make no preparation. We have trouble enough controlling viruses and Some Limits to Global Ecophagy fruit flies. by Biovorous Nanoreplicators, with Among the cognoscenti of nanotechnology, this threat has become known as the "gray goo problem." Though masses of uncontrolled Public Policy Recommendations replicators need not be gray or gooey, the term "gray goo" emphasizes that replicators able to obliterate life might be less inspiring than a single species of crabgrass. They might be superior in an evolutionary Robert A. Freitas Jr. sense, but this need not make them valuable. Research Scientist, Zyvex LLC , 1321 North Plano Road, The gray goo threat makes one thing perfectly clear: We cannot afford Richardson, TX 75081 © April 2000 Robert A. Freitas Jr. certain kinds of accidents with replicating assemblers. http://www.foresight.org/nano/Ecophagy.html Gray goo would surely be a depressing ending to our human adventure on Earth, far worse than mere fire or ice, and one that could Abstract stem from a simple laboratory accident.

The maximum rate of global ecophagy by biovorous self- Lederberg [ 3] notes that the microbial world is evolving at a replicating nanorobots is fundamentally restricted by the fast pace, and suggests that our survival may depend upon replicative strategy employed; by the maximum dispersal embracing a "more microbial point of view." The emergence velocity of mobile replicators; by operational energy and of new infectious agents such as HIV and Ebola demonstrates chemical element requirements; by the homeostatic resistance that we have as yet little knowledge of how natural or of biological ecologies to ecophagy; by ecophagic thermal technological disruptions to the environment might trigger pollution limits (ETPL); and most importantly by our mutations in known organisms or unknown extant organisms determination and readiness to stop them. Assuming current [81 ], producing a limited form of "green goo" [ 92 ]. and foreseeable energy-dissipative designs requiring ~100 MJ/kg for chemical transformations (most likely for biovorous However, biovorous nanorobots capable of comprehensive systems), ecophagy that proceeds slowly enough to add ~4°C ecophagy will not be easy to build and their design will to global warming (near the current threshold for immediate require exquisite attention to numerous complex specifications climatological detection) will require ~20 months to run to and operational challenges. Such biovores can emerge only completion; faster ecophagic devices run hotter, allowing after a lengthy period of purposeful focused effort, or as a quicker detection by policing authorities. All ecophagic result of deliberate experiments aimed at creating general- scenarios examined appear to permit early detection by purpose artificial life, perhaps by employing genetic vigilant monitoring, thus enabling rapid deployment of algorithms, and are highly unlikely to arise solely by accident. effective defensive instrumentalities. 2.0 The Ecophagic Threat 1.0 Introduction Classical molecular nanotechnology [ 2, 4] envisions Recent discussions [ 1] of the possible dangers posed by future nanomachines predominantly composed of carbon-rich technologies such as artificial intelligence, genetic engineering diamondoid materials. Other useful nanochemistries might and molecular nanotechnology have made it clear that an employ aluminum-rich sapphire (Al 2O3) materials, boron-rich intensive theoretical analysis of the major classes of (BN) or titanium-rich (TiC) materials, and the like. TiC has environmental risks of molecular nanotechnology (MNT) is one the highest possible operating temperatures allowed for warranted. No systematic assessment of the risks and commonplace materials (m.p. ~3410°K [ 5]), and while limitations of MNT-based technologies has yet been diamond can scratch TiC, TiC can be used to melt diamond. attempted. This paper represents a first effort to begin this analytical process in a quantitative fashion. However, atoms of Al, Ti and B are far more abundant in the Earth's crust (81,300 ppm, 4400 ppm and 3 ppm, respectively Perhaps the earliest-recognized and best-known danger of [5]) than in biomass, e.g., the human body (0.1 ppm, 0 ppm, molecular nanotechnology is the risk that self-replicating and 0.03 ppm [ 6]), reducing the direct threat of ecophagy by nanorobots capable of functioning autonomously in the natural such systems ( Section 8.3 ). On the other hand, carbon is a environment could quickly convert that natural environment thousand times less abundant in crustal rocks (320 ppm, (e.g., "biomass") into replicas of themselves (e.g., mostly carbonates) than in the biosphere (~230,000 ppm). "nanomass") on a global basis, a scenario usually referred to as the "gray goo problem" but perhaps more properly termed Furthermore, conversion of the lithosphere into "global ecophagy." nanomachinery is not a primary concern because ordinary rocks typically contain relatively scarce sources of energy. For As Drexler first warned in Engines of Creation [ 2]: instance, natural radioactive isotopes present in crustal rocks vary greatly as a function of the geological composition and "Plants" with "leaves" no more efficient than today's solar cells could history of a region, but generally range from 0.15-1.40 out-compete real plants, crowding the biosphere with an inedible mGy/yr [ 7], giving a raw power density of 0.28-2.6 ×10 −7 foliage. Tough omnivorous "bacteria" could out-compete real bacteria: W/m 3 assuming crustal rocks of approximately mean They could spread like blowing pollen, replicate swiftly, and reduce the 3 biosphere to dust in a matter of days. Dangerous replicators could terrestrial density (5522 kg/m [ 5]). This is quite insufficient easily be too tough, small, and rapidly spreading to stop - at least if we to power nanorobots capable of significant activities; current nanomachine designs typically require power densities on the extracted can no longer be alive but would instead become order of 10 5-10 9 W/m 3 to achieve effective results [ 6]. lifeless chemical sludge. (Biological systems typically operate at 10 2-10 6 W/m 3 [ 6].) Solar power is not readily available below the surface, and the 3.0 Exponential Replication Rate mean geothermal heat flow is only 0.05 W/m 2 at the surface [6], just a tiny fraction of solar insolation. Subsurface pressure Ignoring thermal pollution considerations for the moment and temperature rise with depth in Earth's crust at the rates of (Section 6.0 ), in theory an optimally designed and k 0.47 atm/meter and q ~ 0.014°K/meter [ 8], exceeding geographically uniformly distributed population of replibots maximum reasonable nanorobot operating limits of 100,000 could increase the mass of their own population at the expense atm and 2000°K at depths of ~210 km and ~120 km well into of the biosphere, via self-replication, according to the simple the upper mantle below a ~50 km crust; however, geothermal 2 −6 3 relation [ 19 ]: power density is only Dp ~ Kt kq kCarnot / ∆T ~ 1-4 ×10 W/m taking thermal conductivity K ~ 2-5 W/m-K for common t M M e(t/τ) (1) crustal minerals [ 9] and ∆T ~ 1°C giving Carnot efficiency repl = init kCarnot = ∆T / T ~ 0.3% at T = 300°K. for maximum exponential growth, where t is elapsed time Hypothesized crustal abiotic highly-reduced petroleum (sec), τ is generation cycle or replication time (sec), Minit (kg) reserves [ 16 ] probably could not energize significant replicator is initial nanorobot mass at time t = 0, and Mrepl (kg) is the nanomass growth due to the anoxic environment deep replicator mass at time t, where Mrepl 0.23 Mbio . In order to underground, although potentially large geobacterial achieve this rate, each completed component of the unit populations have been described [ 10 −16 ] and in principle currently being built must be put to full productive use some unusual though highly limited bacterial energy sources immediately, instead of waiting for the final completion of the could also be tapped by nanorobots. For example, some unit. There are a few design configurations where something anaerobic bacteria use metals (instead of oxygen) as electron- close to this can be achieved efficiently, but as a practical acceptors [ 13 ], with iron present in minerals such as pyroxene matter and to retain simplicity it will usually be preferable to or olivine being converted to iron in a more oxidized state in await the completion of a unit before pressing it into magnetic minerals such as magnetite and maghemite, and replicative service, a mode of operation called discrete using geochemically produced hydrogen to reduce CO to replication, in which case the exponential term in Eqn. 1 2 (t/τ ) methane [ 11 ]. Underground bacteria in the Antrim Shale should be replaced with 2 discrete -- which, all else equal, deposit produce 1.2 ×10 7 m 3/day of natural gas (methane) by will be a slightly slower function. (Discrete replication can be consuming the 370 MY-old remains of ancient algae [17 ]. faster than pure exponential replication only if τdiscrete < τ Bioremediation experiments have also been done by ln(2).) Replicating populations limited to activity only at the Envirogen and others in which pollution-eating bacteria are perimeter of the expansion wave, or in regions of high replibot purposely injected into the ground to metabolize organic number density, may achieve only polynomial growth rates toxins; in field tests it has proven difficult to get the bacteria to [19 ], which are even slower. move through underground aquifers, because the negatively- charged cells tend to adhere to positively charged iron oxides In order to estimate t = tconv , the time required for total in the soil [ 18 ]. conversion of the biosphere to replibots plus waste sludge, we must first estimate τ. Drexler [ 4] has calculated that a readily- However, the primary ecophagic concern is that runaway envisioned multistage molecular manufacturing system could nanorobotic replicators or "replibots" will convert the entire manufacture its own mass in τ ~ 1000 seconds. However, surface biosphere (the ecology of all living things on the nanoreplicators need not be capable of general purpose surface of the Earth) into alternative or artificial materials of manufacturing, but may be optimized solely for replication of some type -- especially, materials like themselves, e.g., more their own substance. A molecular manipulator designed by self-replicating nanorobots. Since advanced nanorobots might Drexler [ 4] that is suitable for molecular assembly pick-and- be constructed predominantly of carbon-rich diamondoid place operations consists of 4 million atoms excluding support materials [ 4], and since ~12% of all atoms in the human body base, power, control, and other necessary structures, and is (representative of biology generally) are carbon atoms [ 6], or designed to perform ~10 6 atomic-precision molecular pick- ~23% by weight, the