In Kofi Annan’s vision of the United States, the superpower is so forceful, so overbearing, that you might think it had just won a war in Iraq. The Secretary-General of the United Nations used his farewell address yesterday to attack the Bush Administration for unilateralism, in a speech that will raise cheers from its critics but was extravagantly unfair.

Annan might drive home a few good points if he were not so indulgent to previous US presidents, from Harry Truman to Bill Clinton, in his efforts to damn George W. Bush. He credits the US with more power than it has had; accuses it of general obstruction of the UN, where its objections have been particular; and blames it for failures that might be better pinned on other countries, on the UN, or indeed, on him.

This competitive mud-slinging is inevitable. Annan steps down on December 31 after ten years in the post. Within two years, four of the five permanent members of the Security Council — the US, Russia, France and Britain — should have new leaders. They are rushing, on similar deadlines, to write their version of history.

Annan’s begins in 1945 and doesn’t get much beyond 1950, before making sorrowful comparison with the present. He glorifies Truman, the “master builder” of the UN, tucking into a sub-clause the acknowledgment that his favourite president gave the order for nuclear weapons to be used, “for the first, and please God, the only time in history”.

For him, it seems, Hiroshima was adequately counterbalanced by Truman’s offer in 1946 to put nuclear energy under international control, a gesture of statesmanship frustrated, as he sketches it, only by Joseph Stalin’s stubbornness.

In that, and other examples, he risks over-personalising clashes between countries, suggesting that only the perversity of these leaders got in the way of the project of international co-operation. That is a hazard of a life lived in the corridors of the UN, where countries are so much personified by their ambassadors. Annan and his team had a poor relationship with John Bolton, the US’s just-departed US Ambassador, who turned an inexhaustible appetite for confrontation to tackling the UN’s own unaccountability.

Bolton embodied, to Annan, the US’s new taste for acting alone, and there is plenty in his personality and US policy to support that. But it is not the whole picture. The US and Bolton have been aggressive in pushing for UN resolutions on Iran and Sudan — where some fear that the slow search for multilateral support may not even be in the best interests of the people of Darfur.

Bush’s approach to the UN has been more mixed than Annan allows; so was Clinton’s. Annan skates over Clinton’s willingness to act alone in military action or trade, which his rhetoric and foreign travel disguised.

He also makes too little of the new complexity of striking deals, given the assertiveness of some rapidly developing countries, who sometimes appear to oppose anything the US backs, for no other reason. The US can be blamed for aggravating those clashes, but not entirely for causing them. Other Western countries have been happy to hide behind the US, but have shared its concerns — that they were granting a lot on the development agenda but getting too little in return on security, terrorism and the Human Rights Council. Annan blames these clashes on Bush but they are also a phenomenon caused by the fall of the Soviet Union and the rise of once-impotent countries.

Annan chides the US for failing abroad to hold to its democratic ideals. If by this he means the US prison camp at Guantanamo Bay, and the justifications it has offered for holding people there indefinitely, then he might as well say so, but he is right. But if he means the Iraq invasion, then he is ignoring the US’s belief that toppling Saddam Hussein would promote democracy across the region — and the UN’s failure to uphold its own sanctions against Iraq. It is easier to accuse the US of too much idealism than too little — and even easier to accuse the UN of confusion and incoherence.

Annan, who shared the 2001 Nobel Peace Prize with the UN, has had a difficult ride. His accusations against Bush would have more weight if he had also turned some of the heat back on the UN and its painful failures to change.

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