Long ago, I decided Northern Ireland was a hopeless conflict.

I grew up in a working-class Irish Catholic neighborhood of Boston where in every bar people collected money for the Irish Republican Army. When I became a journalist, I avoided the Irish question because there seemed no chance to solve it. I’ve spent 30 years focused on the Israeli-Palestinian issue.

That’ll teach me. On Monday, the impossible happened.

“We all saw something today that people, never, ever thought would happen,” said British Secretary of State Peter Hain. The two most important leaders of Northern Ireland’s hard-line Protestants and Catholics, who fought for decades, finally agreed to share power in a joint government.

Ian Paisley, the 80-year-old Protestant head of the Democratic Unionist Party sat for the first time with Sinn Fein’s Gerry Adams, reputedly a veteran IRA leader. Their deal culminates a torturous peace process, during which more than 3,600 people died.

What was most moving and thrilling about the scene were the words of the curmudgeonly Paisley: “We must not allow our justified loathing of the horrors and tragedies of the past become a barrier to create a better and more stable future for our children.”

Watching this stooped white-haired man reverse a lifetime’s course made one feel that change might be possible in other intractable situations, like the Israeli-Palestinian conundrum. This very week, more than 100 leading Israeli and Palestinian figures signed a statement endorsing a 2002 Saudi peace plan that will be reconfirmed at an Arab summit convening Wednesday in Riyadh.

The plan offers Israel recognition and permanent peace with all Arab countries in return for full Israeli withdrawal from land captured in the 1967 Six-Day War. It calls for a Palestinian state with East Jerusalem as its capital. There are many serious loopholes, notably the issue of whether Arabs would demand that Palestinian refugees be allowed to return to former homes in Israel. This would effectively end the Jewish state and is an uncrossable line for Israel.

Perhaps it’s a political feint, but Israeli Prime Minister Ehud Olmert has said positive things about the Saudi initiative. The sight of Paisley and Adams together should remind us that things, times and people do change.

Brendan O’Leary, head of the Solomon Asch Center for Study of Ethnopolitical Conflict at the University of Pennsylvania, has vast experience with conflicts from Northern Ireland to Iraq.

I asked O’Leary what brought Paisley and Adams to that table. “Both sides had to believe they couldn’t win the conflict” by the tactics they were using, O’Leary said. Sinn Fein recognized it couldn’t defeat the British by using politics plus violence. And the Unionists recognized that demography wasn’t on their side, as the Catholic population in the north gradually approached parity with the Protestants.

A second key factor was leadership. Sinn Fein’s leaders, and ultimately Paisley, were strong enough to choose compromise over violence. In the case of Sinn Fein, it took so-called hard men – leaders reputedly connected to the IRA – to persuade radicals to lay down arms.

Outside parties – Tony Blair’s Britain and the United States under Bush the father and Bill Clinton – also were key. “In Northern Ireland, the Brits gently but firmly squeezed the Protestants into power-sharing,” says O’Leary. And the Irish government played a constructive role in nudging Sinn Fein.

Can these lessons be applied to the Middle East? Of course, geography matters. It helped that Northern Ireland is part of a stable, prosperous Europe.

But some elements of the Irish case apply. The Palestinians seemed to grasp in the 1990s that they couldn’t win a state by force. Most Israelis understand that demography isn’t on their side – if they keep the West Bank and effective control of Gaza’s borders, they will ultimately face a Palestinian population that outnumbers Israeli Jews.

On the minus side, many Palestinians still believe demographics and violence can defeat Israel. Israeli settlers continue to build in Palestinian areas where they are outnumbered. Leaders on both sides are weak.

This makes it imperative that other parties play a constructive role. “Decisive action by Arab countries to support a peaceful Palestinian movement, and work actively to help it,” is crucial, O’Leary notes. So is the need for decisive U.S. action to encourage Israel on the path toward two states.

Monday’s meeting between Adams and Paisley shows it is premature to say “never.” May that turn out to be a lesson with meaning for Israelis and Palestinians.