global biological carbon inventory may and-place operations per second, assuming arm-tip movement support the self-manufacture of a final mass of replicating at 1 cm/sec over minimal 10-nm arcs each cycle. Freitas [ 6] diamondoid nanorobots on the order of ~0.23 Mbio , where Mbio estimates that a basic autonomous nanoassembler using two is the total global biomass. Drexler manipulator arms and incorporating a simple onboard nanocomputer might require at least ~70 million atoms (~1 Unlike almost any other natural material, biomass can serve gigadalton), suggesting a minimum replication time τ ~ 100 both as a source of carbon and as a source of power for seconds. (The smallest independently viable cells are thought nanomachine replication. Ecophagic nanorobots would regard to have a molecular weight of order ~1 gigadalton, e.g., living things as environmental carbon accumulators, and minimum diameter ~140 nm[ 72 , 73 ].) biomass as a valuable ore to be mined for carbon and energy. Of course, biosystems from which all carbon has been It is difficult to imagine how an ecophagic replicator capable of successfully assimilating natural biomatter of all existing varieties could be much simpler than this. However, it is of digesting only certain limited forms of biological matter possible that molecular manipulators might be slewed at and have very severe operational restrictions including proper speeds up to ~100 cm/sec, perhaps giving τ ~ 1 sec, but at the temperature, pH, and so forth. They are not bio-omnivorous. cost of steeply rising energy dissipation [ 4] which greatly increases waste heat production and system operating 4.0 Dispersal Velocity Limitation temperatures, and reduces nanoreplicator reliability due to larger thermally-excited displacements, thermal damage rates, The expansion of any population of replicating systems is also and phonon-mediated drag [ 4]. For example, a 10-nm force fundamentally restricted by the expansion velocity of the sensor measuring 10 pN at an operating temperature of 300°K outermost envelope which defines the maximum physical has a 0.2% probability of erroneous measurement; this extent or dispersion of the growing population. No population probability jumps to 3% at 500°K and 16% at 1000°K [ 4]. of ecophagic objects can disperse more quickly than its growth Hence, τ ~ 1 sec appears to be a rather aggressive and medium -- in this case, the terrestrial biosphere -- will permit. probably unachievable lower limit. Thus for a two-dimensional growth medium on the surface of a sphere (e.g., the Earth), the time required for complete Table 1. Terrestrial Carbon Sources biospheric conversion starting from a single initial release site Form of Worldwide must be at least the minimum time required for the replibots to Location of the Quantity travel exactly half of a great circle route across the spherical the Carbon Carbon of Carbon surface, since the expanding wavefront of conversion is a 15 moving around the globe in all compass directions Biosphere CHON 1.1 ×10 kg simultaneously. This minimum conversion time may be b 14 Atmosphere CO 2, CH 4 5.2 ×10 kg crudely approximated as: c 16 Hydrosphere CO 2 3.8 ×10 kg d 16 v -1 2 ½ CH 4 1-2 ×10 kg tspread ≥ repl (4 πREarth / N) (2) Lithosphere Petroleum e 1-3 ×10 14 kg f 16 Coal 1-2 ×10 kg assuming tspread >> τ, where the mean planetary radius REarth = 6.37 ×10 6 meters, N is the number of initial replibot release Carbonates 19 g ~1 ×10 kg sites, and v is the maximum nanoreplicator linear dispersal repl velocity. For isolated replibots lacking significant aeromotive capabilities, dispersal velocity will be limited approximately a. estimated carbon inventory in the global biomass to the mean global wind speed, perhaps vrepl ~ 10 m/sec, [20 , 21 ] ignoring the narrow 30-75 m/sec jet streams at 9-16 km b. atmospheric carbon inventory, mostly CO 2 at 362 altitude [ 94 ]. This is also near the maximum feasible velocity ppm [ 22 ] and CH 4 at 1.7 ppm [ 46 ] for nanorobotic flyers operating in the viscous regime, based c. total ocean-dissolved carbon as CO 2, assuming a on maximum attainable endogenous power densities [ 6]. mean concentration of 2300 micromoles CO 2 per kg of seawater [ 26 ] and an ocean mass of 1.36 × 10 21 kg Assuming a single initial release site ( N = 1) and taking vrepl ~ [6] 6 10 m/sec, then tspread ~ 2 ×10 sec. However, a more efficient d. global undersea carbon storage on continental biosphere conversion strategy would incorporate the margins as CH 4 gas hydrates and gas trapped benea th simultaneous release of numerous "seed" replibots distributed [24 ] uniformly throughout the terrestrial biomass, thus reducing the e. Earth's total original underground petroleum required maximum extension of each expanding replication 14 14 endowment was 2-4 × 10 kg, of which ~1 × 10 kg domain from neighboring replibot release sites. Large has already been consumed [ 23 ] numbers of replibots could be transported by high-velocity f. all identified and undiscovered global coal reserves airborne macroscale carrier vehicles to distant sites around the [25 ] world and then released, crudely analogous to a jet aircraft g. assumes 320 ppm C in crustal rocks [ 5] to ~50 km scattering printed leaflets over a civilian area during wartime. depth Nanoreplicator progeny tasked with the conversion of biomass to nanomass within such smaller substrate domains have much less distance to travel to complete their purpose. Minimum ½ Carbon inventory in the global biomass has been estimated as biomass conversion time scales roughly as N , where N is the 1.1 ×10 15 kg ( Table 1 ). Life is ~23% carbon by weight, so the number of independent initial replicator domains, as reflected 15 in Table 2 generated from Eqn. 2 : total global biomass can be estimated as Mbio ~ 5 ×10 kg. Starting from a single 70-million-atom replicator of mass ~1 −18 gigadalton [ 6] or Minit ~ 1.7 ×10 kg, and taking τ ~ 1 sec and 15 Mrepl = 0.23 Mbio ~ 1.2 ×10 kg, then tconv ~ 76 sec. Adopting a more reasonable τ ~ 100 sec, tconv ~ 7600 sec. For comparison, the fastest known replicators found in nature are certain bacteria which have a mean generation time of τ ~ 900-1200 sec (15-20 minutes) [ 27 ]. However, these bacteria are capable the biosphere. For example, a biomass density of ~10 kg/m 2 on land [ 20 , 21 ] typically having ~10 7 J/kg of recoverable Table 2. chemical energy [ 6] implies an available energy density of ~10 8 J/m 2 at the terrestrial surface. By comparison, visible- Minimum Replibot Dispersal Time as a Function of the spectrum sunlight at noon on a cloudless day ( I ~ 100-400 Number of Uniformly-Distributed Replibot Release Sites solar W/m 2 [ 6]) may provide at most ~10 7 J/m 2 over the course of Min. Global Mean Distance an 8-hour work day. Other sources of scavengable energy such Dispersal Time, # of Release Sites Between as radionuclides are much scarcer ( Section 2.0 ). Note that the tspread (N) Neighboring complete combustion in air of a mass of glucose equal to Mbio (for vrepl = 10 15 18 Release Site would consume ~5.3 ×10 kg O 2, only 0.5% of the ~1.1 ×10 m/sec) kg of oxygen contained within Earth's ~21% O 2 atmosphere. 1 2 × 10 7 meters 30 days Hence oxygen-dependent ecophagy will not be oxygen- 10 2 2 × 10 6 meters 3 days limited. 10 4 2 × 10 5 meters 6 hours Interestingly, diamond has the highest known oxidative 10 6 2 × 10 4 meters 40 minutes chemical storage density because it has the highest atom 8 3 10 2 × 10 meters 200 sec number (and bond) density per unit volume. Organic materials 10 10 2 × 10 2 meters 20 sec store less energy per unit volume, from ~3 times less than 10 12 2 × 10 1 meters 2 sec diamond for cholesterol, to ~5 times less for vegetable protein, to ~10-12 times less for amino acids and wood [ 6]. Since replibots must build energy-rich product structures (e.g. This analysis suggests that the limitations on biosphere diamondoid) by consuming relatively energy-poor feedstock conversion rate imposed by dispersal velocity are readily structures (e.g., biomass), it may not be possible for biosphere overcome by employing a sufficient number of release sites, conversion to proceed entirely to completion (e.g., all carbon and do not, by themselves, prohibit ecophagic conversion atoms incorporated into nanorobots) using chemical energy times on the order of ~1000 seconds or less. In principle, very alone, even taking into account the possible energy value of sophisticated biovores could facultatively aggregate into the decarbonified sludge byproduct, though such unused macroscale assemblages to escape the viscous flight regime, carbon may enter the atmosphere as CO 2 and will still be lost theoretically permitting aerodynamic or even suborbital flight to the biosphere. velocities up to 100-1000 m/sec. Replicators incapable of aerial transport will experience significantly longer dispersal The speed of biospheric conversion can also be limited by the times. abundances of chemical elements available in the environment for conversion into nanomass, as compared to the relative In practical surface deployments, major distribution quantities of each element that are required by the nanorobot nonuniformities will exist because some areas have for replication. (In replicator engineering, this is the "materials significantly larger carbon inventories than others [ 28 ]. For closure" issue [ 19 ]; in chemistry, it is called "stoichiometry.") example, a map of the global annual net primary production In the gray goo scenario, nanorobot replication occurs on the (NPP) of photosynthetically fixed carbon on land shows NPP 2 Earth's surface, so any elements which are in short supply in ranging from 0.1-1.5 kg/m -yr of carbon, with 25% of the land the biosphere might alternatively be obtained from nearby surface area without permanent ice supporting an NPP > 0.5 2 2 topsoil or crustal rocks, although this may impose an kg/m -yr and an average of 0.426 kg/m -yr on land [ 21 ]. The additional logistical overhead on replicative processes. Hence oceans, which cover ~70% of Earth's surface and show carbon 2 only the concentration of the most abundant of these two fixation activity averaging only 0.14 kg/m -yr [ 21 ], contain a sources may act as a significant limit to replication speed. mere 0.02% of the entire planetary biomass, compared to Traditional diamondoid nanomachinery designs [ 4] have 99.98% on land. employed 8 primary chemical elements, as summarized in Table 3 (more details in Table 5 ); Table 3 also gives the The uneven geographical distribution of carbon inventories associated biological [ 6] and crustal [ 5] abundances for each [28 ] and solar power availability [ 83 ] along with possible element. element shortages (Tables 3 and 5) may produce significant geographical variation in replication rates. A detailed analysis of such variation is beyond the scope of this paper but likely would place upper limits on replication speed in many environments.

