So what would it take to bring the Taliban into a settlement? First, he said, stop killing them. Second, an end to foreign military presence, the one thing that always mobilizes the occupied in that part of the world. Third, an Afghan constitution framed to give more local autonomy, so that Pashtun regions could be run by Pashtuns.

On the face of it, as my breakfast companion surely knows, those sound like three nonstarters, and taken together they sound rather like surrender. Even Clinton is not calling for a break in hostilities, which the Americans see as the way to drive the Taliban to the bargaining table. As for foreign presence, both the Americans and the Afghans expect some long-term residual force to stay in Afghanistan, to backstop the Afghan Army and carry out drone attacks against Al Qaeda. And while it is not hard to imagine a decentralized Afghanistan — in which Islamic traditionalists hold sway in the rural areas but cede the urban areas, where modern notions like educating girls have already made considerable headway — that would be hard for Americans to swallow.

Clinton herself sounded pretty categorical on that last point when she told Pakistani interviewers: “I cannot in good faith participate in any process that I think would lead the women of Afghanistan back to the dark ages. I will not participate in that.”

To questions of how these seemingly insurmountable differences might be surmounted, Marc Grossman, who replaced Holbrooke as Clinton’s special representative, replies simply: “I don’t know whether these people are reconcilable or not. But the job we’ve been given is to find out.”

If you look at reconciliation as a route to peace, it requires a huge leap of faith. Surely the Taliban have marked our withdrawal date on their calendars. The idea that they are so deeply weary of war — – let alone watching YouTube and yearning to join the world they see on their laptops — feels like wishful thinking.

But if you look at reconciliation as a step in couples therapy — a shared project in managing a highly problematic, ultimately critical relationship — it makes more sense. It gives Pakistan something it craves: a seat at the table where the future of Afghanistan is plotted. It gets Pakistan and Afghanistan talking to each other. It offers a supporting role to other players in the region — notably Turkey, which has taken on a more active part as an Islamic peace broker. It could drain some of the acrimony and paranoia from the U.S.-Pakistan rhetoric.

It might not save Afghanistan, but it could be a helpful start to saving Pakistan.

What Clinton and company are seeking is a course of patient commitment that America, frankly, is not usually so good at. The relationship has given off some glimmers of hope — with U.S. encouragement, Pakistan and India have agreed to normalize trade relations; the ISI has given American interrogators access to Osama bin Laden’s wives — but the funerals of those Pakistani troops last month remind us that the country is still a graveyard of optimism.

At least the U.S. seems, for now, to be paying attention to the right problem.

“If you stand back,” said one American who is in the thick of the American strategy-making, “and say, by the year 2020, you’ve got two countries — 30 million people in this country, 200 million people with nuclear weapons in this country, American troops in neither. Which matters? It’s not Afghanistan.”