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However, maps are static, whereas navi gation—whether in physical or cognitive space103—is dynamic. Without motion, there is no grounding; distances and durations cannot be calibrated, and therefore neuronal patterns cannot acquire meaning. Motion is sensed by velocity detectors. During real-world navigation, the rate of change within the assembly sequences is controlled by the animal’s velocity. In brains of increasing complexity, many environmentally driven functions become internalized104 and the rate of change—for example, during memory recall, imagination, or planning—may become under the control of a hypothetical mechanism known as ‘attention’, in lieu of velocity. In a thinking brain, therefore, attention may be the substitute for velocity, which can maintain the grid dynamics in the absence of locomotion. This speculation is supported by the presence of hexagonal grid-like dynamics organizing both spatial and nonspatial conceptual representations in a variety of higher-order cortical regions without overt motion. Grid dynamics can, therefore, also support abstract knowledge102,105, not only maps.