I think that you may be significantly underestimating the minimum possible doubling time of a fully automated, self replicating factory, assuming that the factory is powered by solar panels. There is a certain amount of energy which is required to make a solar panel. A self replicating factory needs to gather this amount of energy and use it to produce the solar panels needed to power its daughter factory. The minimum amount of time it takes for a solar panel to gather enough energy to produce another copy is known as the energy payback time, or EPBT.
Energy payback time (EPBT) and energy return on energy invested (EROI) of solar photovoltaic systems: A systematic review and meta-analysis is a meta-analysis which reviews a variety of papers to determine how long it takes various types of solar panels to produce the amount of energy needed to make another solar panel of the same type. It also provides energy returns on energy invested, which is a ratio which signifies the amount of excess energy you can harvest from an energy producing device before you need to build another one. If its less than 1, then the technology is not an energy source.
The energy payback time for solar panels varies between 1 and 4 years, depending on the technology specified. This imposes a hard limit on a solar powered self replicating factory’s doubling time, since it must make all the solar panels required for its daughter to be powered. Hence, it will take at least a year for a solar powered fully automated factory to self replicate. Wind has similar if less severe limitations, with Greenhouse gas and energy payback times for a wind turbine installed in the Brazilian Northeast finding an energy payback time of about half a year. This means that a wind powered self replicating factory must take at least half a year to self-replicate.
Note that neither of these papers account for how factories are not optimized to take advantage of intermittent energy and as such, do not estimate the energy cost of the energy storage required to smooth out intermittencies. Since some pieces of machinery, such as aluminumsmelters and chipfabs, cannot tolerate a long shutdown, a significant amount of energy storage will be required to keep these machines idling during cloudy weather or wind droughts. Considerations such as this will significantly increase the length of time it will take for a fully automated factory to self-replicate. Accounting for energy storage and the amount of energy needed to build a fully automated factory, I estimate that it would take years for a factory powered by solar or wind to self replicate.
I expect fusion will outperform solar and is reasonably likely to be viable if there is an abundance of extremely superhuman AIs.
Notably, there is no hard physical reason why the payback time required for solar panels has to a year rather e.g. a day or two. For instance, there exist plants which can double this quickly (see e.g. duckweed) and the limits of technology could allow for much faster double times. So, I think your analysis holds true for current solar technology (which maybe relevant to part of this post), but certainly doesn’t hold in the limit of technology and it may or may not be applicable at various points in a takeoff depending on how quickly AIs can advance relevant tech.
I mostly agree with your thinking. If there are multiple superintelligent AIs then one of then will likely figure out a method of viable fusion with a short payback period.
On the payback time of solar, it probably can be reduced significantly. Since the efficiency of solar panels cannot be increased much more (Shockley-Queisser limit for single junction cells, thermodynamic limit for any solar panel), then the only way to reduce the payback period will be to reduce the amount of embodied energy in the panel. I expect that the embodied energy of solar panels will stop falling once they start being limited by their fragility. If a solar panel cannot survive a windstorm, then it cannot be useful on Earth.
Your mention of biological lifeforms with a faster doubling time sent me on a significant tangent. Biological lifeforms provide an alternative approach, though any quickly doubling lifeform needs to either use photosynthesis for energy or eat photosynthetic plants. I expect there to be two main challenges to this approach. First, for the lifeform to be useful to a superintelligence, it needs to be hypercompetitive relative to native Earth life. This means that it needs to be much better at photosynthesis or digesting plant material compared to native Earth life. Such traits would allow it to fulfill the second requirement while remaining a functional lifeform. Second, the superintelligence needs to be able to effectively control the lifeform and have it produce arbitrary biomolecules on demand. Otherwise, the lifeform is not very useful to the superintelligence. I believe the first challenge is almost certainly solvable since photosynthesis on Earth is at best 5% efficient. The second will be more difficult. If the weakness in an organism a superintelligence needs to use to produce arbitrary biomolecules is too easily exploited, a virus, bacteria or parasite will evolve to exploit it, causing the population of the shackled synthetic organism to crash. If the synthetic organism has been designed such that it cannot evolve, its predators will keep it in check. Contrastingly, if the organism’s weakness is not sufficiently embedded in the genome, then the synthetic organism will evolve to lose its weakness. Variants of the synthetic organism which will not produce arbitrary biomolecules on demand will outcompete those which will since producing arbitrary biomolecules costs energy.
