Preprint Article Version 1 This version is not peer-reviewed

The Banach-Tarski Paradox Dictates Snyergistic Routes for Scale-Free Neurodynamics

Version 1 : Received: 4 April 2020 / Approved: 6 April 2020 / Online: 6 April 2020 (11:36:49 CEST)

How to cite: Tozzi, A.; Peters, J.F. The Banach-Tarski Paradox Dictates Snyergistic Routes for Scale-Free Neurodynamics. Preprints 2020, 2020040050 (doi: 10.20944/preprints202004.0050.v1). Tozzi, A.; Peters, J.F. The Banach-Tarski Paradox Dictates Snyergistic Routes for Scale-Free Neurodynamics. Preprints 2020, 2020040050 (doi: 10.20944/preprints202004.0050.v1).

Abstract

Neuroscientists are able to detect physical changes in information entropy in available neurodata. However, the information paradigm is inadequate to fully describe nervous dynamics and mental activities such as perception. This paper provides an effort to build explanations to neural dynamics alternative to thermodynamic and information accounts. We recall the Banach–Tarski paradox (BTP), which informally states that, when pieces of a ball are moved and rotated without changing their shape, a synergy between two balls of the same volume is achieved instead of the original one. We show how and why BTP might display this physical and biological synergy meaningfully, making it possible to tackle nervous activities. The anatomical and functional structure of the central nervous system’s nodes and edges allows to perform a sequence of moves inside the connectome that doubles the amount of available cortical oscillations. In particular, a BTP-based mechanism permits scale-invariant nervous oscillations to amplify and propagate towards far apart brain areas. Paraphrasing the BPT’s definition, we could state that: when a few components of a self-similar nervous oscillation are moved and rotated throughout the cortical connectome, two self-similar oscillations are achieved instead of the original one. Furthermore, based on topological structures, we illustrate how, counterintuitively, the amplification of scale-free oscillations does not require information transfer.

Subject Areas

Banach–Tarski paradox; brain; power law; fractal; oscillations; information

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