Arturo Tozzi

Center for Nonlinear Science, Department of Physics, University of North Texas, Denton, Texas 76203, USA


  • DOI
  • 10.13140/RG.2.2.27238.93769



Recent claims point towards the brain dynamics as equipped with further functional dimensions, apart from the classical three spatial-plus time (1-6).  Is it feasible to assess how such hypothetical multidimensional nervous activity can be generated by the brain electric (or solitonic) oscillations?

A recent paper throws a possible bridge between the spatial four-dimensional (plus time) detection of quantum phenomena and the multidimensional biophysical neuronal activity.  Indeed, Lohse et al. (7) found a (relatively) simple way to probe 4D physical phenomena, starting from artificial, two-dimensional dynamical systems. 

We start from a 2D lattice, consisting of superlattices along the x and y axes.  Each superlattice is created by superimposing two standing waves of different wavelength, so that a reticulum is build (Figure A). 

When a third wave is introduced along the x direction (an operation corresponding to moving the long lattice along x) with the proper inclination (Figure 2), we achieve dynamics that are equivalent to movements in 4D.  Indeed, the third wave leads to two responses: a linear response along the axis x and a nonlinear response along y (Figure C). 


Lohse et al. provide all the measurements (wavelengths, angles, equations) required in order to detect the quantum Hall effect and the second Chern number; therefore, their approach holds true for the assessment of peculiar multidimensional phenomena occurring in the field of quantum dynamics.  However, with the proper corrections, their “4D building machine” could be used also in order to assess the possible presence of further brain dimensions.  Indeed, taking into account the neuroscientific field, the required waves might stand for slow- and high-frequency nervous electric activities.  The superimposition of these brain waves of different wavelengths might give rise to the required superlattices.  When such functional reticulum is crossed by other brain waves equipped with the proper angulation, both (2D) linear and (4D) nonlinear nervous dynamics might take place. 




Figure.  4D physical activities on a 2D superlattice.  Figure A depicts a topological lattice equipped with two waves of different wavelength.  Figure B: another wave with the proper wavelength and angulation (not shown here) is superimposed to the lattice in the direction x.  Figure C: the three waves give rise to two different motions: a linear one along the axis x (yellow arrow), and a nonlinear one along the axis y (red arrow).  Such motions can be quantified, in order to check whether the currently-known brain dynamics match them.  




1)       Tozzi A, Peters JF. 2016.  Towards a Fourth Spatial Dimension of Brain Activity.  Cognitive Neurodynamics 10 (3): 189–199. doi:10.1007/s11571-016-9379-z.

2)       Tozzi A, Peters JF. 2016.  A Topological Approach Unveils System Invariances and Broken Symmetries in the Brain.  Journal of Neuroscience Research 94 (5): 351–65. doi:10.1002/jnr.23720.

3)       Peters JF, Ramanna S, Tozzi A, İnan E.  2017.  Bold-Independent Computational Entropy Assesses Functional Donut-Like Structures in Brain fMRI Images.  Front Hum Neurosci. 2017 Feb 1;11:38. doi: 10.3389/fnhum.2017.00038. eCollection 2017.

4)       Peters JF, Tozzi A, Ramanna S, Inan E.  2017. The human brain from above: an increase in complexity from environmental stimuli to abstractions.  Cognitive Neurodynamics,11(4), 391–394.  DOI: 10.1007/s11571-0­17-9428-2.

5)       Tozzi A, Peters JF, Fingelkurts AA, Fingelkurts AA, Marijuán PC.  2017.  Topodynamics of metastable brains.  Physics of Life Reviews, 21, 1-20.

6)       Tozzi A, Peters JF, Fingelkurts AA, Fingelkurts AA, Marijuán PC.  2017.  Brain projective reality: novel clothes for the emperor.  Reply to comments on “Topodynamics of metastable brains”by Tozzi et al.  Physics of Life Reviews, 21, 46-55.

7)       Lohse M, Schweizer C, Price HM, Zilberberg O, Bloch I.  2018.  Exploring 4D quantum Hall physics with a 2D topological charge pump.  Nature 553, 55–58. doi:10.1038/nature25000.