O Relógio da Mente: Formalismo Matemático e Modelagem Física da Percepção Temporal

Abstract

This article proposes a unified way of understanding human time perception, contrasting the linear, mechanical time of clocks (t) with the fluid, non-linear way our mind actually experiences it (τ). The investigation approaches this phenomenon through two interrelated perspectives: a macroscopic one and a microphysical one. At the macroscopic level, we use ordinary differential equations to mathematically translate the common sensation that time speeds up as we age. At the microphysical level, everyday fluctuations — such as moments of danger or novelty seeming to last an eternity — are explained by linking Claude Shannon's Information Entropy to statistical thermodynamics, drawing on Carlo Rovelli's thermal time hypothesis. In addition, Arrhenius kinetics is integrated to show how the human "internal clock" is closely tied to metabolism and body temperature. The mathematical model constructed suggests, at a theoretical level, that time perception is not an abstract illusion but rather the direct result of how the brain processes information and dissipates energy — a hypothesis consistent with the formalism presented, still pending direct empirical validation. Finally, we explored how these formulas could be applied in practice: in the design of more comfortable and efficient Brain-Machine Interfaces (BMIs), in the development of early medical tests for neurodegenerative diseases, and in the design of artificial intelligence algorithms able to manage their attention as intelligently and economically as the human brain.