Aspiring to the Abstract: Pure Space and Geometry

Abstract This chapter argues that geometry carried profound cultural significance for the early 19th century by representing space in its purest form. Geometry offered access to space set free from the clumsiness and limitation of human perception. Geometry's space of pure thought gave the most certain and secure rational knowledge possible and was used as a yardstick for other claims to truth and universality. Euclidean geometry had traditionally enjoyed enormously high prestige as the foundation not only for a scientific education but for any kind of systematic thought. Its authority was appropriated by many other discourses claiming cultural power. But by the early 19th century cracks were appearing in its status as groups with no geometrical training and no belief in its relevance to their educational needs denounced its prestige as a repressive outdated shibboleth. Even much more moderate writers, with vested interests in retaining geometry and other kinds of mathematical education at the heart of the British elite educational system, offered suggestions for reforming its teaching, and for making it more usefully applicable to the needs of industrial and technological workers. Geometry was the unlikely locus of important struggles in the class politics of education in the early 19th century: at stake was the privileging of ideal over actual space, and of abstract over practical science. Readings of contemporary writing on geometry are interwoven in this chapter with a study of Victorian geometry textbooks for both elite and artisan readers.