Where j is dissipating power per area and sigma is Stephan-Boltzmann constant.
We can estimate j as
Gsc×πR2Earth4πR2Earth×(1−albedo)
Where GSC is a solar constant 1361 W/m^2. We take all incoming power and divide it by Earth surface area. Earth albedo is 0.31.
After substitution of variables, we get Earth temperature 254K (-19C), because we ignore greenhouse effect here.
How much humanity power consumption contributes to direct warming? In 2023 Earth energy consumption was 620 exajoules (source: first link in Google), which is 19TW. Modified rough estimation of Earth temperature is:
jsolar+JhumanSEarthσ1/4
Human power production per square meter is, like, 0.04W/m^2, which gives us approximately zero effect of direct Earth heating on Earth temperature. But what happens if we, say, increase power by factor x1000? We are going to get increase of Earth temperature to 264K, by 10K, again, we are ignoring greenhouse effect. But qualitatively, increasing power consumption x1000 is likely to screw the biosphere really hard, if we count increasing amount of water vapor, CO2 from water and methane from melting permafrost.
How is it realistic to get x1000 increase in power consumption? Well, @Daniel Kokotajlo at least thought that we are likely to get it somewhere in 2030s.
The power density of nanotech is extremely high (10 kW/kg), so it only takes 16 kilograms of active nanotech per person * 10 billion people to generate enough waste heat to melt the polar ice caps. Literally boiling the oceans should only be a couple more orders of magnitude, so it’s well within possible energy demand if the AIs can generate enough energy. But I think it’s unlikely they would want to.
Roughly, Earth average temperature:
jσ1/4
Where j is dissipating power per area and sigma is Stephan-Boltzmann constant.
We can estimate j as
Gsc×πR2Earth4πR2Earth×(1−albedo)
Where GSC is a solar constant 1361 W/m^2. We take all incoming power and divide it by Earth surface area. Earth albedo is 0.31.
After substitution of variables, we get Earth temperature 254K (-19C), because we ignore greenhouse effect here.
How much humanity power consumption contributes to direct warming? In 2023 Earth energy consumption was 620 exajoules (source: first link in Google), which is 19TW. Modified rough estimation of Earth temperature is:
jsolar+JhumanSEarthσ1/4
Human power production per square meter is, like, 0.04W/m^2, which gives us approximately zero effect of direct Earth heating on Earth temperature. But what happens if we, say, increase power by factor x1000? We are going to get increase of Earth temperature to 264K, by 10K, again, we are ignoring greenhouse effect. But qualitatively, increasing power consumption x1000 is likely to screw the biosphere really hard, if we count increasing amount of water vapor, CO2 from water and methane from melting permafrost.
How is it realistic to get x1000 increase in power consumption? Well, @Daniel Kokotajlo at least thought that we are likely to get it somewhere in 2030s.
The power density of nanotech is extremely high (10 kW/kg), so it only takes 16 kilograms of active nanotech per person * 10 billion people to generate enough waste heat to melt the polar ice caps. Literally boiling the oceans should only be a couple more orders of magnitude, so it’s well within possible energy demand if the AIs can generate enough energy. But I think it’s unlikely they would want to.
Source: http://www.imm.org/Reports/rep054.pdf