© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

6.5.7 Global Hypsithermal Limit

Finally, it is possible to derive a limit to the total planetary active nanorobot mass by considering the global energy balance. Total solar insolation received at the Earth's surface is ~1.75 x 10¹⁷ watts (I_Earth ~ 1370 W/m² + 0.4% at normal incidence⁸⁸⁷). Global energy consumption by mankind reached an estimated 1.2 x 10¹³ watts (~0.02 W/m²) in 1998. This latter figure may also be regarded as the total heat dissipation of all human technological civilization worldwide, as distinct from the ~10¹² watt metabolic output of the global human biomass. The evidence for global warming remains controversial,⁸⁸⁷ but it is clear that as the waste heat from human-built machinery continues to grow, the climate will begin to change. Technological heat plumes from asphalt-covered major cities already have demonstrable impact on local weather and thermal patterns.

Leaving aside all considerations of changing concentrations of various atmospheric components (e.g., CO₂, H₂O, O₃), one might ask at what point anthropogenic energy releases could begin to seriously affect the global energy balance. (Climatologists sometimes call this the "hypsithermal limit.") Global warming data remain inconclusive but certainly suggest that the present ~10¹³ watts may lie within an order of magnitude of an important threshold. The power dissipation of all terrestrial vegetation is ~10¹⁴ watts,* and it is well-known that such vegetation plays a major role in the planetary energy equation. Climatologists have speculated that an anthropogenic release of ~2 x 10¹⁵ watts (~1% solar insolation) might cause the polar icecaps to melt. A high upper limit is provided by Venus, which receives ~3.3 x 10¹⁷ watts at its cloudtops, producing a surface temperature of ~700 K and a hellish ~100 atm sulfurous atmosphere -- despite its close geological and size similarity to Earth. As a fairly liberal estimate,^3100,3101 the maximum hypsithermal limit for Earth is taken to be ~10¹⁵ watts.

* Global photosynthetic fixation of CO₂ by plants is ~3.85 x 10¹⁴ kg CO₂/yr, ~46% by ocean flora;¹⁷²⁰ CO₂ fixation requires ~794 zJ/molecule (Eqn. 6.16) or ~1.1 x 10⁷ J/kg CO₂, giving a global vegetative total of ~1.4 x 10¹⁴ watts.

The hypsithermal ecological limit in turn imposes a maximum power limit on the entire future global mass of active nanomachinery or "active nanomass." Assuming the typical power density of active nanorobots is ~10⁷ W/m³, the hypsithermal limit implies a natural worldwide population limit of ~10⁸ m³ of active functioning nanorobots, or ~10¹¹ kg at normal densities. Assuming the worldwide human population stabilizes near ~10¹⁰ people in the 21st century and assuming a uniform distribution of nanotechnology, the above population limit would correspond to a per capita allocation of ~10 kg of active continuously-functioning nanorobotry, or ~10¹⁶ active nanorobots per person (assuming 1 micron³ nanorobots developing ~10 pW each, and ignoring nonactive devices held in inventory).* Whether a ~10-liter per capita allocation (~100 KW/person) is sufficient for all medical, manufacturing, transportation and other speculative purposes is a matter of debate.

* Note that a global population limit of ~10²⁶ 10-pW nanorobots represents only ~100 moles of active devices; for 1000-pW devices (~10⁹ W/m³ power density), the upper population limit is only ~1 mole of 1-micron³ active nanorobots worldwide. Facile talk of controlling localized "mole quantities" of nanodevices is thus highly misleading.

The hypsithermal active nanorobot population limit cannot be defeated by heroic artifices of planetary engineering such as giant Earth-orbiting sunscreens or planetary-scale heat pumps, which would devastate global photosynthetic activity or climate while not significantly reducing thermal energy density at the Earth's surface. Likewise, significantly reducing the atmospheric concentration of the most important natural greenhouse gases, especially CO₂ and H₂O, on a worldwide basis is not possible if the present ecology is to remain essentially undisturbed, but even the complete elimination of such gases would raise the hypsithermal limit by at most a factor of 10-20. Specifically, if Earth had no atmosphere at all, then to maintain the global mean surface temperature at its current value of T_Earth ~ 288 K,³⁰⁹⁷ an additional nanorobogenic power of P_noatm ~ p R_Earth² (4 s T_Earth⁴ - I_Earth) ~ 2 x 10¹⁶ watts could be released at the Earth's surface, where R_Earth = 6.37 x 10⁶ m (radius of Earth) and s = 5.67 x 10^-8 W/m²-K⁴ (Stefan-Boltzmann constant). Still more unrealistically, if Earth's surface were an atmosphere-free black body surrounded by a perfect mirror (e.g., albedo = 1.00, vs. ~0.31 for natural Earth), an additional nanorobogenic power release (underneath the mirrored barrier) of P_mirror <~ 4 p R_Earth² (s T_Earth⁴ - I_geol) ~ 2 x 10¹⁷ watts would allow maintenance of the current mean global surface temperature T_Earth; I_geol = 0.05 W/m²,³¹²³ the mean geological heat flow at Earth's surface due to radioactive decay (e.g., U²³⁸, K⁴⁰) in the crust. Reductions in nanorobot waste heat made possible by low-dissipative molecular manufacturing and reversible computing may be offset by popular insistence on adherence to a more conservative global limit, perhaps ~10¹³ watts (today's level), to better preserve the terrestrial habitat. Consistent with long-term ecological maintenance the hypsithermal limit ultimately can only be avoided by continuing human technological progress in space, which seems an excellent idea in any case.

Last updated on 18 February 2003