The Gap Between Mathematical Description and Existential Cognition —A Consideration from Quantum Mechanics and the Structure of Human Perception—

This paper examines the structural discrepancy between the mathematical formulations of physics—particularly those of quantum mechanics—and the conditions under which human beings recognize existence and establish observation. The fundamental equations of quantum mechanics do not require sensory distinctions such as whether a particle is “moving” or “at rest”; the same formalism allows both dynamic and static states. In contrast, human perceptual structures presuppose continuous change or motion for the recognition of existence and the establishment of observation. A completely unchanging entity does not readily emerge within the sensory world. Focusing on this discrepancy, this paper argues that mathematical equations describe the consistency of states rather than the conditions of existential recognition or generative processes. Furthermore, concepts such as “will” and “choice” do not belong to the third-person domain described by mathematical formalism, but instead function as first-person preconditions. Accordingly, this paper does not claim that there exist phenomena that cannot be expressed mathematically; rather, it clarifies that there are layers of reality that mathematics does not, by design, attempt to describe. This distinction does not indicate a limitation of mathematics, but instead reveals a layered structure of world-description, offering a new perspective for connecting physics, cognitive science, and philosophy.