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Some Limits to Global Ecophagy
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28 February 2001: Thanks to work done by Patrick Macé, "Ecophagy" has been translated into French and can be downloaded in rich text format (288 Kb). |
The maximum rate of global ecophagy by biovorous self-replicating nanorobots is fundamentally restricted by the replicative strategy employed; by the maximum dispersal velocity of mobile replicators; by operational energy and chemical element requirements; by the homeostatic resistance of biological ecologies to ecophagy; by ecophagic thermal pollution limits (ETPL); and most importantly by our determination and readiness to stop them. Assuming current and foreseeable energy-dissipative designs requiring ~100 MJ/kg for chemical transformations (most likely for biovorous systems), ecophagy that proceeds slowly enough to add ~4°C to global warming (near the current threshold for immediate climatological detection) will require ~20 months to run to completion; faster ecophagic devices run hotter, allowing quicker detection by policing authorities. All ecophagic scenarios examined appear to permit early detection by vigilant monitoring, thus enabling rapid deployment of effective defensive instrumentalities.
Recent discussions [1] of the possible dangers posed by future technologies such as artificial intelligence, genetic engineering and molecular nanotechnology have made it clear that an intensive theoretical analysis of the major classes of environmental risks of molecular nanotechnology (MNT) is warranted. No systematic assessment of the risks and limitations of MNT-based technologies has yet been attempted. This paper represents a first effort to begin this analytical process in a quantitative fashion.
Perhaps the earliest-recognized and best-known danger of molecular nanotechnology is the risk that self-replicating nanorobots capable of functioning autonomously in the natural environment could quickly convert that natural environment (e.g., "biomass") into replicas of themselves (e.g., "nanomass") on a global basis, a scenario usually referred to as the "gray goo problem" but perhaps more properly termed "global ecophagy."
As Drexler first warned in Engines of Creation [2]:
"Plants" with "leaves" no more efficient than today's solar cells could out-compete real plants, crowding the biosphere with an inedible foliage. Tough omnivorous "bacteria" could out-compete real bacteria: They could spread like blowing pollen, replicate swiftly, and reduce the biosphere to dust in a matter of days. Dangerous replicators could easily be too tough, small, and rapidly spreading to stop - at least if we make no preparation. We have trouble enough controlling viruses and fruit flies.
Among the cognoscenti of nanotechnology, this threat has become known as the "gray goo problem." Though masses of uncontrolled 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 sense, but this need not make them valuable.
The gray goo threat makes one thing perfectly clear: We cannot afford certain kinds of accidents with replicating assemblers.
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 stem from a simple laboratory accident.
Lederberg [3] notes that the microbial world is evolving at a fast pace, and suggests that our survival may depend upon embracing a "more microbial point of view." The emergence of new infectious agents such as HIV and Ebola demonstrates that we have as yet little knowledge of how natural or technological disruptions to the environment might trigger mutations in known organisms or unknown extant organisms [81], producing a limited form of "green goo" [92].
However, biovorous nanorobots capable of comprehensive ecophagy will not be easy to build and their design will require exquisite attention to numerous complex specifications and operational challenges. Such biovores can emerge only after a lengthy period of purposeful focused effort, or as a result of deliberate experiments aimed at creating general-purpose artificial life, perhaps by employing genetic algorithms, and are highly unlikely to arise solely by accident.
Classical molecular nanotechnology [2, 4] envisions nanomachines predominantly composed of carbon-rich diamondoid materials. Other useful nanochemistries might employ aluminum-rich sapphire (Al2O3) materials, boron-rich (BN) or titanium-rich (TiC) materials, and the like. TiC has one the highest possible operating temperatures allowed for commonplace materials (m.p. ~3410°K [5]), and while diamond can scratch TiC, TiC can be used to melt diamond.
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 [5]) than in biomass, e.g., the human body (0.1 ppm, 0 ppm, and 0.03 ppm [6]), reducing the direct threat of ecophagy by such systems (Section 8.3). On the other hand, carbon is a thousand times less abundant in crustal rocks (320 ppm, mostly carbonates) than in the biosphere (~230,000 ppm).
Furthermore, conversion of the lithosphere into nanomachinery is not a primary concern because ordinary rocks typically contain relatively scarce sources of energy. For instance, natural radioactive isotopes present in crustal rocks vary greatly as a function of the geological composition and history of a region, but generally range from 0.15-1.40 mGy/yr [7], giving a raw power density of 0.28-2.6 ×10-7 W/m3 assuming crustal rocks of approximately mean terrestrial density (5522 kg/m3 [5]). This is quite insufficient to power nanorobots capable of significant activities; current nanomachine designs typically require power densities on the order of 105-109 W/m3 to achieve effective results [6]. (Biological systems typically operate at 102-106 W/m3 [6].) Solar power is not readily available below the surface, and the mean geothermal heat flow is only 0.05 W/m2 at the surface [6], just a tiny fraction of solar insolation. Subsurface pressure and temperature rise with depth in Earth's crust at the rates of 0.47 atm/meter and kq ~ 0.014°K/meter [8], exceeding maximum reasonable nanorobot operating limits of 100,000 atm and 2000°K at depths of ~210 km and ~120 km well into the upper mantle below a ~50 km crust; however, geothermal power density is only Dp ~ Kt kq2kCarnot / DT ~ 1-4 ×10-6 W/m3 taking thermal conductivity Kt ~ 2-5 W/m-K for common crustal minerals [9] and DT ~ 1°C giving Carnot efficiency kCarnot = DT / T ~ 0.3% at T = 300°K.
