What question did this study set out to answer?

The research aims to explore how recursive divergence affects language expression and conceptual gaps.

April 5, 20260 citationsOpen Access

The Exergy of the Word: Recursive Divergence and the Thermodynamic Ceiling of Languages

Key Points

The research aims to explore how recursive divergence affects language expression and conceptual gaps.
Analyzed semantic entropy using Classical Latin as a baseline.
Construed decomposition trees for 12 modern concepts at varying depths.
Utilized the Abrams-Strogatz simulation to assess language collapse dynamics.
Found a cost structure for expressing concepts as C(d) = 7.8 × 1.94^d.
Identified two regimes of conceptual expression: flat O(1) and recursive O(b^d).
Demonstrated that vocabulary depth could accelerate language collapse by up to 85% at equal prestige.

Abstract

This repository contains the paper, analysis scripts, simulation code, and data for a study of recursive divergence in semantic entropy. Using Classical Latin as a frozen baseline, decomposition trees for 12 modern concepts (depth 0 to 5) demonstrate that the cost of expressing a concept across a conceptual gap grows as C (d) = 7. 8 × 1. 94ᵈ (R² = 0. 93). Two regimes are identified: flat O (1) when sub-concepts are available, and recursive O (bᵈ) when the conceptual infrastructure is absent. An extended Abrams-Strogatz simulation shows that vocabulary depth accelerates language collapse by up to 85% at equal prestige. The unified equation C (d, A) = bᵈ × C₀ (A) links conceptual depth and phonemic inventory size in a single expression for the lexical carrying capacity of a language.

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