In a more typical endogenous growth model, output is the product of physical capital (e.g. how many computers you have) and a technology factor (e.g. how smart you are). You can either invest in producing more capital (building more computers) or doing research (becoming smarter). On these models, even returns of xϵ still lead to a mathematical singularity (while constant technology leads to exponential growth).
From this perspective, you are investigating whether there is an intelligence explosion with finite capital. If productivity grows sublinearly with inputs, you need to build more machines (and ultimately extract more resources from nature) in order to grow really fast. This might suggest that getting to a singularity would take years rather than weeks, but doesn’t much change the qualitative conclusion or substantially change the urgency (especially given that the early phase of takeoff would be driven by moving resources over from lower productivity areas into higher productivity areas).
In a more typical endogenous growth model, output is the product of physical capital (e.g. how many computers you have) and a technology factor (e.g. how smart you are). You can either invest in producing more capital (building more computers) or doing research (becoming smarter). On these models, even returns of xϵ still lead to a mathematical singularity (while constant technology leads to exponential growth).
From this perspective, you are investigating whether there is an intelligence explosion with finite capital. If productivity grows sublinearly with inputs, you need to build more machines (and ultimately extract more resources from nature) in order to grow really fast. This might suggest that getting to a singularity would take years rather than weeks, but doesn’t much change the qualitative conclusion or substantially change the urgency (especially given that the early phase of takeoff would be driven by moving resources over from lower productivity areas into higher productivity areas).