5.0 Energy and Materials Requirements Limitations

The need for energy is another fundamental limit on the speed at which biospheric conversion can take place. During ecophagy, the richest source of energy is likely to be chemical energy derived from the assimilation of biomolecules found in tire rubber and asphalt tar binder; cars, trucks and airplanes roll on roads and tarmacs worldwide. If the ~4 million miles of paved roads in the U.S. [ 80 ] represent ~25% of the global Table 3. 13 Chemical Element Usages by Weight in Classical total, then road asphalt mass worldwide is ~3 ×10 kg, or M Diamondoid Nanorobot Designs Compared to ~0.6% bio ; the global rubber tire population of ~10 billion Biological and Terrestrial Crustal Chemical Element tires stockpiled, in use or discarded in scrap heaps [ 80 , 82 ] adds another ~0.003% M . Other vectors with similar Abundances bio properties include cotton, polyester or other uniform textiles % by % by Wt. % by [79 ], insulation on electrical wiring, and paper money. Wt. in Range Chemical in Wt. in Regular monitoring and decontamination procedures may Human of Element Nanorobot Earth's thwart these threats. Body τ Designs Crust ττmult (biology) 6.0 Ecophagic Thermal Pollution Limits (ETPL) 3.95% - O 61.1% 46.6% 1 7.20% A more restrictive limitation on the maximum speed of 0.58% - H 10.01% 0.14% 1 biomass conversion to nanomass is the generation and release 1.35% of process waste heat into the environment during ecophagy. 4.13% - If there are too many nanoreplicators working all at once, the Si 27.7% 1 - 2 52.60% 0.0259% waste heat they generate can begin to warm up the 19.87% - environment. In some cases, the environment could become so C 22.9% 1 - 3 57.71% 0.032% hot that the biospheric conversion process can no longer proceed.

P 0% - 9.43% 0.706% 0 - 13 0.118% In the crude analysis that follows, we assume that after some 3.56% - N 1.30% 3 - 19 number of prior replication cycles, the replibots have 25.19% 0.0046% converted roughly half of the biosphere to nanoreplicator

F 0% - 0.77% 0 - 26 mass. In the next and final replication cycle, the energy 0.00374% 0.030% extractable from the remaining half of the global biomass will 3.65% - 19 - be consumed as each existing nanorobot replicates itself once S 0.197% 7.98% 0.052% 41 more for the last time, thus promptly doubling the existing population and completing the global conversion of biomass into nanomass. Dividing the lowest and highest nanorobot requirement by the highest available environmental abundance gives τmult , the required increase in replication time due to scarcity of a In this case, the total heat energy released at Earth's surface is chemical element required for replication. Inspection of Table Ptotal = Pnano + Psolar , where Pnano is the waste heat generated by 3 reveals that sulfur appears to be in the shortest supply the replibots as they emit Ehalf joules in the last replicative relative to nanorobot requirements (at least for current cycle of duration τlast , with Pnano = Ehalf / τlast , and where the total solar insolation on Earth's cloudless surface that is primitive designs), possibly increasing replication time τ by a 17 factor of up to 41 while the device waits for sufficient sulfur subsequently thermalized is Psolar ~ 1.75 ×10 W. Neglecting atoms to be accumulated from the environment. Other the heat-trapping effects of greenhouse gases and the minor elements possibly in somewhat limited supply include P, N contributions from the geological heat flow at Earth's surface, and F, although the impact of any of these elements on the temperature at the terrestrial surface is given replication time can probably be minimized by judicious approximately by the Stefan-Boltzmann relation: nanorobot composition design choices.

2 4 As a general rule, ecophagic nanorobot replication time is Ptotal = 4 πREarth erσTEarth (3) longer in direct proportion to the extent that nanorobot where er is terrestrial surface emissivity, taken here as 0.97 elemental requirements exceed the availability of the scarcest (e.g. carbon black) to maximize heat emission at the lowest element in the consumable substrate, in comparison to the possible temperature, σ is the Stefan-Boltzmann constant theoretical nanorobot replication time on a perfectly −8 2 4 (5.67 ×10 W/m -K ), and TEarth is the mean surface compositionally-matched substrate [ 19 ]. This phenomenon is temperature of Earth. The minimum last-replication time that commonplace in biology. For instance, it is well-known that will allow a global temperature of TEarth or lower to be phytoplanktonic growth in the open oceans is iron-limited maintained throughout the final conversion cycle is given by: [29 ]. 2 4 τlast = Ehalf / [4 πREarth erσTEarth −Psolar ] (4) The highest near-term risk could come from relatively simple single-behavior replibots whose niche is a high-energy ~ E / [ (2.8 ×10 7) T 4− half Earth substrate of uniform composition which affords a rapid vector (1.75 ×10 17 ) ] for the dispersal of the replicators [ 79 ]. The classic example is What is an appropriate maximum operating temperature limit a future theoretical study. However, near-term for nanoreplicators that must forage for organic substrate in nanochemistries are unlikely to be significantly more efficient order to replicate? The softening point for sapphire, an oft- than natural enzyme chemistries, which have been evolving mentioned substitute building material for diamond because of for efficiency over eons; the terrestrial biosphere fixes ~1.2 its high strength, high-temperature tolerance, and inability to ×10 14 kg/yr of biomass carbon [ 21 ] with a ~1.4 ×10 14 watt burn in oxygen, is 2070°K [ 30 ], probably near the upper limit energy input [ 6], or Ediss ~ 38 MJ/kg of carbon. in any reasonable ecophagic nanorobot design scenario especially given the seriously negative impact of higher Using Eqn. 4 , the minimum last-replication time can be temperatures on nanorobot reliability and functionality calculated for various plausible values of Ediss , wherein the (Section 3.0 ). The combustion temperature of diamond in air mean terrestrial temperature will not exceed the chosen value is usually given as 870-1070°K [ 31 ]. of TEarth during ecophagy, as given in Table 4 :

