Regarding the first point, I apologize for the error made by the LLM during translation. The original phrase I provided was “the difference is not too significant” but it seems some words were omitted. However, I admit my example was weak and not suitable. First, birds have higher body temperatures, allowing for faster heat dissipation (so the hummingbird, compared to the elephant, is actually closer to the ^2/3 scaling law and deviates more from Kleiber’s law). Second, evolution has favored lower resting metabolic rates to conserve energy, whereas our goal is maximum growth speed, so comparing basal metabolic rates is beside the point. We don’t need to reduce specific surface area for the sake of energy conservation to avoid hypothermia; on the contrary, we should design structures to be flat. So, I’d like to rephrase my argument with a few clearer points: 1. Specific surface area (for heat dissipation and material intake) is, of course, very important. 2. However, the size of the replication unit is not the most critical factor affecting the specific surface area. The geometry of the entire system is. Even if the replication units are small, when they pile up and obstruct each other, unless you have a massive heat sink (like an ocean) to temporarily store the heat, the effective surface area for achieving true thermal equilibrium will converge to that of a macroscopic structure. Multicellular organisms are essentially large collections of micro-machines, but they are forced to slow down because they are not individually dispersed in water or air. For a planetary industrial system, the mass at which this mutual obstruction becomes a necessary consideration is not very large. The total mass of the human technosphere is currently 1.1 Tt, and if spread evenly over the Earth’s surface, it would already be a centimeter-scale layer. Conversely, even macroscopic replication units can be made flat. In fact, our industrial systems are indeed spread out across the planet’s surface.
Regarding the second point, this is worth a more in-depth discussion.
First, concerning the replication cycle of duckweed, the “in hours” figure might be a bit off. The results from DOI: 10.1111/plb.12184 show a range of 1.34 to 4.54 days. There are a few records of biomass doubling times under 24 hours, but not by much. Second, duckweed has a very simple structure, so it doesn’t need to expend energy maintaining stems, branches, root systems, lignified support structures, or searching for salt ions in soil. It consists of one or a few fronds, and nearly all its cells are involved in photosynthesis or direct nutrient absorption. Furthermore, it doesn’t require sexual reproduction. Single-celled algae are even more extreme in this regard. They have an advantage in these aspects, so comparing them to consumers, which “have low energy costs for food but waste a lot of energy on things other than doubling,” is unfair. I believe we cannot deny that the energy cost of raw materials remains a factor that influences the outcome by an order of magnitude. Third, and this is something I missed before, we should actually categorize raw material sources into three tiers. Tier 1: Sourcing from pre-processed biomass. These materials can even carry their own energy. Tier 2: Sourcing from liquid or gaseous phases, mainly C, N, O, H. Other elements are also dissolved in a dispersed medium, allowing for direct extraction by molecular machines with specific affinities, which is low in energy cost. Tier 3: Sourcing from solid phases. The key here is purification, which becomes considerably more energy-intensive. Gaseous CO₂, abundant water, and salts mean organisms don’t need to perform this purification (otherwise, they’d have to gnaw on carbonate rocks). In contrast, an industrial system has to process large amounts of rock (consuming tens of MJ/kg for every kilogram) to extract a small fraction of useful elements. (Of course, for modern human industry, there’s another negative factor: current production is not optimized for energy efficiency, so the energy efficiency of the production process itself is low).
So, we would first exhaust the biosphere (~few MJ/kg, total mass ~1 Tt), then all the carbon sources in the dispersed media (~tens of MJ/kg; water is abundant, but CO₂ is the limiting step. Atmospheric carbon is less than terrestrial biomass, while dissolved ocean carbon is ~100 Tt). To purify solid materials, we always need to break the surrounding chemical bonds to extract the desired elements, for example, by melting or pulverizing, which increases the cost by another order of magnitude.
Regarding the third point, I’d be happy to provide sources. https://ntrs.nasa.gov/citations/19830007081, https://arxiv.org/abs/2110.15198 and https://doi.org/10.2514/6.2023-4636 all contain rough calculations for the average specific energy and specific power of Von Neumann probes, although the first is in a lunar environment, and the latter two are in asteroid environments. The first two also describe primary seed factories that don’t heavily consider the electronics industry, but given its mass fraction, I think this can be overlooked.
As for a complete industrial system on Earth, perhaps due to its complexity, I’ve rarely seen estimates. However, a rough order-of-magnitude estimation method is to consider only the power generation system. This is because the power generated must equal the total power consumed by all other facilities. If the power generation system isn’t specifically optimized to have values far exceeding other equipment (like thin-film photovoltaics), then we can assume its parameters are within the same order of magnitude as those of the entire industrial system we’re considering. And there is a large body of research available on the energy payback period of power generation equipment.
