Chapter II — Tracking Orders of Embodiment

Axiom 2: Physical technologies scale logistically, but the mid-phase approximates a logarithmic curve.

In Aschenbrenner's compute world, each "Order of Magnitude (OOM)" of compute delivered a discontinuous capability leap. In robotics, we can define Orders of Embodiment (OOE) or its normalized equivalent, Embodied Productivity Index (EPI).

Plot the growth of robot-hours, unit deployments, and capability per robot — the mid-band of the logistic curve (when deployment accelerates but before saturation) appears linear on a log scale. That log-linear window is the pseudo-OOM regime of robotics.

Evidence

• China installed >50% of global industrial robots in 2024 (IFR 2024 data: 290,000 new units).
• Robot density in Chinese manufacturing has doubled since 2018, now 470 robots per 10,000 workers.
• Humanoid companies such as Unitree, UBTECH, and AgiBot are scaling 20–40% annually.
• The U.S. lags, adding ~40,000–50,000 units per year, constrained by energy, financing, and regulation.

Mathematical Framing

EPIₜ = (Units)ₜ × (Utilization)ₜ × (Capability Factor)ₜ

log₁₀(EPIₜ) = a + bt

where b = "orders per year." A b = 0.2 implies 1.6× productivity growth per year — fast enough to feel exponential, slow enough to remain governed by physical bottlenecks.

Next: Chapter III — Inflection Point: The Race to the Time Bank