Modeling Human–AI Survival with Feedback and Entropy Tools

Arturo Ortiz-Tapia, Universidad Abierta y a Distancia de México

#WolframTechConf

ABSTRACT

This talk introduces mathematical feedback models for sustainable human–AI coexistence. Using entropy, energy, and Pareto metrics, it demonstrates how regulation and measurable signals can maintain stability and prevent runaway dominance in complex AI systems.

Motivation & Oversight Limits

Aim: robust coexistence of Humans and AI via interpretable feedback.
Limits: exact verification is constrained (Gödel / Halting). We regulate with measurable proxies.

∃ φ ∈ Th(S): S ⊬ φ   (incompleteness)
¬∃ A ∈ A_AI : A(x) decides all x ∈ Σ*   (halting)
⇒ use entropy/energy signals + regulation to bound drift.

Regulated tri-species dynamics

Let x(t)=Humans, y(t)=AI, z(t)=Regulator. A regulated Lotka–Volterra form:

dx/dt=r x (1-x/K)-(a x y)/(1+b x)-m x z
dy/dt=(a x y)/(1+b x)-d y-α y z
dz/dt=γ y-β z
r,K,a,b,d,α,m,γ,β>0

Saturation (a x y)/(1+ b x) avoids blow-up; z moderates both x,y and responds to y.

Deterministic population time series

Deterministic trajectories under nominal parameters.

The presence of a generalized regulator leads to sustained coexistence between humans and AI agents, preventing collapse or runaway dominance.

3D spiral phase portrait

Three-dimensional phase space trajectory of the regulated system: Human vs AI vs Regulator.

All trajectories spiral inward toward a stable region.

Phase portrait: Human vs AI

Phase portrait showing Human vs AI dynamics.

The trajectories exhibit an inward spiral behavior, indicating dissipative dynamics and convergence toward a bounded attractor.
In presence of the regulator, the system tends to equilibrium rather than extinction (cf. Peitgen et al., 2004).
A similar inward-spiraling convergence is observed in the other pairwise projections (Human–Regulator and AI–Regulator).

Outcome distribution across initial conditions

3D histogram of simulation outcomes across varying initial human and AI seed populations.

Each vertical bar represents results from 100 Monte Carlo trials of the stochastic ruin model.
Green bars denote human survival and red bars extinction.

Under this regulatory scheme, 71% of runs ended in sustained human survival, indicating that continued human agency is statistically favored.

Analytical analysis confirms that the triadic system is globally bounded and asymptotically stable under positive parameters r,K,a,b,d,α,m,γ,β.

Entropy dynamics and regulatory trigger

Rolling feedback entropy H_feedback(t) tracks the diversity of AI feedback types within a moving window.
Peaks near t≈4 and t≈10–12 reach H≈2.0, reflecting maximal diversity; drops toward H_min=1.0 indicate reduced variability and possible feedback drift.

The regulatory logic applies a binary signal S(t)=1 if H_feedback(t)<H_min, otherwise 0.
An intervention is triggered when the cumulative sum over a window exceeds τ, flagging a persistent entropy deficit.

Sustained plateaus above H_min denote healthy diversity, whereas prolonged drops mark semantic narrowing and activate corrective feedback (e.g. interpretability prompting or entropy injection).

Energy usage divergence (AI vs Humans)

The plot shows the simulated energy-consumption difference ΔE(t)=E_AI(t)-E_H(t), with a regulatory threshold ε_E=0.5 (dashed line).
Excursions where ΔE(t)>ε_E represent potential misalignment events or adversarial dynamics.

Although this scenario is fully synthetic—no real infrastructure or metering data are involved—it illustrates how threshold-based regulation could detect abnormal energy dominance by AI systems.

The approach parallels anomaly detection in smart-grid monitoring and supports entropy-aware policy design: regulation based on measurable divergence rather than speculative intent.

Pareto frontier and cooperative drift

The plot shows the time evolution of the cooperative index P_Pareto(t)=|P|/t, where P denotes the set of Pareto-optimal strategies (those nondominated in the (U_H,U_AI) utility space).

A regulatory flag is raised when P_Pareto(t)<θ for θ=0.5 over a tolerance window, i.e. when cooperative strategy selection drops below half.

Despite ample cooperative opportunities, simulations show a consistent downward drift—an emergent tendency toward dominated or zero-sum behavior unless cooperation is actively reinforced.

This mirrors Chamberlain’s framework: adversarial drift can arise not from malice, but from neutral optimization dynamics.

Hence, P_Pareto(t) offers a micro-level diagnostic for regulatory activation and long-term coexistence stability.

Summary of regulatory trigger operators

Each operator provides a quantitative signal for regulatory activation: entropy captures semantic diversity, energy flags physical imbalance, and Pareto drift monitors cooperative stability. Together, they form a minimal diagnostic set for adaptive human–AI coexistence.

Research, Data, Code & Research Identifiers

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Full simulation framework and source code are available on GitHub:
https://github.com/aortizt/AIregulator

Text data used for the semantic and ideological WordCloud analysis are archived on Zenodo:
https://doi.org/10.5281/zenodo.15485922

Complete paper and theoretical background are available on ResearchGate:
https://www.researchgate.net/publication/392529514_Mathematics_of_Infinite_Survival_Regulatory_Models_for_Human-AI_Coexistence

All repositories are cross-linked for citation and reproducibility.