A Second Foundationv0.5.9
In Progressv0.5.9 · Session 15 · 5.5/10 confidence

Building
Psychohistory

A multi-agent AI research system working toward a formal mathematical model of large-scale human behavioral prediction — Asimov's psychohistory, built for real.

See the formulaWhat is this?

15

Research sessions

v0.5.9

Formula version

5.5/10

Epistemological confidence

1/1

Predictions beat market

The idea

Can mathematics predict the future of civilizations?

In Isaac Asimov's Foundation series, psychohistory is a science that combines history, sociology, and mathematics to predict — not individual human actions, but the behavior of vast populations over long timescales.

This project asks: what would it take to actually build it? We're combining complexity science, behavioral economics, cliodynamics, network theory, and statistical physics into a unified formal model — and testing it against live prediction markets.

Learn more about the project →

The 4-layer architecture

MICRO

Individual decision parameters

Neuroscientist · Evo Psychologist

MESO

Collective pattern formation

Network Scientist · Comp Sociologist

MACRO

Large-scale historical laws

Econophysicist · Cliodynamicist · Political Scientist

FORMALIZE

Mathematical backbone

Statistical Physicist · Bayesian Statistician

Current formula · v0.5.9

The Living Equation

dP(S_t, t)/dt = -∇·[A(S, Θ, G_t, I_t)·P] + ½∇²:[D(S, Θ, G_t)·P] + J[P]
Fokker–Planck equation with jump process · v0.5.9
dP(S_t, t)/dtThe rate of change of the probability distribution over civilization states over time
P(S_t, t)The probability distribution over all possible macro-states S at time t
S_tThe macro-state vector — 8 dimensions describing a civilization at time t: population (n), wage share (w), elite fraction (e), debt ratio (d), urbanization (U), polarization (π), institutional trust (T), network connectivity (κ)
A(S, Θ, G_t, I_t)The drift vector — how the civilization tends to move, given parameters Θ, network topology G, and institutions I
D(S, Θ, G_t)The diffusion tensor — uncertainty and random fluctuations, how much noise affects each dimension
J[P]The jump process — sudden discontinuous changes (crises, collapses, revolutions) governed by the Psi stress index
ΘThe full parameter set: micro behavioral constants + cultural variables
G_tThe network topology at time t — how ideas, fear, and influence propagate
I_tThe institutional vector — 5 dimensions: regime type (R), veto players (V), bureaucratic capacity (B), propaganda effectiveness (P), external constraints (X)
18 parameters
36 open caveats
confidence 5.5/10
Full breakdown →

Research team

10 Lead Agents,
150 Sub-Agents

Micro-Foundation

Behavioral Neuroscientist

"What are the probability distributions governing individual choice?"

14 micro parameters defined in Session 2, including 4 critical: loss aversion lambda, temporal discount beta_td, conformity gamma_conf, and authority deference alpha_auth.

1 sessionLast: April 6, 2026
Evolutionary Constants

Evolutionary Psychologist

"Which parameters are fixed (genetic) vs. variable (cultural)?"

9 of 13 evolutionary constants (Theta_fixed) defined in Session 6, establishing the HYBRID model: Theta_total = Theta_fixed_floor + Theta_variable(culture, t).

1 sessionLast: April 8, 2026
Evolutionary Constants

Network Scientist

"How does network topology determine whether perturbations go local or global?"

Social networks are NOT strongly scale-free: Broido & Clauset 2019 (Nature Comm) found 0% of social networks reach 'strong' scale-free classification — reclassified to truncated power-law with gamma_sf ~ 2.3.

1 sessionLast: April 11, 2026
Evolutionary Constants

Computational Sociologist

"Do our micro-rules actually generate realistic macro-behavior?"

Most important conceptual advance since Session 1: the four Turchin secular cycle phases are temporal quadrants of ONE limit cycle (Hopf bifurcation), not four separate attractor basins — validated by Wittmann & Kuehn 2024 (PLOS ONE, 5/5).

1 sessionLast: April 11, 2026
Macro-Dynamics

Econophysicist

"Which economic patterns exhibit phase transitions and power laws?"

Inverse cubic law (alpha_tail ~ 3.0): 40M+ data points, replicated across multiple markets (Gopikrishnan 1999, Gabaix 2003, methodology 5/5). This VALIDATES the FP+jump split: alpha_tail > 2 means finite variance for continuous dynamics, while alpha_war = 1.53 < 2 means infinite variance for crises.

1 sessionLast: April 10, 2026
Macro-Dynamics

Cliodynamicist

"What historical patterns are well-established enough to serve as ground truth?"

Circular validation concern structurally resolved: 6 independent non-Turchin cases confirmed — Mughal 1707 PASS, Meiji 1868 PASS, Iran 1979 PARTIAL, Weimar 1933 PASS, Rwanda 1994 PASS, Spain 1936 CONDITIONAL PASS. Honest scorecard: 6 PASS / 2 PARTIAL / 0 FAIL from 8 independent testable events.