I think that you may be significantly underestimating the minimum possible doubling time of a fully automated, self replicating factory, assuming that the factory is powered by solar panels. There is a certain amount of energy which is required to make a solar panel. A self replicating factory needs to gather this amount of energy and use it to produce the solar panels needed to power its daughter factory. The minimum amount of time it takes for a solar panel to gather enough energy to produce another copy is known as the energy payback time, or EPBT.
Energy payback time (EPBT) and energy return on energy invested (EROI) of solar photovoltaic systems: A systematic review and meta-analysis is a meta-analysis which reviews a variety of papers to determine how long it takes various types of solar panels to produce the amount of energy needed to make another solar panel of the same type. It also provides energy returns on energy invested, which is a ratio which signifies the amount of excess energy you can harvest from an energy producing device before you need to build another one. If its less than 1, then the technology is not an energy source.
The energy payback time for solar panels varies between 1 and 4 years, depending on the technology specified. This imposes a hard limit on a solar powered self replicating factory’s doubling time, since it must make all the solar panels required for its daughter to be powered. Hence, it will take at least a year for a solar powered fully automated factory to self replicate. Wind has similar if less severe limitations, with Greenhouse gas and energy payback times for a wind turbine installed in the Brazilian Northeast finding an energy payback time of about half a year. This means that a wind powered self replicating factory must take at least half a year to self-replicate.
Note that neither of these papers account for how factories are not optimized to take advantage of intermittent energy and as such, do not estimate the energy cost of the energy storage required to smooth out intermittencies. Since some pieces of machinery, such as aluminum smelters and chip fabs, cannot tolerate a long shutdown, a significant amount of energy storage will be required to keep these machines idling during cloudy weather or wind droughts. Considerations such as this will significantly increase the length of time it will take for a fully automated factory to self-replicate. Accounting for energy storage and the amount of energy needed to build a fully automated factory, I estimate that it would take years for a factory powered by solar or wind to self replicate.
I expect fusion will outperform solar and is reasonably likely to be viable if there is an abundance of extremely superhuman AIs.
Notably, there is no hard physical reason why the payback time required for solar panels has to a year rather e.g. a day or two. For instance, there exist plants which can double this quickly (see e.g. duckweed) and the limits of technology could allow for much faster double times. So, I think your analysis holds true for current solar technology (which maybe relevant to part of this post), but certainly doesn’t hold in the limit of technology and it may or may not be applicable at various points in a takeoff depending on how quickly AIs can advance relevant tech.
I mostly agree with your thinking. If there are multiple superintelligent AIs then one of then will likely figure out a method of viable fusion with a short payback period.
On the payback time of solar, it probably can be reduced significantly. Since the efficiency of solar panels cannot be increased much more (Shockley-Queisser limit for single junction cells, thermodynamic limit for any solar panel), then the only way to reduce the payback period will be to reduce the amount of embodied energy in the panel. I expect that the embodied energy of solar panels will stop falling once they start being limited by their fragility. If a solar panel cannot survive a windstorm, then it cannot be useful on Earth.
Your mention of biological lifeforms with a faster doubling time sent me on a significant tangent. Biological lifeforms provide an alternative approach, though any quickly doubling lifeform needs to either use photosynthesis for energy or eat photosynthetic plants. I expect there to be two main challenges to this approach. First, for the lifeform to be useful to a superintelligence, it needs to be hypercompetitive relative to native Earth life. This means that it needs to be much better at photosynthesis or digesting plant material compared to native Earth life. Such traits would allow it to fulfill the second requirement while remaining a functional lifeform. Second, the superintelligence needs to be able to effectively control the lifeform and have it produce arbitrary biomolecules on demand. Otherwise, the lifeform is not very useful to the superintelligence. I believe the first challenge is almost certainly solvable since photosynthesis on Earth is at best 5% efficient. The second will be more difficult. If the weakness in an organism a superintelligence needs to use to produce arbitrary biomolecules is too easily exploited, a virus, bacteria or parasite will evolve to exploit it, causing the population of the shackled synthetic organism to crash. If the synthetic organism has been designed such that it cannot evolve, its predators will keep it in check. Contrastingly, if the organism’s weakness is not sufficiently embedded in the genome, then the synthetic organism will evolve to lose its weakness. Variants of the synthetic organism which will not produce arbitrary biomolecules on demand will outcompete those which will since producing arbitrary biomolecules costs energy.