However, such elevated surface temperatures, while perhaps Table 4. acceptable for diamondoid nanomachines in some Minimum Last-Cycle Replication Time for Ecophagic circumstances, will immediately volatize and incinerate most Nanorobots as a of the natural organic feedstock upon which the Function of Replication Energy Efficiency and the nanoreplicators must feed. The minimum ignition point of Resulting Global Temperature wood, paper, or diesel fuel in air has been given as low as Min. Last-Cycle Replication ~500°K [ 68 ], and glucose caramelizes [ 6] at 433°K -- Mean Terrestrial Time τττ (sec) for E = caramelization is not oxidation but rather is a decomposition Temperature last diss reaction that includes polymerizations and covalent 0.1 1.0 10. 100 (TEarth ) bondmaking that could render this substrate material MJ/kg MJ/kg MJ/kg MJ/kg somewhat less accessible to the replibots. A still lower 281°K ∞ ∞ ∞ ∞ temperature threshold is the boiling point of water at 373°K; 4 5 6 7 above this temperature, living things will boil, thus denying 285°K 5 × 10 5 × 10 5 × 10 5 × 10 4 5 6 7 ecophagic nanoreplicators access to solution-based chemical 300°K 1 × 10 1 × 10 1 × 10 1 × 10 processes at normal atmospheric pressures, which could be an 320°K 4 × 10 3 4 × 10 4 4 × 10 5 4 × 10 6 important restriction. 373°K 1 × 10 3 1 × 10 4 1 × 10 5 1 × 10 6 400°K 9 × 10 2 9 × 10 3 9 × 10 4 9 × 10 5 The waste heat energy released globally in the last replicative 500°K 3 × 10 2 3 × 10 3 3 × 10 4 3 × 10 5 cycle may be estimated as Ehalf (q Dbio ) Mbio , where Dbio is 2 × 10 1 the energy density of the organic feedstock material and q is 1000°K 2 × 10 2 2 × 10 3 2 × 10 4 the energy conversion ratio for its transformation into * 0 1 nanomass. For example, Dbio = 16 MJ/kg for glucose, 17 1 × 10 1 × 10 2000°K 1 × 10 2 1 × 10 3 MJ/kg for vegetable protein, 18 MJ/kg for animal protein, 19 * * MJ/kg for wood, and 39 MJ/kg for fats [ 6]. However, these 0 1 3 × 3 × 3 × 10 3 × 10 figures refer to the energy content of the organic feedstock, 5000°K * * 10 −2 * 10 −1 * not to the energy that must be consumed (and the waste heat * subsequently thermalized) in order to build a kilogram of Actual last-cycle replication time limited to exponential τ ~ nanomass. Drexler [ 4] estimates that the typical energy 100 sec ( Section 3.0 ). dissipation caused by chemical transformations involving carbon-rich materials will be Ediss = ( q Dbio ) ~ 100 MJ/kg of final product using readily-envisioned irreversible methods in Setting aside Merkle's conjecture, Table 4 suggests that if systems where low energy dissipation is not a primary design phenomenally efficient reversible molecular manufacturing objective. This figure corresponds roughly to the strongest techniques become available -- e.g., Ediss ~ 0.1 MJ/kg -- the covalent bond energies (e.g., 1190 zJ/bond for C=C, 1327 final replicative cycle of global ecophagy could proceed as zJ/bond for C=O, and 1594 zJ/bond for C ≡C [ 4]), and is quickly as ~1000 seconds while just avoiding incinerating the roughly of the same order as the thermodynamic heat of organic feedstock or boiling environmental water. However, formation of diamond from CO 2(g), ~33 MJ/kg [ 5]. there currently exist no known designs which would be capable of achieving such highly energy-efficient Drexler [ 4] claims that energy dissipation may in theory be as nanoassembly operations. low as Ediss ~ 0.1 MJ/kg "if one assumes the development of a set of mechanochemical processes capable of transforming More probably, highly dissipative molecular manufacturing feedstock molecules into complex product structures using designs are likely to be implemented during the early and only reliable, nearly reversible steps." 0.1 MJ/kg of diamond intermediate years of molecular nanotechnology development. corresponds roughly to the minimum thermal noise at room Such designs are also likely to be necessary for the very temperature (e.g., kT ~ 4 zJ/atom at 298°K). R. Merkle [ 32 ] complex machines needed to implement biovorous replication also conjectures that near-zero energy dissipation is in given the enormous variety of chemically diverse natural principle possible in certain special circumstances, a biological substrates. Assuming current and foreseeable possibility that should be investigated in the present context in energy-dissipative designs requiring ~100 MJ/kg for chemical transformations (most likely for biovorous systems), complete materials (e.g. wood, rubber, etc.) is ~2 MJ/m 3-K [ 6], or ~800 ecophagy that proceeds slowly enough to add ~4°C to global J/kg-K for the biomass/nanomass aggregate as dry mass or up warming (near the current threshold for immediate to 3200 J/kg-K assuming 70% water content. Taking the climatological detection) will require ~20 months to run to higher figure, the total heat capacity of the biomass/nanomass 19 completion. Faster ecophagic devices will run hotter, allowing aggregate is Cbn ~ 3200 J/kg-K × Mbio = 2 ×10 J/K. Adding quicker detection by policing authorities. Qwaste to this aggregate would raise its temperature by ∆T ~ Qwaste / Cbn ~ 5,000ºK. The conversion of biomass to nanomass may proceed according to Eqn. 1 up to the ecophagic thermal pollution limit Similarly, air conduction is unlikely to significantly reduce the (ETPL) whereupon the specified maximum global temperature ETPL limits. Waste energy can be absorbed by atmospheric 18 21 TEarth is attained, after which the replication time must heat capacity (5.27 ×10 kg [ 6] at 988 J/kg-K [ 6] = 5 ×10 approximately double after each population doubling, J/K) only if said heat energy is delivered to the atmosphere ultimately reaching τlast in the final doubling, as described by and thoroughly mixed via conduction, convection, or radiative Eqn. 4 . Total time spent in the ETPL-limited regime is ~ 2 transfer. But the thermal conductivity ( Kt) of air is very poor. τlast . For example, taking τ = 100 sec, TEarth = 300°K, and Ediss Consider a layer of air H meters thick and area A, with ~ 100 MJ/kg, the transition to the ETPL regime occurs when temperature differential ∆T on opposite faces, with power flow 10 total global nanomass reaches ~5 ×10 kg, or only 0.001% of through the layer of P = Kt A∆T / H = Qwaste / tburn , where total global biomass, and the last ~17 population doublings power is generated by consuming the ecosphere in a time tburn , 7 remain to be completed over a time span of ~2 τlast = 2 ×10 so the temperature differential across the layer is ∆T = Qwaste H sec (~7 months). This is also the optimum strategy for an / ( Kt At burn ). With a thin layer of replibots coating the foliage ecophagic population that is attempting to evade premature on Earth's surface, generating heat only on the "skin" of the detection by maintaining a low thermal emissions profile. biosphere, there will be a nonconvective stagnant layer of air Constant ecological surveillance for any evidence of trapped for long periods near the surface that is poorly mixed ecophagic activity is an appropriate policing measure to by winds. In weather modeling this viscous sublayer, called provide adequate early warning to the existence of this threat. the roughness parameter, may be ~0.01-300 cm thick [ 84 -86 ] (e.g., 0.01 cm over water surface, 0.1 cm over short grain, 10 Note further that the presence of natural and anthropogenic cm over prairie grass, 100 cm over grain crops [ 85 ]), and greenhouse gases in the Earth's atmosphere will amplify any sometimes is taken as ~10% of the height of the obstacle [ 87 ]. 23 heating effects, helping to make ecophagic activities more Assuming H ~ 1 cm layer and taking Qwaste = 10 J, Kt = 2.5 immediately visible in its earlier stages. (In theory, a large ×10 -2 W/m-K for air [ 6], A = 5.10 ×10 14 m 2 for Earth, then ∆T 7 4 enough replibot population could actively manage terrestrial ~ 7 ×10 / tburn . Thus, consuming Mbio in tburn = 10 sec albedo or global greenhouse gas concentrations, but these nominally produces a temperature differential across the 1 cm activities would themselves generate still more waste heat.) layer of ∆T ~ 7000ºK (and violates our nonconvection Additionally, using the actual current mean value of er = 0.69 assumption); assuming tburn = 6 months, then ∆T ~ 4ºK, for terrestrial emissivity in Eqns. 3 and 4, rather than the much detectable using current orbital surveillance assets given a higher value of er = 0.97 for carbon black assumed in normal tropospheric thermal gradient of 0.006-0.009ºK/m calculating Table 4 , the last-cycle time τlast increases by [88 ]. (Vertical temperature gradients below 0.010ºK/m are another ~40%, giving still more time for defensive considered subadiabatic, producing downward buoyancy instrumentalities to be brought to bear on the situation. forces [ 89 ].) These crude estimates provide an approximate indication of the magnitudes involved, but the details of Assuming the surface biomass is compositionally similar to convective vertical mixing and its possible meteorological consequences during ecophagy are beyond the scope of this wood ( Dbio ~ 19 MJ/kg), prompt consumption (e.g., paper and should be investigated further. combustion) of the entire biosphere would release Qwaste = 23 Mbio Dbio ~ 10 J of energy. The combined heat capacity of planetary oceans (1.36 ×10 21 kg [ 6] at 4200 J/kg-K [ 6] = 6 7.0 Homeostatic Resistance to Ecophagy ×10 24 J/K) and land (~4 ×10 20 kg/km crustal landmass at, e.g., 23 25 833 J/kg-K for silica [ 90 ] = 3 ×10 J/km-K) is ~10 J/K, so in Over long time periods, natural ecosystems are believed to principle Qwaste , ideally distributed, could be absorbed with a have a nearly balanced carbon budget, with photosynthetic negligible rise in global temperature, ~0.01ºK -- although even uptake equal to respiratory release [ 33 ]. From the ecological a slight rise in ocean temperature could increase mean perspective, the insertion of carbon-absorbing artificial worldwide humidity, greatly amplifying global warming devices into the environment represents a new sink in the because water vapor is the most effective greenhouse gas homeostatic global carbon cycle, in addition to the natural [91 ]. However, in the instant scenario, the replibots are carbon sinks such as forests [ 34 , 35 ]. Most of terrestrial assumed to be in intimate contact with the biomass which they biomass consists of plants, especially trees, though nearly half are consuming -- not with the vast volumes of sea or land. Air of all biomass may consist of bacteria, mostly in soils (up to is an excellent insulator (see below), and the thermal ~10 15 cells/m 3) and subsurface sediments and rocks down to conductivity of wood is ~4 times higher than for air, so ~3 km depth [ 12 , 38 ]; there are ~5 ×10 30 bacteria on Earth replication waste heat energy will be conducted primarily into [39 ]. Conversion of living plant biomass to diamondoid the nanorobot population and the proximate biomass that is nanomass by nanoreplicators thus may reduce the ability of being consumed. The heat capacity of diamond and organic the surviving plant population to remove carbon dioxide from the atmosphere. Unless carbon dioxide levels in the subsequent colonization of the land-based carbon-rich ecology atmosphere are directly regulated by the active robotic by a large and hungry seabed-grown replicator population is nanomass, CO 2 levels will begin to rise, which in turn may the "gray plankton" scenario. (Phytoplankton, 1-200 microns increase the growth rate of plants. In a few experimental in size, are the particles most responsible for the variable studies [ 40 ], elevated CO 2 has been shown to stimulate plant optical properties of oceanic water because of the strong growth at least temporarily, even under serious nutrient absorption of these cells in the blue and red portions of the shortage, although one experiment [ 41 ] challenges this optical spectrum [ 37 ].) supposition. If slow-moving nanoreplicators consume biomass only very slowly, the consumed biomass may be regenerated The gray plankton replicator waste heat signature is readily as new plant growth is stimulated worldwide. detected at an early stage. The temperature of most of the ocean is near ~4°C -- for example, ~1.6°C at 3627 m on the What is the minimum ecophagic biomass removal rate floor of Monterey Bay [ 44 ]. Typical ocean column thermal necessary to overcome the resulting carbon-sequestration gradients are ~0.02°K/m in the top 300 m (1-30 atm) and response of the natural ecology? One study [ 20 ] found that ~0.006°K/m from 300-1000 m depth (30-100 atm) [ 44 ]. A deforestation in the low latitudes during 1990 resulted in forest near-seafloor water temperature change of ∆T = 1°K over a area expansion and growth in mid- and high-latitude forest depth range of L = 100 m would be clearly distinguishable that sequestered ~7 ×10 11 kg of carbon (e.g., creating ~3 ×10 12 from natural variations even using contemporary kg of extra biomass) in one year. Estimates of unrealized instrumentation [ 44 ], and would evidence an increased seabed 2 global forest carbon conservation and sequestration potential power release of Irepl ~ Kt ( ∆T / L) ~ 0.005 W/m , taking 12 suggest a biologic capability of 1-3 ×10 kg/yr (e.g., 4-13 thermal conductivity as Kt ~ 0.5 W/m-K for seawater at 4°C. 12 ×10 kg/yr of biomass) for more than a century [ 20 ]. Global Thus the threshold for seafloor replibot detectability, assuming 12 2 14 2 oceans are believed to absorb ~2 ×10 kg/yr of global seabed area is Aseabed ~ (70%) 4 π REarth = 3.6 ×10 m , 12 12 anthropogenically-produced carbon, creating ~9 ×10 kg of is Pmin = Irepl Aseabed ~ 2 ×10 watts worldwide or a global new biomass per year [ 20 ]. This gives a worldwide carbon 6 replibot population of mass Mmin ~ Pmin τ / Ediss ~ 20 ×10 kg sink of ~5 ×10 12 kg/yr of carbon [ 42 ] and thus a global 13 assuming Ediss ~ 100 MJ/kg and τ = 1000 sec. (Faster biomass recovery of at least ~2 ×10 kg/yr. The upper limit is replicators are detectable at lower population masses.) Thus probably closer to the global net primary biomass production 14 14 bottom-dwelling gray plankton can be detected before they of ~5 ×10 kg/yr [ 21 ]. (Indeed, natural variations of ~10 kg −9 14 have consumed more than 10 of the total oceanic abiotic of atmospheric carbon (equivalent to ~6 ×10 kg of biomass) carbon supply. were recorded over a ~600-year period during the last three glaciation cycles [ 43 ].) Thus it appears that a long-term ecophagic biomass removal rate exceeding 0.2-5 ×10 14 kg/yr Direct census sampling of the seafloor may also allow early (~0.4%-10%/yr of the global biomass) may be necessary to detection, although nanorobotic samplers will have to contend overpower the natural ecological restorative forces. with a significant number of false targets in the oceanic environment. These false targets may include 0.1 micron small colloids (~7 ×10 14 m −3) and viruses (~3 ×10 13 m −3), 0.2-0.3 8.0 Additional Scenarios micron heterotrophic bacteria (~10 12 m −3), 0.3 micron large colloids (~10 13 m −3), 1 micron cyanobacteria (~10 10 m −3), 2-3 Four related scenarios which may lead indirectly to global 8 −3 micron small phytoplankton (~10 m ), larger phytoplankton ecophagy have been identified and are described below. In all (e.g., 10 micron cells ~10 6 m −3), and zooplankton (e.g., 50 cases, early detection appears feasible with advance 3 −3 preparation, and adequate defenses are readily conceived micron cells ~10 m ) [ 36 -38 ]. At the minimum detectable M 6 using molecular nanotechnologies of comparable global mass of min = 20 ×10 kg estimated above, the number density of gray plankton on the seabed floor is Ngp ~ Mmin / sophistication. 7 −2 (Aseabed mgp ) ~ 2 ×10 m , assuming ~1 micron gray plankton replicators each of mass m ~ 3 ×10 −15 kg. In this scenario, the 8.1 Gray Plankton gp bottommost 1 mm of the ocean column above the seabed

