Map engineering targets onto Barrow's complexity scale alongside the Kardashev scale — and see why Phase 5 computronium is electromagnetically invisible.
John D. Barrow (1998, Impossibility, Oxford UP) proposed a complementary scale to Kardashev's. Where Kardashev measures outward mastery — total power commanded — Barrow's scale measures inward mastery: how deeply a civilization has penetrated the structure of matter itself. The scale descends from macroscopic (Type I) to Planck-scale (Type −∞), with each step representing a different physical regime.
The key divergence from Kardashev: a civilization can increase its Kardashev number without improving its Barrow level (just build more Dyson spheres), but a high Barrow level enables dramatic efficiency gains that make high-K civilizations nearly thermally invisible.
OCS Phase 5 involves compressing computation into Planck-scale micro black holes (kugelblitz). At Barrow −1, essentially all energy is stored in quantum gravitational degrees of freedom rather than being emitted as radiation. The waste heat fraction approaches zero — not because the total power is low, but because the computational substrate has near-100% energy-to-computation efficiency. A K=2.5 civilization at Barrow −1 would emit perhaps ~10²⁵ W as waste heat (10⁻⁶ × total throughput of ~10³¹ W) — vastly less than a Barrow I civilization at the same K which wastes ~10²⁷ W. This falls below JWST detection thresholds for sources at globular cluster distances.
The Kardashev number K is defined here as: K = log₁₀(P) / 10 − 0.6, inverted to give P = 10^(10×(K+0.6)) W. At K=1: P ≈ 10¹⁶ W; K=2: P ≈ 10²⁶ W; K=3: P ≈ 10³⁶ W.
The tool uses approximate efficiency ceilings by Barrow level. These are rough order-of-magnitude estimates, not precise calculations:
Barrow I (bulk thermodynamics): ~0.01% efficiency ceiling (Carnot-limited heat engines)
Barrow II (molecular nanotechnology): ~1% ceiling (reversible molecular computing, near-Landauer-limited)
Barrow III (quantum computing, nuclear-scale): ~50% ceiling (quantum coherent operations)
Barrow IV (vacuum engineering, Casimir): ~99% ceiling
Barrow −1 (Planck-scale, kugelblitz): ~99.9999% (approaching Bekenstein-Landauer theoretical maximum)
JWST's mid-infrared sensitivity (MIRI) can detect thermal emission from sources at globular cluster distances (~5 kpc) down to roughly ~10²⁴ W equivalent isotropic luminosity. This is the value used as the "JWST limit" in this tool. A civilization radiating more than this amount would leave a detectable waste-heat signature; below it, detection is not feasible with current instruments.