Things farther away appear smaller, and two-point linear perspective is taken to approximate the eye. That entire phenomenology is Archimedean geometry. This paper asks what changes if the metric of physical space were instead non-Archimedean and ultrametric. Why a reader should care: smooth perspective does not rule out a discrete world — it only rules out direct perception of one — and the distinction marks the exact boundary between physics and phenomenology for the live p-adic/ultrametric research program. Four moves: (1) the Archimedean anatomy of perspective (similar triangles, additive distance, projective closure over R); (2) the ultrametric demolition (strong triangle inequality kills rays, angles, boundaries, and smooth scaling — the naive direct-reading model is falsified by ordinary vision, recorded as C3-C4); (3) the rendering lemma (perception is a surjective interface; the Monna map is the explicit candidate); (4) the underdetermination theorem (first-person vision cannot decide the substrate metric; the continuum is a rendering, not a fact about the rendered). Premise depth: the theorem rests on two imported premises — the Kantian interface premise (corpus anchor: Unified Theory of Non-Archimedean Ontology) and the existence of the Monna map (established mathematics, Weiß 2406.13255); given both, the conclusion follows at theorem level. v0.2 (2026-08-16): post-publication red-team corrections — the Monna-map discontinuity justification was corrected (H1: the invalid 'totally disconnected, hence discontinuous' shorthand is replaced by the digit argument), the code-availability declaration was corrected and the verification script deposited (H2), the §5 rendering maps coordinate-wise into R^3, Monna's original 1952 construction is cited (ref 12), and inline refs 1-5 authors were corrected to match the live records. The underdetermination theorem, the falsifiability register, and the ontology claims are unchanged.