Euclid's heritage

The three spatial characteristics of length, height, and depth are commonly used by laymen, technicians, and scientists to describe forms, positions, and measurements of bodies. However, the question of why our space has these three dimensions has intrigued philosophers and scientists since antiquity. Proposed answers have often become more presumptuous, losing sight of everyday intuitions and sacrificing explanatory power. The author demonstrates that explanations of three-dimensionality rely on an unreflective geometrical language that accepts only three types of entities—points, lines, and planes—that define extended entities—lines, planes, and solids. This reflects a dual heritage from Euclid, who adopted geometrical language from figure drawing and established a tradition of geometry involving planimetry and stereometry through the rotation of plane figures. The systematic approach presented begins with operational definitions of spatial forms—plane, straight edge, and perpendicularity—and proves that only three planes can intersect pairwise orthogonally. This constructive solution within the frame theory of action provides a clear characterization of spatial relations in the physical world. Ultimately, the traditional order of geometric concepts emerges as a significant obstacle to methodically organizing everyday scientific concepts.