When I meet Foster, he is quite the dandy in a plum-coloured velvet suit, modish large-check shirt, and perfectly contrasting sage knitted tie. It’s clear he’s been enjoying the fun of the chase, directing and designing the show and pulling it all together at the last minute, with some of the models arriving only days before the opening. "There’s been a number of challenges - inevitable when you’re putting something like this together at short notice," he acknowledges right away. "But we’ve got a big list of people who’ve sent material in. It’s like a mini RA within the RA."

Let’s face it, if you’re an architect anywhere in the world and a big name like Foster rings up to ask for a loan of your model, you are not going to say no. Unless, that is, you are Daniel Libeskind, whose winning scheme for the World Trade Center is conspicuously absent. But that, says Foster, was simply because the model was needed for consultations in New York. He has two of the other Ground Zero contenders in the show (and two versions of his own design in the generalist architecture room outside) as well as a model of Minoru Yamasaki’s original Twin Towers. What concerned him more was a simple matter of scale. It clearly vexed him at first that the models came in all shapes and sizes. "You get some of the shortest tall buildings in the world which come as big models, and you get the tallest in the world, which come as small models. You get very elegant Perspex things, and cruder wooden things, all coming from all directions."

As a noted control freak, Foster had to impose order on this chaos. The bilateral division into East and West was his first big move - demonstrating that the East now challenges the States as the spiritual home of the skyscraper. "Asia and the Pacific Rim has seized the initiative of the skyscraper tradition and really captured the dynamic," he observes. "For us, tall buildings are only one weapon in the armoury - there are other ways of achieving density - but for so many people in the world the high-rise residential building is a lifeline out of the slums and the ghettoes." And then there’s the question of precious land. "Take Singapore - if they want land to build on, they have to buy it from Malaysia and dump it in the water. Or take Hong Kong with its airport, the size of Heathrow, created by dumping earth in the sea." A Foster airport, naturally. Such places are not going to waste their costly space with suburban low-rise sprawl. And the results can be spectacular: the evocative skyline of Hong Kong forms one of the two giant wall-hangings at Sky High. Or take Sydney, where a very fine Renzo Piano skyscraper now graces the skyline. The other wall-hanging at the exhibition is very Look and Learn: the tall buildings of the world, arranged not by chronology, but height.