This essay is part of the Volumetric Sovereignty forum.

ines are willfully ignorant of volume. Precisely because of this, lines are forced to confront volume at every turn. As they strive to abstract themselves down to one dimension, lines must negotiate endlessly with all three stubbornly material dimensions. Their linearity is never more than a bargain of convenience, a tolerable approximation of an abstract ideal. Abstraction is not itself an abstract process.

Railway lines offer a vivid demonstration of this tension. The first rail line to Chengdu, capital of China’s Sichuan province, was completed only in 1952. Traveling the recently opened high-speed rail line makes the reason for this late date viscerally apparent: for what seems like hours, the train passes through an unbroken series of bridges over gorges and tunnels under mountains, one after the other. Engineers have built and excavated a wholly novel path through air and stone, in flagrant, laborious disregard for what the terrain offers (Elden, 2017). This path is described with precise mathematics: how sharply it may curve, how much it may rise or fall, how much each meter of track may stray from its neighbors. Yet at each point, the intervention necessary to produce this path depends wholly on the particularities of Sichuan’s uneven topography. Making lines requires a constant negotiation of volumes.

This tense negotiation has always been at the heart of rail construction. Early English rail made extensive use of cuttings and embankments, bridges and tunnels to produce a straight, level, and smooth line for the railway (see figure 1). The abstract Newtonian logic of the rail line was perceptibly at odds with the surrounding landscape: passengers felt as though they belonged to “another sphere,” that they were “shut out from all communication with the world” (see Schivelbusch, 1986: 23–24). More than one balance could be struck between abstraction and the world, however: American lines, in contrast, took advantage of cheaper land and a novel axle design to curve around obstacles rather than cut through them (Schivelbusch, 1986: 96).

The engineering constraints of early rail—both real and supposed—exhibited a spatial logic at odds with the surrounding terrain. (Source: View of the Deep Cutting in the Olive Mount, 1830. Courtesy of the London Science Museum.)

The rail line does not encounter volumes only in the world through which it travels, but must define and regulate its internal dimensionality as well. One early, vital yet arbitrary decision rail engineers must make is that of gauge, the width of the track. A standardized gauge links rail and locomotive both intimately and universally: the fit must be exact, but enables free circulation within the network it bounds. Just as vital is the consideration of leeway: the height and width above and to each side of the track that must be kept free of obstacles. While the importance of leeway is self-evident in the context of tunnels, an obstacle at any point along the track could be disastrous; gauge and leeway thus sweep a two-dimensional cross-section along the length of the track, a tunnel through open air. The purely one-dimensional abstraction of the rail line is revealed, step by step, as a volume in its own right. As lines join up, the rail network merges into a singular, contiguous volume, cut apart from the world by velocity and iron. Within the carriage, the world outside the windows seems to slow to a standstill. Space is, if not annihilated by time, then relegated to second class.

The new-built internal volume of the rail line gives rise to radically new affective dimensions, shaping new social, emotional and mental spaces (see figure 2). The railway carriage brings together a wide cross-section of society and packs them together like “living parcels” (see Schivelbusch, 1986: 54, fn 8). Rail travel is, in a way, the experience of industrialization not from the perspective of the worker or consumer, but from that of the commodity. The anxieties of enforced passivity in this novel space required inventing entirely new ways of relating—to the carriage itself, to the landscapes whipping by outside, and most of all, to one’s fellow passengers. The proliferation of rail travel went hand-in-hand with the development of new social technologies like the paperback novel. In China today, the smartphone plays a similar role, staving off boredom and providing a means of avoiding unwanted social intercourse.

The internal volume of Zhengzhou station is so vast that the far end is hazed by air pollution. (February 2017. Photo by author.)

Despite the best efforts of engineers and passengers to separate the internal and external volumes of the rail network, it is always an imperfect abstraction. As the train whips into tunnels in mountainous Sichuan, the speed of the train creates a wave of pressure that is felt within the carriages, within the inner ear of every passenger. As tunnel follows tunnel, discomfort gives way to fatigue. This discomfort is what shapes the futuristic profiles of high-speed trains: the sharp nose attenuates the pressure wave, allowing for higher speeds without exceeding the tolerance of passengers.

Considered volumetrically, the array of practical conundrums that railways must handle—engineering in both the social and technical sense—are the problem of abstraction made concrete. In theory, rail connects nodes within a topology that is measured by time and connection rather than a topography of extension and territory. In practice, it is only through careful attention to material volumes that this abstraction can be approximated. These approximations are never settled: what counts as sufficient abstraction—“straight enough,” “level enough,” “smooth enough”—is only ever an arrangement of convenience. The original line from Chongqing to Chengdu was 505 kilometers; high speed rail required straightening it down to 307 kilometers. As technological demands grow and tolerances narrow, engineers perforce return to the material world and re-abstract their standards anew.

Abstractions are always imperfect—a limit felt most viscerally when trains collide, in an existential betrayal of unidimensionality. These horrifying accidents led to another confrontation between reality and abstraction: with its strong commitment to laissez faire, nineteenth-century England only with great reluctance acknowledged the necessity of an operational monopoly along the railway. Abstraction matters because it is real: abstractions come to be only through re-arrangements of the material world. Abstraction from terrain is made possible precisely through a series of forceful, even violent intercessions upon terrain. Lines cut through volumes, but never transcend them.


Schivelbusch W (1986) The railway journey: the industrialization of time and space in the 19th century. Berkeley: University of California Press.