Hi Ben, thanks for your kind words, and so sorry for the delayed response. Thanks for your questions!
Yes, this could definitely be the case. In terms of what the most effective intervention is, I don’t know. I agree that more work on this would be beneficial. One important consideration would be what intervention has the potential to raise the level of safety in the long run. Safety spending might only lead to a transitory increase in safety, or it could enable R&D that improves improves the level of safety in the long run. In the model, even slightly faster growth for a year means people are richer going forward forever, which in turn means people are willing to spend more on safety forever.
At least in terms of thinking about the impact of faster/slower growth, it seemed like the eta > beta case was the one we should focus on as you say (and this is what I do in the paper). When eta < beta, growth was unambiguously good; when eta >> beta, existential catastrophe was inevitable.
In terms of expected number of lives, it seems like the worlds in which humanity survives for a very long time are dramatically more valuable than any world in which existential catastrophe is inevitable. Nevertheless, I want to think more about potential cases where existential catastrophe might be inevitable, but there could still be a decently long future ahead. In particular, if we think humanity’s “growth mode” might change at some stage in the future, the relevant consideration might be the probability of reaching that stage, which could change the conclusions.
Regarding your question, yes, you have the right idea. Growth of consumption per capita is growth in consumption technology plus growth in consumption work per capita — thus, while the fraction of workers in the consumption sector declines exponentially, consumption technology grows (due to increasing returns) quickly enough to offset that. This yields positive asymptotic growth of consumption per capita overall (on the specific asymptotic paths you are referring to). Note that the absolute total number of people working consumption *research* is still increasing on the asymptotic path: while the fraction of scientists in the consumption sector declines exponentially, there is still overall population growth. This yields the asymptotic growth in consumption technology (but this growth is slower than what would be feasible, since scientists are being shifted away from consumption). Does that make sense?
Sorry to hear that! I’m not sure why it’s doing that—it’s just hosted on Github. Try this direct link: https://leopoldaschenbrenner.github.io/xriskandgrowth/ExistentialRiskAndGrowth050.pdf
Thanks. I generally try to explain the intuition of what is going on in the body of the text—I would recommend focusing on that rather than on the exact mathematical formulations. I am not planning to write a summary at the moment, sorry.
Thank you for your kind words!