This article links the rise of non-Euclidean geometry with the ascent of theories of evolution in the second half of the nineteenth century, and argues that the upsurge of speculations on higher dimensional space figures as a corollary of the pre-eminence of Darwinian ideas in the late Victorian imaginary. It first provides a short sketch of the development of thinking in higher dimensions from Plato's 'allegory of the cave' to the late Victorian popularisation of the subject in the works of Charles Hinton and H.G. Wells. On this basis, it goes on to examine two literary texts from the 1880s, Edwin A. Abbott's novel Flatland and May Kendall's poem 'A Pure Hypothesis'. Both texts are premised on the assumption that there are different versions of the world with different numbers of spatial dimensions, and that through the faculty of dreaming it is possible to transcend the boundaries between these worlds. This article shows how both texts use this central conceit to pose serious questions about contemporary class hierarchies as well as the ethical implications of scientific progress.