The term "neo-conservative" has many usages, including "former liberal" and "Jewish conservative". In recent years, however, it has taken on clearer definition as a philosophy of aggressive unilateralism and the attempt to impose democratic ideas on the Arab world. The neo-conservatives also constitute a distinct group around George W. Bush, the US president. They pushed for the invasion of Iraq and remain identified with hardline positions on Iran, Syria and North Korea.
Outside the administration, the chief fulcrum of neo-conservatism is the American Enterprise Institute. The day after vice-president Dick Cheney's former aide Scooter Libby was convicted of perjury, AEI held its annual black-tie gala. I did not go expecting contrition, but under the circumstances it seemed possible that self-examination might feature on the menu. Once a lazy pasture for moderate Republicans hurtled into the private sector by Gerald Ford's 1976 defeat, AEI has turned in recent years into a kind of Cheney family think-tank. It had not been a good week, year, or second term for any of these people and I thought a few cocktails might cause them to consider their predicament.
This was fantasy on my part. From the stage, one took no hint that matters were not working out as anticipated. All rose to salute the arrival of Mr and Mrs Cheney, herself a longtime fellow at the institute. The vice-president looked on from the head table as his friend, Bernard Lewis, perhaps the most significant intellectual influence behind the invasion of Iraq, came up to accept an award.
In his address, the 90-year-old Mr Lewis did not revisit his argument that regime change in Iraq could provide the jolt needed to modernise the Middle East. Instead, he spoke about the millennial struggle between Christianity and Islam. Mr Lewis argues that Muslims have adopted migration, along with terror, as the latest strategy in their "cosmic struggle for world domination". This is a familiar framework from the original author of the phrase "the clash of civilisations". What did surprise me was Mr Lewis's denunciation of Pope John Paul II's 2000 apology for the crusades as political correctness run amok, which drew clapping. Mr Lewis's view is that the Muslims started the trouble by invading Europe in the eighth century; the crusades were merely a failed imitation of Muslim jihad in an endless see-saw of conquest and reconquest.
Were one to start counting ironies here, where would one stop? Here was a Jewish scholar criticising the Pope for apologising to Muslims for a holy war against Muslims, which was also a massacre of the Jews. Here were the theorists of the invasion of Iraq, many of them also Jewish, applauding the notion that the crusades were not so terrible and embracing a time horizon that makes it impossible to judge their war an error. And here was the clubhouse of the neo-conservatives, throwing itself a lavish party when the biggest question in American politics is how to escape the hole they have dug.
But whether or not the neo-cons are prepared to face it, there are increasing signs that their moment is finally over. At the Defence department, Donald Rumsfeld has been replaced by Robert Gates, a member of the Iraq Study Group and an affiliate of the realist school associated with the previous President Bush. Paul Wolfowitz, the architect who wanted to build a new Middle East on Saddam's rubble, has been moved to the World Bank, where he observes a Robert McNamara-like silence on the failure of his war. Another former Pentagon official, Douglas Feith, is under investigation for misrepresenting intelligence data to make the case for the invasion.
At the State department, Condoleezza Rice is returning to her realist roots and now actually seems to direct policy. She has embraced shuttle diplomacy in the Israeli- Palestinian conflict, is considering conversation with Syria and Iran and even made a nuclear deal with North Korea. These steps signify a broader shift away from what the neo-con defector Francis Fukuyama calls "hard Wilsonian" ideas and back towards the less principled, more effective pragmatism of Brent Scowcroft, former national security adviser, and James Baker, former secretary of state.
The most important sign of all is the fading influence of Mr Cheney, who for six years dominated foreign policy in a way no previous vice-president ever has. Mr Cheney is discredited, unwell and facing various congressional investigations. He was badly damaged by the Libby trial, which exposed his ruthless mania to justify a war gone wrong.
But the larger factor in Mr Cheney's demise is that his neo-conservative hypotheses have been falsified by events. Invading Iraq did not catalyse a new Middle East; isolating North Korea advanced its nuclear programme; high-handed unilateralism has reduced American power. At the outset of his presidency, Mr Bush thought himself lucky to have a number two who did not aspire to his job. He may now grasp the hazard of lending so much power to someone with no incentive to test his views in the political marketplace.
As disciples of Bernard Lewis, it is unlikely Mr Cheney and the neo-con crusaders will apologise for what they have wrought. Like Mr Bush, they look to the long span of history for vindication. It will indeed be eons before anyone trusts them again.