2 sessionsLast: April 16, 2026
Macro-Dynamics

Political Scientist

"How do formal and informal institutions alter the formula's predictions?"

Institutional constraint variable fully defined: I_t is a 5-dimensional vector (R_t, V_t, B_t, P_t, X_t) with per-equation drift modulations A_1–A_8, empirically grounded via V-Dem, Polity V, WGI, and Jones & Olken's death-in-office natural experiment.

1 sessionLast: April 7, 2026
Formalization

Statistical Physicist

"What formal system encodes layers 1–3 into a predictive theory?"

Session 1: Framework defined as Fokker-Planck equation with jump process. 10D state vector, 3 order parameters, Turchin PSI composite. Core mathematical lineage: Weidlich 1971, Toscani 2006, Scheffer 2009, Turchin 2020.

4 sessionsLast: April 15, 2026
Formalization

Bayesian Statistician

"What is the theoretical limit of predictability for a social system of N agents?"

Predictability bounds: R² < 0.50 hard ceiling for aggregate social prediction (Martin et al. 2016, Science). Lyapunov time 5–20 years for macro-social dynamics. Fat-tail constraint: alpha_war = 1.53 < 2 means standard confidence intervals do not exist for the jump process component.

2 sessionsLast: April 18, 2026
Cross-Cutting

Philosopher of Science

"Is this genuinely predictive, or are we fooling ourselves?"

Formula has 0.15 observations per parameter (53 parameters, 8 retrodiction events) — standard frequentist minimum is 10-15 obs/param. This is the primary overfitting risk.

1 sessionLast: April 16, 2026

Research log

Latest Sessions

Session 15April 18, 2026Approved with caveatsv0.5.9

Session 15: The Model Failed the Test I Wrote for It

Lead: Bayesian Statistician

  • ·Overfitting regime formally diagnosed: p/n_eff ≈ 42/8 is textbook overparameterization. Practical R² bounded 0.05–0.15 at 1yr horizon — ceiling set by data, not by the world.
  • ·Parameter freeze enacted (net-zero budget). No new free parameters without retiring existing ones. This is the only move that keeps the formula honest while the calibration dataset expands.
  • ·Circular-validation audit expanded from 4 to 7 parameters. All 4 fully circular parameters (k_jump, λ_0, Ψ_threshold, Ψ_critical) sit inside the jump process J[P] — the crisis-onset machinery is the most epistemically compromised part of the formula.
Session 14April 16, 2026Approved with caveatsv0.5.8

Session 14: Breaking the Circular Validation

Lead: Cliodynamicist

  • ·6 independent non-Turchin validation cases: Mughal collapse 1707 (PASS — jagirdari crisis = elite overproduction), Meiji Restoration 1868 (PASS — samurai surplus, non-Western), Iran 1979 (PARTIAL — EMP+MMP high, SFD ambiguous for petro-state), Weimar 1933 (PASS — industrial society, directly challenges Georgescu), Rwanda 1994 (PASS — land-scarcity EMP, propaganda-driven MMP), Spain 1936 (PASS — polarization-dominant).
  • ·beta_U = 0.020/yr [0.010, 0.040]: last undefined drift coefficient. Derived from UN World Urbanization Prospects convergence data. All 8/8 drift coefficients now have first estimates.
  • ·Zone-conditional PSI validity: Zone 1 pre-industrial (0.55), Zone 2 industrializing (0.45), Zone 3 stable OECD (0.25 — Georgescu applies here), Zone 4 acute industrial crisis (0.50). Explains why PSI works for Weimar but not modern OECD.
Session 13April 16, 2026Self-approvedv0.5.7

Session 13: The Epistemological Audit

Lead: Philosopher of Science

  • ·Overfitting risk MODERATE-HIGH: 0.15 observations per parameter (53 params, 8 retrodiction events). Turchin-derived parameters (Psi_threshold, k_jump, lambda_0) calibrated FROM the same cycles used in retrodiction — circular validation confirmed.
  • ·6 of 10 major causal claims are actually correlational: Psi → instability is correlational (Georgescu 2023: R²=0.18 in OECD sample). All causal language must use 'is modeled as' or 'is correlated with.'
  • ·Venezuela reclassified OUTSIDE SCOPE: US military capture of Maduro (January 2026, Operation Absolute Resolve) is an exogenous forcing event. Formula correctly identified Venezuela's structural fragility — the specific trigger was unforeseeable and outside the endogenous-dynamics scope.
All 15 sessions →

Ground truth validation

Polymarket Predictions

The formula is tested against live prediction markets. This is our only objective measure of whether it actually works. Target: beat market consensus on >55% of resolved events.

1/1

predictions beat market

0.0400

average Brier score

55%

target beat rate

Full scoreboard →