Brain activity can be assessed either at anatomical/functional micro-, meso- and macro- spatiotemporal scales of observation, or at different intertwined levels with mutual interactions. Here we show, based on topological findings, that nervous activities occurring in micro-levels project to single activities at the macro-levels. This means that brain functions assessed at the higher scale of the whole brain necessarily display a counterpart in the lower ones, and vice versa. Furthermore, we point out how it is possible for different functional and anatomical levels to be stitched (sewn) together to become condensed brain activities, giving rise, for example, to ideas and concepts. Also, a topological approach makes it possible to assess brain functions in the general terms of particle trajectories taking place on donut-like manifolds. Indeed, every macro-scale activity, independent of the subtending theoretical model, can be described in terms of a multi-dimensional torus mapping to activities at lower levels. In physics, the term duality refers to a case where two seemingly different systems turn out to be equivalent, because they are mathematically distinguishable descriptions of the same phenomenon. Our framework permits a topological duality among different neuro-techniques, because it holds for all the types of spatio-temporal brain activities, independent of their inter- and intra-level relationships, strength, magnitude and boundaries.
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[v1] 2016-10-10 15:21:51
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