Regarding the first point,
I apologize for the error made by the LLM during translation. The original phrase I provided was “the difference is not too significant” but it seems some words were omitted. However, I admit my example was weak and not suitable. First, birds have higher body temperatures, allowing for faster heat dissipation (so the hummingbird, compared to the elephant, is actually closer to the ^2/3 scaling law and deviates more from Kleiber’s law). Second, evolution has favored lower resting metabolic rates to conserve energy, whereas our goal is maximum growth speed, so comparing basal metabolic rates is beside the point. We don’t need to reduce specific surface area for the sake of energy conservation to avoid hypothermia; on the contrary, we should design structures to be flat.
So, I’d like to rephrase my argument with a few clearer points:
1. Specific surface area (for heat dissipation and material intake) is, of course, very important.
2. However, the size of the replication unit is not the most critical factor affecting the specific surface area. The geometry of the entire system is.
Even if the replication units are small, when they pile up and obstruct each other, unless you have a massive heat sink (like an ocean) to temporarily store the heat, the effective surface area for achieving true thermal equilibrium will converge to that of a macroscopic structure. Multicellular organisms are essentially large collections of micro-machines, but they are forced to slow down because they are not individually dispersed in water or air.
For a planetary industrial system, the mass at which this mutual obstruction becomes a necessary consideration is not very large. The total mass of the human technosphere is currently 1.1 Tt, and if spread evenly over the Earth’s surface, it would already be a centimeter-scale layer.
Conversely, even macroscopic replication units can be made flat. In fact, our industrial systems are indeed spread out across the planet’s surface.
Regarding the second point, this is worth a more in-depth discussion.
First, concerning the replication cycle of duckweed, the “in hours” figure might be a bit off. The results from DOI: 10.1111/plb.12184 show a range of 1.34 to 4.54 days. There are a few records of biomass doubling times under 24 hours, but not by much.
Second, duckweed has a very simple structure, so it doesn’t need to expend energy maintaining stems, branches, root systems, lignified support structures, or searching for salt ions in soil. It consists of one or a few fronds, and nearly all its cells are involved in photosynthesis or direct nutrient absorption. Furthermore, it doesn’t require sexual reproduction. Single-celled algae are even more extreme in this regard. They have an advantage in these aspects, so comparing them to consumers, which “have low energy costs for food but waste a lot of energy on things other than doubling,” is unfair. I believe we cannot deny that the energy cost of raw materials remains a factor that influences the outcome by an order of magnitude.
Third, and this is something I missed before, we should actually categorize raw material sources into three tiers.
Tier 1: Sourcing from pre-processed biomass. These materials can even carry their own energy.
Tier 2: Sourcing from liquid or gaseous phases, mainly C, N, O, H. Other elements are also dissolved in a dispersed medium, allowing for direct extraction by molecular machines with specific affinities, which is low in energy cost.
Tier 3: Sourcing from solid phases. The key here is purification, which becomes considerably more energy-intensive. Gaseous CO₂, abundant water, and salts mean organisms don’t need to perform this purification (otherwise, they’d have to gnaw on carbonate rocks). In contrast, an industrial system has to process large amounts of rock (consuming tens of MJ/kg for every kilogram) to extract a small fraction of useful elements. (Of course, for modern human industry, there’s another negative factor: current production is not optimized for energy efficiency, so the energy efficiency of the production process itself is low).
So, we would first exhaust the biosphere (~few MJ/kg, total mass ~1 Tt), then all the carbon sources in the dispersed media (~tens of MJ/kg; water is abundant, but CO₂ is the limiting step. Atmospheric carbon is less than terrestrial biomass, while dissolved ocean carbon is ~100 Tt).
To purify solid materials, we always need to break the surrounding chemical bonds to extract the desired elements, for example, by melting or pulverizing, which increases the cost by another order of magnitude.
Regarding the third point, I’d be happy to provide sources. https://ntrs.nasa.gov/citations/19830007081, https://arxiv.org/abs/2110.15198 and https://doi.org/10.2514/6.2023-4636 all contain rough calculations for the average specific energy and specific power of Von Neumann probes, although the first is in a lunar environment, and the latter two are in asteroid environments. The first two also describe primary seed factories that don’t heavily consider the electronics industry, but given its mass fraction, I think this can be overlooked.
As for a complete industrial system on Earth, perhaps due to its complexity, I’ve rarely seen estimates. However, a rough order-of-magnitude estimation method is to consider only the power generation system. This is because the power generated must equal the total power consumed by all other facilities. If the power generation system isn’t specifically optimized to have values far exceeding other equipment (like thin-film photovoltaics), then we can assume its parameters are within the same order of magnitude as those of the entire industrial system we’re considering. And there is a large body of research available on the energy payback period of power generation equipment.