Why Spatial Axes Are Perpendicular: A Derivation from Wave Information and Isotropy

Every physical theory uses coordinate systems with perpendicular axes, but none explain why. Orthogonal coordinates are taken as a mathematical convenience, not derived from physical principles.

In the canvas model, spatial axes are not abstract—they are the physical directions along which fundamental oscillators vibrate. This paper proves that these axes must be mutually perpendicular.

The proof has two parts. First, wave independence: the information content of each spatial axis is maximized when the axes are perpendicular. Non-perpendicular axes introduce redundancy—the projection of one wave onto another means the information channels are not independent. The effective information available to specify physical quantities is reduced by the overlap, and the observed cosmological constant requires the full information capacity of the universe. Perpendicularity is forced by information saturation.

Second, isotropy: the voxel lattice formed by intersecting waves must be isotropic to match observation. If axes are not perpendicular, voxel spacings differ in different directions, creating a preferred orientation. In three dimensions, the only configuration that produces equal spacing in all directions is mutual perpendicularity.

Together with the proof that space has three dimensions, this completes the geometry of the canvas: space is three-dimensional with three mutually perpendicular axes. Both properties are theorems, not postulates.