This math problem is relevant, although maybe the assumptions aren’t realistic. Basically, under certain assumptions, either our population has to increase without bound, or we go extinct.
EDIT: The main assumption is effectively that extinction risk is bounded below by a constant that depends only on the current population size, and not the time (when the generation happens). But you could imagine that even for a stable population size, this risk could be decreased asymptotically to 0 over time. I think that’s basically the only other way out.
So, either:
1. We go extinct,
2. Our population increases without bound, or
3. We decrease extinction risk towards 0 in the long-run.
Of course, extinction could still take a long time, and a lot of (dis)value could happen before then. This result isn’t so interesting if we think extinction is almost guaranteed anyway, due to heat death, etc..
re: 3 — to be more precise, one can show that $\prod_i (1 - p_i) > 0$ iff $\sum p_i < ∞$, where $p_i \in [0, 1)$ is a probability of extinction in a given year.
I’ve seen and liked that book. But i don’t think there really is enough information about risks (eg earth being hit by a comet or meteor that kills everything) to really say much—maybe if cosmology makes major advances or in other fields one can say somerthing but that might takes centuries.
This math problem is relevant, although maybe the assumptions aren’t realistic. Basically, under certain assumptions, either our population has to increase without bound, or we go extinct.
EDIT: The main assumption is effectively that extinction risk is bounded below by a constant that depends only on the current population size, and not the time (when the generation happens). But you could imagine that even for a stable population size, this risk could be decreased asymptotically to 0 over time. I think that’s basically the only other way out.
So, either:
1. We go extinct,
2. Our population increases without bound, or
3. We decrease extinction risk towards 0 in the long-run.
Of course, extinction could still take a long time, and a lot of (dis)value could happen before then. This result isn’t so interesting if we think extinction is almost guaranteed anyway, due to heat death, etc..
Source for the screenshot: Samuel Karlin & Howard E. Taylor, A First Course in Stochastic Processes, 2nd ed., New York: Academic Press, 1975.
re: 3 — to be more precise, one can show that $\prod_i (1 - p_i) > 0$ iff $\sum p_i < ∞$, where $p_i \in [0, 1)$ is a probability of extinction in a given year.
Should that be ∑ilog(1−pi)>−∞? Just taking logarithms.
This is a valid convergence test. But I think it’s easier to reason about \sum p_i < ∞. See math.SE for a proof.
I’ve seen and liked that book. But i don’t think there really is enough information about risks (eg earth being hit by a comet or meteor that kills everything) to really say much—maybe if cosmology makes major advances or in other fields one can say somerthing but that might takes centuries.