The Circuit Model of Historical Progression: A Dynamical RLC and Network Laplacian Framework

Abstract

Abstract This upload establishes a formal mathematical framework for the Circuit Model of Historical Progression. By establishing a direct analogy between macro-historical state variables and electrical circuit parameters (Voltage, Current, Resistance, Inductance, and Capacitance), societal evolution is mapped to dynamic second-order differential systems. The repository includes both the theoretical manuscript (compiled PDF and LaTeX source) and the full Python computational script verifying the numerical stability, phase transitions, and network dynamics of the system. Core Theoretical Mapping Systemic Tension (Voltage): Societal pressure driving structural change across a polity. Progression Rate (Current): Event density and the speed of structural modification (the rate of change of accumulated progress over time). Institutional Friction (Resistance): Bureaucratic inertia, regulatory friction, and institutional resistance opposing change. Cultural Momentum (Inductance): Inertia of generational memory, tradition, and collective habitus. Absorptive Capacity (Capacitance): Storage of capital, economic reserves, and institutional knowledge. Accumulated State (Charge): The total time integral of net technological, legal, and cultural progress. Key Mathematical Formulations Governing RLC Differential Model: Relates cultural momentum, institutional friction, and absorptive capacity directly to incoming systemic tension shocks over time. Canonical State-Space Model: Formulates accumulated progress and progression velocity into a standard matrix differential system suitable for control theory and numerical integration. Multi-Polity Graph Laplacian Model: Connects individual polities across a spatial network to simulate cross-border technology diffusion, trade coupling, and geopolitical tension cascades. Repository Contents circuit_model_paper.pdf: Peer-review ready compiled manuscript containing all theoretical derivations, frequency-domain transfer functions, Hamiltonian energy dissipation equations, and network Laplacian formulations. multi_node_historical_rlc.py: Complete executable Python simulation script modeling 3 single-polity damping regimes (underdamped, critically damped, overdamped) and a 4-node spatial network simulation. circuit_model_paper.tex: Standalone LaTeX source code for complete academic replication and journal submission. Execution & Replication The Python code can be executed locally using standard numerical packages (NumPy, SciPy, Matplotlib) or copied directly into a Google Colab notebook cell to generate all manuscript figures in the browser.