In mathematical physics, “oblique” refers to non-orthogonal coordinate systems or bases that imply interaction and interdependence.

In mathematical physics, “oblique” refers to non-orthogonal coordinate systems or bases that imply interaction and interdependence. Orthogonal coordinates assume flat Euclidean space, whereas oblique coordinates feature tilted axes, introducing off-diagonal components in the metric tensor ( g_{\mu\nu} ). These components express curvature—space where time and distance vary depending on the observer. Thus, obliqueness is a mathematical sign of curved or non-inertial space, representing gravity itself in general relativity. In such frames, time and spatial axes mix (( g_{0i} \neq 0 )), meaning time and space are no longer perpendicular. In quantum mechanics, non-Hermitian systems also exhibit non-orthogonal eigenstates, forming “biorthogonal” pairs that capture non-conservation and irreversibility. In field theory and differential geometry, oblique coordinates describe couplings like electromagnetism and gravity, where torsion or gauge connections arise from these non-orthogonal terms. In essence, obliqueness formalizes the fact that observation alters the space observed—an interdependent structure between observer and world. Yoshimoto Takaaki’s “non-orthogonality” of expression and reference parallels this physical obliqueness.