The hippocampus participates in multiple functions, including spatial navigation, adaptive timing and declarative (notably, episodic) memory. How does it carry out these particular functions? The present article proposes that hippocampal spatial and temporal processing are carried out by parallel circuits within entorhinal cortex, dentate gyrus and CA3 that are variations of the same circuit design. In particular, interactions between these brain regions transform fine spatial and temporal scales into population codes that are capable of representing the much larger spatial and temporal scales that are needed to control adaptive behaviors. Previous models of adaptively timed learning propose how a spectrum of cells tuned to brief but different delays are combined and modulated by learning to create a population code for controlling goal-oriented behaviors that span hundreds of milliseconds or even seconds. Here it is proposed how projections from entorhinal grid cells can undergo a similar learning process to create hippocampal place cells that can cover a space of many meters that are needed to control navigational behaviors. The suggested homology between spatial and temporal processing may clarify how spatial and temporal information may be integrated into an episodic memory. The model proposes how a path integration process activates a spatial map of grid cells. Path integration has a limited spatial capacity, and must be reset periodically, leading to the observed grid cell periodicity. Integration-to-map transformations have been proposed to exist in other brain systems. These include cortical mechanisms for numerical representation in the parietal cortex. As in the grid-to-place cell spatial expansion, the analog representation of number is extended by additional mechanisms to represent much larger numbers. The model also suggests how visual landmarks may influence grid cell activities via feedback projections from hippocampal place cells to the entorhinal cortex.