Hypothesized crustal abiotic highly-reduced petroleum reserves [16] probably could not energize significant replicator nanomass growth due to the anoxic environment deep underground, although potentially large geobacterial populations have been described [10-16] and in principle some unusual though highly limited bacterial energy sources could also be tapped by nanorobots. For example, some anaerobic bacteria use metals (instead of oxygen) as electron-acceptors [13], with iron present in minerals such as pyroxene or olivine being converted to iron in a more oxidized state in magnetic minerals such as magnetite and maghemite, and using geochemically produced hydrogen to reduce CO2 to methane [11]. Underground bacteria in the Antrim Shale deposit produce 1.2 ×107 m3/day of natural gas (methane) by consuming the 370 MY-old remains of ancient algae [17]. Bioremediation experiments have also been done by Envirogen and others in which pollution-eating bacteria are purposely injected into the ground to metabolize organic toxins; in field tests it has proven difficult to get the bacteria to move through underground aquifers, because the negatively-charged cells tend to adhere to positively charged iron oxides in the soil [18].
However, the primary ecophagic concern is that runaway nanorobotic replicators or "replibots" will convert the entire surface biosphere (the ecology of all living things on the surface of the Earth) into alternative or artificial materials of some type -- especially, materials like themselves, e.g., more self-replicating nanorobots. Since advanced nanorobots might be constructed predominantly of carbon-rich diamondoid materials [4], and since ~12% of all atoms in the human body (representative of biology generally) are carbon atoms [6], or ~23% by weight, the global biological carbon inventory may support the self-manufacture of a final mass of replicating diamondoid nanorobots on the order of ~0.23 Mbio, where Mbio is the total global biomass.
Unlike almost any other natural material, biomass can serve both as a source of carbon and as a source of power for nanomachine replication. Ecophagic nanorobots would regard living things as environmental carbon accumulators, and biomass as a valuable ore to be mined for carbon and energy. Of course, biosystems from which all carbon has been extracted can no longer be alive but would instead become lifeless chemical sludge.
Ignoring thermal pollution considerations for the moment (Section 6.0), in theory an optimally designed and geographically uniformly distributed population of replibots could increase the mass of their own population at the expense of the biosphere, via self-replication, according to the simple relation [19]:
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(1)
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for maximum exponential growth, where t is elapsed time (sec), t is generation cycle or replication time (sec), Minit (kg) is initial nanorobot mass at time t = 0, and Mrepl (kg) is the replicator mass at time t, where Mrepl 0.23 Mbio. In order to achieve this rate, each completed component of the unit currently being built must be put to full productive use immediately, instead of waiting for the final completion of the unit. There are a few design configurations where something close to this can be achieved efficiently, but as a practical matter and to retain simplicity it will usually be preferable to await the completion of a unit before pressing it into replicative service, a mode of operation called discrete replication, in which case the exponential term in Eqn. 1 should be replaced with 2(t/tdiscrete) -- which, all else equal, will be a slightly slower function. (Discrete replication can be faster than pure exponential replication only if tdiscrete < t ln(2).) Replicating populations limited to activity only at the perimeter of the expansion wave, or in regions of high replibot number density, may achieve only polynomial growth rates [19], which are even slower.
In order to estimate t = tconv, the time required for total conversion of the biosphere to replibots plus waste sludge, we must first estimate t. Drexler [4] has calculated that a readily-envisioned multistage molecular manufacturing system could manufacture its own mass in t ~ 1000 seconds. However, nanoreplicators need not be capable of general purpose manufacturing, but may be optimized solely for replication of their own substance. A molecular manipulator designed by Drexler [4] that is suitable for molecular assembly pick-and-place operations consists of 4 million atoms excluding support base, power, control, and other necessary structures, and is designed to perform ~106 atomic-precision molecular pick-and-place operations per second, assuming arm-tip movement at 1 cm/sec over minimal 10-nm arcs each cycle. Freitas [6] estimates that a basic autonomous nanoassembler using two Drexler manipulator arms and incorporating a simple onboard nanocomputer might require at least ~70 million atoms (~1 gigadalton), suggesting a minimum replication time t ~ 100 seconds. (The smallest independently viable cells are thought to have a molecular weight of order ~1 gigadalton, e.g., minimum diameter ~140 nm[72, 73].)
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 possible that molecular manipulators might be slewed at speeds up to ~100 cm/sec, perhaps giving t ~ 1 sec, but at the cost of steeply rising energy dissipation [4] which greatly increases waste heat production and system operating temperatures, and reduces nanoreplicator reliability due to larger thermally-excited displacements, thermal damage rates, and phonon-mediated drag [4]. For example, a 10-nm force sensor measuring 10 pN at an operating temperature of 300°K has a 0.2% probability of erroneous measurement; this probability jumps to 3% at 500°K and 16% at 1000°K [4]. Hence, t ~ 1 sec appears to be a rather aggressive and probably unachievable lower limit.
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Location of
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Form of
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Worldwide Quantity
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Carbon inventory in the global biomass has been estimated as 1.1 ×1015
kg (Table 1). Life is ~23% carbon by weight, so the
total global biomass can be estimated as Mbio
~ 5 ×1015 kg. Starting from a single 70-million-atom
replicator of mass ~1 gigadalton [6] or Minit
~ 1.7 ×10-18 kg, and taking
t
~ 1 sec and
The expansion of any population of replicating systems is also fundamentally restricted by the expansion velocity of the outermost envelope which defines the maximum physical extent or dispersion of the growing population. No population of ecophagic objects can disperse more quickly than its growth medium -- in this case, the terrestrial biosphere -- will permit. Thus for a two-dimensional growth medium on the surface of a sphere (e.g., the Earth), the time required for complete biospheric conversion starting from a single initial release site must be at least the minimum time required for the replibots to travel exactly half of a great circle route across the spherical surface, since the expanding wavefront of conversion is moving around the globe in all compass directions simultaneously. This minimum conversion time may be crudely approximated as:
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(2)
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assuming tspread >> t, where the mean planetary radius REarth = 6.37 ×106 meters, N is the number of initial replibot release sites, and vrepl is the maximum nanoreplicator linear dispersal velocity. For isolated replibots lacking significant aeromotive capabilities, dispersal velocity will be limited approximately to the mean global wind speed, perhaps vrepl ~ 10 m/sec, ignoring the narrow 30-75 m/sec jet streams at 9-16 km altitude [94]. This is also near the maximum feasible velocity for nanorobotic flyers operating in the viscous regime, based on maximum attainable endogenous power densities [6].
