of that serape and its double reappears in my mind's eye. This is what it means to do art now: Art travels, artists travel, you travel. Things are in motion: You may be asleep but your double is awake. You see so much art that your dreams are strangely, newly upholstered for a while. In one dark room in Istanbul, there was a work of art by an artist who lived in Seattle until recently moving to Nashville, Vesna Pavlovi: She showed old travel slides projected onto a patchwork of screens that weren't correctly lined up with the projectors. The images overlapped each other and bled across the borders of the different screens. Each image became a new picture with mixed-up colors, located in multiple zones at once.

The piece in Venice that's emblematic of the whole trip is a dim series of rooms, a warren really, that the artist Mike Nelson built inside the British Pavilion. Nelson physically obliterated the British Pavilion in order to create the illusion of, as it happens, a chunk of Istanbul. It has the feeling of a haunted house. A heap of dusty crystals lies on a dirty table. Along with the dusty crystals and dirty tables are uneven false floors, rickety steep stairs, old tools, a makeshift sleeping area, burned-out lamps, and Turkish posters, including one of the original Turk, Atatürk, who bizarrely has blond hair and blue eyes (a cultural footnote we picked up from the expat couple in Istanbul). I read later that Nelson's inspiration was a novel by Turkish author Orhan Pamuk, in which a Venetian character discovers he has a Turkish double. On the wall, it is scrawled in English, "Is this art or is it me?" recommended