Barack Obama normally likes to talk about hope. Last week at the United Nations he had the audacity to fear. The US president conjured up a vision of a dystopian world: “Extremists sowing terror…Protracted conflicts that grind on and on. Genocide and mass atrocities. More and more nations with nuclear weapons. Melting ice caps and ravaged populations.” That is our collective future, according to Mr Obama, unless the world’s leaders co-operate to find “global solutions to global problems”.

As if to illustrate his point about this dangerous new world, two days later it was revealed that Iran has a second, secret, nuclear site. The mental image of bearded mullahs watching spinning centrifuges in a secret nuclear-facility hidden in a mountain sounds like something out of a James Bond film. It is, however, exactly the kind of international challenge Mr Obama was referring to. The question is whether the world’s leaders can rise to the occasion.

If the major powers can establish a united front and force a change in Iranian behaviour, it would be a triumph for the co-operative internationalism that underpins Mr Obama’s foreign policy. Unfortunately, the odds are on failure.

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Angela Merkel’s victory in the German elections last night is both a triumph and a paradox. In 2005 she campaigned as an economic liberal but ended up in a coalition with the Social Democrats, which forced her towards the centre. This time around she campaigned as a centrist and a champion of the traditional German social market economy, and has ended up in a coalition with the economic liberals of the Free Democrats.

So the next question is will this new coalition finally free Merkel to be Merkel, and to push through the free-market policies that she put at the centre of her programme in 2005? Or has the chancellor really changed?

I think there are two big tests to look out for. First, tax cuts; both the CDU and the Free Democrats promised tax cuts – will they, can they, deliver? Second, what are they going to do about the Opel bail-out. Securing the future of a big car manufacturer was an important achievement for Merkel in the last days before the vote; but leading figures in the Free Democrats expressed misgivings about such a costly, anti-market measure. Whose views will prevail?

Watching television in America is always educational – a useful reminder of what a bizarre country this is. Earlier this week, I tuned into a CNN discussion in which an orthodox rabbi – Rabbi Shmuley – was demanding that Iran be thrown out of the UN, and the world body be turned into a league of democracies. Then last night, I turned on and there was Rabbi Shmuley again – only this time, he was flogging a book based on thirty hours of interviews he had recorded with Michael Jackson.

There are so many questions raised by this – should I take Shmuley’s views on UN reform, more or less seriously, because he was a confidant of the king of pop?; why did Jackson, a former Jehovah’s witness, choose to confide in a Lubavitch rabbi?; is Shmuley rushing the bookout for the benefit of mankind, or does he have baser motives?

I have to say the tapes made fascinating listening. Jackson comes across as unhappy, narcisistic and slighly unhinged. Who would have thought it? He was also horrified by the idea of getting old, and said that when he looked in the mirror, he saw “an ugly lizard“.

As for Shmuley, he has another best-selling book out, called “the Kosher Sutra”. But I’m feeling too weak to check it out, at the moment.

The subject matter at the G20 is undeniably important. But now that the immediate fear that the world economy is going to implode has died down, discussions about financial regulation and global economic imbalances are once again rather dry and technocratic. This morning, however, some real drama intruded on the economic discussions – with the revelations about Iran’s second and secret nuclear plant. Obama, Brown and Sarkozy appeared before the cameras looking stern and threatening tough action, unless Iran changes course.

In an odd way, the new revelations were both feared and hoped for. On the one hand, they confirm the fears of the West that there is much more to the Iranian nuclear programme than had been declared. On the other hand – since that was always thought to be the case, anyway - it is useful to have confirmation, to brandish in the face of the reluctant Chinese and Russians, who must agree to any further sanctions.

So what happens next? The first stage is the meeting of the Perm 5+1 (the US, UK, France, Russia, China and Germany) with Iran next week. This is going to be a bit awkward for Iran – and they might agree to new international inspections. But I would be very surprised if they made any serious concessions. A regime that is content to shoot demonstrators down in the streets, can brush off a little diplomatic embarrassment.

I am sitting in a cavernous press centre in Pittsburgh at the G-20, watching television pictures on a big screen of anarchist demonstrators being tear-gassed in a suburb about four miles from here. Now I understand one of the reasons for putting the summit in Pittsburgh. You can throw an exclusion zone around the centre of the city, in a way that just isn’t possible in New York.

Obama has also chosen Pittsburgh for reasons of tact. It would just have been too much of a snub to the other 170-plus members of the UN General Assembly, if a select group of 20 nations had snuck off to hold a separate, exclusive meeting in another part of Manhattan. It would have been like one of those New York night clubs, where the hoi polloi are held back behind a rope, while the favoured few are waved through the VIP entrance.

Pittsburgh is also regarded as a showcase for post-industrial recovery. The city was decimated by the shrinkage of the steel industry. Half the population has moved away, as the jobs disappeared. Pittsburgh’s population, which was 676,000 in 1950, is now a little over 300,000. The city’s champion football team, the Steelers, are well supported all around the country because there are so many Pittsburghers in exile. However, these days, the local economy is regarded as a success story. New industries have sprung up in medical services, robotics and computing. The unemployment rate is “only” 7.7%, which is lower than the rest of the US. They should hand-out t-shirts at the summit, with the slogan – “You can survive globalisation”

Approaching the UN today, I came across pro and anti-Gaddafi demonstrators. The “pros” were American members of the Nation of Islam, in their trademark suits and bow ties, who seemed to regard Gaddafi as “the leader of Africa”. The opposition was provided by real Libyans, protesting about human-rights abuses.

As it happens the UN General Assembly is currently being chaired by a Libyan diplomat, Ali Treki. He had insisted that all heads of state speak for no longer than 15 minutes. But he did not apply this to Gaddafi, who he introduced in neutral style as “king of kings and leader of the revolution.” The Libyan leader rambled on for some 96 minutes, reading off scraps of paper, and throwing the UN schedule into chaos.

Now clearly Gaddafi is going to get bad reviews in the morning papers here in the US. But I have to say that some of what he had to say made perfect sense. It is entirely true that the structure of the UN Security Council is anomalous and outdated (although it was perhaps a bit harsh to call it “the terror council”). Gaddafi’s analysis of why it is so hard to reform the council was also bang on the money – each time you suggest one country, you trigger a demand from the next one in the queue. (So if you suggest Germany, Italy jumps up and down.) And his proposed solution – a Security Council of regional organisations such as the EU, Asean, the African Union – sounded like an elegant way out. Gaddafi was even quite witty. I liked his comparison of the UN General Assembly to Speakers Corner in London; you can speak as much as you like, it is just that you will be ignored.

New York is even more chaotic and noisy than normal, when the UN comes to town. Trying to deal with the security arrangements for 88 heads-of-state in a few square miles of midtown Manhattan turns the city into a mad-house of road blocks and blaring police sirens.

The locals are reasonably tolerant. But, inevitably, Fox News is trying to use the occasion to whip up a bit of anti-UN sentiment. I watched a broadcast in which a TV anchor listed all the “crazies” and anti-American leaders who are in town, and invited his audience to share in his disgust that they are being funded by “your tax dollars”. The implication was that it was clearly in American interests to save some cash by slinging the UN out of New York and barring the likes of Hugo Chavez, Gaddafi and Ahmadi-Nejad from ever entering the country.

ADJ is still the number one villain. Fox helpfully pointed out that he is staying at the Intercontinental. Gaddafi has not found anywhere to pitch his tent, so is staying at the Libyan mission. And Obama is at the Waldorf Astoria. I was at the Waldorf last night and by American standards, the security is reasonably relaxed. You can wander around the lobby unmolested. Its only the upper floors that are barred.