Assuming a single initial release site (N
= 1) and taking vrepl
~ 10 m/sec, then tspread
~ 2 ×106 sec. However, a more efficient biosphere conversion
strategy would incorporate the simultaneous release of numerous "seed"
replibots distributed uniformly throughout the terrestrial biomass, thus
reducing the required maximum extension of each expanding replication domain
from neighboring replibot release sites. Large numbers of replibots could
be transported by high-velocity airborne macroscale carrier vehicles to
distant sites around the world and then released, crudely analogous to
a jet aircraft scattering printed leaflets over a civilian area during
wartime. 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 biomass conversion time scales
roughly as N½, where
N
is the number of independent initial replicator domains, as reflected in
Table
2 generated from Eqn. 2:
This analysis suggests that the limitations on biosphere conversion rate imposed by dispersal velocity are readily overcome by employing a sufficient number of release sites, and do not, by themselves, prohibit ecophagic conversion times on the order of ~1000 seconds or less. In principle, very sophisticated biovores could facultatively aggregate into macroscale assemblages to escape the viscous flight regime, theoretically permitting aerodynamic or even suborbital flight velocities up to 100-1000 m/sec. Replicators incapable of aerial transport will experience significantly longer dispersal times.
In practical surface deployments, major distribution nonuniformities
will exist because some areas have significantly larger carbon inventories
than others [28]. For example, a map of the global
annual net primary production (NPP) of photosynthetically fixed carbon
on land shows NPP ranging from 0.1-1.5 kg/m2-yr of carbon, with
25% of the land surface area without permanent ice supporting an
The uneven geographical distribution of carbon inventories [28]
and solar power availability [83] along with
possible 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.
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 the biosphere. For example, a biomass density of ~10 kg/m2 on land [20, 21] typically having ~107 J/kg of recoverable chemical energy [6] implies an available energy density of ~108 J/m2 at the terrestrial surface. By comparison, visible-spectrum sunlight at noon on a cloudless day (Isolar ~ 100-400 W/m2 [6]) may provide at most ~107 J/m2 over the course of an 8-hour work day. Other sources of scavengable energy such as radionuclides are much scarcer (Section 2.0). Note that the complete combustion in air of a mass of glucose equal to Mbio would consume ~5.3 ×1015 kg O2, only 0.5% of the ~1.1 ×1018 kg of oxygen contained within Earth's ~21% O2 atmosphere. Hence oxygen-dependent ecophagy will not be oxygen-limited.
Interestingly, diamond has the highest known oxidative chemical storage density because it has the highest atom number (and bond) density per unit volume. Organic materials store less energy per unit volume, from ~3 times less than 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. diamondoid) by consuming relatively energy-poor feedstock structures (e.g., biomass), it may not be possible for biosphere conversion to proceed entirely to completion (e.g., all carbon atoms incorporated into nanorobots) using chemical energy alone, even taking into account the possible energy value of the decarbonified sludge byproduct, though such unused carbon may enter the atmosphere as CO2 and will still be lost to the biosphere.
The speed of biospheric conversion can also be limited by the abundances
of chemical elements available in the environment for conversion into nanomass,
as compared to the relative quantities of each element that are required
by the nanorobot for replication. (In replicator engineering, this is the
"materials closure" issue [19]; in chemistry,
it is called "stoichiometry.") In the gray goo scenario, nanorobot replication
occurs on the Earth's surface, so any elements which are in short supply
in the biosphere might alternatively be obtained from nearby topsoil or
crustal rocks, although this may impose an additional logistical overhead
on replicative processes. Hence only the concentration of the most abundant
of these two sources may act as a significant limit to replication speed.
Traditional diamondoid nanomachinery designs [4]
have employed 8 primary chemical elements, as summarized in Table
3 (more details in Table 5); Table
3 also gives the associated biological [6]
and crustal [5] abundances for each element.
Dividing the lowest and highest nanorobot requirement by the highest available environmental abundance gives tmult, the required increase in replication time due to scarcity of a chemical element required for replication. Inspection of Table 3 reveals that sulfur appears to be in the shortest supply relative to nanorobot requirements (at least for current primitive designs), possibly increasing replication time t by a factor of up to 41 while the device waits for sufficient sulfur atoms to be accumulated from the environment. Other elements possibly in somewhat limited supply include P, N and F, although the impact of any of these elements on replication time can probably be minimized by judicious nanorobot composition design choices.
As a general rule, ecophagic nanorobot replication time is longer in direct proportion to the extent that nanorobot elemental requirements exceed the availability of the scarcest element in the consumable substrate, in comparison to the theoretical nanorobot replication time on a perfectly compositionally-matched substrate [19]. This phenomenon is commonplace in biology. For instance, it is well-known that phytoplanktonic growth in the open oceans is iron-limited [29].
The highest near-term risk could come from relatively simple single-behavior
replibots whose niche is a high-energy substrate of uniform composition
which affords a rapid vector for the dispersal of the replicators [79].
The classic example is 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 total, then road asphalt mass worldwide is
A more restrictive limitation on the maximum speed of biomass conversion to nanomass is the generation and release of process waste heat into the environment during ecophagy. If there are too many nanoreplicators working all at once, the waste heat they generate can begin to warm up the environment. In some cases, the environment could become so hot that the biospheric conversion process can no longer proceed.
In the crude analysis that follows, we assume that after some number of prior replication cycles, the replibots have converted roughly half of the biosphere to nanoreplicator mass. In the next and final replication cycle, the energy extractable from the remaining half of the global biomass will be consumed as each existing nanorobot replicates itself once more for the last time, thus promptly doubling the existing population and completing the global conversion of biomass into nanomass.
