SergeakaAimate/Ontology-Lab: Propertyness (𝒩ₚ) — Metric of Ontological Complexity

Propertyness (𝒩ₚ) — Metric of Ontological Complexity A Core Primitive of the MPO-System 𝒩ₚ is a numerical measure of the "saturation" of an object or system with properties within the MPO-System. A higher 𝒩ₚ corresponds to a richer, more multifaceted reality of the object. 🔗 Read the specification: 𝒩ₚ-Propertyness.pdf 🔖 DOI (Zenodo): Abstract 𝒩ₚ is a numerical measure of the "saturation" of an object or system with properties within the MPO-System. A higher 𝒩ₚ corresponds to a richer, more multifaceted reality of the object. Core Definition 𝒩ₚ quantifies ontological depth by counting how many properties (from the 36+1 set of the MPO-System) are meaningfully instantiated in a given object across relevant ChORs (ontological regimes). Conceptual Anchoring Exemplary Values: Electron: 𝒩ₚ ≈ 3 (mass, charge, spin) Human being: 𝒩ₚ ≈ 10⁹ (biological, cognitive, social strata) Table with a hole: 𝒩ₚ = 8 (4 legs + tabletop + hole + its boundaries + function) Key Characteristics Nonlinear Scaling: 𝒩ₚ grows exponentially with the emergence of new organizational levels (e.g., neurons → consciousness). ChOR-Dependence: An object manifests different 𝒩ₚ across distinct worlds (e.g., water in W₁ vs. W₂). Measurable via Thought Experiment: Determined through analysis of connectivity (KSS) and paradoxical permeability (PPU). Distinction from Classical Complexity Metrics 𝒩ₚ incorporates not only physical parameters, but also: Semantics (the meaning of a "hole" for an observer), Dynamics (how properties transform under Γ-actualization), Hierarchies (e.g., 𝒩ₚ of a society > Σ𝒩ₚ of its individuals). Systemic Significance 𝒩ₚ functions as the fundamental "currency" of the MPO-System, enabling: Cross-domain complexity comparison (from quarks to love), Prediction of significance thresholds (𝒯𝒫), Detection of novel ChOR emergence. "𝒩ₚ is not merely a number—it is a measure of reality's depth. Like a microscope's resolution: the higher the 𝒩ₚ, the more properties become discernible." Context Part of: Ontology Lab Related to: MPO-System (v1.0.0) — formal axiomatics Uniqueness of Space — 𝒩ₚ of spacetime points INTELLECTUAL-THRILLER.pdf — 𝒩ₚ of identity in word games License Text: CC BY-SA 4.0 Conceptual framework: © Serge Magomet aka Aimate, 2025