The Ng Operator: Mathematical Formalization and Operational Definition of Narrative Gravity

The Narrative Gravity operator (Ng) has been criticized as lacking operational definition — as a conceptual label rather than a calculable variable. This paper provides the complete mathematical formalization of Ng, operationalizes its two input variables (Narrative Mass Ma and Narrative Entropy Sn), defines the conditions of its application, and demonstrates its calculability through three worked examples drawn from canonical literary texts.

Narrative Mass (Ma) is operationalized through four sub-variables scored on a 0.0-2.5 scale: Causal Density (Cd), Informational Opacity (Io), Temporal Persistence (Tp), and Structural Centrality (Sc). Narrative Entropy (Sn) is operationalized through Information Friction (If) and Causal Branching (Cb). The Vacuum Variable — the most powerful form of Ng attractor — is formally defined and distinguished from Hitchcock's MacGuffin through precise mathematical criteria.

Three benchmark cases demonstrate the formula's calculability: Pulp Fiction (Ng = 0.031 — edge of structural collapse through maximum entropy), Crime and Punishment (Ng = 0.312 — high stability through controlled entropy), and Moby Dick (Ng = 0.167 — intermediate stability through mass-based gravity). Four testable predictions are derived from the formula, falsifiable through standard reader response methodology without biometric equipment.

The paper further demonstrates that the Ng operator constitutes a genuine structural contribution distinct from Shannon's Information Theory: it introduces temporal integration of entropy across the narrative arc, a formal counterforce mechanism absent from Shannon, and a squared denominator relationship capturing the exponential attractor requirements of high-entropy narrative systems.