In this case, the total heat energy released at Earth's surface is Ptotal
= Pnano + Psolar,
where Pnano is the waste
heat generated by the replibots as they emit Ehalf
joules in the last replicative cycle of duration tlast,
with Pnano = Ehalf
/ tlast,
and where the total solar insolation on Earth's cloudless surface that
is subsequently thermalized is Psolar
~ 1.75 ×1017 W. Neglecting the heat-trapping effects of
greenhouse gases and the minor contributions from the geological heat flow
at Earth's surface, the temperature at the terrestrial surface is given
approximately by the Stefan-Boltzmann relation:
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(3)
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where er is terrestrial surface emissivity, taken here as 0.97 (e.g. carbon black) to maximize heat emission at the lowest possible temperature, s is the Stefan-Boltzmann constant (5.67 ×10-8 W/m2-K4), and TEarth is the mean surface temperature of Earth. The minimum last-replication time that will allow a global temperature of TEarth or lower to be maintained throughout the final conversion cycle is given by:
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(4) | |
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What is an appropriate maximum operating temperature limit for nanoreplicators that must forage for organic substrate in order to replicate? The softening point for sapphire, an oft-mentioned substitute building material for diamond because of its high strength, high-temperature tolerance, and inability to burn in oxygen, is 2070°K [30], probably near the upper limit in any reasonable ecophagic nanorobot design scenario especially given the seriously negative impact of higher temperatures on nanorobot reliability and functionality (Section 3.0). The combustion temperature of diamond in air is usually given as 870-1070°K [31].
However, such elevated surface temperatures, while perhaps acceptable for diamondoid nanomachines in some circumstances, will immediately volatize and incinerate most of the natural organic feedstock upon which the nanoreplicators must feed. The minimum ignition point of wood, paper, or diesel fuel in air has been given as low as ~500°K [68], and glucose caramelizes [6] at 433°K -- caramelization is not oxidation but rather is a decomposition reaction that includes polymerizations and covalent bondmaking that could render this substrate material somewhat less accessible to the replibots. A still lower temperature threshold is the boiling point of water at 373°K; above this temperature, living things will boil, thus denying ecophagic nanoreplicators access to solution-based chemical processes at normal atmospheric pressures, which could be an important restriction.
The waste heat energy released globally in the last replicative cycle may be estimated as Ehalf (q Dbio) Mbio, where Dbio is the energy density of the organic feedstock material and q is the energy conversion ratio for its transformation into nanomass. For example, Dbio = 16 MJ/kg for glucose, 17 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 figures refer to the energy content of the organic feedstock, not to the energy that must be consumed (and the waste heat subsequently thermalized) in order to build a kilogram of nanomass. Drexler [4] estimates that the typical energy 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 systems where low energy dissipation is not a primary design objective. This figure corresponds roughly to the strongest covalent bond energies (e.g., 1190 zJ/bond for C=C, 1327 zJ/bond for C=O, and 1594 zJ/bond for CºC [4]), and is roughly of the same order as the thermodynamic heat of formation of diamond from CO2(g), ~33 MJ/kg [5].
Drexler [4] claims that energy dissipation may in theory be as low as Ediss ~ 0.1 MJ/kg "if one assumes the development of a set of mechanochemical processes capable of transforming feedstock molecules into complex product structures using only reliable, nearly reversible steps." 0.1 MJ/kg of diamond corresponds roughly to the minimum thermal noise at room temperature (e.g., kT ~ 4 zJ/atom at 298°K). R. Merkle [32] also conjectures that near-zero energy dissipation is in principle possible in certain special circumstances, a possibility that should be investigated in the present context in a future theoretical study. However, near-term nanochemistries are unlikely to be significantly more efficient than natural enzyme chemistries, which have been evolving for efficiency over eons; the terrestrial biosphere fixes ~1.2 ×1014 kg/yr of biomass carbon [21] with a ~1.4 ×1014 watt energy input [6], or Ediss ~ 38 MJ/kg of carbon.
Using Eqn. 4, the minimum last-replication time
can be calculated for various plausible values of Ediss,
wherein the mean terrestrial temperature will not exceed the chosen value
of TEarth during ecophagy,
as given in Table 4:
* Actual last-cycle replication time limited to exponential t ~ 100 sec (Section 3.0).
Setting aside Merkle's conjecture, Table 4
suggests that if phenomenally efficient reversible molecular manufacturing
techniques become available -- e.g., Ediss
~ 0.1 MJ/kg -- the final replicative cycle of global ecophagy could proceed
as quickly as ~1000 seconds while just avoiding incinerating the organic
feedstock or boiling environmental water. However, there currently exist
no known designs which would be capable of achieving such highly energy-efficient
nanoassembly operations.
More probably, highly dissipative molecular manufacturing designs are likely to be implemented during the early and intermediate years of molecular nanotechnology development. Such designs are also likely to be necessary for the very complex machines needed to implement biovorous replication given the enormous variety of chemically diverse natural biological substrates. Assuming current and foreseeable energy-dissipative designs requiring ~100 MJ/kg for chemical transformations (most likely for biovorous systems), complete ecophagy that proceeds slowly enough to add ~4°C to global warming (near the current threshold for immediate climatological detection) will require ~20 months to run to completion. Faster ecophagic devices will run hotter, allowing quicker detection by policing authorities.
The conversion of biomass to nanomass may proceed according to Eqn. 1 up to the ecophagic thermal pollution limit (ETPL) whereupon the specified maximum global temperature TEarth is attained, after which the replication time must approximately double after each population doubling, ultimately reaching tlast in the final doubling, as described by Eqn. 4. Total time spent in the ETPL-limited regime is ~ 2 tlast. For example, taking t = 100 sec, TEarth = 300°K, and Ediss ~ 100 MJ/kg, the transition to the ETPL regime occurs when total global nanomass reaches ~5 ×1010 kg, or only 0.001% of total global biomass, and the last ~17 population doublings remain to be completed over a time span of ~2 tlast = 2 ×107 sec (~7 months). This is also the optimum strategy for an ecophagic population that is attempting to evade premature detection by maintaining a low thermal emissions profile. Constant ecological surveillance for any evidence of ecophagic activity is an appropriate policing measure to provide adequate early warning to the existence of this threat.
