When will androids outnumber humans?

Abstract

Humanoid robots are increasingly discussed not only as machines but also as a potential technological population. We develop a nonlinear population-dynamical framework to examine their possible diffusion relative to humans, without assuming that large-scale adoption or numerical crossover is inevitable. The human population $H(t)$ is calibrated to the United Nations World Population Prospects 2024 median trajectory. The android population $A(t)$ is represented through the normalized stock $a=A/A_s$. A conventional, human-organized manufacturing and adoption channel is calibrated to a conditional scenario spanning approximately $10^4$ humanoids in 2025 to $10^9$ in 2050 and follows $\dot a=(q_M+r_Ma)\exp(K_Ma^γ)$. We separately introduce a hypothetical autonomous channel in which installed androids contribute materially to producing additional androids. Under the minimal canonical TZ closure, the corresponding production--feedback number is $\mathcal{P}(a)=(r_A/δ_A)\exp(K_Ra)$, where $r_A$ is the gross robot-mediated production coefficient, $δ_A$ the retirement rate, and $K_R$ the autonomous feedback parameter. This channel is locally self-amplifying if and only if $\mathcal{P}>1$, whereas numerical human--android parity, $A=H$, is a separate cumulative condition. Global uncertainty analysis shows that crossover dates remain strongly scenario-dependent, while the production--feedback threshold is more robust. An extreme early-autonomy stress test can produce parity by 2050, but this represents a conditional dynamical boundary rather than a technological forecast.