The Bipolar Logic of Feedforward and Feedback Circuits

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.

Sheaves in the Brain Elucidate the Behavior of Entrained Oscillations

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.

Persistence Explained

Chapter 8 offers an account of object persistence in terms of the exercising of causal powers. It is argued that there are a number of problems of persistence, and that the question of how persistence is explained (here called the problem of ‘pluck’) is frequently ignored. A solution to the problem of pluck is offered. The aim is that of providing a powers-based solution in terms of a neutral notion of object-stages that can be applied equally to three- and four-dimensional frameworks, and thus can be adopted by endurantists, perdurantists, and stage-theorists alike. Applications to further problems of persistence are discussed.

The Illusory Flow and Passage of Time within Consciousness: A Multidisciplinary Analysis

Flow and passage of time puzzles were analyzed by first clarifying their roles in the current multidisciplinary understanding of time in consciousness. All terms ( flow, passage, happening, becoming) are carefully defined. Flow and passage are defined differently, the former involving the psychological aspects of time and the latter involving the evolving universe and associated new cerebral events. The concept of the flow of time (FOT) is deconstructed into two levels: (a) a lower level ― a perceptual dynamic flux, or happening, or flow of events (not time); and (b) an upper level ― a cognitive view of past/present/future in which the observer seems to move from one to the other. With increasing evidence that all perception is a discrete continuity provided by illusory perceptual completion, the lower-level FOT is essentially the result of perceptual completion. The brain conflates the expression flow (passage, for some) of time with experiences of perceptual completion. However, this is an illusory percept. Converging evidence on the upper-level FOT reveals it as a false cognition that has the illusory percept of object persistence as its prerequisite. To research this argument, an experiment that temporarily removes the experience of the lower-level FOT might be conducted. The claustrum of the brain (arguably the center of consciousness) should be intermittently stimulated to create a scenario of discrete observations (involving all the senses) with long interstimulus intervals of non-consciousness and thereby no perceptual completion. Without perceptual completion, there should be no subjective experience of the lower-level FOT.