Note further that the presence of natural and anthropogenic greenhouse gases in the Earth's atmosphere will amplify any heating effects, helping to make ecophagic activities more immediately visible in its earlier stages. (In theory, a large enough replibot population could actively manage terrestrial albedo or global greenhouse gas concentrations, but these activities would themselves generate still more waste heat.) Additionally, using the actual current mean value of er = 0.69 for terrestrial emissivity in Eqns. 3 and 4, rather than the much higher value of er = 0.97 for carbon black assumed in calculating Table 4, the last-cycle time tlast increases by another ~40%, giving still more time for defensive instrumentalities to be brought to bear on the situation.
Assuming the surface biomass is compositionally similar to wood (Dbio
~ 19 MJ/kg), prompt consumption (e.g., combustion) of the entire biosphere
would release Qwaste = MbioDbio
~ 1023 J of energy. The combined heat capacity of planetary
oceans (1.36 ×1021 kg [6]
at 4200 J/kg-K [6] =
Similarly, air conduction is unlikely to significantly reduce the ETPL
limits. Waste energy can be absorbed by atmospheric heat capacity
Over long time periods, natural ecosystems are believed to have a nearly balanced carbon budget, with photosynthetic uptake equal to respiratory release [33]. From the ecological perspective, the insertion of carbon-absorbing artificial devices into the environment represents a new sink in the homeostatic global carbon cycle, in addition to the natural carbon sinks such as forests [34, 35]. Most of terrestrial biomass consists of plants, especially trees, though nearly half of all biomass may consist of bacteria, mostly in soils (up to ~1015 cells/m3) and subsurface sediments and rocks down to ~3 km depth [12, 38]; there are ~5 ×1030 bacteria on Earth [39]. Conversion of living plant biomass to diamondoid nanomass by nanoreplicators thus may reduce the ability of the surviving plant population to remove carbon dioxide from the atmosphere. Unless carbon dioxide levels in the atmosphere are directly regulated by the active robotic nanomass, CO2 levels will begin to rise, which in turn may increase the growth rate of plants. In a few experimental studies [40], elevated CO2 has been shown to stimulate plant growth at least temporarily, even under serious nutrient shortage, although one experiment [41] challenges this supposition. If slow-moving nanoreplicators consume biomass only very slowly, the consumed biomass may be regenerated as new plant growth is stimulated worldwide.
What is the minimum ecophagic biomass removal rate necessary to overcome
the resulting carbon-sequestration response of the natural ecology? One
study [20] found that deforestation in the low
latitudes during 1990 resulted in forest area expansion and growth in mid-
and high-latitude forest that sequestered ~7 ×1011 kg
of carbon (e.g., creating ~3 ×1012 kg of extra biomass)
in one year. Estimates of unrealized global forest carbon conservation
and sequestration potential suggest a biologic capability of
Four related scenarios which may lead indirectly to global ecophagy have been identified and are described below. In all cases, early detection appears feasible with advance preparation, and adequate defenses are readily conceived using molecular nanotechnologies of comparable sophistication.
The existence of 1-2 ×1016 kg [24] of global undersea carbon storage on continental margins as CH4 clathrates and a like amount (3.8 ×1016 kg) of seawater-dissolved carbon as CO2 represent a carbon inventory more than an order of magnitude larger than in the global biomass (Section 3.0). Methane and CO2 can in principle be combined to form free carbon and water, plus 0.5 MJ/kg C of free energy. (Some researchers are studying the possibility of reducing greenhouse gas accumulations by storing liquid [44] or solid [45] CO2 on the 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 buoyancy transport, with the conversion of carbon clathrates to nanomass taking place on the seabed below. The subsequent colonization of the land-based carbon-rich ecology by a large and hungry seabed-grown replicator population is the "gray plankton" scenario. (Phytoplankton, 1-200 microns in size, are the particles most responsible for the variable optical properties of oceanic water because of the strong absorption of these cells in the blue and red portions of the optical spectrum [37].)
The gray plankton replicator waste heat signature is readily 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 floor of Monterey Bay [44]. Typical ocean column thermal gradients are ~0.02°K/m in the top 300 m (1-30 atm) and ~0.006°K/m from 300-1000 m depth (30-100 atm) [44]. A near-seafloor water temperature change of DT = 1°K over a depth range of L = 100 m would be clearly distinguishable from natural variations even using contemporary instrumentation [44], and would evidence an increased seabed power release of Irepl ~ Kt (DT / L) ~ 0.005 W/m2, taking thermal conductivity as Kt ~ 0.5 W/m-K for seawater at 4°C. Thus the threshold for seafloor replibot detectability, assuming global seabed area is Aseabed ~ (70%) 4p REarth2 = 3.6 ×1014 m2, is Pmin = Irepl Aseabed ~ 2 ×1012 watts worldwide or a global replibot population of mass Mmin ~ Pmint / Ediss ~ 20 ×106 kg assuming Ediss ~ 100 MJ/kg and t = 1000 sec. (Faster replicators are detectable at lower population masses.) Thus bottom-dwelling gray plankton can be detected before they have consumed more than 10-9 of the total oceanic abiotic carbon supply.
