A Repetitive Modular Oscillation Underlies Human Brain Electric Activity

ABSTRACT The modular function j, central in the assessment of abstract mathematical problems, describes elliptic, intertwined trajectories that move in the planes of both real and complex numbers. Recent clues suggest that the j-function might display a physical counterpart, equipped with a quantifiable real component and a hidden imaginary one, currently undetectable by our senses and instruments. Here we evaluate whether the real part of the modular function can be spotted in the electric activity of the human brain. We assessed EEGs from five healthy males, eyes-closed and resting state, and superimposed the electric traces with the bidimensional curves predicted by the j-function. We found that the two trajectories matched in more than 85% of cases, independent from the subtending electric rhythm and the electrode location. Therefore, the real part of the j-function’s peculiar wave is ubiquitously endowed all over normal EEGs paths. We discuss the implications of such correlation in neuroscience and neurology, highlighting how the j-function might stand for the one of the basic oscillations of the brain, and how the still unexplored imaginary part might underlie several physiological and pathological nervous features. SIGNIFICANCE STATEMENT Our results point towards the brain as ubiquitously equipped with j-function’s oscillations, which movements take place on the plane of the complex numbers. It means that there must be, in brain electric activity, also a veiled complex part, which can be assessed with the help of imaginary numbers. The modular j-function provides further dimensions to the real numbers, in order to enlarge their predictive powers: it suggests the possible presence of hidden (functional or spatial) brain extra-dimensions. Furthermore, j-oscillations could be disrupted during pathologies, paving the way to novel approaches to central nervous system’s diseases.