IT IS hardly news that the city of Detroit has been in long-term decline, a victim of everything from the problems of the “big three” carmakers to family breakdown, crime and middle-class flight, both black and white. But the scale of the recent collapse has caught even hardened Detroiters by surprise. When the results from the most recent decennial census appeared earlier this year, they showed that in the decade from 2000 to 2010 Detroit lost an astonishing 25% of its population, a demographic catastrophe (New Orleans apart) without parallel in the developed world.

With a population falling this far, this fast, come terrible problems. There are now about 60,000 empty houses in Detroit, says its mayor, Dave Bing. Vacant properties are magnets for crime, and once one house in a block has been vandalised, and often set alight, the problem tends to spread. As property prices in the city collapse, so too does the rate-base that is used to collect the taxes that go to pay for schools; so the schools decline too, encouraging yet more people to move across “8 Mile”, the road that marks the city's main northern limit, or to plusher suburbs like Dearborn to the west or Grosse Pointe to the east. Those who are left are likely to be the poorest, least-skilled and so least mobile. Only 11% of Detroiters aged between 25 and 34 has a college degree; in Seattle, the equivalent figure is 63%. Around 50% of the city's adult black males are unemployed, and 38% of all Detroiters live below the poverty line.

Yet physically, of course, the city remains the same size, imposing most of the same requirements of road maintenance, street lighting, rubbish collection and emergency-service response times. Detroit is a sprawling place, with the city itself (not the wider metro area) covering an area of 139 square miles, as it did in the 1950s when just under 2m people lived there, rather than the 714,000 it has now. You could fit Miami, Minneapolis and San Francisco into its city limits, and still have room left over. “We have a city that ought to be half its size,” says Mr Bing. He would like to concentrate his citizens, boosting the population density in areas that are still economically viable, while encouraging people to move out of districts that are not.

Politically, though, that has proved very hard to do. People, funnily enough, like their neighbourhoods and either do not want, or cannot afford, to move. Mr Bing is almost halfway through his four-year term, and faces re-election in 2013. Yet while he has drawn up a sensible-sounding plan, Detroit Works, which will help boost three pilot viable areas, with more to come next year, there is still no flipside plan for what to do about places that everyone knows are simply not saveable.

In areas like Brightmoor in the north-west, or Osborn in the north-east, you can see scenes of vandalism, decay and abandonment unparalleled in America. But it has fallen not to the mayor, but to the Kresge Foundation, one of the big philanthropic outfits that are Detroit's main suppliers of funds for redevelopment (since the mayor is, in effect, broke and little help is available from the also-stressed state authorities of Michigan), to pay for the drawing up of a city-wide plan; and after a number of public consultations turned nasty, that plan remains still very much in development. Meanwhile, well-meaning charities and the city itself continue to pump good money after bad into Brightmoor.

Yet despite all the gloom, there is a bit of a sense that things might just be starting to turn, and the reason is simple: Detroit is now incredibly cheap. And that has drawn some admittedly rather pioneering types back into town.

The most remarkable of these is Dan Gilbert. A 49-year-old native of Detroit whose motto is “We can do well by doing good”, Mr Gilbert is reshaping Detroit's centre. Last year he moved his main business, Quicken Loans, the largest internet mortgage company in America, from the quiet suburbs into a building on Campus Martius park, the heart of downtown. His 1,700 staff there were joined, earlier this month, by another 2,000 people whom he moved into a second building nearby. From his window Mr Gilbert points to some of his other acquisitions, including one, of 800,000 square feet, that he bought for just $8m and intends to let out. It is hard to beat $10 a square foot for downtown office space. Mr Gilbert is buying other buildings for internet start-ups, and is planning a big new residential development and lots of retail space in the area as well. “The intellectual energy of a city depends on livability,” he says. “We have to create a hot urban core, and it is going to happen.” Miles of new river-walks and cycle-lanes help. So too will the planned construction of M1, a new light-rail system that will run in a north-south corridor from the Detroit river to 8 Mile Road. Since the city has no money, the $100m for its first stage is coming from investors, philanthropists and the federal government. Ideally, it would then link up with services reaching deep into the suburbs; but bureaucratic and political rivalries between the various municipal and county governments involved have so far stymied attempts to do it. It really should fall to Michigan's governor to bang the necessary heads together, but this has not yet happened. The M1 railway will run along Woodward Avenue, the main axis of Detroit's planned redevelopment. With the river and downtown at one end, the “Woodward Corridor” stretches north to one of the other great hopes for the city, a cluster of universities and business parks. David Egner, who runs Detroit's New Economy Initiative (founded three years ago with a $100m budget by a group of ten non-profit organisations) has high hopes for TechTown, a business accelerator his organisation helped set up on the corridor to take advantage of Wayne State University, the Detroit Medical Centre and the Henry Ford Hospital. So far, a lot of the business TechTown has incubated has not been particularly high-tech: dry-cleaning businesses and art restoration, as well as a cryogenic tissue-storage facility. But arguably Detroit needs dry-cleaners just as much as stem-cell researchers: any business development at all in the city is not to be sneered at. TechTown, at any rate, appears to be thriving. It has 250 businesses on its books, and a waiting list of 40 would-be start-ups; it is considering a number of additional buildings for expansion. Its neighbourhood is littered with affordable jewels from Detroit's mighty past: the building where the electric iron was developed and a factory where Cadillacs used to be built are both possibilities.