But out on the streets yesterday there was little talk of celebration. "Not yet - not for a while", was a common response. You could search long and hard for an out-and-out optimist in recent days.
"If it stops any killings, it will be good. But I don't believe it will. The bottom line is: there's still guys in the background with guns."
"I'm pleased that there's an agreement. But the violence will pick up. When the emotions are strong, it's like a tinderbox."
Those two reactions - from a Catholic on the Falls Road and a Protestant on the Shankill Road respectively - were typical.
Politicians and commentators vied with each other in their use of superlatives: "I have to pinch myself", "It's like the fall of the Berlin wall" and "I cannot believe what has happened"were phrases that observers and participants grasped for to convey the magnitude of what was taking place.
Others are still wondering. Jayne and Kenny Knox both desperately want the peace process to work. Jayne, a 35-year-old teacher, cannot remember peace. "I find it difficult to imagine," she said yesterday. As the peace talks reached their climax, and as the broadcasters went into overdrive, they had decided to switch the radio off. "We always have the news on in the morning. But we were just so fed up. Everybody is a bit weary." They bought a batch of yesterday's newspapers with their banner headlines, to give to their five-year-old son when he grows up - "in case it is a moment of history". But neither of them are betting heavily.
In the lead-up to the deal, the mood of scepticism was even stronger. Watching the television news in a pub in heart of Catholic Derry at Thursday lunchtime, I expected imaginations to be gripped. In reality, almost nobody looked up when the news came on; one man gave a contemptuous grunt, and looked the other way. In Protestant Portadown, it was the same story: everyone scoffed when the evening news came on. Some were contemptuous, saying that even if agreement was achieved, "it is going nowhere". Others, like Martin, a 35-year-old engineer, were regretful, but equally pessimistic: "Somebody has to win or lose. And whichever side thinks they have lost the most - all hell will be let loose."
By Friday morning, when the story of a possible peace deal after 30 years of violence was dominating television news bulletins around the globe, there was a surreal dissonance between two almost irreconcilable worlds - even stranger than the weather, which zigzagged between snow and warm sunshine. Listening to the car radio or watching the unfolding television news, it seemed impossible not to be caught up in the drama and the excitement. Then, when I talked to people, the balloon of hope seemed to be deflated.
A Protestant waitress in Craigavon declared that the fuss being made about a deal was "a load of rubbish". Her comments, together with similar remarks from her colleagues ("I don't believe it'll make a bit of difference", "They'll not bring peace here, through that") are scribbled on the same page in my notebook as the comments that I noted down off the television news a few minutes earlier - "historic", "without parallel", "amazing".
It is curiously unsettling to look at the two sets of reactions side by side - like one of those computer-created illustrations that shows an entirely different picture, depending on how you focus your eyes.
Not everybody was so downbeat. In fiercely nationalist Crossmaglen, in south Armagh, an elderly shop-owner was so busy listening to the radio coverage that she scarcely had time for her customers.
"I'm listening and listening and listening. It's fantastic. I thought it would be a good Good Friday - but not this good." But she also had a pessimistic postscript: "Even if it's not good for us, it will be good for those who come after."
The events of last week may eventually seem to have been the defining moment for future peace. In that respect, comparisons with the fall of the Berlin Wall are entirely valid. The local reaction, however, could hardly be more different. Many people point out that it has not always been gloomy like this. When the IRA declared their first ceasefire, in 1995 - that was a moment to treasure. "You really felt jubilation. That was different then," said one man yesterday. Now, there is a prickly vulnerability.
In the little village of Poyntzpass, near Newry, the mood remains deeply sombre, following the recent killing there of two friends, a Catholic and a Protestant. There had been no inter-community violence here before. Many say that the killings have brought the community even closer than before. Here, too, however, there is little belief in a peaceful future.
"That's all waffle. It's just talk. I've heard it all before," said one villager with bleak finality, as the i's were dotted and the t's were being crossed at Stormont. (Like many others, his refusal to believe in a new dawn means that he does not want to be quoted by name. "Otherwise, someone can come through the door and say: 'You spoke'. Bang!") Even as the politicians argued their way to a final deal on Good Friday, he declared: "There's no hope until the guns are taken out of politics." That phrase is repeated, almost mantra-like. It is half-fear, half-prayer. Hope is still running a cautious third.
Across the world, the best advice is to ignore the politicians and listen to the street. At the beginning of the Balkan wars Western politicians prattled about a peace deal, while villagers and ordinary townspeople talked of the impending apocalypse. It was depressingly obvious that the villagers were right and the politicians wrong.
But in Ulster, maybe this rule of thumb can be reversed. Pessimism may be a form of protective shell, to prevent further disappointment. A minority still seem proud of their hatreds - like the Catholic and Protestant in Derry who both said that they would forbid their daughter to marry somebody from the other side ("I would kill her," boasted the Protestant). Others seem wary of building up too much hope, only to see it crushed once more.
The events of the past few days do show that the pessimists are not always right. Polls suggested that 90 per cent had believed a settlement to be out of the question.
One Londonderry electrician will be suffering from severe indigestion today, if he has fulfilled a promise he made on Thursday afternoon. Less than 24 hours before Tony Blair walked out to announce that "courage has triumphed", he insisted: "I'll eat that pillar if David Trimble signs."
The "Mandela moment" in South Africa - the release of the jailed nationalist leader - marked the beginning of a giant shift towards democracy that is still astonishing to contemplate. At the time, however, scepticism and fears of future violence were widespread.
Ulster could be the same. Again and again, people say that the distrust is buried too deep. Like the retired teacher in the cathedral city of Armagh ("city of saints and scholars", in the official phrase) who wistfully declared: "It doesn't feel like a moment of history. Everything is too ingrained. It'll take generations."
Equally, however, there is a yearning for that distrust to be at an end. In many respects, the distrust and the yearning are incompatible. The violent fish can only survive if they have some water to swim in. The Good Friday peace ought to help to dry out the pool.
Optimism is perhaps strongest among those who already lead more or less mixed lives, especially in Belfast. In a lively bar close to the university in south Belfast, Catholics and Protestants were eating, drinking and joking together on Friday night.
Steve, a 36-year-old Catholic businessman, insisted that now is the time to celebrate. "It's not going to be an Alice in Wonderland transformation, where everything changes overnight. But there will be change. And that's brilliant."Reuse content