I really like this post. I totally agree that if x-risk mitigation gets credit for long-term effects, other areas should as well, and that global health & development likely has significantly positive long-term effects. In addition to the compounding total utility from compounding population growth, those people could also work on x-risk! Or they could work on GH&D, enabling even more people to work on x-risk or GH&D (or any other cause), and so on.
One light critique: I didn’t find the theoretical infinity-related arguments convincing. There are a lot of mathematical tools for dealing with infinities and infinite sums that can sidestep these issues. For example, since ∑∞t=1f(t) is typically shorthand for limt→∞∑tx=1f(x), we can often compare two infinite sums by looking at the limit of the sum of differences, e.g., ∑∞t=1f(t)−∑∞t=1g(t)=limt→∞∑tx=1(f(x)−g(x)). Suppose f(t),g(t) denote the total utility at time t given actions 1 and 2, respectively, and f(t)=2g(t). Then even though ∑∞t=1f(t)=∑∞t=1g(t)=∞, we can still conclude that action 1 is better because limt→∞∑tx=1(f(x)−g(x))=limt→∞∑tx=1g(t)=∞.
This is a simplified example, but my main point is that you can always look at an infinite sum as the limit of well-defined finite sums. So I’m personally not too worried about the theoretical implications of infinite sums that produce “infinite utility”.
P.S. I realize this comment is 1.5 years late lol but I just found this post!
I really like this post. I totally agree that if x-risk mitigation gets credit for long-term effects, other areas should as well, and that global health & development likely has significantly positive long-term effects. In addition to the compounding total utility from compounding population growth, those people could also work on x-risk! Or they could work on GH&D, enabling even more people to work on x-risk or GH&D (or any other cause), and so on.
One light critique: I didn’t find the theoretical infinity-related arguments convincing. There are a lot of mathematical tools for dealing with infinities and infinite sums that can sidestep these issues. For example, since ∑∞t=1f(t) is typically shorthand for limt→∞∑tx=1f(x), we can often compare two infinite sums by looking at the limit of the sum of differences, e.g., ∑∞t=1f(t)−∑∞t=1g(t)=limt→∞∑tx=1(f(x)−g(x)). Suppose f(t),g(t) denote the total utility at time t given actions 1 and 2, respectively, and f(t)=2g(t). Then even though ∑∞t=1f(t)=∑∞t=1g(t)=∞, we can still conclude that action 1 is better because limt→∞∑tx=1(f(x)−g(x))=limt→∞∑tx=1g(t)=∞.
This is a simplified example, but my main point is that you can always look at an infinite sum as the limit of well-defined finite sums. So I’m personally not too worried about the theoretical implications of infinite sums that produce “infinite utility”.
P.S. I realize this comment is 1.5 years late lol but I just found this post!