Riding around in the Rolls, I couldn’t tell whether Ibrahimov was indeed a brilliant strategist or someone who just had the capital to create a vision on a piece of tissue paper and turn it into a construction project. Or perhaps both. As we neared the site of what will be the ritziest restaurant at Khazar Islands, he became very excited. The concrete and aluminum skeleton of the restaurant resembles a Viking helmet, and when it’s done, it will include a microbrewery, which Ibrahimov mentioned two or three times. “We have a guy from Austria,” he said. Nearby, there were more men in hard hats and jumpsuits, and trucks carting rocks. “In my head,” he said, “this project is already done.”

Ibrahimov is not the only developer in Baku, and Khazar Islands is not the only major development. Flame Towers, which features three flamelike towers, includes a five-star hotel and, at night, will be lighted in red. The Heydar Aliyev Center, designed by Zaha Hadid, includes a museum and looks a little like the starship Enterprise. Baku White City will encompass 500-plus acres of new apartments and parking lots and is supposed to be the opposite of Black City, where the oil barons built their refineries a century ago. Finally, there’s Crystal Hall, a 23,000-seat arena overlooking the Caspian.

Nearly three years after Ibrahimov’s initial vision on the Azerbaijan Airlines flight, Khazar Islands has grown to 4 fake islands, 1 bridge and 13 apartment buildings. All this development can feel a bit weird, or at least incongruous. As the Rolls careered through the outskirts of Baku, Ibrahimov became quiet. Unlike the United Arab Emirates, which was, until recently, a desert, Baku has a rich architectural history, with centuries-old mansions, mosques, palaces, squares and esplanades. (Some sites date to at least the seventh century.) Baku has a grace and cosmopolitanism; it feels like an amalgam of Paris and Istanbul, albeit dustier. It also feels like a gateway to the East, distant places, mythologies and many other things that the new Azerbaijan doesn’t have much appetite for. I interpreted Ibrahimov’s silence as a sign of melancholy, but in the front seat, Huseynli, who was fielding calls on two or possibly three cellphones, each with its own hip-hop ring tone, turned around excitedly. Glancing at the beige facades, the narrow streets, the old women selling apricots and nuts and pirated DVDs, she said: “All of this soon will be gone. Then we will have a new city. I like the old, of course, the historic. . . . But this will be gone, and then it will be a different country.”

When we pulled up to the Avesta Concern Tower, in central Baku, several men in tweed jackets were assembled on the curb and ready to escort us inside. After lunch in Ibrahimov’s private dining room, we decamped to the office and sat on a red silk divan with miniature Sphinx armrests. Ibrahimov pointed out his artifacts: his desk, which, he said, is Spanish and the same kind used by Vladimir Putin; a chess set from Italy; a sculpture of his father.

Ibrahimov segued back to Ilham Aliyev, the Boss of All Bosses, whom he called a great supporter, an ally, the son of the savior of the people of Azerbaijan. I asked him about other features of his regime: the lack of transparency, the lack of civil liberties, the detention of opposition activists. Ibrahimov said what oligarchs have been saying since Mikhail Khodorkovsky, the Russian industrialist, was exiled to Siberia in 2003: “I don’t know anything about politics.” But “biznessmen” are much more intimately woven into the political fabric of Russia or Azerbaijan than C.E.O.’s in the West. They may wear crocodile-skin shoes, but they rely on the state for pipelines and extraction rights.

Ibrahimov, like other successful men in this part of the world, knows his place, and he knows it is best to be philosophical about these things. “Don’t ask me about politics,” he said. “I’m afraid I’ll make a mistake. This is not what I’m good at. This is not what I do.” Then his semismile semiwidened, and he started talking about his next big idea, which features more stratospheric buildings and superlong canals and eight-star hotel-palaces and heliports and yacht clubs. He was sure all these things could be done. He knew it. There were important people — “political people,” he said — who support him.