16 would contain roughly equal numbers of > ~1-micron natural The existence of 1-2 ×10 kg [ 24 ] of global undersea carbon cells and ~1-micron artificial bottom-dwelling gray plankton storage on continental margins as CH 4 clathrates and a like 16 devices. If not largely confined to the sea floor during most of amount (3.8 ×10 kg) of seawater-dissolved carbon as CO 2 their replication cycle, the natural cell/device ratio could represent a carbon inventory more than an order of magnitude increase by many orders of magnitude, requiring a more larger than in the global biomass ( Section 3.0 ). Methane and diligent census effort. Census-taking nanorobots can CO 2 can in principle be combined to form free carbon and alternatively be used to identify, disable, knapsack or destroy water, plus 0.5 MJ/kg C of free energy. (Some researchers are the gray plankton devices. studying the possibility of reducing greenhouse gas accumulations by storing liquid [ 44 ] or solid [ 45 ] CO on the 2 8.2 Gray Dust (Aerovores) ocean floor, which could potentially enable seabed replibots to more easily metabolize methane sources.) Oxygen could also be imported from the surface in pressurized microtanks via Traditional diamondoid nanomachinery designs [ 4] have buoyancy transport, with the conversion of carbon clathrates employed 8 primary chemical elements, as detailed in Table 5 to nanomass taking place on the seabed below. The along with the associated atmospheric abundances [ 46 ] of 3 each element. (Silicon is present in air as particulate dust (molecules/m ), where aatm = atmospheric fractional 23 which may be taken as ~28% Si for crustal rock [ 5], with a abundance, TSTP = 273.15°K, NA = 6.023 ×10 global average dust concentration of ~0.0025 mg/m 3). The molecules/mole (Avogadro's number), and molar volume at −3 3 requirement for elements that are relatively rare in the STP is Vmolar = 22.4141 ×10 m /mole of an ideal gas. The atmosphere greatly constrains the potential nanomass and replication time τ = Mnano / Mcurrent , where Mnano = 3 3 growth rate of airborne replicators. However, note that at least (4/3) πρaelement Rnano , taking ρ ~ 2000 kg/m as nanorobot one of the classical designs exceeds 91% CHON by weight. density and aelement as the fraction of nanorobot mass Although it would be very difficult, it is at least theoretically comprised of a given element. Hence: possible that replicators could be constructed almost solely of CHON, in which case such devices could replicate relatively rapidly using only atmospheric resources, powered by τ = [( Nencounter ρVmolar aelemnt Rnano ) / (3 f aatm TSTP NA)] ½ (6) sunlight. A worldwide blanket of airborne replicating dust or [( πT) / (2 kmgas )] (sec) "aerovores" that blots out all sunlight has been called the "gray dust" scenario [ 47 ]. (There have already been numerous Taking Rnano = 1 micron and allocating each aelement for the experimental aerial releases of recombinant bacteria [ 48 ].) hypothetical CHON replicator as indicated in the second column of Table 6 gives the values of τ shown at far right in Table 5. Table 6 . The limiting elements are H and C, but C has the Element Usages by Weight in Classical Diamondoid strongest impact on replication time, requiring a τ ~ 12,300

