This article pursues the hypothesis that a scale-invariant representation of history could support performance in a variety of learning and memory tasks. This representation maintains a conjunctive representation of what happened when that grows continuously less accurate for events further and further in the past. Simple behavioral models using a few operations, including scanning, matching and a "jump back in time" that recovers previous states of the history, describe a range of behavioral phenomena. These behavioral applications include canonical results from the judgment of recency task over short and long scales, the recency and contiguity effect across scales in episodic recall, and temporal mapping phenomena in conditioning. A growing body of neural data suggests that neural representations in several brain regions have qualitative properties predicted by the representation of temporal history. Taken together, these results suggest that a scale-invariant representation of temporal history may serve as a cornerstone of a physical model of cognition in learning and memory.