Primary Evidence of a Donut-like, Fourth Spatial Dimension in the Brain

We introduce a novel method for the measurement of information in fMRI neuroimages, i.e., nucleus clustering’s Rényi entropy derived from strong proximities in feature-based Voronoï tessellations, e.g., maximal nucleus clustering (MNC). We show how MNC is a novel, fast and inexpensive image-analysis technique, independent from the standard blood-oxygen-level dependent signals, which facilitates the objective detection of hidden temporal patterns of entropy/information in zones of fMRI images generally not taken into account by the subjective standpoint of the observer. In order to evaluate the potential applications of MNC, we looked for the presence of a fourth dimension’s distinctive hallmarks in a temporal sequence of 2D images taken during spontaneous brain activity. Indeed, recent findings suggest that several brain activities, such as mind-wandering and memory retrieval, might take place in the functional space of a four dimensional hypersphere, which is a double donut-like structure undetectable in the usual three dimensions. We found that the Rényi entropy is higher in MNC areas than in the surrounding ones, and that these temporal patterns closely resemble the trajectories predicted by the possible presence of a hypersphere in the brain.