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For decades, one rule of American politics has been that the political power of the Cuban-American lobby in Miami (which is to say, in swing-state Florida) made rapprochement with Castro’s country impossible. But when the breakthrough finally came on Wednesday, there was little objection at all. “No one is marching in the streets,” the Washington Post’s great Joel Achenbach reported from Little Havana, for decades the global center of anti-Castroism. On cable television, you could hear exasperation from Ted Cruz and Marco Rubio (who argued, not incorrectly, that the objectionable things about Cuba hadn’t really changed: “No freedom of organization. No elections”). But on the streets Achenbach, like others, saw little of that — “a far cry from the throngs that clogged the streets during the Elian Gonzalez controversy 15 years ago.” Even the titans of Little Havana were adapting themselves to the inevitable. Last winter, for instance, the Cuban-American sugar tycoon Alfonso Fanjul, whose family had long helped to fund the anti-Castro movement, told the Washington Post that he was giving up the fight and had begun scouting investment opportunities back on the island. The pope prodded Obama and Raul Castro, urging the two men together, but it couldn’t have hurt that Rand Paul and the U.S. Chamber of Commerce supported the reconciliation, along with, the Times reported, “major agricultural interests.”

In part because of the broad consensus in its favor — at home and abroad — Obama’s announcement has been seen this week as the welcome end of the era, the banishing of the last vestiges of the Cold War. And yet it was striking to hear the President talking about this move in different terms — not as an end but as a beginning — and not really about Cuba. The hope, President Obama said in his address Wednesday, pointedly, is “to begin a new chapter among the nations of the Americas.” This was what seemed to most excite the Latin America experts this week — the possibility of a new posture to the continent generally. It’s too early to know whether that will happen in any meaningful way. But if it does, it would be something historic, both for the president and the country. It would be a return to the scene of the crime.

America has nothing so bleak and ugly as the colonial history of Britain or France or Belgium, no dark era of oppression and direct political control. But for more than a century — really, ever since the Monroe Doctrine — Americans have been the invisible hand in Latin America: the engineers of banana republics and proxy wars, the hypocrites who experiment with drug legalization at home while requiring Latin presidents to launch full-scale wars against growers and traffickers, the supporters of brutal regimes indefensible except for their loyalty to Washington. As far as our activities overseas go, many of the very worst things that America has done have been done in Latin America.

But the politics of anti-Americanism — always there in many places in this hemisphere, ebbing and flowing — have become a little more powerful and strategic during the past decade, as the politics of the Latin left were both revived and somewhat modernized and moderated, in a wealthier era. The political consensus that the U.S. has been working to build since the end of the Cold War (for open markets and democracy and security cooperation) has seemed during the past two years on the verge of collapse. The Cuba embargo has held an outsize symbolic significance in these debates, because it has served as a signal that no matter how putatively liberal our president, the United States will continue to act as it always has, as continental bullies. “In coming months,” Richard Feinberg of the Brookings Institute wrote in September, “the United States is going to face a tough choice: either alter its policy toward Cuba or face the virtual collapse of its diplomacy toward Latin America.” If America wanted to “not have this kind of left-right divide and the loss of Latin America be one of the president’s legacy,” the great Cuba analyst Julia Sweig said on Wednesday, then it had to realize that “the path to fixing that is through Cuba.”

Those relationships have become more important, because of events that run deeper than politics. The United States is becoming more diverse, but it is especially becoming more Latin, which means that problems emanating south of the border now land closer to home. Washington has paid comparatively little attention to Latin crises during the Obama years. Its gaze has been farther afield, on the bleak aftermath of the civilizational struggle the Bush White House launched with radical Islam, on the problem of Putin, and on the notional obscurity of Hillary Clinton’s “pivot to Asia.” But Latin America has grown impossible to ignore, because during the Obama years, Latin Americans have kept arriving: the ebb and flow of Mexican economic migrants; the lurid scenes from the cartel ascendency south of the border and the displacement of many members of the Mexican middle class to San Diego and San Antonio; the thousands of Honduran and Salvadoran children who turned up unaccompanied at the Texas border, fleeing cities so violent that the state could not protect them; the Brazilian oligarchs in Brickell or midtown east. American politics have always been able to affect Latin America, but now Latin American politics, thanks to simple human movement, have the ability to affect the United States. We need Latin help. Maybe Cuba, belatedly, is the price.

A future, more cautious America may not so casually involve itself in Afghanistan or Ukraine or Vietnam. But we will always be involved in Latin America — the human ties are too many, and the history too deep. This fall, I spent some time reading Telex From Cuba, Rachel Kushner’s novel about Americans on the island on the eve of the revolution. To read it is to experience a kind of temporal displacement: The novel is set in 1960 — the modern era, or nearly — but the scenes are flatly imperial: the insular community of American corporate barons (sugar, mining) in their little clubs with native servants; the brutal conditions in the mines and cane fields where Cubans labored for American bosses; the whole island outside was beginning to rage, buckle, and burn. And yet this wasn’t so long ago. The Castro brothers are characters in the novel: Kushner has Fidel as the passionate, charismatic front man, and Raul Raúl as the fey, patient strategist, pulling the important strings.

Raúl, of course, is still around. And there remain relationships between north and south that don’t look so different than those, and maybe if the opening of Cuba is an enticement to Western investment and sugar barons, there will soon be more of them. But the Cold War is over, the drug war nearly so, and the political battle for Hispanic votes in the United States is only growing more important. One of the least consistent parts of Obama’s presidency has been his perspective on American power: The White House has long insisted that the U.S. can’t permanently serve as the world’s policeman, while giving the CIA and other intelligence agencies broad new powers to try to do exactly that. But this declaration seemed to suit him. Obama built his political career on a magnificent sensitivity to the tones of very long political arcs (race, the country’s division into red states and blue) and from the podium he acknowledged that many Cubans “have seen us as a former colonizer, intent on controlling your future.” Then he quoted the Cuban theorist and revolutionary José Martí: “Liberty is the right of every man to be honest.” This was an indispensable step, politically and ethically the decent and honest thing to do, many years too late. But it contained the hope of another project, farther off: that we might someday return to this region with different intent, to clean up our own mess.