The critical dimension of memory engrams and an optimal number of senses

In this work, we analyse the fundamental question: how many senses are optimal for memory and learning. To answer this question, we introduce and analyse a novel kinetic model of memory engrams. The model, built on basic general principles and phenomenology, captures the engrams' emergence and evolution driven by their interaction with external environment, learning, and forgetting. We derive the corresponding kinetic equation governing the dynamics and evolution of engrams over time. We then solve this equation analytically and numerically through Monte Carlo simulations. We observe the formation of a steady state with a steady number of different engrams covering a fraction of the conceptual space. We analyze the impact of the dimension of the conceptual space on the steady state and discover the existence of a critical dimension, at which the number of different engrams is maximal; we provide a theoretical explanation of this observation. If each feature is associated with a different sense, the critical dimension corresponds to an optimal number of senses for a system aiming at keeping the maximal number of different concepts in its memory. We also reveal an apparent tension between the system's receptivity to new stimuli and concept sharpness-the higher the receptivity, the less sharp the learned concept becomes.