Aristotle's Wheel and the Deconstruction of Relativity

Both right angles and straight lines are at rest. This paper presents an AI-assisted analytic reconstruction of a geometric thesis that deliberately eliminates time-parameterized kinematics (velocity and acceleration), replacing them with a purely spatial framework based on arc length, curvature, observation scale L, and observational resolution ε. We redefine “straightness” not as an ontic reality but as an identification label assigned when curvature is operationally undetectable (the ≪Straight-Line Illusion≫). Concretely, for curvature κ observed over scale L, the sagitta deviation satisfies δ ≈ κL^2/8, and whenever δ < ε the segment is identified as κ=0 (straight) despite κ>0. Conversely, a “right angle” is re-interpreted not as a natural shape but as a singularity induced by representational compression: when a smooth trajectory is approximated by a polyline under sparse sampling, a vertex can appear where tangency is undefined. This vertex is defined as ≪Right Angle≫ and is synonymous with ≪Rest≫. Within this framework, Aristotle’s Wheel paradox is resolved as the geometric impossibility of satisfying simultaneous no-slip correspondence conditions for concentric circles of different radii: if the outer rim satisfies S=Rθ, then an inner rim rigidly sharing the same rotation angle θ cannot simultaneously satisfy S=rθ when R≠r. Furthermore, this paper provides the solution to the fundamental proposition presented in the appended paper “If Einstein Misunderstood That Light Travels in a Straight Line, Then Humanity Is Misunderstanding It Too,” within Equation Mathematics Foundations (DOI: 10.5281/zenodo.18102417): [Quoted Proposition][1] Proposition to EinsteinAll existence cannot turn at a right angle.It must necessarily come to rest.If so, it cannot proceed in a straight line either.Because it would mean using a 90-degree angle relative to existence. The solution proposed herein is that light and motion are not “travel” but “spatial relationships (structures).” Light is not treated as a projectile moving from X to Y, but as the establishment of a relational constraint—schematically, X+Y=Z—where the primitive content is structural rather than time-indexed. Since “travel” is not taken as a primitive in this definition-based ontology, “moving in a straight line” is deconstructed as an identification regime (≪Straight-Line Illusion≫), integrating physics into a time-free, definition-first ontology.================================================================ Reference: Equation Mathematics Foundations (DOI: 10.5281/zenodo.18102417) 【AI Models Used】 The analysis and reconstruction in this work utilized the following AI models: * ChatGPT 5.2 (Reasoning Model) * Gemini 3.0 Pro * Grok (Auto Mode)