In his geographical treatise of 1537, the Portuguese cosmographer Dom João de Castro explained that it would be possible to correlate all newly discovered lands with astronomical markers to produce an accurate map of the world. The result would be, he wrote, a “true and perfect geography.” The movement toward this vision, from the cartographic revolution of thirteenth-century portolan charts to the use of surveying to map colonial territories in the nineteenth century, is a compelling narrative of the rationalization of space, and of the reinforcement of this trend by the pursuit of European imperial interests.

This narrative needs to be placed alongside the history of imperfect geographies and the production in empire of variegated spaces with an uncertain relation to imperial power. Territorial control was, in many places, an incidental aim of imperial expansion. While an iconic association with empire is the pink shading of British imperial possessions in nineteenth- and early twentieth-century maps, that image, and others like it, obscures the many variations of imperial territories. Empires did not cover space evenly but composed a fabric that was full of holes, stitched together out of pieces, a tangle of strings. Even in the most paradigmatic cases, an empire's spaces were politically fragmented; legally differentiated; and encased in irregular, porous, and sometimes undefined borders. Although empires did lay claim to vast stretches of territory, the nature of such claims was tempered by control that was exercised mainly over narrow bands, or corridors, and over enclaves and irregular zones around them.