Direct census sampling of the seafloor may also allow early detection,
although nanorobotic samplers will have to contend with a significant number
of false targets in the oceanic environment. These false targets may include
0.1 micron small colloids (~7 ×1014 m-3)
and viruses (~3 ×1013 m-3),
0.2-0.3 micron heterotrophic bacteria (~1012 m-3),
0.3 micron large colloids (~1013 m-3),
1 micron cyanobacteria (~1010 m-3),
2-3 micron small phytoplankton (~108 m-3),
larger phytoplankton (e.g., 10 micron cells ~106 m-3),
and zooplankton (e.g., 50 micron cells ~103 m-3)
[36-38]. At
the minimum detectable global mass of Mmin
= 20 ×106 kg estimated above, the number density of gray
plankton on the seabed floor is Ngp
~ Mmin / (Aseabedmgp)
~ 2 ×107 m-2, assuming
~1 micron gray plankton replicators each of mass mgp
~ 3 ×10-15 kg. In this scenario,
the bottommost 1 mm of the ocean column above the seabed would contain
roughly equal numbers of > ~1-micron natural cells and ~1-micron artificial
bottom-dwelling gray plankton devices. If not largely confined to the sea
floor during most of their replication cycle, the natural cell/device ratio
could increase by many orders of magnitude, requiring a more diligent census
effort. Census-taking nanorobots can alternatively be used to identify,
disable, knapsack or destroy the gray plankton devices.
Traditional diamondoid nanomachinery designs [4] have employed 8 primary chemical elements, as detailed in Table 5 along with the associated atmospheric abundances [46] of each element. (Silicon is present in air as particulate dust which may be taken as ~28% Si for crustal rock [5], with a global average dust concentration of ~0.0025 mg/m3). The requirement for elements that are relatively rare in the atmosphere greatly constrains the potential nanomass and growth rate of airborne replicators. However, note that at least one of the classical designs exceeds 91% CHON by weight. Although it would be very difficult, it is at least theoretically 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 sunlight. A worldwide blanket of airborne replicating dust or "aerovores" that blots out all sunlight has been called the "gray dust" scenario [47]. (There have already been numerous experimental aerial releases of recombinant bacteria [48].)
Two independent constraints on gray dust replication speed are materials and energy availability, and both methods suggest that t ~ 10,000 sec for 1-micron replicators and ~1000 sec for 0.1-micron replicators. The analyses are as follows.
First, the mass current Mcurr
through the surface of a spherical nanorobot of radius Rnanois
equal to the number of gas molecules/sec that collide with the fraction
f
~ 10% of the 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 Nencounter
~ 100 [6]; that is:
|
(5)
|
where k = 1.381 ×10-23
J/molecule-K (Boltzmann's constant) and T
~ 300°K is ambient temperature in kelvins. The concentration of gas
is
|
(6)
|
Taking Rnano = 1 micron
and allocating each aelement
for the hypothetical CHON replicator as indicated in the second column
of Table 6 gives the values of t
shown at far right in Table 6. The limiting elements
are H and C, but C has the strongest impact on replication time, requiring
a t ~ 12,300 sec.
Since t scales
as Rnano, reducing Rnano
to 100 nm reduces
t
to ~1230 sec for this device. (Mechanical precompression and sortation
[6] of gas molecules might reduce
Second, the solar energy flux into the nanorobot, assuming that a fraction
f
of its surface is photosensitive with energy conversion efficiency e,
is
|
(7)
|
Taking r = 2000
kg/m3, Ediss
~ 100 MJ/kg,
f = 50%, e
= 10%, and Isolar = 100-400
W/m2, then for Rnano
= 1 micron,
Since replication of an airborne CHON replibot is primarily carbon-limited,
in theory the entire global atmospheric carbon mass of ~5.2 ×1014
kg C is available for conversion into Mgd
= 8.4 ×1014 kg of CHON nanomass, assuming a 62% carbon
content by weight (Table 6). However, because the
machines are solar powered, the active population of gray dust nanorobots
is restricted to one optical depth of such devices. To a very crude first
approximation (e.g., ignoring contributions from scattered and reflected
photons), one optical depth occurs when the cumulative cross-sectional
area of the nanorobot population equals the surface area of Earth, so the
maximum total mass of continuously active CHON airborne nanorobots is:
|
(8)
|
|
|
||
|
||
|
Once the expanding nanorobot population reaches one optical depth (requiring ~0.2% of all atmospheric carbon, or ~3 months of current anthropogenic airborne carbon releases), the replication rate of the gray dust ceases to grow exponentially and becomes essentially constant -- a phenomenon which may be called the "opacity brake effect." (One optical depth of uniformly distributed Rnano = 275 nm aerovores represents a particle number density of ~5 ×108 m-3.) After the opacity brake point has been reached, a constant nanomass production rate of Mtotal/t ~ 1.4 ×108 kg/sec ensues until exhaustion of the limiting atmospheric carbon resource. Current instrumentation can detect ~1% variations in the solar constant, so the limit for early bolometric detection is probably ~1% Mtotal, when ~0.002% of atmospheric carbon has been converted to nanomass.
Dust monitors in late 20th-century wafer-fab clean rooms regularly measure dust densities of ~10 particles/m3 at 0.5 microns and larger [49], potentially allowing detection as early as <10-8 Mtotal if more highly discriminating monitors can be developed. If the replibots settle out on the planetary surface and continue replicating there (Section 8.3), they could deprive the ecology of needed sunlight without darkening the sky, but their effects (e.g., a fine gray dust covering everything on the surface) would also be detectable far sooner than the 1% Mtotal point.
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 will have the minimum possible size. (Replication time varies
with thickness for a sheetlike nanorobot configuration.) The minimum replibot
size is driven by UV radiation damage rates on nanomachinery [4].
