This article explores the relationships that disabled people have with the space surrounding them. Extending Jacques Lévy’s work on various non-Euclidean spatialities, we study the discontinuous and discrete nature of space as inhabited by disabled people, with a focus on people with physical impairments. We start at a local scale, with perceptions of one’s body, of one’s environment, and the algorithmic nature of conscious movement. Lack of autonomy, often a consequence of society’s (lack of) accessibility, creates an experience of disjointed spaces, connected not by continuous paths which the subject can explore at will, but by fixed A to B routes. This happens at multiple levels, from the occupation of space within a dwelling or office to national travel patterns, and contributes to crips’ lack of visibility in social spaces. We follow with a study of discontinuities and discreteness in the perception of time, with an analysis of spoon theory, and discuss potential extensions to discontinuous perceptions of the self.