A few suburbs away, Paddington-Moore Park (4394 people a sq km) most closely resembles the Tokyo-Yokohama urban area (4400 people a sq km), while the Concord-Mortlake-Cabarita precinct (3706 people a sq km) in the inner west is the closest match to Paris (3700 people a sq km). And by 2030, Green Square's projected population density of 22,000 people a sq km will rival General Santos, Philippines (21,500 people a sq km) and Ranchi, India (22500 people a sq km). Increasing density in at least some parts of the city is central to the government's strategy to improve housing affordability. While there are limits to the comparisons that can be drawn between small neighbourhoods and large urban areas, it helps to illustrate how differently people in, say, Pyrmont-Ultimo (15,346 people a sq km) experience Sydney, compared with those in Rouse Hill (612 people a sq km), for example.

It also shows that in many pockets of Sydney, people are already living at densities far higher than the city average. "It's one of the good things about really big cities: you get a choice about the lifestyle you want to live," says Terry Rawnsley, an economist at consultancy SGS Economics and Planning. Sydney is more crowded than ever. Since 2000 – the year former NSW premier and federal foreign minister Bob Carr famously declared that Sydney was "full" – the population of Greater Sydney has swelled by 22 per cent, while the total area has expanded by less than 2 per cent. In 2016, 38 sq km of the city exceeded 8000 people a sq km, up from 21 sq km in 2011, and 131 sq km had between 5000 and 8000 people a sq km, up from 93 sq km in 2011, according to the latest ABS figures.

To put the figures in perspective, however, Greater Sydney covers 12,368 sq km, which means less than 1.4 per cent of the city exceeds 5000 people a sq km. The notion that a neighbourhood, a city, or even an entire country is "full" can seem absurd in Australia, where our most packed metropolitan areas (Greater Melbourne at 465 people a sq km and Greater Sydney at 405 people a sq km) seem like sprawling deserts compared with world megacities such as Dhaka, Bangladesh (44,100 people a sq km) or Mumbai, India (26,000 people a sq km). And in one sense, there's no such thing as a city of neighbourhood being "full", says Kristian Ruming, an associate professor of Macquarie University's Department of Geography and Planning. "A city is not a container. The boundaries are not fixed," he says. "We can move the fringe of the city out. We can increase the density in particular locations. Using that sort of metaphor, the city is never full because what the city is can change."

However, the fact that many world cities cope with much higher densities doesn't mean we can simply dismiss concerns about density in Australia. "Many residents groups are characterised as selfish NIMBYs," Associate Professor Ruming says. "But these people can make really positive changes to a city. They can oppose poor development. They can increase the level of local democracy and participation, which might not have been part of the process." Bigger cities benefit from economies of scale that create more services and job opportunities, but those benefits can be wasted if infrastructure doesn't keep pace with growth, Rawnsley says.

"People complain about a city being too full when they can't get on a train or they can't find a spot in childcare," he says. "It's often the lack of infrastructure they're are really complaining about, rather than too many people." On the other hand, it is foolish not to recognise how cultural norms and expectations – chiefly, the "great Australian dream" of the quarter-acre block – influence public debates about higher-density living. But even these seem to be changing, partly in response to the housing market, says Bill Randolph, director of the City Futures Research Centre at UNSW. "Essentially, it's about what you can persuade people to accept," he says.

Take the swing to urban living,for example. "We're told that we're all more inclined to live in multi-unit dwellings," he says. "Well, maybe we are but, if there's no alternative or you've never lived anywhere else, then you're more willing to accept that." Part of the problem is that Australians are surrounded by bad examples of higher-density living, Ruming says. Good design is key to changing attitudes. "People's perceptions of high density come from the buildings they see in their everyday life," he says. "Many of them are very poor examples, not just in terms of design and construction but also how they fit in the city, where they're located and how they link to infrastructure and services." Tim Williams, chief executive of the Committee for Sydney, says concerns about densification are understandable but "high density doesn't always mean high-rise".

"The romantic notion of families living on a quarter-acre block can feel jarring alongside Hong Kong style high-rise. But we should remember that Sydney has traditionally low levels of density - only around 40 per cent as dense as London," Williams says. "The challenge for Sydney is not whether to densify but how ... Densification does not need to mean a reduction in quality of life. Indeed, it can mean the opposite if done well."