Cycling home on Tuesday afternoon, the asphalt of the bike path was slick with rain and shimmering with the last light of the afternoon filtering in beyond the clouds. My route home takes me west, so I didn’t have a chance to look east until I was walking to my building – and there, in the light, was a double rainbow. Of course, I ran up to my building’s roof to take this photograph.

Standing on the roof, I saw all of Frederiksberg below me, with the spires of the center city further in the distance and the suburbs of Brøndby and Hvidøvre lying behind. It was a landscape of buildings, an artificial ecology punctuated only by a few occasional trees. Looking out, I began thinking about how small and how fragile this city really is.

A thought experiment. Freeze time, then begin to remove objects from the city, one by one. Take away a brick from a church, a wheel from a train of the Metro, an apple from the fruit stand. Eventually, everything will be gone. What does that landscape look like? The impermeable surface of the city is gone, leaving behind holes in the ground, exposed soil. There are tunnels deeper still, empty and collapsed. This negative shape extends in a reticulate pattern across the landscape, leaving behind pockets of agricultural fields, parks, and bits of forgotten land. The negative shape is probably no deeper than a few meters in most places, a few tens of meters in the inner city. We are surface-builders, layering cities on top of earlier cities, but never delving deep. From this perspective, the impact of a city is quite minor. The structures removed, the filamentous scar is removed and the land can recover.

But I think that this story is too simple. First, think of all the objects that were imagined away. Imagine now sorting these objects into their places of origin. Think of the the tons of rock from nearby quarries, the countless beams of wood from local forests and further afield, the metal wiring and plumbing mined from deep places, the fruits and animals from all around the world, the artifacts from other countries hidden in storage-rooms of the museums… and so on. The city reflects the combined efforts of millions of people over hundreds of years – efforts that have caused these particular objects to be brought together and arranged in just the right way to build a city. The impact of the city is not just in its self, but also in its origin, through the many lands it depends on for its existence.

The idea of an ecological footprint reflects this notion – cities are resource-concentrators, requiring vast areas of land to subsidize their continued existence. Sanderson et al. (2002) summarize this impact – we use more than 40% of all plant productivity and 35% of coastal shelf productivity, as well as more than 60% of freshwater runoff each year. Usage of these resources is by far the highest in cities, but the source of these resources is far away from cities, leading to footprints for individual cities that are a patchwork of landscapes (Luck 2001). This patchwork is likely to expand and converge over the next century – more than half the world’s population now live in cities, and the number is likely to reach 80% by the end of the century (Grimm 2008). This growth will inevitably lead to an increasingly large fraction of the Earth’s surface being built into cities, and the capture of an increasingly large fraction of the earth’s resources.

The natural question is then the same thought experiment, but in reverse. How many resources are available globally, and how much negative space can be transformed into the built environments of cities before the resources run out? Now the city becomes more like an infectious diseases, using up all the land to fuel its own growth. The projections are not so encouraging – macroecology puts hard limits on the amount of natural resources available (Burger 2012), ultimately constraining economic growth (Brown 2011).

And we are living on borrowed time. Cities are not only resource concentrators, but also resource dissipators. The food demands of a city must be met by agriculture – and the agriculture we depend on requires large nutrient inputs of nitrogen and phosphorus. Once these fertilizers are used, they dissipate into the environment and are nearly impossible to recapture. Nitrogen fertilizers are renewable, insofar as we have the fossil fuel energy to synthesize them from atmospheric sources, but phosphorus is not. Most phosphorus comes from mineral sources, and these will likely be depleted within a century (Cordell 2009), with no feasible alternative. Conservation measures only put off the inevitable decline in resource availability. Continued urbanization depends on these resources, but our cities are rapidly exhausting them.

So it was with mixed emotions that I looked into the city on that rainy Tuesday afternoon. Building a city is a marvelous achievement, but it is an achievement bought with exploitation of lands far away, and an achievement reflective of a future trajectory we cannot afford to sustain.

To close, a recent New York Times editorial by Ellis paints a different picture of the situation, arguing that greater efficiencies (not lower populations) are the key to the earth’s future. It is an optimistic viewpoint that suggests transformation of landscapes has been an ongoing and necessary fact of human civilization. This latter point is true, but I don’t think the editorial provides a convincing argument against the hard limits to growth we are rapidly reaching. Efficiency gains put off the inevitable problem we are still very far away from solving.