Many, perhaps most, international disputes are solved ultimately not by compromise and reconciliation but because one side wins and one side loses, or at least becomes exhausted.
This dynamic is assisted if the outside world also loses interest and thereby stops encouraging the losing side from continuing the fight.
Something like this has produced the cold, strange, angry, yet so far effective peace of Northern Ireland. I have just spent a week travelling in Ireland and found it, as they say of Israel, a land of limitless impossibilities.
In Northern Ireland, in the great historic dispute between Catholic nationalists and Protestant Unionists, the Unionists won. The nationalists wanted all of the island of Ireland to be one nation, ruled by a national parliament in Dublin. When Ireland won its independence from Britain in 1921, after a brilliant and ruthless military campaign led by Michael Collins, London retained control of six of the nine counties of Ulster. These became part of the United Kingdom of Great Britain and Northern Ireland. Ulster's Unionists are determined to stay part of the UK.
Tony Blair oversaw the Good Friday Agreement of 1998, which led to the effective end of large-scale sectarian killings in Ulster. Blair deserves great honour for his role in Anglo-Irish relations, especially for his 1987 apology for the British government's responsibility in the Irish famine of the mid-19th century. This was a kind of proto-genocide in which a million Irishmen died and a million emigrated.
Of the Good Friday Agreement, Blair reflected that the Unionists were too stupid to realise they'd won, and the Republicans were too clever to tell them. For the Republic of Ireland gave up its historic territorial claim to the north. Previous institutions, such as the all-Ireland Council, designed to give Dublin some say in the running of the north, were abandoned. Ulster's status as part of the UK was guaranteed, unless a clear majority of its citizens should vote otherwise in some future plebiscite. And the Irish Republican Army gave up violence.
In return, Ulster's Catholics got extensive cultural rights and an absolute guarantee of civic equality, which they had certainly not enjoyed in previous decades. A power-sharing agreement gives the leaders of both sides an effective veto.
But here is a startling paradox. Having won the war, the Unionists, 16 years later, appear to be losing the peace. For a start, the Protestants have lost their majority. The 2011 census showed 48 per cent Protestant and 45 per cent Catholic. Given higher Catholic birthrates and higher Protestant migration to mainland Britain, there are probably already more Catholics than Protestants in Northern Ireland. The Catholic population is substantially younger. In time these demographic trends will lead to a clear nationalist majority.
But that almost certainly won't lead to any short-term change in constitutional arrangements. Since the bust of the Celtic Tiger economy in the Republic of Ireland and the associated Irish banking crisis, there has been little appetite among northern Catholics for political union with the south. British health, education and salary provisions are better than the republic's. But the biggest winner from the Good Friday Agreement in the north has been the Catholic middle class. Northern Ireland was a state designed to perpetuate Protestant privilege. Now the state is committed to being a meritocracy.
And what do we find in that meritocracy? The cohort that does best at school is middle-class Catholic girls (middle class defined as not qualifying for a free school lunch). They do so well they are challenging the best performing cohort in all UK schools, ethnic Chinese kids. And the cohort that performs worst in Northern Irish schools is working-class Protestant boys, many of whom go on to marching bands and violence.
A lot of Ulster's middle-class Protestant kids go to university in northern English and Scottish cities and don't come home. They feel out of place in Northern Ireland. They can never identify with the Gaelic Irishness of the republic and the northern nationalists, but neither do they identify with the old-style unionism of their grandfathers.
As they lose their electoral majority, the Unionists are steadily losing their symbols, and it's driving them nuts. Already, there are more Catholics than Protestants in Belfast. So the city council is not inclined to fly the Union Jack. Polls show that only about 40 per cent of Northern Irish regard their primary civic identity as British. Twenty per cent say they are Northern Irish and another 20 per cent say they are just Irish. So while the nationalists cannot take Northern Ireland out of the UK, they are taking the UK out of Northern Ireland.
Although broadly peaceful, and certainly preferable to "the Troubles", this is still a situation full of danger for everyone. Gaelic cultural nationalism is flourishing in the north. Ireland's history suggests that cultural nationalism is the surest route to political nationalism. If the Scots should vote to leave the UK in December, unlikely but by no means impossible, or even if Edinburgh keeps pressing for ever greater devolved powers, the dynamic for Gaelic separatism in the north must be affected.
And Northern Ireland is still a bitterly and profoundly divided society. There are still physical barriers between Catholic and Protestant communities in Belfast. Very few children attend mixed schools. Hundreds of people still receive assistance because they are forced to sell their homes - they are the wrong religion in someone else's patch.
And while Northern Irish politics has domesticated the extremists, it has also empowered them. Sinn Fein and the Democratic Unionist Party have replaced the more moderate political parties that once dominated their respective communities. Most Catholics, though full of grievance for their unequal treatment in the past, never supported violence. But many of them vote Sinn Fein now because they think Gerry Adams and Martin McGuinness are tough, effective negotiators. If politics is to be a communal arm wrestle, let's put some muscle into it, as one wag observes.
Politics, like life, is full of anomalies, of formulas that should work but don't, and of situations that should never work but do. Northern Ireland could continue as it is, with all its demographic and political trends unfolding, uncomfortably but peacefully, for many years.
On the other hand, it could easily get very ugly again.