When moving, the spatiotemporal unfolding of events is bound to our physical trajectory, and time and space become entangled in episodic memory. When imagining past or future events, or being in different geographical locations, the temporal and spatial dimensions of mental events can be independently accessed and manipulated. Using time-resolved neuroimaging, we characterized brain activity while participants ordered historical events from different mental perspectives in time (e.g., when imagining being 9 years in the future) or in space (e.g., when imagining being in Cayenne). We describe 2 neural signatures of temporal ordinality: an early brain response distinguishing whether participants were mentally in the past, the present or the future (self-projection in time), and a graded activity at event retrieval, indexing the mental distance between the representation of the self in time and the event. Neural signatures of ordinality and symbolic distances in time were distinct from those observed in the homologous spatial task: activity indicating spatial order and distances overlapped in latency in distinct brain regions. We interpret our findings as evidence that the conscious representation of time and space share algorithms (egocentric mapping, distance, and ordinality computations) but different implementations with a distinctive status for the psychological "time arrow."