Consider the smallest possible replicator with mass
|
(9)
|
for replibots that produce nt
offspring before failing. The number of generations needed to replicate
one optical depth of nanorobots worldwide, starting from a single device,
is nt
= ln(Mtotal / Minit)
= 65-60 for Rnano = 0.1-1
microns. Taking nt
~ 64, Eqn. 9 defines the smallest gray dust replibot
as Rnano ~275 nm (mass ~
1.7 ×10-16 kg) with a d
~ 215 nm thick graphite UV shield assuming Ncleave
= 1. The smallest replibot that can replicate only once before it fails
(e.g., nt
= 1) has Rnano ~ 230 nm
with a
d ~ 170 nm shield taking
From Eqns. 1 and 8, and neglecting
dispersal velocity limitations (Section
4.0) the minimum possible time to reach some fraction fopac
of global atmospheric opacity is:
|
(10)
|
For airborne CHON replibots with Rnano = 275 nm and t ~ 2750 sec, 1% of opacity is reached in topac ~ 1.85 days, 100% opacity in 2.0 days, leaving a response time of ~3.5 hours between first detection at 1% opacity and complete opacity at 100%. If uniformly distributed throughout the atmosphere, the dust density at 100% opacity would amount to ~0.085 mg/m3 for 275-nm nanorobots, about equal to the typical ~0.05 mg/m3 dust density normally found in the air of most industrialized Western cities [69].
After 100% opacity is reached, another tend = t (Mgd-Mtotal) / Mtotal = 72 days would be required to convert the remaining atmospheric carbon resource into nanomass. However, post-opacity the gray dust replication rate is no longer exponentiating so the defensive nanorobots can quickly catch up.
The most efficient cleanup strategy appears to be the use of air-dropped
non-self-replicating nanorobots equipped with prehensile microdragnets.
Consider a planetwide dragnet comprised of a square mesh of fibers, with
mesh aperture size lmesh,
mesh fibers of thickness dfiber,
and total dragnet area Anet
covering Earth's entire surface area AEarth
= 4pREarth2
= Anet. Minimum fiber thickness
is
|
(11)
|
Taking Anet = AEarth
= 5.10 ×1014 m2, lmesh
= 460 nm and dfiber = 1
nm, then
Vdragnet = 2200
m3. This dragnet may be carried aloft by a fleet of
The total machine volume of one optical depth of 275-nm gray dust replibots is 1.9 ×108 m3, making an average cleanup requirement of only ~4500 micron3 of targets per defensive nanorobot. A spherical knapsack comprised of additional mesh material having an enclosed volume of 4500 micron3 adds only 11% to the onboard mesh storage requirement. Each defensive nanorobot deploys a (110 micron)2 ~ 12,100 micron2 section of the planetwide dragnet. In theory, if this section were curved into a huge spherical knapsack, it would make a storage volume of 125,000 micron3 -- enough to hold the equivalent of ~28 optical depths of gray dust replibots during passage through locally dense clouds of target airborne nanoreplicators.
Each defensive nanorobot requires ~66 nN of motive force and ~6600 pW of onboard power to overcome drag loss [6] on the ~5.3 cm length of dragnet fiber that it is passing through the air at 0.1 m/sec. This power is provided by a rear-deployed, 30% efficient, 55 micron2, ~10 nm thick solar collector film that stows in a 0.55 micron3 volume before deployment and adds only ~45 pW to drag power after deployment. When fully deployed, the defensive fleet contributes <0.5% additional atmospheric opacity, and clears air for an energy cost of ~5.8 J/m3 of contaminated atmosphere, per pass. Defensive nanorobot locomotion in the viscous flight regime may be provided by screw drives, viscous anchoring via the prehensile dragnet, or other means [6].
The Stokes settling velocity [6] in air is ~240 micron/sec for Rnano = 1 micron, ~20 micron/sec for Rnano = 275 nm and ~5 micron/sec for Rnano = 100 nm, giving 10-km passive fall times (in still atmosphere) of 1.3 years, 16 years and 67 years, respectively.
Alternative airborne or ground-based atmospheric filtration configurations
that could permit more rapid filtering are readily envisioned. For example,
since drag power varies as the square of the velocity, then by increasing
mesh volume 10,000-fold while decreasing airflow velocity 100-fold, total
drag power remains unchanged but whole-atmosphere turnover proceeds 100-fold
faster, e.g., ~15 minutes.
a There are
~1018-1019 insects on Earth [75-77].
The average insect devotes ~35% of body volume to its respiratory system
[78], which is mostly gas-phase diffusional
but with some very primitive active ventilation. If average insect
volume is ~0.6 mm3 [77], then the worldwide
insect population has
b There are ~300
billion birds on Earth [70]. The average
bird devotes 20% of body volume to its respiratory system [71],
mostly unidirectional airflow unlikely to permanently trap gray dust, but
~20% of the bird respiratory volume consists of tidally exchanged air in
8-9 anterior and posterior air sacs, and air spaces in the bones [71].
Assuming dead air in birds represents 38% of tidal volume as in humans
[6], and that the average bird is ~500 cm3
in volume, then the worldwide bird population has ~2 × 106
m3 of respiratory dead air which could accumulate ~1013
aerovores if the birds are breathing replibot-contaminated air at
a concentration equivalent to ~1% atmospheric opacity. In this case
~10-12 of the global aerovore population resides inside
bird respiratory systems (~40 replibots per bird at 1% opacity), necessitating
specialized quarantine or inspection and release protocols for birds passing
through the dragnet. Under similar exposure,
Colonies of symbiotic algae and fungi known as lichens (which some have called a form of sub-aerial biofilm) are among the first plants to grow on bare stone, helping in soil formation by slowly etching the rock [55]. Lithobiontic microbial communities such as crustose saxicolous lichens penetrate mineral surfaces up to depths of 1 cm using a complex dissolution, selective transport, and recrystallization process sometimes termed "biological weathering" [56]. Colonies of epilithic (living on rock surfaces) microscopic bacteria produce a 10 micron thick patina on desert rocks (called "desert varnish" [57]) consisting of trace amounts of Mn and Fe oxides that help to provide protection from heat and UV radiation [57-59]. In theory, replicating nanorobots could be made almost entirely of nondiamondoid materials including noncarbon chemical elements found in great abundance in rock such as silicon, aluminum, iron, titanium and oxygen (Section 2). The subsequent ecophagic destruction of land-based biology by a maliciously programmed noncarbon epilithic replicator population that has grown into a significant nanomass is the "gray lichen" scenario.