Nanorobot Designs sec. Since τ scales as Rnano , reducing Rnano to 100 nm reduces τ Compared to Atmospheric Element Abundances to ~1230 sec for this device. (Mechanical precompression and Fine Neon Total sortation [ 6] of gas molecules might reduce τ by up to an order Chemical Differential Motion Gas Atmospheric of magnitude but may impose partially offsetting internal Element Gear Controller Pump Abundance volume utilization inefficiencies.). N 25.19% 3.56% 5.91% 7.81 × 10 −1 O 7.20% 6.66% 3.95% 2.1-2.4 × 10 −1 Table 6. Replication Times of Airborne CHON Replicators C 57.71% 24.84% 19.87% −5 9.87 × 10 as Restricted Solely by Chemical Element Abundances −5 H 1.35% 2.05% 0.58% 1-300 × 10 Used Main Source Chemical Source Replication in Source Molecule Element Abundance Time CHON 91.45% 37.11% 30.31% >1 × 10 −5 Device Gas Mass m a a gas (τ) element atm (kg) Si 4.13% 52.20% 52.60% ~5 × 10 −10 −10 4.6 × S 3.65% 7.98% 7.66% N 28% N2 78.1% −26 0.9 sec ~5 × 10 10 −14 F 0.77% 0% 0% ~3 × 10 5.3 × O 8% O 21.0% 0.9 sec P 0% 2.71% 9.43% ~1 × 10 −20 2 10 −26 Total: 100.00% 100.00% 100.00% 1 7.3 × C 62% CO 0.0099% 12,300 sec 2 10 −26 Two independent constraints on gray dust replication speed 0.001- 3.0 × H 2% H O 20-6130 sec are materials and energy availability, and both methods 2 0.3% 10 −26 suggest that τ ~ 10,000 sec for 1-micron replicators and ~1000 sec for 0.1-micron replicators. The analyses are as follows. Second, the solar energy flux into the nanorobot, assuming that a fraction f of its surface is photosensitive with energy First, the mass current M through the surface of a spherical 2 curr conversion efficiency ε, is Pnano = εIsolar f π Rnano . The energy nanorobot of radius R is equal to the number of gas nano required to build a nanorobot is Enano ~ Mnano Ediss , hence the molecules/sec that collide with the fraction f ~ 10% of the replication time is τ = Enano / Pnano , or: nanorobot surface that consists of binding sites for those molecules, times the mass per gas molecule mgas , divided by the number of collisions required for binding to occur, or τ = (4 ρEdiss Rnano ) / (3 f εIsolar ) (sec) (7) Nencounter ~ 100 [ 6]; that is: 3 Taking ρ = 2000 kg/m , Ediss ~ 100 MJ/kg, f = 50%, ε = 10%, 2 2 Mcurrent = (4 πRnano fc gas / Nencounter ) (2 kTm gas / and Isolar = 100-400 W/m , then for Rnano = 1 micron, τ ~ ½ (5) π) (kg/sec) 11,000-53,000 sec; for Rnano = 100 nm, τ = 1100-5300 sec. where k = 1.381 ×10 −23 J/molecule-K (Boltzmann's constant) Since replication of an airborne CHON replibot is primarily carbon-limited, in theory the entire global atmospheric carbon and T ~ 300°K is ambient temperature in kelvins. The 14 mass of ~5.2 ×10 kg C is available for conversion into Mgd = concentration of gas is cgas = aatm TSTP NA / ( Vmolar T) 14 2 8.4 ×10 kg of CHON nanomass, assuming a 62% carbon πRnano qytlife D0exp(-4πkxd / λ), where qy is quantum yield content by weight ( Table 6 ). However, because the machines (bonds cleaved / photons absorbed), tlife is mean time to are solar powered, the active population of gray dust failure, and kx is extinction coefficient. kx ~ 2.26 for graphite nanorobots is restricted to one optical depth of such devices. at 280 nm [ 50 ], a 2250 kg/m 3 semimetal that is probably the −4 −1 To a very crude first approximation (e.g., ignoring most UV-absorptive CHON shield material. qy = 10 to 10 contributions from scattered and reflected photons), one for CHON polymers [ 51 ] and various proteins, viruses and optical depth occurs when the cumulative cross-sectional area phages [ 52 ]; following Drexler [ 4], we adopt qy ~ 0.01 here of the nanorobot population equals the surface area of Earth, (the exact choice is not critical to our conclusions). From Eqn. 10 so the maximum total mass of continuously active CHON 7, τ ~ cτRnano , where cτ ~ 10 sec/m. Taking tlife = τ nτ, where airborne nanorobots is: nτ is the number of offspring constructed before replibot failure, and assuming that Ncleave ≥ 1 implies device failure [ 4], 2 Mtotal ~ (16 π / 3) ρ Rnano REarth (kg) (8) then: 12 = 1.4 ×10 kg for Rnano = 1 micron 11 = 3.7 ×10 kg for Rnano = 275 nm (Rcore + d) ≤Rnano ≤ [ Ncleave (exp(4 πkxd / λ)) / 1/3 (9) 11 (πqynτ cτD0)] = 1.4 ×10 kg for Rnano = 100 nm

Once the expanding nanorobot population reaches one optical for replibots that produce nτ offspring before failing. The depth (requiring ~0.2% of all atmospheric carbon, or ~3 number of generations needed to replicate one optical depth of months of current anthropogenic airborne carbon releases), the nanorobots worldwide, starting from a single device, is nτ = replication rate of the gray dust ceases to grow exponentially ln( Mtotal / Minit ) = 65-60 for Rnano = 0.1-1 microns. Taking nτ ~ and becomes essentially constant -- a phenomenon which may 64, Eqn. 9 defines the smallest gray dust replibot as Rnano ~275 −16 be called the "opacity brake effect." (One optical depth of nm (mass ~ 1.7 ×10 kg) with a d ~ 215 nm thick graphite uniformly distributed Rnano = 275 nm aerovores represents a UV shield assuming Ncleave = 1. The smallest replibot that can 8 -3 particle number density of ~5 ×10 m .) After the opacity replicate only once before it fails (e.g., nτ = 1) has Rnano ~ 230 brake point has been reached, a constant nanomass production nm with a d ~ 170 nm shield taking Ncleave = 1, or Rnano ~ 175 8 rate of Mtotal /τ ~ 1.4 ×10 kg/sec ensues until exhaustion of the nm with a d ~ 115 nm shield taking Ncleave = 100 for more limiting atmospheric carbon resource. Current instrumentation robust devices. can detect ~1% variations in the solar constant, so the limit for early bolometric detection is probably ~1% Mtotal , when From Eqns. 1 and 8, and neglecting dispersal velocity ~0.002% of atmospheric carbon has been converted to limitations ( Section 4.0 ) the minimum possible time to reach nanomass. some fraction fopac of global atmospheric opacity is:

Dust monitors in late 20th-century wafer-fab clean rooms t = τ ln(4 f R 2 / R 2) (sec) (10) regularly measure dust densities of ~10 particles/m3 at 0.5 opac opac Earth nano microns and larger [ 49 ], potentially allowing detection as early −8 For airborne CHON replibots with R = 275 nm and τ ~ as <10 Mtotal if more highly discriminating monitors can be nano developed. If the replibots settle out on the planetary surface 2750 sec, 1% of opacity is reached in topac ~ 1.85 days, 100% and continue replicating there ( Section 8.3 ), they could opacity in 2.0 days, leaving a response time of ~3.5 hours deprive the ecology of needed sunlight without darkening the between first detection at 1% opacity and complete opacity at sky, but their effects (e.g., a fine gray dust covering everything 100%. If uniformly distributed throughout the atmosphere, the 3 on the surface) would also be detectable far sooner than the dust density at 100% opacity would amount to ~0.085 mg/m for 275-nm nanorobots, about equal to the typical ~0.05 1% Mtotal point. mg/m 3 dust density normally found in the air of most industrialized Western cities [ 69 ]. Since replication rate and opacity per unit nanomass vary inversely with Rnano , the most efficient gray dust replibot tasked with opacifying the atmosphere as quickly as possible After 100% opacity is reached, another tend = τ ( Mgd −Mtotal ) / will have the minimum possible size. (Replication time varies Mtotal = 72 days would be required to convert the remaining with thickness for a sheetlike nanorobot configuration.) The atmospheric carbon resource into nanomass. However, post- minimum replibot size is driven by UV radiation damage rates opacity the gray dust replication rate is no longer on nanomachinery [ 4]. Consider the smallest possible exponentiating so the defensive nanorobots can quickly catch −18 up. replicator with mass Minit = 1.7 ×10 kg ( Section 3.0 ); constructed as a spherical shape of density ρ = 2000 kg/m 3, the radius of this core replicator is Rcore ~ 59 nm. The core is The most efficient cleanup strategy appears to be the use of surrounded by a radiation shield of thickness d and density ~ ρ. air-dropped non-self-replicating nanorobots equipped with The most dangerous is UV-B at λ ~ 280 nm which will prehensile microdragnets. Consider a planetwide dragnet conservatively be taken as ~5 W/m 2 intensity near ground comprised of a square mesh of fibers, with mesh aperture size 18 2 l , mesh fibers of thickness d , and total dragnet area A level [ 4], equivalent to D0 = 7 ×10 photons/m -sec. The mesh fiber net 2 number of bonds cleaved inside the nanorobot is Ncleave = covering Earth's entire surface area AEarth = 4 πREarth = Anet . 2 ½ Minimum fiber thickness is dfiber ( pair lmesh / 4 σfiber ) , where Each defensive nanorobot requires ~66 nN of motive force pair 2 atm is the maximum air pressure resisting movement and ~6600 pW of onboard power to overcome drag loss [ 6] on of the net through the air and fiber failure strength is very the ~5.3 cm length of dragnet fiber that it is passing through 10 2 conservatively taken as σfiber ~ 10 N/m for carbon the air at 0.1 m/sec. This power is provided by a rear- 2 nanotubes. For lmesh 460 nm (smallest possible gray dust deployed, 30% efficient, 55 micron , ~10 nm thick solar collector film that stows in a 0.55 micron 3 volume before replibot, see above), dfiber 1 nm. Simple geometry gives the total volume of required square-grid dragnet as: deployment and adds only ~45 pW to drag power after deployment. When fully deployed, the defensive fleet

