Brain activity takes place in three spatial-plus time dimensions. This rather obvious claim has been recently questioned by papers (including this foremost one by Stringer et al.) that, taking into account the big data outburst, are starting to unveil a more intricate state of affairs (see: https://www.sciencedirect.com/science/article/pii/S1571064519300089 ).
Various brain activities and their correlated mental functions can be assessed in terms of trajectories embedded in phase spaces of dimensions higher than the canonical ones. It has been proposed that further dimensions may not just represent a convenient methodological tool that allows a better mathematical treatment of otherwise elusive cortical activities, but may also reflect genuine functional or anatomical relationships among real nervous functions.
In particular, the observed multidimensional representations of behavior reported by Stringer et al. subtend a spontaneous nervous activity that has been recently described as taking place inside a four-dimensional donut-like manifold.