The growth rate of gray lichens on the surface of the Earth will be primarily energy-limited, not materials-limited. While it is true that chemolithotrophic microorganisms such as Thiobacillus ferrooxidans use reduced iron and sulfur compounds for their energy source [60-62], and that other chemolithotrophic bacteria can metabolize inorganic carbon (e.g., assimilating CO2 from carbonate rock) using a pathway similar to green plants [63], such energy sources appear to be far less plentiful than ambient sunlight because most rocks are already fully oxidized. (For example, the oxidation of Fe++ to Fe+++ by chemolithotrophs liberates only 0.75 MJ/kg [64], as compared to ~16 MJ/kg for the combustion of glucose in oxygen [6].) Assuming that up to 400 W/m2 in the visible spectrum is harvested with 30% efficiency for 8 hours/day over the entire landmass of Earth, the 6 ×1015 watts theoretically available could produce at most ~6 ×107 kg/sec of mineral nanomass taking Ediss ~ 100 MJ/kg as before. Even assuming an optimal dispersal pattern, ~2.6 years would be required for the growing mineral nanomass to equal the terrestrial biomass (~5 ×1015 kg; Section 3), whereupon the top ~1 cm of Earth's entire continental land area would have been converted to nanomass.
Continuous direct census sampling of the Earth's land surfaces will
almost certainly allow early detection, since mineralogical nanorobots
should be easily distinguishable from inert rock particles and from organic
microbes in the top 3-8 cm of soil, typically
More difficult scenarios involve ecophagic attacks that are launched not to convert biomass to nanomass, but rather primarily to destroy biomass. The optimal malicious 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 with maximum stealth up to some critical population size by consuming local environmental substrate to build nanomass. In the second phase, the now-large replibot population ceases replication and exclusively undertakes its primary destructive purpose. More generally, this strategy may be described as Build/Destroy.
During the Build phase of the malicious "badbots," and assuming technological equivalence, defensive "goodbots" enjoy at least three important tactical advantages over their adversaries:
However, once the badbots enter their Destroy phase, only the first advantage
of the defenders (i.e., preparation) remains fully effective. Of course,
a total mass Mgoodbots of
nonreplicating defensive nanorobots can hold constant a population Mbadbots
of self-replicating biovorous nanorobots if Mgoodbots
Nevertheless it is most advantageous to engage a malicious ecophagic threat while it is still in its Build phase. This requires foresight and a commitment to extensive surveillance by the defensive authorities. A complete analysis is beyond the scope of this paper, but two simple examples will suffice to illustrate the level of surveillance required.
First, consider a population of Nbot
replibots that have infested a human body and are about to enter their
Destroy phase. 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 mass fraction fdest
of the biomass must be destroyed to produce death. The time required
to kill is:
|
(12)
|
where Mbody is body mass
and rbody
is mean body density. Power is provided by combustion at conversion
efficiency
|
(13)
|
where h is mean
tissue viscosity. The mass fraction of badbots that can produce death
in a time tkill is fn
= Mbadbot / Mbody,
where total badbot mass is
|
(14)
|
The number of attacking badbots is then:
|
(15)
|
Taking fdest = 0.1 (10%),
ke
= 0.5 (50%), e
= 0.5 (50%), ffuel = 0.1
(10%), Rnano = 1 micron,
rnano
= 2000 kg/m3, h
~ 1000 kg/m-sec [6], and rbody
= Mbody / Vbody
where Mbody = 70 kg and
body volume Vbody = 0.06
m3 [6], then a kill time tkill
= 1 sec requires fn = 6
×10-4 and
Second, consider the defense of the entire eukaryotic biosphere. Excluding
bacteria assumed to represent about half of global biomass and assuming
an average eukaryotic cell size of 20 microns, there are ~3 ×1026
eukaryotic cells on Earth. If each cell is visited and examined,
on average, about once a year with time spent per cell ctime
= 100 sec/cell as before, this implies a global examination rate of Xcell
~ 1019 cells/sec and a requirement for
The smallest plausible biovorous nanoreplicator has a molecular weight of ~1 gigadalton and a minimum replication time of perhaps ~100 seconds, in theory permitting global ecophagy to be completed in as few as ~104 seconds. However, such rapid replication creates an immediately detectable thermal signature enabling effective defensive policing instrumentalities to be promptly deployed before significant damage to the ecology can occur. Such defensive instrumentalities will generate their own thermal pollution during defensive operations. This should not significantly limit the defense strategy because knapsacking, disabling or destroying a working nanoreplicator should consume far less energy than is consumed by a nanoreplicator during a single replication cycle, hence such defensive operations are effectively endothermic.
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 completion, which is plenty of advance warning to mount an effective defense.
Ecophagy that progresses slowly enough to evade easy detection by thermal monitoring alone would require many years to run to completion, could still be detected by direct in situ surveillance, and may be at least partially offset by increased biomass growth rates due to natural homeostatic compensation mechanisms inherent in the terrestrial ecology.
Ecophagy accomplished indirectly by a replibot population pre-grown on nonbiological substrate may be avoided by diligent thermal monitoring and direct census sampling of relevant terrestrial niches to search for growing, possibly dangerous, pre-ecophagous nanorobot populations.
Specific public policy recommendations suggested by the results of the present analysis include:
The author thanks Robert J. Bradbury, J. Storrs Hall, James Logajan, Markus Krummenacker, Thomas McKendree, Ralph C. Merkle, Christopher J. Phoenix, Tihamer Toth-Fejel, James R. Von Ehr II, and Eliezer S. Yudkowsky for helpful comments on earlier versions of this manuscript; J. S. Hall for the word "aerovore"; and R. J. Bradbury for preparing the hypertext version of this document.
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