Dubai, the city of the 21st century

You are standing on the raised walkways of Trade Centre 2, above the highway that made modern Dubai. Until the 1990s it carried a plainer name; when it was widened through that decade the city's ruler renamed it for Sheikh Zayed, the first president of the UAE, and most of Dubai's skyscrapers have lined it ever since. The twin Emirates Towers beside you opened on 15 April 2000, the office tower and the hotel joined at their feet by a two-storey retail arcade. Up here the traffic is a hum below your feet and the shade comes from the towers themselves. Look for the ring: a silver torus with the sky showing through its middle, floating on a green mound beside the towers. From it you set off along Al Boursa Street.

Follow the walkways along the towers and drop to Al Boursa Street, about a quarter of an hour. You are entering the Dubai International Financial Centre, a free zone opened in 2004 that is, in law, very nearly an island: it runs on English-language common law with its own courts and its own independent regulator, though the city's criminal law and immigration regulations still reach in from outside. The towers around you hold banks, law firms and funds, the plazas are polished stone and the lunch crowd is in office dress. It is the quietest stretch of the walk. Gate Avenue is the landscaped promenade that threads beneath the towers, and you have reached it when the great square-cut arch of the Gate building closes the view, a frame with nothing inside it but sky.

The long leg, and the only one that asks for patience: Al Mustaqbal Street and then Sheikh Mohammed bin Rashid Boulevard carry you out of the financial district into Downtown, about forty minutes. This is the high street that loops the whole development. Emaar built it and first named it after itself; in December 2012 the developer renamed it for Dubai's ruler. Downtown is a developer's city from kerb to skyline, and even its street names were the developer's to give. The glass tube on stilts beside you at the end is Metro Link, the air-conditioned footbridge opened in late 2012 so metro passengers could ride moving walkways to the mall. Two slim towers joined at the top by a horizontal bar of glass rise over it; that bar is the observatory.

Retrace Metro Link, then let the boulevard swing you into the Opera District, a quarter of an hour. Emaar planned Downtown Dubai in two registers: high-rise glass for most of the district and, around the lake, the Old Town, built deliberately in a low-rise Arabic vernacular of sand-coloured walls and shaded passages. The Opera District sits between the two, and this is where the scale drops: the towers step away, the pavement widens into a promenade and the first water appears. Burj Khalifa fills the sky the whole way, closer with every minute. The Opera is the faceted glass front at the edge of the lake, looking across the water to the fountain and the tower.

The tower grows the whole way along the lakeside walkways, ten minutes of it, until you have to tip your head back. The water you are rounding is Burj Khalifa Lake, and the green ground at the tower's foot is Burj Park, built on a man-made island in that lake and opened with the tower in 2010 to the designs of the landscape firm SWA. It is where Dubai fires the Ramadan cannon each evening and where the New Year fireworks are watched from. The grass is real; the shade is thin. The stop is the tower's foot, where it stands directly overhead and its base, a spread of low glass podiums, finally reads as a building instead of a line in the sky.

Barely a leg at all: the fountain's edge is a few minutes further along the water. Beside you the whole way is Burj Khalifa Lake, an artificial lake of about thirty acres dug at the centre of Downtown, the one feature Emaar built the entire district around: the mall on one bank, hotels and the Old Town's low sand-coloured blocks on another, the tower on its island. Everything faces the water, the point of a city in the desert that spent a fortune on a lake. By day the surface is calm enough to pick out the lines of nozzles beneath it; after dark the crowds gather here. Straight ahead across the water stand the mall's terraces, and the long line of jets runs the length of the near shore: this is the stop.

The lake is bigger than it looks: it takes nearly twenty minutes to round it to the mall's waterfront doors. All of this, the lake, the towers, the opera, the mall, stands on ground that was still called Umm Al Tarif until 2000. Emaar has since built on it a district costed at twenty billion dollars. Walking the shoreline you can read the plan: glass on the skyline, low Arabic-style walls at the water, the tower in the middle, and every path bending so the water stays in view. The mall announces itself as a long wall of terraces stacked above the promenade, with wide steps and glass doors beneath them and the fountain lake lapping at its foot.

Two minutes inside the building: this is the end of the walk and its one leg in air-conditioning. The Dubai Mall is among the largest shopping centres on earth by floor area, more than twelve hundred shops under a single roof, and the walk through it is a corridor of marble, cool air and polished light after the heat outside. People slow down as they near the end of it, phones raised, children pressed to the glass. You have arrived when the corridor opens onto a wall of blue water three storeys high, with large fish and rays drifting past the reflections of the shoppers.