2 ½ 3 contributes <0.5% additional atmospheric opacity, and clears Vdragnet ~ 2 dfiber [( Anet ) + ( Anet / lmesh )] (m ) (11) air for an energy cost of ~5.8 J/m 3 of contaminated atmosphere, per pass. Defensive nanorobot locomotion in the 14 2 Taking Anet = AEarth = 5.10 ×10 m , lmesh = 460 nm and dfiber = viscous flight regime may be provided by screw drives, 3 1 nm, then Vdragnet = 2200 m . This dragnet may be carried viscous anchoring via the prehensile dragnet, or other means aloft by a fleet of Nbot = Vdragnet / fvVbot spherical defensive [6]. nanorobots, each of which uses some fraction fv of its internal storage volume to hold a piece of the dragnet, where The Stokes settling velocity [ 6] in air is ~240 micron/sec for 3 individual defensive nanorobot volume is Vbot = (4/3) π Rnano . Rnano = 1 micron, ~20 micron/sec for Rnano = 275 nm and ~5 3 Taking fv = 5% and Rnano = 0.62 micron, Vbot = 1 micron and micron/sec for Rnano = 100 nm, giving 10-km passive fall times 22 Nbot = 4.4 ×10 defensive nanorobots of total mass ~ Vbot ρNbot (in still atmosphere) of 1.3 years, 16 years and 67 years, = 8.8 ×10 7 kg (of which ~4.4 ×10 6 kg is dragnet). Thus a respectively. single 88-kg payload of non-self-replicating defensive 6 nanorobots launched from each of 10 deployment sites Alternative airborne or ground-based atmospheric filtration worldwide (mean site separation ~23 km, ~one per town) to an configurations that could permit more rapid filtering are altitude just above the gray dust replibots can deploy an Earth- readily envisioned. For example, since drag power varies as covering net, which then descends through the air, selectively the square of the velocity, then by increasing mesh volume filtering out the gray dust replibots. The time required for this 10,000-fold while decreasing airflow velocity 100-fold, total dragnet to sweep the entire atmospheric volume of Earth once drag power remains unchanged but whole-atmosphere 2v is tsweep ~ Vair / (4 πREarth nano ) ~ 24 hours, taking nanorobot turnover proceeds 100-fold faster, e.g., ~15 minutes. aeromotive velocity vnano ~ 0.1 m/sec for power densities appropriate to solar powered nanodevices [ 6] and Vair ~ 4.36 18 3 ×10 m at ~1 atm pressure and room temperature. Possible false targets that may be encountered during the sweep include a There are ~10 18 -10 19 insects on Earth [ 75 -77 ]. The average airborne fungal spores at 10-500 m −3 indoors and 100-1000 −3 −3 insect devotes ~35% of body volume to its respiratory system m outdoors [ 53 ]; bacteria at 0-500 m indoors, 179-1083 [78 ], which is mostly gas-phase diffusional but with some −3 −3 m outdoors [ 53 ], and ~140 m up to ~3 km altitude [ 38 ]; very primitive active ventilation. If average insect volume is and inert dust particles of various sizes peaking in number ~0.6 mm 3 [ 77 ], then the worldwide insect population has ~2 × density near ~20 nm [ 46 ], in concentrations ranging from 10 10 9 m 3 of tracheal air volume which could accumulate ~10 16 −3 7 −3 m in semiconductor fab plant clean rooms up to 2 ×10 m aerovores if insects are exposed to replibot-contaminated air at in quiet country air, 6 ×10 7 m −3 over residential city air, 1.5 a concentration equivalent to ~1% atmospheric opacity. In ×10 8 m −3 in the worst congested downtown city air, and >2.7 this case ~10 -9 of the global aerovore population resides inside ×10 8 m −3 in rooms with smokers present [ 49, 54 ]. Of course, insects (~1 replibot per 1000 insects at 1% opacity), requiring multiple cleansing sweeps may be required, insect a and bird b careful quarantine or inspection and release protocols for management and biocompatibility protocols must be devised, insects passing through the dragnet. exterior surfaces must be appropriately hydrophobic to avoid providing condensation nuclei for cloud and fog formation, b There are ~300 billion birds on Earth [ 70 ]. The average bird and so forth. devotes 20% of body volume to its respiratory system [ 71 ], mostly unidirectional airflow unlikely to permanently trap The total machine volume of one optical depth of 275-nm gray gray dust, but ~20% of the bird respiratory volume consists of dust replibots is 1.9 ×10 8 m 3, making an average cleanup tidally exchanged air in 8-9 anterior and posterior air sacs, and requirement of only ~4500 micron 3 of targets per defensive air spaces in the bones [ 71 ]. Assuming dead air in birds nanorobot. A spherical knapsack comprised of additional represents 38% of tidal volume as in humans [ 6], and that the mesh material having an enclosed volume of 4500 micron 3 average bird is ~500 cm 3 in volume, then the worldwide bird adds only 11% to the onboard mesh storage requirement. Each population has ~2 × 10 6 m 3 of respiratory dead air which could defensive nanorobot deploys a (110 micron) 2 ~ 12,100 accumulate ~10 13 aerovores if the birds are breathing replibot- micron 2 section of the planetwide dragnet. In theory, if this contaminated air at a concentration equivalent to ~1% section were curved into a huge spherical knapsack, it would atmospheric opacity. In this case ~10 -12 of the global aerovore make a storage volume of 125,000 micron 3 -- enough to hold population resides inside bird respiratory systems (~40 the equivalent of ~28 optical depths of gray dust replibots replibots per bird at 1% opacity), necessitating specialized during passage through locally dense clouds of target airborne quarantine or inspection and release protocols for birds nanoreplicators. passing through the dragnet. Under similar exposure, ~7 × 10 13 aerovores (~3 × 10 -12 of the total) could reside in all More difficult scenarios involve ecophagic attacks that are human lungs worldwide, or ~10,000 aerovores/person. launched not to convert biomass to nanomass, but rather primarily to destroy biomass. The optimal malicious 8.3 Gray Lichens ecophagic attack strategy appears to involve a two-phase process. In the first phase, initial seed replibots are widely distributed in the vicinity of the target biomass, replicating Colonies of symbiotic algae and fungi known as lichens with maximum stealth up to some critical population size by (which some have called a form of sub-aerial biofilm) are among the first plants to grow on bare stone, helping in soil consuming local environmental substrate to build nanomass. formation by slowly etching the rock [ 55 ]. Lithobiontic In the second phase, the now-large replibot population ceases replication and exclusively undertakes its primary destructive microbial communities such as crustose saxicolous lichens purpose. More generally, this strategy may be described as penetrate mineral surfaces up to depths of 1 cm using a Build/Destroy. complex dissolution, selective transport, and recrystallization process sometimes termed "biological weathering" [ 56 ]. Colonies of epilithic (living on rock surfaces) microscopic During the Build phase of the malicious "badbots," and bacteria produce a 10 micron thick patina on desert rocks assuming technological equivalence, defensive "goodbots" (called "desert varnish" [ 57 ]) consisting of trace amounts of enjoy at least three important tactical advantages over their Mn and Fe oxides that help to provide protection from heat adversaries: and UV radiation [ 57 -59 ]. In theory, replicating nanorobots could be made almost entirely of nondiamondoid materials 1. Preparation -- defensive agencies can manufacture and including noncarbon chemical elements found in great position in advance overwhelming quantities of (ideally, abundance in rock such as silicon, aluminum, iron, titanium non-self-replicating) defensive instrumentalities, e.g., and oxygen ( Section 2 ). The subsequent ecophagic destruction goodbots, which can immediately be deployed at the first of land-based biology by a maliciously programmed sign of trouble, with minimal additional risk to the noncarbon epilithic replicator population that has grown into a environment; significant nanomass is the "gray lichen" scenario. 2. Efficiency -- while badbots must simultaneously replicate and defend themselves against attack (either actively or The growth rate of gray lichens on the surface of the Earth by maintaining stealth), goodbots may concentrate will be primarily energy-limited, not materials-limited. While exclusively on attacking badbots (e.g., because of their it is true that chemolithotrophic microorganisms such as large numerical superiority in an early deployment) and Thiobacillus ferrooxidans use reduced iron and sulfur thus enjoy lower operational overhead and higher compounds for their energy source [ 60 -62 ], and that other efficiency in achieving their purpose, all else equal; and chemolithotrophic bacteria can metabolize inorganic carbon 3. Leverage -- in terms of materials, energy, time and sophistication, fewer resources are generally required to (e.g., assimilating CO 2 from carbonate rock) using a pathway similar to green plants [ 63 ], such energy sources appear to be confine, disable, or destroy a complex machine than are far less plentiful than ambient sunlight because most rocks are required to build or replicate the same complex machine already fully oxidized. (For example, the oxidation of Fe ++ to from scratch (e.g., one small bomb can destroy a large Fe +++ by chemolithotrophs liberates only 0.75 MJ/kg [ 64 ], as bomb-making factory; one small missile can sink a large compared to ~16 MJ/kg for the combustion of glucose in ship). oxygen [ 6].) Assuming that up to 400 W/m 2 in the visible spectrum is harvested with 30% efficiency for 8 hours/day However, once the badbots enter their Destroy phase, only the over the entire landmass of Earth, the 6 ×10 15 watts first advantage of the defenders (i.e., preparation) remains 7 theoretically available could produce at most ~6 ×10 kg/sec fully effective. Of course, a total mass Mgoodbots of of mineral nanomass taking Ediss ~ 100 MJ/kg as before. Even nonreplicating defensive nanorobots can hold constant a assuming an optimal dispersal pattern, ~2.6 years would be population Mbadbots of self-replicating biovorous nanorobots if required for the growing mineral nanomass to equal the Mgoodbots (tdestroy / τ) Mbadbots , where tdestroy is the time required terrestrial biomass (~5 ×10 15 kg; Section 3 ), whereupon the for a goodbot to find and permanently restrain, disable or top ~1 cm of Earth's entire continental land area would have destroy a badbot (which has a replication time τ); usually, been converted to nanomass. tdestroy << τ.

Continuous direct census sampling of the Earth's land surfaces Nevertheless it is most advantageous to engage a malicious will almost certainly allow early detection, since mineralogical ecophagic threat while it is still in its Build phase. This nanorobots should be easily distinguishable from inert rock requires foresight and a commitment to extensive surveillance particles and from organic microbes in the top 3-8 cm of soil, by the defensive authorities. A complete analysis is beyond 13 −3 12 −3 typically 2.1 ×10 m of aerobic bacteria, 5.6 ×10 m of the scope of this paper, but two simple examples will suffice actinomycetes, 5.2 ×10 12 m −3 of anaerobic bacteria, 3.2 ×10 11 to illustrate the level of surveillance required. m−3 fungi, and 6.7 ×10 10 m −3 of algae [ 64 ].

