Information as Force: A Vector Theory of Cognitive Dynamics in Semantic Space

Classical information theory, as established by Shannon, treats information as a scalar quantity that reduces uncertainty in a static sense. However, this perspective is insufficient to describe the temporal dynamics of understanding, learning, and belief change in cognitive systems, especially in the age of artificial intelligence and "post-truth". In this paper, we propose a vector-based theory of information and cognition in which information is treated as a force that drives the evolution of a cognitive state vector in a semantic space. Drawing an analogy to Newtonian mechanics, we formalize a differential equation of cognitive dynamics with parameters representing the inertia of beliefs and damping (forgetting). We show that this model can qualitatively reproduce known empirical phenomena such as the Ebbinghaus forgetting curve and learning curves under constant information input. We analyze the system's behavior in different damping regimes (underdamped, critically damped, overdamped) and discuss the qualitative implications for how beliefs change (or resist change) under various conditions. Furthermore, we extend the model to multiple coupled agents to explore information exchange in a network and demonstrate convergence (or oscillation) toward consensus.The proposed framework yields three principles of "information physics":(1) Principle of Continuity (truth as a continuous trajectory rather than a static point),(2) Semantic Inertia (entrenched beliefs correspond to a large mass resisting change),(3) Differential Nature of Reality (changes and differences drive cognition more fundamentally than static states). We argue that this vector paradigm can bridge information theory and cognitive dynamics, providing insight into memory, learning, and the spread of information in social networks.