Metrics of Time and Space are of great importance for an organism to thrive in its environment. Estimating object positions and memorizing important locations and their temporal relationships is mostly studied behaviourally. But recently, advances have benefitted from analyzing actual neural responses. Deciphering this activity using neuro-dynamical models provides an exciting playground for physicists, as illustrated in three examples. I first describe distance estimation in a velocity-independent manner, and the importance of tuning cells near boundaries between dynamical regimes, namely, oscillations vs chaos. I then discuss recent work on a true “2D cognitive map” in the mouse brain that allows the inference of shortcuts between places along un-rehearsed trajectories. Time is an adjacent quantity whose neuro-physical embodiment is still vague. I discuss a compelling proposal whereby elapsed time is encoded through depletion of neural signalling resources.

The development of quantitative neural circuit models in this era of large scale recordings and AI often faces the problem of model degeneracy, where many satisfactory fits arise based on similar likelihood metrics. One can improve model inference by incorporating known constraints in a physics-informed manner. I finally introduce a method that enhances this model selection using the distribution of model risk derived from the accounting for experimental uncertainty, a technique that can be broadly applied across the sciences.