First, consider a population of Nbot replibots that have infested a human body and are about to enter their Destroy phase. 8.4 Malicious Ecophagy These badbots are assumed to be motile spherical nanorobots of radius Rnano , capable of drilling through tissue at velocity vnano ; encountered tissue is destroyed with efficiency ke, and a of global biomass and assuming an average eukaryotic cell 26 mass fraction fdest of the biomass must be destroyed to produce size of 20 microns, there are ~3 ×10 eukaryotic cells on death. The time required to kill is: Earth. If each cell is visited and examined, on average, about once a year with time spent per cell ctime = 100 sec/cell as 19 2 before, this implies a global examination rate of Xcell ~ 10 tkill = fdest Mbody / ( keπρbody Rnano vnano Nbot ) (12) 21 cells/sec and a requirement for Xcell ctime ~ 10 cell-monitoring nanorobots, representing a total worldwide nanomachine 3 where Mbody is body mass and ρbody is mean body density. volume of ~1000 m of 1-micron nanorobots consuming ~10 Power is provided by combustion at conversion efficiency ε of GW (~0.1% total current human global power generation) 10 3 onboard H 2/O 2 fuel (energy density Efuel ~ 4.5 ×10 J/m [ 6]) assuming ~10 pW/device. In this surveillance regime, a ~1 compressed to 10,000 atm, stored in tanks representing some mg infestation of 1-micron badbots in a 3 meter wide, 30 -11 fraction ffuel of nanorobot volume. The power produced is meter tall redwood tree ( fn ~ 10 ) is first detected in ~100 3 Pnano = (4 π / 3) Rnano ffuel Efuel ε / tkill , exhausting the stored fuel millisec -- again, triggering a prompt corrective response. after tkill . Setting this available power Pnano equal to Stokes 2 drag power Pdrag = 6 π ηRnano vnano and substituting for tkill 9.0 Conclusions and Public Policy gives maximum drilling velocity: Recommendations

4 vnano (2 π keρbody ffuel Efuel εNbot Rnano ) / (9 The smallest plausible biovorous nanoreplicator has a (13) molecular weight of ~1 gigadalton and a minimum replication ηfdest Mbody ) time of perhaps ~100 seconds, in theory permitting global ecophagy to be completed in as few as ~10 4 seconds. where η is mean tissue viscosity. The mass fraction of However, such rapid replication creates an immediately badbots that can produce death in a time tkill is fn = Mbadbot / detectable thermal signature enabling effective defensive Mbody , where total badbot mass is Mbadbot = (4/3) π policing instrumentalities to be promptly deployed before 3 ρnano Rnano Nbot and ρnano is nanorobot density. Obtaining Nbot significant damage to the ecology can occur. Such defensive by solving Eqn. 13 for Nbot , then substituting vnano obtained instrumentalities will generate their own thermal pollution from Eqn. 12 , gives: during defensive operations. This should not significantly limit the defense strategy because knapsacking, disabling or f = [(4 f ρ ) / ( k ρ )] [ η / (2 f E εt )] ½ (14) destroying a working nanoreplicator should consume far less n dest nano e body fuel fuel kill energy than is consumed by a nanoreplicator during a single replication cycle, hence such defensive operations are The number of attacking badbots is then: effectively endothermic.

3 Nbot = 3 fnMbody / (4 πρnano Rnano ) (15) Ecophagy that proceeds near the current threshold for immediate climatological detection, adding perhaps ~4°C to global warming, may require ~20 months to run to Taking fdest = 0.1 (10%), ke = 0.5 (50%), ε = 0.5 (50%), ffuel = 3 completion, which is plenty of advance warning to mount an 0.1 (10%), Rnano = 1 micron, ρnano = 2000 kg/m , η ~ 1000 effective defense. kg/m-sec [ 6], and ρbody = Mbody / Vbody where Mbody = 70 kg and 3 body volume Vbody = 0.06 m [ 6], then a kill time tkill = 1 sec -4 12 Ecophagy that progresses slowly enough to evade easy requires fn = 6 ×10 and Nbot = 5 ×10 badbots. However, if the body is monitored continuously such that a whole-body detection by thermal monitoring alone would require many -8 years to run to completion, could still be detected by direct in badbot dose as small as 1 mg can be detected, then fn ~ 10 8 situ surveillance, and may be at least partially offset by (Nbot ~ 10 badbots) and tkill increases dramatically to ~60 years, giving plenty of time for defense. If the potential increased biomass growth rates due to natural homeostatic 14 compensation mechanisms inherent in the terrestrial ecology. victim's body (comprised of Ncell ~10 native and foreign cells [6]) contains a continuously-circulating population NbotM of cell-monitoring nanorobots each requiring ctime ~ 100 sec/cell Ecophagy accomplished indirectly by a replibot population to enter and examine a cell for badbot intruders, and if every pre-grown on nonbiological substrate may be avoided by 5 cell in the body is to be checked once every day ( tbody ~ 10 diligent thermal monitoring and direct census sampling of 11 sec), then NbotM = ctime Ncell / tbody ~ 10 cell-monitors, with relevant terrestrial niches to search for growing, possibly 3 total fleet volume ~ 0.1 cm assuming Rnano = 1 micron. At fn dangerous, pre-ecophagous nanorobot populations. ~ 10 -8, a badbot resides, on average, in one of every 10 6 cells, assuming uniform distribution. The hypothesized monitoring Specific public policy recommendations suggested by the system examines ~10 6 cells every 0.001 sec, so a badbot results of the present analysis include: infection of this magnitude is first detected in ~1 millisec, allowing a massive and immediate "immune" response. 1. an immediate international moratorium on all artificial life experiments implemented as nonbiological hardware. Second, consider the defense of the entire eukaryotic In this context, "artificial life" is defined as autonomous biosphere. Excluding bacteria assumed to represent about half foraging replicators, excluding purely biological implementations (already covered by NIH guidelines [ 65 ] 5. Robert C. Weast, Handbook of Chemistry and Physics, 49th Edition, tacitly accepted worldwide) and also excluding software CRC, Cleveland OH, 1968. simulations which are essential preparatory work and 6. Robert A. Freitas Jr., Nanomedicine, Volume I , Landes Bioscience, should continue. Alternative "inherently safe" replication Georgetown, TX, 1999. See at: http://www.nanomedicine.com . strategies such as the broadcast architecture [ 66 ] are 7. Edward L. Alpen, Radiation Biophysics , Second Edition, Academic already well-known. Press, New York, 1998. 2. continuous comprehensive infrared surveillance of Earth's 8. Walter M. Elsasser, "Earth," Encyclopedia Britannica 7(1963):845-852. surface by geostationary satellites, both to monitor the 9. G. Buntebarth, A. Gliko, "Heat Flow in the Earth's Crust and Mantle," in current biomass inventory and to detect (and then A.S. Marfunin, ed., Advanced Mineralogy, Volume 1: Composition, investigate) any rapidly-developing artificial hotspots. Structure, and Properties of Mineral Matter: Concepts, Results, and This could be an extension of current or proposed Earth- Problems , Springer-Verlag, New York, 1994, pp. 430-435. monitoring systems (e.g., NASA's Earth Observing 10. Karsten Pedersen, "The deep subterranean biosphere," Earth Sci. Rev. System [ 67 ]and disease remote-sensing programs [ 93 ]) 34 (1993):243-260. originally intended to understand and predict global 11. Todd O. Stevens, James P. McKinley, "Lithoautotrophic Microbial warming, changes in land use, and so forth -- initially Ecosystems in Deep Basalt Aquifers," Science 270 (20 October using non-nanoscale technologies. Other methods of 1995):450-454; see also: G. Jeffrey Taylor, "Life Underground," PSR detection are feasible and further research is required to Discoveries, 21 December 1996, at: http://www.soest.hawaii.edu/PSRdiscoveries/Dec96/LifeUnderground.ht identify and properly evaluate the full range of ml . alternatives. 3. initiating a long-term research program designed to 12. Stephen Jay Gould, Life's Grandeur: The Spread of Excellence from Plato to Darwin , Jonathan Cape, 1996. acquire the knowledge and capability needed to counteract ecophagic replicators, including scenario- 13. Bill Cabage, "Digging Deeply," September 1996; see: building and threat analysis with numerical simulations, http://www.ornl.gov/publications/labnotes/aug96/phelps.htm . measure/countermeasure analysis, theory and design of 14. James K. Fredrickson, Tullis C. Onstott, "Microbes Deep Inside the global monitoring systems capable of fast detection and Earth," Sci. Am. 275 (October 1996):68-73. response, IFF (Identification Friend or Foe) 15. Richard Monastersky, "Deep Dwellers: Microbes Thrive Far Below discrimination protocols, and eventually the design of Ground," Science News 151 (29 March 1997):192-193. relevant nanorobotic systemic defensive capabilities and 16. Thomas Gold, The Deep Hot Biosphere , Copernicus Books, 1999; "The infrastructure. A related long-term recommendation is to deep, hot biosphere," Proc. Natl. Acad. Sci. 89 (1992):6045-6049. See initiate a global system of comprehensive in situ also: P.N. Kropotkin, "Degassing of the Earth and the Origin of ecosphere surveillance, potentially including possible Hydrocarbons," Intl. Geol. Rev. 27 (1985):1261-1275. nanorobot activity signatures (e.g. changes in greenhouse 17. Karl Leif Bates, "Michigan's natural gas fields: Blame it on underground gas concentrations), multispectral surface imaging to bacteria," The Detroit News , 12 September 1996; see at: http://www.detnews.com/1996/menu/stories/64795.htm . detect disguised signatures, and direct local nanorobot census sampling on land, sea, and air, as warranted by the 18. JoAnn Gutin, "Making bacteria move," Princeton Weekly Bulletin , 17 pace of development of new MNT capabilities. November 1997; see at: http://www.princeton.edu/pr/pwb/97/1117/1117-dig.html . 19. Robert A. Freitas Jr., William P. 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