Two-Dimensionality as the Ontological Foundation of Mathematics: The RIT as the Necessary Base Object from the Standpoint of Neurophysiology, Physics, and the Structure of Provability

This work develops a single thesis: two-dimensionality is not an arbitrary choice of Δ-ontology but a necessary consequence of the nature of human perception and the structure of mathematics itself. We argue that: 1. Neurophysiological argument. Most human sense organs — the retina, skin, eardrum, olfactory epithelium, cochlea — are topologically two-dimensional surfaces (S², S¹×I). Spatial information reaches the brain only through two-dimensional slices. The brain is a machine for reconstructing three-dimensionality from two-dimensional projections, not for directly perceiving it. Smell and taste are exceptions: they work not through spatial relations but through valent (valence) bonds, and carry information of a different type. 2. Physical argument. Light is a plane-transverse wave; electromagnetic oscillations occur in the plane perpendicular to the direction of propagation. The fundamental channel of spatial information about the world is two-dimensional. Pressure — the primary quantity measured by receptors — is defined through a plane: p = F/S. 3. Mathematical argument. Self-similarity with invertible gluing (Φ ∘ Ψ = id) is possible only in dimension 2. In dimensions ≥ 3, cutting and gluing inevitably produce halves that are not similar to the original figure. Fermat's Last Theorem for n > 2 is an algebraic manifestation of this geometric fact. Complex analysis, Kähler manifolds, the Hodge Conjecture, knot theory via 2D diagrams, the holographic principle — all point to one thing: the arena of spatial provability is two-dimensional. 4. Consequence. The right isosceles triangle △₁ₓ₁ is not chosen arbitrarily. It is the only figure simultaneously satisfying: (a) 2D self-similarity with invertible decomposition, (b) orthogonality from the gravity vector, (c) irrationality √2 from the Pythagorean theorem, (d) minimal encoding energy. This makes it the necessary base object of spatial mathematics. A remark on smell and taste. Smell and taste occupy a special place: their reception does not reduce to spatial geometry but is determined by the valent (valence) bonds of molecules. This does not contradict the main line of the paper but refines it: spatial mathematics has a 2D foundation, while chemical information has a different nature. This distinction is funda mental.