The enrichment paradox: critical capability thresholds and irreversible dependency in human-AI symbiosis

Abstract

As artificial intelligence assumes cognitive labor, no quantitative framework predicts when human capability loss becomes catastrophic. We present a two-variable dynamical systems model coupling capability (H) and delegation (D), grounded in three axioms: learning requires capability, practice, and disuse causes forgetting. Calibrated to four domains (education, medicine, navigation, aviation), the model identifies a critical threshold K* approximately 0.85 (scope-dependent; broader AI scope lowers K*) beyond which capability collapses abruptly-the "enrichment paradox." Validated against 15 countries' PISA data (102 points, R^2 = 0.946, 3 parameters, lowest BIC), the model predicts that periodic AI failures improve capability 2.7-fold and that 20% mandatory practice preserves 92% more capability than the simulation baseline (which includes a 5% background AI-failure rate). These findings provide quantitative foundations for AI capability-threshold governance.

Figures (7)

• Figure 1: Parameter estimation across four empirical domains. Model-predicted capability decline (solid curves) versus empirical observations (points with error bars) for A, education (Bastani et al., $\beta = 0.047$/session, 17% decline after 4 sessions), B, medical endoscopy (Budzyn et al., $\beta = 0.02$/week, 21% decline after 12 weeks), C, spatial cognition (Dahmani & Bohbot, $\beta = 0.01$/month, 30% decline over 36 months), and D, aviation (Casner & Schooler, $\beta = 0.002$/month, 38% decline over $\sim$240 months of career-long autopilot exposure). Shaded regions: 95% confidence intervals from ABM ensemble ($n = 50$ replicates).
• Figure 2: Multi-country PISA analysis (15 countries, 102 data points, 3 global parameters). A, Normalized PISA trajectories colored by mean internet adoption (blue: low, red: high). Solid lines: observed; dashed: ODE predictions. High-adoption countries (Finland, Sweden) show steeper declines; low-adoption countries (Indonesia, Turkey) show modest gains. B, Profile likelihood of $\alpha$: single OECD average (red, flat) versus 15-country panel (blue, peaked near the MLE ($\alpha = 0.013$, 95% CI: 0.008--0.038)). Cross-country variation in technology exposure resolves the parameter identifiability problem. C, Predicted versus observed scores across all countries and time points ($R^2 = 0.946$, 3 parameters).
• Figure 3: Model discrimination. A, Four models fitted to PISA mathematics scores (2003--2022). The ODE ($R^2 = 0.9207$, AIC $= -69.2$) outperforms linear ($R^2 = 0.82$), exponential ($R^2 = 0.82$), and logistic ($R^2 = 0.88$) decay models with the same parameter count ($k = 2$). B, Recovery prediction after AI removal: linear, exponential, and logistic models predict symmetric recovery (dashed/dash-dotted), while the ODE predicts near-irreversible stagnation below the saddle point (solid)---the dependent attractor traps capability near zero. C, Equilibrium capability versus AI capability $K$: the ODE uniquely predicts a sharp phase transition at $K^* \sim 0.85$, whereas all three alternatives show smooth, gradual decline.
• Figure 4: Critical threshold and policy space. A, Equilibrium human capability $H$ versus AI capability $K$, showing the critical threshold $K^* \sim 0.85$ (dashed red line) where $|dH/dK|$ is maximized at 12.0 (50 grid points, $K$ from 0.50 to 0.99). Shaded band: interquartile range across 50 ABM replicates. B, Two-dimensional phase diagram of $K$ (x-axis) versus crisis frequency (y-axis). Color encodes equilibrium $H$. Dashed contours mark the $H = 0.5$ boundary. Red triangle: current AI trajectory (high $K$, no crisis planning).
• Figure 5: Operationalizing the capability parameter $K$. A, Mean capability ratio $\bar{K}$ for five frontier AI models over time. The critical threshold $K^* = 0.85$ (dashed red line) was approached by GPT-4 in March 2023. Green shading: safe region ($\bar{K} < K^*$); red shading: dependency-risk region ($\bar{K} \geq K^*$). B, Domain-specific $K$ values across four professional benchmarks, showing that medical and knowledge domains entered the critical region before coding and legal domains.