I am struggling to follow this anthropic shadow argument. Perhaps someone can help me see what I am getting wrong.
Suppose that every million years on the dot, some catastrophic event happens with probability P (or fails to happen with probability 1-P). Suppose that if the event happens at one of these times, it destroys all life, permanently, with probability 0.1. Suppose that P is unknown, and we initially adopt a prior for it which is uniform between 0 and 1.
Now suppose that by examining the historical record we can discover exactly how many times the event has occurred in Earth’s history. Naively, we can then update our prior based on this evidence, and we get a posterior distribution sharply peaked at (# of times event has occurred) / (# of times event could have occurred). I will call this the ‘naive’ approach.
My understanding of the paper is that they are claiming this ‘naive’ approach is wrong, and it is wrong because of observer selection effects. In particular they claim it gives an underestimate of P. Their argument for this appears to be the following: if you pick a fixed value of P, and simulate history a large number of times, then in the cases where an observer like us evolves, the observer’s calculation of (# of times event has occurred) / (# of times event could have occurred) will on average be significantly below the true value of P. This is because observers are more likely to evolve after periods of unusually low catastrophic activity.
What I am currently not happy with is the following: shouldn’t you run the simulation a large number of times, not with fixed value of P, but with P chosen from the prior? And if you do that, I find their claim less obvious. Suppose for simplicity that instead of having a uniform prior, P is equally likely to take the value 0.1 or 0.9. Simulate history some large number of times. Half will be 0.1 worlds and half will be 0.9 worlds. Under the naive approach, more 0.9 world observers will think they are in the 0.1 world than in the paper’s approach, so they are more wrong, but there are also very few 0.9 world observers anyway (there is approximately a 10% chance of extinction per million years in this world). The vast majority of observers are 0.1 world observers, confident that they are 0.1 world observers (overconfident according to the paper), and they are right. If you just look at fixed values of P you seem to be ignoring the fact that observers are more likely to arise in worlds where P is smaller. When you take this fact into account, maybe it can justify the ‘naive’ underestimate?
This is a bit vague, but I’m just trying to explain my feeling that simulating the world many times at fixed P is not obviously the right thing to do (I may also be misunderstanding the argument of the paper and this isn’t really what they are doing).
To state my issue another way, although their argument seems plausible from one point of view, I am struggling to understand WHY the ‘naive’ argument is wrong. All you are doing is applying Bayes theorem, and conditioning on the evidence, which is the historical record of when the event did or did not occur. What could be wrong with that? I can only see it being wrong if there is some additional evidence you should be conditioning on as well which you are missing out, but I can’t see what that additional evidence could be in this context. It cannot be your existence, because the probability of your existence loses its dependence on P once the number of past occurrences of the event is given.
Yes, it seems that self-indication assumption is exactly compensating the anthropic shadow: the stronger is the shadow, the less likely I will be in such a world.
However, it works only if worlds with low p and no shadow actually exist somewhere in the multiverse (and in sufficiently large numbers). If there is a universal anthropic shadow, it will still work.
I am struggling to follow this anthropic shadow argument. Perhaps someone can help me see what I am getting wrong.
Suppose that every million years on the dot, some catastrophic event happens with probability P (or fails to happen with probability 1-P). Suppose that if the event happens at one of these times, it destroys all life, permanently, with probability 0.1. Suppose that P is unknown, and we initially adopt a prior for it which is uniform between 0 and 1.
Now suppose that by examining the historical record we can discover exactly how many times the event has occurred in Earth’s history. Naively, we can then update our prior based on this evidence, and we get a posterior distribution sharply peaked at (# of times event has occurred) / (# of times event could have occurred). I will call this the ‘naive’ approach.
My understanding of the paper is that they are claiming this ‘naive’ approach is wrong, and it is wrong because of observer selection effects. In particular they claim it gives an underestimate of P. Their argument for this appears to be the following: if you pick a fixed value of P, and simulate history a large number of times, then in the cases where an observer like us evolves, the observer’s calculation of (# of times event has occurred) / (# of times event could have occurred) will on average be significantly below the true value of P. This is because observers are more likely to evolve after periods of unusually low catastrophic activity.
What I am currently not happy with is the following: shouldn’t you run the simulation a large number of times, not with fixed value of P, but with P chosen from the prior? And if you do that, I find their claim less obvious. Suppose for simplicity that instead of having a uniform prior, P is equally likely to take the value 0.1 or 0.9. Simulate history some large number of times. Half will be 0.1 worlds and half will be 0.9 worlds. Under the naive approach, more 0.9 world observers will think they are in the 0.1 world than in the paper’s approach, so they are more wrong, but there are also very few 0.9 world observers anyway (there is approximately a 10% chance of extinction per million years in this world). The vast majority of observers are 0.1 world observers, confident that they are 0.1 world observers (overconfident according to the paper), and they are right. If you just look at fixed values of P you seem to be ignoring the fact that observers are more likely to arise in worlds where P is smaller. When you take this fact into account, maybe it can justify the ‘naive’ underestimate?
This is a bit vague, but I’m just trying to explain my feeling that simulating the world many times at fixed P is not obviously the right thing to do (I may also be misunderstanding the argument of the paper and this isn’t really what they are doing).
To state my issue another way, although their argument seems plausible from one point of view, I am struggling to understand WHY the ‘naive’ argument is wrong. All you are doing is applying Bayes theorem, and conditioning on the evidence, which is the historical record of when the event did or did not occur. What could be wrong with that? I can only see it being wrong if there is some additional evidence you should be conditioning on as well which you are missing out, but I can’t see what that additional evidence could be in this context. It cannot be your existence, because the probability of your existence loses its dependence on P once the number of past occurrences of the event is given.
Yes, it seems that self-indication assumption is exactly compensating the anthropic shadow: the stronger is the shadow, the less likely I will be in such a world.
However, it works only if worlds with low p and no shadow actually exist somewhere in the multiverse (and in sufficiently large numbers). If there is a universal anthropic shadow, it will still work.