History as a dynamical system
Computational Macrohistory is a formal framework for studying the long-term dynamics of human societies: eight axioms, a 25-dimensional state space, and an explicit account of what can and cannot be predicted.
Computational Macrohistory (CMH) builds stochastic models of large-scale historical change that estimate probability distributions over critical socio-political transitions — never point predictions of events.
Societies are not laboratories. They can still be studied as systems.
Historical change cannot be re-run under controlled conditions, and the people inside a society react to the predictions made about it. CMH takes both constraints as starting points rather than obstacles: it asks which questions about large-scale social dynamics remain scientifically tractable once those limits are made explicit.
The answer is built in three parts. A set of axioms defines which models are admissible. An operational state space turns the axioms into measurable variables and dynamic equations. And a precise theory of the predictive horizon separates what the framework claims from what it deliberately refuses to claim.
Eight axioms
Formulated in WP-2026-001 as admissibility constraints: they do not describe the world as it is, they define the conditions under which historical systems become scientifically tractable. Select an axiom to read what it requires.
A 25-dimensional state space
WP-2026-002 translates the axioms into an operational apparatus: twenty-five variables across five domains, each with an operationalization protocol and specified data sources. Select a domain to isolate its variables.
Each node is a state variable; links indicate coupling within and across domains in the CMH dynamic equations. Schematic representation — the full variable list and coupling structure are specified in WP-2026-002.
Three levels of analysis
The same state space is read at three levels of resolution, from transparent composite indices to the full stochastic dynamics. Each level trades interpretability against dynamical detail.
Composite indices
Weighted combinations of state variables that summarise structural pressure in a single interpretable number, with uncertainty quantification and robustness analysis across alternative weighting schemes.
Systemic Stress Index · Elite Pressure IndexCoupled dynamic equations
The equations of motion governing how the state variables evolve and interact over time — the level at which feedbacks, thresholds and slow structural drift are made explicit.
Defined in WP-2026-002Full stochastic dynamics
Stochastic differential equations with endogenous noise, supporting probabilistic event functions for instability episodes and regime transitions — and, beyond the predictive horizon, spectral analysis of the dynamics themselves.
Probabilistic event functions · Koopman-CMHThe Lyapunov Wall, live
Ten copies of the same chaotic system, started from initial conditions that differ by one part in a billion. For a while they are indistinguishable — then chaos amplifies the difference and the trajectories scatter. The wall is where quantitative prediction of individual trajectories ends. No amount of data or computing power moves it.
Demonstration uses the logistic map in its chaotic regime; the same divergence mechanism, formalised in Axioms A5 and A7, bounds the CMH forecasting horizon to roughly five to fifteen years. Each run applies a fresh random perturbation of order 10-9.
Event prediction
Which country, which year. Possible only within the horizon, and only as a probability — never as a point forecast.
Regime probability
Probability distributions over classes of outcomes: how likely a system is to remain in, or exit, a structural regime.
Spectral persistence
Persistent cyclic structures in the dynamics, identified through Koopman operator methods at the level where chaos no longer destroys the signal.
Start here
Two ways into the framework: the introductory guides assume no mathematical background; the working papers carry the full formal apparatus.
Computational Macrohistory: A Guide for Everyone
The accessible introduction — core concepts, methodological foundations and applications, with no mathematics assumed.
Axiomatic Foundations
The formal starting point: the eight axioms as admissibility constraints, with a minimal toy model demonstrating joint satisfiability.
Operational Framework
The state space, the variables and the dynamic equations — where the axioms become a measurable apparatus.
The framework at work: the Arab Spring
From a three-country proof of concept to an eleven-country structural analysis, with the misses analysed in as much detail as the hits.
Beyond the Lyapunov Wall
The predictive horizon made precise, and the spectral methods that ask what lies on the other side of it.
Koopman–CMH
The spectral theory proved as a theorem, then put to its first pre-registered empirical test on two centuries of European data.