This part of things intrigued Foster because it threw up some surprises. Such as the fact the 14th century Ulm Cathedral is taller than an iconic New York skyscraper, Mies van der Rohe’s Seagram tower of 1957. Which in turn is only a few feet taller than the Great Pyramid of Cheops (2500BC). But the other thing that struck him, once he’d got all these famous tall buildings in order, was how the rate of growth of skyscrapers slowed right down from the mid 20th century.

"The thing I find staggering is that the jump in height from the Empire State Building to the supertall ones like the Sears Tower in Chicago or to the World Trade Center is really not that big, over a long period of time", he says. True enough: even the very high ones being planned and built now - such as Kohn Pedersen Fox’s World Financial Center in Shanghai with its big hole in the top, are not hugely taller than the great names of the 1930s. And whereas Foster’s own unbuilt "Millennium Tower" of 1989, envisaged for Tokyo, ups the ante a fair bit, it is still only the second tallest ever designed. The palm belongs to Frank Lloyd Wright with his "Mile-High Sky City" of 1956, planned for Illinois.

Such vertical cities, particularly if they can be designed to generate their own power as Foster believes they can, will eventually happen. In the meantime, the shape of the high-density future is in the hands of such emerging architects as Hong Kong’s Andrew Ng, whose models show you how very tall, ultra-dense housing can also be surprisingly humane. "Sky High", then, may have been flung together in a hurry, may have a bit too much Foster in it, but is not just a flash one-liner kind of exhibition. It’s got content, and it’s accessible. It might even give you a reason to risk a visit to the Summer Show.

"Sky High: vertical architecture" is at the Royal Academy Summer Show, June 2 - August 10 2003. www.royalacademy.org.uk.