The Principle of Persistence, Leibniz's Law, and the Computational Task of Object Re-Identification

Fields, Chris

doi:10.1159/000350206

Cited by 10 publications

(6 citation statements)

References 78 publications

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“…Since the size of the globular sets may vary, presheaves can be used for the assessment of different coarse-grained nervous structures at the micro-, meso-and macro-levels of observation. The human ability to re-identify objects at different times and across observation gaps leads to the phenomenon termed "object persistence" (Fields, 2013). The computational tasks required by object persistence can be tackled in terms of presheaf theory both at the microscopic level of histological microcolumns (Tozzi et al, 2017b) and at the macroscopic level of brain functional/anatomical areas.…”

Section: Discussionmentioning

confidence: 99%

The Bipolar Logic of Feedforward and Feedback Circuits

Tozzi¹

2021

Preprint

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Instead of the conventional 0 and 1 values, bipolar reasoning uses -1, 0, +1 to describe double-sided judgements in which neutral elements are halfway between positive and negative evaluations (e.g., “uncertain” lies between “impossible” and “totally sure”). We discuss the state-of-the-art in bipolar logics and recall two medieval forerunners, i.e., William of Ockham and Nicholas of Autrecourt, who embodied a bipolar mode of thought that is eminently modern. Starting from the trivial observation that “once a wheat sheaf is sealed and tied up, the packed down straws display the same orientation”, we work up a new theory of the bipolar nature of networks, suggesting that orthodromic (i.e., feedforward, bottom-up) projections might be functionally coupled with antidromic (i.e., feedback, top-down) projections via the mathematical apparatus of presheaves/globular sets. When an entrained oscillation such as a neuronal spike propagates from A to B, changes in B might lead to changes in A, providing unexpected antidromic effects. Our account points towards the methodological feasibility of novel neural networks in which message feedback is guaranteed by backpropagation mechanisms endowed in the same feedforward circuits. Bottom-up/top-down transmission at various coarse-grained network levels provides fresh insights in far-flung scientific fields such as object persistence, memory reinforcement, visual recognition, Bayesian inferential circuits and multidimensional activity of the brain. Implying that axonal stimulation by external sources might backpropagate and modify neuronal electric oscillations, our theory also suggests testable previsions concerning the optimal location of transcranial magnetic stimulation’s coils in patients affected by drug-resistant epilepsy.

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Section: Discussionmentioning

confidence: 99%

The Bipolar Logic of Feedforward and Feedback Circuits

Tozzi¹

2021

Preprint

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“…The size of the globular sets may vary, so that presheaves can be used for the description of different coarse-grained nervous structures, both at the micro-and at the macro-levels of observation. Human ability to reidentify objects through time and across gaps in observation leads to the effect termed object persistence (Fields, 2013). The computational task of object persistence can be tackled in terms of presheaf theory, both at the microscopic level of histological microcolumns (Tozzi et al, 2017b) and at the macroscopic level of brain functional and anatomical areas.…”

Section: Conclusion: More Abstract Possibilitiesmentioning

confidence: 99%

Sheaves in the Brain Elucidate the Behavior of Entrained Oscillations

Tozzi¹

2019

Preprint

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Once a wheat sheaf has been sealed and tied up, its packed down straws display the same orientation and zero-divergence. This observation brings us to the mathematical notion of presheaf, i.e., a topological structure in which diverging functions are locally superimposed. We show how the concepts of presheaves and the correlated globular sets, borrowed from category theory and algebraic topology, allow a well-founded mathematical approach to otherwise elusive activities of the brain. The mathematical assessment of brain functions in terms of presheaves: a) explains why spontaneous random spikes synchronize; b) leads to the counterintuitive intuition of antidromic effects in neuronal spikes: when an entrained oscillation propagates from A to B, changes in B lead to changes in A. We provide testable previsions: a) we suggest the proper locations of transcranial magnetic stimulation’s coils to improve the clinical outcomes of drug-resistant epilepsy; b) we advocate that axonal stimulation by external sources backpropagates and alters the neuronal electric oscillatory frequency. Further, we describe how the hierarchical information transmission inside globular sets provides fresh insights concerning different issues at various coarse-grained scales, such as object persistence, memory reinforcement in spite of random noise, Bayesian inferential circuits.

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“…It is, moreover, just an item of faith, sometimes explicitly propped up by appeals to Occam's razor, that systems do not undergo more radical alterations or even substitutions of one for another while we are not observing them. The cognitive mechanisms underlying this item of faith are becoming better understood, largely by studying their points of failure (Fields, 2012;Fields, 2013b;Fields, 2014b). Both cybernetics and quantum theory reminds us that this faith-driven inference of object identity through time is unsupportable, in principle, by finite observations.…”

Section: Physics Without Systems?mentioning

confidence: 99%

Decompositional Equivalence: A Fundamental Symmetry Underlying Quantum Theory

Fields¹

2016

Axiomathes

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Decompositional equivalence is the principle that there is no preferred decomposition of the universe into subsystems. It is shown here, by using a simple thought experiment, that quantum theory follows from decompositional equivalence together with Landauer's principle. This demonstration raises within physics a question previously left to psychology: how do human -or any -observers identify or agree about what constitutes a "system of interest"?

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The Principle of Persistence, Leibniz's Law, and the Computational Task of Object Re-Identification

Cited by 10 publications

References 78 publications

The Bipolar Logic of Feedforward and Feedback Circuits<strong> </strong>

The Bipolar Logic of Feedforward and Feedback Circuits<strong> </strong>

Sheaves in the Brain Elucidate the Behavior of Entrained Oscillations<strong> </strong>

Decompositional Equivalence: A Fundamental Symmetry Underlying Quantum Theory

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