What Does a Mirror Really Reverse? — Visualization Through a Comparison of a Plane Reflection Map and the Rotated Coordinate System of a Person Standing Face-to-Face

This paper formulates a mirror image as a one-axis reversal along the normal to the mirror plane and visualizes how the direction of reversal is determined by the arrangements of the mirror and the person. Using body coordinate systems, it classifies mirror-person relationships into six basic arrangements and the resulting reversals into three types: front-back, left-right, and up-down. The coordinate systems of Persons A and B, the corresponding coordinate system of mirror image A′, and the mirror-plane coordinate system are explicitly illustrated. These illustrations also incorporate a three-finger embodiment of coordinate axes to aid intuitive understanding of their spatial relationships. It further defines a "cognitive twist" as comparing the mirror image not with the present self facing the mirror directly in front, but with the front-facing image of the self obtained by a 180° yaw rotation, and proposes the hypothesis that this operation produces the perception of left-right reversal. A flowchart contrasts this "cognitive twist" with "correct cognition," in which the mirror image is compared with the present self.This is the English-language version of the author's Japanese paper.