Geography has historically imagined a flat world: “territory, sovereignty and human experience have long been flattened by a paradoxical reliance on flat maps—and, more recently, aerial and satellite images—projected or imaged from the disembodied bird's or God's eye view from high above,” writes Stephen Graham in Verical (1). He claims that “the key geographical idea dominating the world from the mid nineteenth to the mid twentieth centuries . . . was that . . . the horizontal and global extent of the earth's surface was both fully explored and fully claimed' (2).

Trouble is, the worlds we actually inhabit aren't flat but three-dimensional, and include resources below the surface and resources and technologies above. Flat geography has treated borders as “abstracted, unhelpfully, as little more than two-dimensional lines on a map. Such a perspective neglects the three-dimensional politics of the worlds above, below, and around borders. It also makes it impossible to understand the increasingly common situation where airspace and subterranean resources are controlled by sovereign powers different to those with notional sovereignty over the surface. Flat imaginations of borders struggle even more to content with occasions where horizontal structures effectively act as political and geopolitical borders—as when horizontal flyovers act to separate Jewish and Palestinian communities in contemporary Palestine” (3).

We live in “stacked” societies where “uses of space are built upwards and downwards with ever-greater intensity within geographic volumes. Thus, housing in many cities is dominated by stacked apartments reaching into the sky. Favela dwellers build houses up perilous mountain slopes directly atop the roots of those below. . . . In Hong Kong the shortage of land is so acute that sports fields, container ports, markets, horse stables, IKEA-like big box retailers and even cemeteries are not routinely stacked within bigger structures which are then linked together and integrated to the wider city through huge arrays of elevators, walkways, escalators and raised highways” (5).

Beneath many cities are “three-dimensional labyrinths which stack and intertwine infrastructures and built spaces as deeply as many cities rise into the sky,” and beyond the highest peak of a skyscraper are “fleets of enigmatic vehicles and sensors that are stacked from ground to orbital levels (and beyond)” (5). Even the ground itself is not ground-level, but increasingly “manufactured and raised up as humans shape the very geology of cities” (9).

Scholarship on cities and urban planning hasn't grasped verticality. Everyone's still theorizing in Flatland. Graham says that he knows of only one book in English that explores city levels, and he argues that flat theorizing dominates urban studies: “Despite a proliferating literature on the architecture of individual tall buildings, such perspectives remain wedded to the traditional idea of urban ground, with its at-grade street networks and public encounters on sidewalks and in traditional public spaces” (8). His book is an effort to fill that gap.

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