Deanna Kreisel of the UBC Department of English delivers an STS colloquium talk titled “‘The Insides of Things’: Higher-Dimensional Geometries and Victorian Theories of Space” on Thursday, February 28, 5:00-6:30pm in Buchanan Tower 1197.
In 1884 Edwin A. Abbott published Flatland, a parable treating an imaginary world of two dimensions and the flat geometrical shapes who live there. The narrator of the tale, A Square, relates how he is visited by an emissary from the world of three dimensions, A Sphere, and gradually comes to understand the limitations of his own perceptions. After attempting unsuccessfully to enlighten his fellow Flatlanders regarding the existence of higher dimensions, he is imprisoned for sedition for the rest of his life. The story ends with him admitting that he is gradually beginning to lose his ability to hold onto faith in the third dimension. Abbott’s novel is a direct response to the creation of higher-dimensional and non-Euclidean geometries in the latter part of the nineteenth century: geometries that either posit the existence of more than three spatial dimensions or treat curved space. This essay will consider Abbott’s tale in its historical context, an ongoing debate in nineteenth-century English mathematics about the truth-status of analytic algebra, and discuss the epistemological crises occasioned by the new mathematics.