Two short words in 67 pages of the peace deal say it all: "or both". The governments, with the endorsement of the Northern parties, "recognise the birthright of all the people of Northern Ireland to identify themselves and be accepted as Irish or British or both, as they may so choose . . ."

In the careful, exquisitely delicate language of the agreement, it is easy to miss the profundity and the originality of this statement.

What is being said is that it is people who identify themselves, not governments or tribes who tell them who they are. That nationality is a matter of choice, not of inescapable destiny.

That, even more extraordinarily, saying who you are is not necessarily a matter of either/or but can also be both/and. Has it ever happened before that two sovereign governments and a range of political parties involved in a bloody conflict have stated such radical things so clearly?

The question is not abstract. The deal agreed on Friday will have to withstand terrible pressures. Fringe terror groups on both sides will test it with atrocities. Two of the most important parties in the process - Gerry Adams's Sinn Fein and David Trimble's Ulster Unionists - will face considerable internal dissent.

The political mechanics of establishing both a workable administration in Northern Ireland and cross-Border bodies with the Republic will be extremely complex. If the deal doesn't have deep roots, it will be blown away.

There are, though, good reasons to believe the peace package arises not from a passing moment, but from some fundamental shifts. For one of the more paradoxical effects of 30 years of conflict has been to give an illusion of continuity to a period of profound change.

The epic language of immemorial and irreconcilable divisions that tends to be used about Northern Ireland has hidden the fact that many of the assumptions that held good in 1968 when the killing began simply no longer apply.

In 1922, when the last attempt at a comprehensive settlement between Ireland and Britain was being debated in the Commons, Winston Churchill famously contrasted the profound changes in Europe after the first World War with the obstinate constancy of religious divisions in Northern Ireland.

Everything else had undergone "violent and tremendous changes in the deluge of the world. But as the deluge subsides and the waters fall short we see the dreary steeples of Fermanagh and Tyrone emerging once again. The integrity of their quarrel is one of the few institutions that has been unaltered in the cataclysm which has swept the world."

Now, as the flood of violence that has washed over Northern Ireland begins to recede, the dreary steeples of sectarian division between British Protestants and Irish Catholics are still the most prominent features on the landscape.

But beneath them, at ground level, almost everything has changed. Only because the quarrel was conducted with such ferocity was it so hard to notice how pointless it was and how rapidly some of its basic assumptions were being dissolved.

When the Northern Ireland conflict got under way in 1968, it was possible to see the war between Irish Catholic nationalism and Protestant British unionism as a clash of civilisations. The categories were, of course, crude. Ordinary lives and attitudes were much more complex than political or religious labels would allow.

There was, nevertheless, a real sense in which Catholics and Protestants belonged to sharply opposed cultures. It was not simply that they worshipped in different churches, or marched behind different flags. They also, on the whole, lived different lives.

The Republic of Ireland, with which Catholics identified, was still a predominantly rural and agricultural society. Northern Irish Protestants, on the other hand, belonged to a strongly urban and industrial world.

In everyday life, the terms "Irish" and "British" were shorthand for a great deal more than national identity. You could use them to guess with reasonable accuracy what kind of work someone did, whether they used contraceptives (and therefore how many children they had) and what sort of sports they played. Yet, even while the conflict was grinding on, those guesses were becoming, year by year, more inaccurate.

When the Troubles started, it made some sense for Northern Protestants to see themselves as part of a modern, prosperous, economy and the Republic of Ireland, by contrast, as an underdeveloped backwater. Even in the early 1970s, gross domestic product per head of population in the Republic was just half what it was in the United Kingdom. And implicit in the contrast was a belief that this was not coincidental. As the Protestants tended to see it, the Irish were poor because they were Catholic. They were, in the Protestant imagination, priest-ridden peasants.

Now, in the late 1990s, the Republic of Ireland has a higher GDP per capita than the UK. It is a predominantly urban society. The political power of the Catholic church is broken.

Irish Catholics, on the whole, take neither their morality nor their politics from their clergy. They use contraceptives and have the same number of children as Protestants. While all of this was going on, the world Irish Protestants knew 30 years ago was disappearing. The North's once mighty heavy industries were becoming obsolete. The shipyards and engineering works that were still the pride of Protestant Belfast in 1968 have long since dwindled.

British identity has been no more stable than Irish identity. In 1968, it was still possible to imagine Britain as an imperial power. The symbols that Northern Irish Protestants valued - the monarchy, the Empire, the United Kingdom - have lost their glamour. After the scandals that culminated in Princess Diana's death, the royal family seems more a source of confusion than a guarantor of eternal stability.

After the handover of Hong Kong last year, Britain's overseas empire now contains just 168,000 people. And after Tony Blair's concession of devolved parliaments for Scotland and Wales, the UK is being transformed into a decentralised federation of nations.

Yet both sides in the conflict tended to collude in a pretence that all of this change was not happening. The images of the Republic of Ireland as an impoverished backwater and of the UK as a mighty imperial power lent an aura of pseudo-epic grandeur to squalid, intimate cruelties.

The Protestant policeman murdered in front of his children wasn't just a soft target for sectarian hatred. He was the representative of a mighty empire. The Catholic shopkeeper murdered behind his counter wasn't just a victim of venomous bigotry. He was an enemy of Her Brittanic Majesty.

Violent division has the strange effect of making people imagine that their enemies, unlike themselves, are powerful and unchanging. Catholics and Protestants could each see that their own community was in flux. Neither could see that what was happening to themselves was also happening to the other side.

One of the wry ironies of Northern Ireland, indeed, is that social surveys consistently show both Protestants and Catholics believe (a) their own side is divided and incoherent and (b) the other side is an impressively unified monolith. Both, of course, were right about themselves and wrong about the others.

The peace deal is really an opportunity to allow each side to see that its own experiences of profound change are mirrored in the other.

It is an attempt to catch up with what we all know in our ordinary lives - that "Irish" and "British" are no longer fixed terms, but open invitations. In the aftermath of empire, on the morning after the long night of ethnic purity, each of us can choose to accept one or the other. Or, preferably, both.

Fintan O'Toole is temporarily based in New York