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.