Friday marked the G20 forum's first big test on a major non-financial crisis. Its performance can only be described as a failure. Not because the St Petersburg summit failed to agree on a solution to the catastrophe in Syria. To expect 20 powerful states (and assorted representatives of multilateral institutions) to shake hands on some kind of a deal was always highly implausible, given that neither Barack Obama nor David Cameron has yet managed to secure the backing of even their own parliaments. Similarly, while all the late-night chest-beatings (aka "candid and constructive conversations"), drippings of poison in journalists' ears and rows over seating plans may have been diverting, they are the meat and drink of international diplomacy. No, the far graver problem exposed this week was that of world leaders palpably losing faith in the very process of international diplomacy that they are meant to be driving forward.

Most striking in this regard was Mr Cameron's call to bypass the UN and press ahead with "action" on Syria. The UK has been a member of the UN since its founding in 1945; it sits permanently on the security council. To talk about this international organisation, as the prime minister did yesterday, as serving only to "contract out our foreign policy, our morality, to the potential of a Russian veto" is frankly silly. But it also speaks of a doubt in the prime minister's mind that he, and the other proponents of imminent military action, can actually win the argument. The same suspicion can be traced in Mr Obama's refusal yesterday to talk about what he would do should next week's congressional vote go against him. Part of what makes multilateralism such a noble ideal is its assertion that countries should not be allowed to get their way merely by bullying, but must argue it out with other nations as equals. Whatever Mr Cameron and Mr Obama's frustrations with Vladimir Putin, it is very dangerous indeed for them to disavow an entire process simply because other participants refuse to do what they want. But for their part, the refusal of Russia and China to engage in serious discussion also knocks the wheels out from under the multilateral vehicle.

Despite the Commons vote, the prime minister was one of President Obama's most outspoken supporters. That, his team will hope, will be the abiding memory of a summit that was predicted to be a humiliation for the prime minister after the almost unprecedented defeat last week. But no one who recalls the George W Bush cheery "Yo, Blair!" moment at a previous St Petersburg summit will doubt how many different messages can emerge from beyond the formal summit news conference at global gatherings. Mr Cameron achieved one small coup when he engaged President Obama in an informal conversation on the fringes of the dinner, during which other world leaders, including Germany's Angela Merkel, joined them. Leveraging more humanitarian relief is another area where Mr Cameron could hope to exercise some power. He chaired a meeting to raise the question of improving access to Syria's estimated 4 million internally displaced people but, despite committing Britain to donate a further £52m, there was no rush to contribute more aid to a UN fund of £4bn that is still less than half funded.

After the fall of the Berlin Wall, it was fashionable to describe this as Washington's "unipolar moment": its chance to reshape the world without resistance from the old Soviet Union. What this week confirmed is that the Bush wars and then the subprime crisis have effectively ended that moment of uncontested supremacy. This is not to say that the US has any equal rivals for global dominance, but nor can it rely any more on always getting its way, or even count on British support. That loss of power and control could be seen quite directly in Mr Obama's impatience yesterday.