Two-Dimensionality as the Base Dimension: A Neurophysiological and Physical Justification for the Infinium △₁ₓ₁ as the Fundamental Object of Mathematics

This work presents a systematic justification for the thesis that two-dimensionality is the base dimension of human cognition and, consequently, of mathematics itself. We show that the receptor surfaces of the organism responsible for perceiving spatial signals (retina, skin, cochlea) are topologically two-dimensional manifolds, that the primary sensory signal is pressure — a quantity defined through a two-dimensional cross-section by the formula p = F/S — and that light is a plane-transverse wave. Three-dimensional (and higher-dimensional) perception is a reconstruction by the brain from two-dimensional input. At the same time, smell and taste form a separate information channel: they encode not spatial but valent (chemical) bonds, depending on the properties of molecules rather than on the geometry of space. This separation strengthens the main thesis: △-ontology describes spatial perception, not chemical specificity. From this we derive that the right isosceles triangle △₁ₓ₁ (the infinium) is not an arbitrary mathematical object but a psychophysical atom of spatial form perception, and that two-dimensionality is the only arena where the discrete (cutting) and the continuous (gluing) are in perfect equilibrium. We prove a theorem within Synthetic Differential Geometry showing that any object admitting an invertible self-similar decomposition into two identical parts must be two-dimensional. We connect this to Fermat's Last Theorem, complex analysis, the Hodge Conjecture, knot theory, the holographic principle, and Einstein's E = MC² formula, showing that all of these are projections of the same 2D-filter principle. The article concludes that △-ontology is not a mathematical invention but an explicit realization of the neurophysiological and physical structure of spatial cognition.