Projective mechanisms subtending real world phenomena wipe away cause effect relationships

Tozzi, Arturo; Papo, David

doi:10.1016/j.pbiomolbio.2019.12.002

Cited by 10 publications

(5 citation statements)

References 107 publications

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“…We described nervous propagation through the Banach Tarski paradox, showing how a sequence of moves related to scale-free brain oscillations allows increases in number of cortical waves. The fact that BTP might work in physical and biological systems would mean, as already suggested by Tozzi and Papo (2020), that topological changes may give rise to modifications devoid of thermodynamic constraints and topological superimposition, so that events may occur that do not require a producing cause. Against all informational odds, it is noteworthy that BPT can be used to describe duplications of nervous oscillations that do not entail information transfer.…”

Section: Discussionmentioning

confidence: 95%

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

Tozzi¹,

Peters²

2020

Preprint

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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.

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Section: Discussionmentioning

confidence: 95%

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

Tozzi¹,

Peters²

2020

Preprint

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“…The occurrence of holes causes the failure of the continuum assumption-based theorems that have been proven useful to investigate a large array of physical and biophysical issues. Amongst them, the hairy ball theorem (colloquially stating that "whenever one attempts to comb a hairy ball flat, there will always be at least one tuft of hair at one point on the ball"), the Brouwer fixed point theorem ("no matter how you slosh the coffee, some point is always in the same position that it was before the sloshing began") and the Borsuk-Ulam theorem ("at any moment, there is always a pair of antipodal points on the Earth's surface with equal temperatures and barometric pressures") should be mentioned (Tozzi and Papo, 2020). Describe genus-0 convex spheres, all these theorems cannot be used to treat manifolds of genus ≥1.…”

Section: Discussionmentioning

confidence: 99%

Topology of Saliva

Tozzi,

Peters

2023

Preprint

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Physical properties like shape, volume and size affect the dynamics of biological systems. Along these lines, we focus on the topological properties of biological fluids and their biochemical and physiological outcomes. We take as a paradigmatic example the salivary fluid and describe how its topological features may affect the physiopathology of the oral cavity. Topological approaches assess the general properties of saliva, ignoring small-scale physical details such as density, flow rate, stiffness, viscosity. Specifically, the mucin aggregates scattered in the salivary fluid can be tackled in terms of topological holes, i.e., vortical clusters that modify the direction, flow, impulse, local rate-of-change and velocity of saliva. While the current methodological approaches are inclined to remove the effects of impurities assessing systems as homogeneous structures, we argue that the occurrence of mucins breaks up the salivary fluid’s homogeneity, leading to unexpected biophysical modifications. We suggest that every collected salivary sample is not reliable for accurate clinical and experimental investigation, since it displays highly local as well as variable chemical, physical and biological features, not reflecting the current physiological state of the oral cavity. Therefore, the assessment of a single salivary sample is not fully reproducible and cannot provide information about the biophysical, enzymatic and microbiological content of the whole saliva. In sum, the very topological features of the saliva - such as volume, shape, antipodal cells, vortex area, whirling fluid mass, segmentation, discretization, triangulation, node numbering - produce unnoticed biological consequences and network connectivity features with intriguing operational implications.

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“…While network features have historically been predicated upon dynamical system and information theory, to render representations more context-independent, network neuroscience will possibly increasingly summon constructs from disciplines such as computational topology (Carlsson, 2009;Edelsbrunner & Harer, 2010;Petri et al, 2014;Reimann et al, 2017;Stolz, 2014;Zomorodian, 2005) or statistical physics (Bianconi & Rahmede, 2016), and explanations at various levels (Marr, 1982) and of different types (Illari & Williamson, 2012;Tozzi & Papo, 2020). New constructs may include neurophysiological properties, such as inherent disorder and lack of translational invariance, and may result in representations with nontrivial emergent geometry (Bianconi & Rahmede, 2017) accounting for phenomenology as yet poorly documented, at least in network terms, for example, topological phase transitions (Santos et al, 2019) or frustration .…”

Section: Discussionmentioning

confidence: 99%

Principles and open questions in functional brain network reconstruction

Korhonen

Zanin

Papo

2021

Human Brain Mapping

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Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network representation involves often covert theoretical assumptions and methodological choices which affect the way networks are reconstructed from experimental data, and ultimately the resulting network properties and their interpretation. Here, we review some fundamental conceptual underpinnings and technical issues associated with brain network reconstruction, and discuss how their mutual influence concurs in clarifying the organization of brain function.

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Projective mechanisms subtending real world phenomena wipe away cause effect relationships

Cited by 10 publications

References 107 publications

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

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

Topology of Saliva

Principles and open questions in functional brain network reconstruction

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