Wuppertal is what engineers call a linear city. The river Wupper runs through a steep narrow valley with hills rising on both sides, and the city is laid out for thirteen kilometers along the valley floor and the lower slopes - the original districts of Elberfeld, Barmen, and Vohwinkel merged in 1929 into a single municipality of about 355,000 people. There was no room for a normal subway. The slopes were too steep for trams in many places. So in 1900 the Wuppertaler Schwebebahn opened: a single overhead rail, twelve meters above the river for much of its run, with elegant green carriages that hang from it like cradles. It has been in continuous service since July 1901. By the time Tuffi made her famous jump it was fifty years old. By now it has carried over a billion passengers. There is nothing else quite like it in the world - the only sister-line is the much-newer Shonan Monorail in Japan, with which the Schwebebahn formally twinned in 2018.

Two-thirds of Wuppertal's municipal area is green - parks, woods, the steep wooded slopes where building was always impractical. The city claims, with statistical support, to be the greenest in Germany. From any address you can be on a woodland footpath in ten minutes. The Nordbahntrasse, a 22-kilometer cycle and walking path opened in stages between 2006 and 2014, runs across the northern hills along a former rail bed; CNN once put Wuppertal on a list of twenty places to visit in 2020, partly for the trail and partly for the Schwebebahn. The Botanischer Garten, the Wuppertal Zoo, and the Skulpturenpark Waldfrieden - founded by the British sculptor Tony Cragg, who has lived in Wuppertal for decades - all sit on the wooded slopes. The city itself is built downhill into the river at every turn, which gives even the suburban streets a sense of small balconies overlooking a slow-moving green spine.

From 1973 until her death in 2009, the choreographer Pina Bausch ran the Tanztheater Wuppertal at the city's opera house, and remade what people meant when they said modern dance. She had a small army of European, Japanese, and South American dancers who stayed with her for decades; she made work that married theater and dance into something the Germans came to call Tanztheater and the rest of the world adopted whole. She insisted on living in Wuppertal because she found it more honest than Cologne or Berlin - smaller, less impressed with itself, with a river to walk along and a strange railway overhead. After her death the company has continued under successive directors. The 2011 Wim Wenders film Pina was shot extensively in and around the city, with dancers performing in unlikely places along the Schwebebahn route. If you happen to ride the suspended monorail and a dancer steps on at one of the stations, do not assume it is a coincidence.

Aspirin was patented here. Felix Hoffmann, working at the Bayer plant in the Elberfeld district, synthesized acetylsalicylic acid in August 1897, and the pharmaceutical industry in Wuppertal has continued without much pause since. The Vorwerk Kobold vacuum cleaner is made here. So are textiles, surgical instruments, automotive components. The Wuppertal Institute for Climate, Environment and Energy is one of the most influential European think tanks on sustainability questions, working out of a low brick building near the railway station. The university - Bergische Universitat Wuppertal - climbs up the slope above Elberfeld. The Junior Uni, a privately funded science-education program for children ages four to eighteen, is a Wuppertal-specific institution unmatched in Germany. Even the city's old industrial buildings, where they survive, have been smartly converted: the Engelsgarten, the Visiodrom planetarium in a former gasometer, the textile-mill complexes turned into apartments and lofts.

It would be dishonest to talk about Wuppertal only in its bright register. The Kemna concentration camp, one of the first Nazi camps, opened in a Wuppertal-Barmen textile factory in July 1933 and ran for six brutal months. The Barmen Declaration of 1934, the great theological resistance to the Nazi co-option of the Protestant churches, was drafted at a Wuppertal synod by Karl Barth and others. The old town centers of Elberfeld and Barmen were both heavily bombed in 1943. Friedrich Engels, born in Barmen in 1820, grew up in a textile family whose mills helped make the working conditions he would later write the book against. The city carries all of this. Walk through it and you will see the markers - small plaques, memorial stones, named squares - that a German city of any seriousness includes in its everyday landscape. And then you will look up, and above your head the green wooden carriages of the Schwebebahn will be sliding by on the rail, on their century-old daily business, and you will remember that a city is also what it does in the present tense.