Arturo Tozzi1, James F. Peters2, Andrew A. Fingelkurts3, Alexander A. Fingelkurts3, Pedro C. Marijuán4


1 Center for Nonlinear Science, University of NorthTexas

1155 Union Circle, #311427Denton, TX76203-5017USA  (corresponding Author)


2 Department of Electrical and Computer Engineering, University of Manitoba

75A Chancellor’s Circle Winnipeg, MB R3T 5V6 CANADA and

Department of Mathematics, AdıyamanUniversity, 02040 Adıyaman, Turkey


3 BM-Science – Brain and Mind Technologies Research Centre, Espoo, Finland  ;


4 Bioinformation Group

Aragon Institute of Health Science (IACS)

Aragon Health Research Institute (IIS Aragon)

Zaragoza, 50009 Spain



This paper (formally a response to the comments of nine highly qualified commenters to our paper: “topodynamics of metastable brains”) introduces a novel paradigm in neuroscience, termed “projectionism”, which assesses projections and mappings among different functional brain dimensions and phase spaces.   We describe recently published papers that confirm our general framework.  Furthermore, we compare brain symmetries with the predictive coding that stands for a sort of Kant a priori located in in our brains. We illustrate the “unreasonable power” of topology in neuroscience, which allows a rationalistic but testable top-down inquiry of the brain activity, in order to mathematically assess the physical and biological dynamics of the human nervous system.  We also propose possible biochemical correlates of a brain fourth dimension, with clues provided by… LSD intake. 

Also, we suggest fresh mathematical approaches to brain topological dynamics, introducing novel theorems and proposing complex functional nervous spaces very different from the classical Euclidean ones. We close our paper with a novel computational scenario that takes into account the tenets of neural Darwinism.