The Ruhr is the smaller river, looping out of the hills to the east. The Rhine is the bigger one, running north toward the sea. Where they join, Duisburg spreads across both banks, the only Rhine-Ruhr city to do so. The Romans drew their imperial boundary somewhere through this floodplain in the fifth century. The Franks built a royal court here in the early Middle Ages, first written into the record in 883. Then around the year 1000 the Rhine quietly shifted its course westward, leaving Duisburg stranded a little inland, connected to its river only by a dying side-channel. For four hundred years the city dwindled back into a farming town, undone by the geography that had made it. It would take the Industrial Revolution to bring the river back to the city, by force.

Look down from cruising altitude and you see the engineering. Twenty-one docks. Forty kilometers of wharf. Cranes the size of small buildings. The Duisburg-Ruhrorter Häfen handles 114 million tonnes of goods every year and counts as a seaport even though the North Sea is two hundred kilometers away. The river vessels that load here are designed to slip down the Rhine and out into ports in Africa and the Middle East. In 2011 the first freight train of the Chongqing-Xinjiang-Europe railway pulled into Duisburg after weeks crossing Eurasia. It has not stopped coming. Walk the Logport complex on the far bank of the Rhine and you can watch containers labeled in Mandarin being shifted onto barges bound for Rotterdam. The map most of us carry in our heads has Hamburg or Antwerp as Europe's freight hubs. The actual map has Duisburg.

Gerardus Mercator was born in Flanders in 1512 but spent the second half of his life in Duisburg, drawing maps under the patronage of the Duke of Cleves. The projection he published in 1569 stretches the world apart at the poles so that any straight line on the chart is also a compass bearing - a small mathematical bargain that made him indispensable to every sea captain for the next four centuries. He is buried in the Salvatorkirche near the inner harbour, in a town he chose because it was Protestant and quiet enough to work in. Duisburg has produced others: the sculptor Wilhelm Lehmbruck, who has a museum here; the composer Ramin Djawadi, who wrote the Game of Thrones theme; the violinist Frank Peter Zimmermann. But Mercator is the one whose lines you still see every time you open a phone map.

The nineteenth century turned the city into a furnace. Coal under the ground, ore brought up the river, the König brewery feeding the workers - Duisburg became one of the engines of German heavy industry, and the Krupps and the Thyssens built fortunes on it. Allied bombers came back to Duisburg 299 times during the Second World War and left eighty percent of its housing destroyed or damaged. The historic cityscape was essentially erased. Then in the mid-1960s the steel and coal began their long retreat. The population peaked near 600,000 in 1975 and slid downward for decades. What happened next is now a case study in industrial heritage: the Landschaftspark Duisburg-Nord, once a Thyssen ironworks, reopened as a public park where climbers scale the old blast furnaces and divers explore a flooded gasometer. The Inner Harbour, Foster-master-planned, became a waterfront of museums and apartments. Industrial bones, civic flesh.

On 24 July 2010 the Love Parade, an electronic music festival that drew vast crowds across Germany, was held in a former freight yard in central Duisburg. The single tunnel approach became a crush. Twenty-one young people died. Six hundred and fifty-two were injured. The city has been processing what happened ever since - through inquiries, trials, memorials, and the slow private grief of families who lost a son or daughter at what was meant to be a summer party. Today Duisburg is a working city of about half a million, with the largest Turkish-German community outside the major capitals, an oceanic climate that keeps the winters mild, the freight trains still arriving from Chongqing, and a quiet understanding that its future, like its past, is built one shipment, one shift, one rebuilt corner at a time.