Brains are Probabilistic, Electrophysiologically Intricate and Triune: A BiasedRandom Walk Perspective on Computational Neuroscience

The pursuit of a unified theory that captures the intricacies of the brain and mind continues to be a significant challenge in theoretical neuroscience. This paper presents a novel, triune framework that utilizes the concept of collective biased random walk (cBRW). Our approach strives to transcend biological specifics, offering a high-level abstraction that remains general and applicable across various neural phenomena. Despite the solid traditional foundation of computational neuroscience, the intricate delicacy of neural processes calls for a renewed probabilistic approach. We aim to utilize the intuitive nature of probability concepts -such as the probability of localization and state, and uniform probability distribution- to study the stochastic organization of electric charges and signals in the brain. This electrophysiological intricacy emerges from the seemingly paradoxical reality that tiny electric events, while random, collectively give rise to predictable, long-range oscillations. These oscillations manifest in three groups of activation states. Our framework categorizes the brain as a triune system, accommodating classical, semiclassical, and non-classical interpretations of both probabilistic phenomena and cBRW models, alongside three groups of states. We conclude that by appreciating, rather than overlooking, the tiny random walks of electric charges and signals in the brain, we can gain a triune mathematical foundation for theoretical brain science, the powerful capabilities of this organ, and the electromagnetic interfaces we can develop.