Differential Entangled Topology: A Mathematical Model for Simulating the Dynamic Nature of Consciousness

This article presents the Differential Entangled Topology (DET) model, a sophisticated mathematical framework designed to simulate the complex, dynamic, and evolving nature of consciousness. By conceptualizing consciousness as an intricate network of entangled points distributed on the surface of a unit sphere, the model captures the fluid and unpredictable interactions that characterize conscious experience. Each point represents a neural region or conscious element, with its position undergoing differential, random shifts that simulate the process of entanglement. These shifts, governed by a specified entanglement factor, reflect the ongoing reconfiguration of consciousness over time. The system's progression is quantitatively analyzed through topological entropy, providing a measure of the system's complexity and the degree of unpredictability inherent in the entanglement process. The model's evolution is visualized in a 3D space, where bright points are projected onto the sphere's surface, and the background is shaded in a soft rosaceous hue, symbolizing the fundus of the system. This framework offers a novel mathematical perspective on the interconnected, non-linear nature of consciousness, providing insight into its continuous transformation and the underlying dynamics that drive cognitive states.