We define qualia space Q to be the space of all possible conscious experience. For simplicity we restrict ourselves to perceptual experience only, though other kinds of experience could also be considered. Qualia space is a highly idealized concept that unifies the perceptual experience of all possible brains. We argue that Q is a closed pointed cone in an infinite-dimensional separable real topological vector space. This quite technical structure can be explained for the most part in a simple, intuitive way. (...) The structure of qualia space allows us to consider and even answer in a precise way such questions as: Is there a continuous path from the sensation of blue to the sensation of pain? Once we fix a desired accuracy of approximation, do there exist finitely many perceptual experiences such that any possible perceptual experience is approximately equal to one of them? What should be meant by ‘fundamentally different’ perceptual experiences? There is the possibility of additional structure, such as a Hilbert space structure on the vector space in which Q is embedded. (shrink)