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I don't know that I agree with this, but it did make me think.
I've never understood the bayesian logic of the anthropic shadow argument. I actually posted a question about this on the EA forum before, and didn't get a good answer. I'd appreciate it if someone could help me figure out what I'm missing. When I write down the causal diagram for this situation, I can't see how an anthropic shadow effect could be possible.
Section 2 of the linked paper shows that the probability of a catastrophic event having occurred in some time frame in the past given that we exist now: P(B_2|E), is smaller than its actual probability of occurring in that time frame, P. The two get more and more different the less likely we are to survive the catastrophic event (they call our probability of survival Q). It's easy to understand why that is true. It is more likely that we would exist now if the event did not occur than if it did occur. In the extreme case where we are certain to be wiped out by the event, then P(B_2|E) = 0.
This means that if you re-ran the history of the world thousands of times, the ones with observers around at our time would have fewer catastrophic events in their past, on average, than is suggested by P. I am completely happy with this.
But the paper then leaps from this observation to the conclusion that our naive estimate of the frequency of catastrophic events (i.e. our estimate of P) must be biased downwards. This is the point where I lose the chain of reasoning. Here is why.
What we care about here is not P(B_2|E). What we care about is our estimate of P itself. We would ideally like to calculate the posterior distribution of P, given both B_1,2 (the occurrence/non-occurrence of the event in the past), and our existence, E. The causal diagram here looks like this:
P -> B_2 -> E
This diagram means: P influences B_2 (the catastrophic event occurring), which influences E (our existence). But P does not influence E except through B_2.
*This means if we condition on B_2, the fact we exist now should have no further impact on our estimate of P*
To sum up my confusion: The distribution of (P|B_2,E) should be equivalent to the distribution of (P|B_2). I.e., there is no anthropic shadow effect.
In my original EA forum question I took the messy anthropics out of it and imagined flipping a biased coin hundreds of times and painting a blue tile red with probability 1-Q (extinction) if we ever get a head. If we looked at the results of this experiment, we could estimate the bias of the coin by simply counting the number of heads. The colour of the tile is irrelevant. And we should go with the naive estimate, even though it is again true that people who see a blue tile will have fewer heads on average than is suggested by the bias of the coin.
What this observation about the tile frequencies misses is that the tile is more likely to be blue when the probability of heads is smaller (or we are more likely to exist if P is smaller), and we should take that into account too.
Overall it seems like our naive estimate of P based on the frequency of the catastrophic event in our past is totally fine when all things are considered.
I'm struggling at the moment to see why the anthropic case should be different to the coin case.
Hi Toby,
Can't we imagine 100 people doing that experiment. People will get different results- some more heads than they "should" and some fewer heads than they "should." But the sample means will cluster around the real rate of heads. So any observer won't know if their result has too many heads or too few. So they go with their naive estimate.
With apocalypses, you know by definition you're one of the observers that wasn't wiped out. So I do think this reasoning works. If I'm wrong or my explanation makes no sense, please let me know!
Thanks for your reply!
If 100 people do the experiment, the ones who end up with a blue tile will, on average, have fewer heads than they should, for exactly the same reason that most observers will live after comparitively fewer catastrophic events.
But in the coin case that still does not mean that seeing a blue tile should make you revise your naive estimate upwards. The naive estimate is still, in bayesian terms, the correct one.
I don't understand why the anthropic case is different.
In the tile case, the observers on average will be correct. Some will get too many heads, some few. But the observers on average will be correct. You won't know whether you should adjust your personal estimate.
In the anthropic case, the observers on average will zero apocalypses no matter how common apocalypses are.
Imagine if in the tile case, everyone who was about to get more heads than average was killed by an assassin and the assassin told you what they were doing. Then when you did the experiment and lived, you would know your estimate was biased.
In the tile case, the observers who see a blue tile are underestimating on average. If you see a blue tile, you then know that you belong to that group, who are underestimating on average. But that still should not change your estimate. That's weird and unintuitive, but true in the coin/tile case (unless I've got the maths badly wrong somewhere).
I get that there is a difference in the anthropic case. If you kill everyone with a red tile, then you're right, the observers on average will be biased, because it's only the observers with a blue tile who are left, and their estimates were biased to begin with. But what I don't understand is, why is finding out that you are alive any different to finding out that your tile is blue? Shouldn't the update be the same?
No, because it's possible you observe blue tile or red tile.
You observe things (alive) or don't observe things (not alive.)
In the first situation, the observer knows multiple facts about the world could be observed. Not so in the second case.
I can see that is a difference between the two cases. What I'm struggling to understand is why that leads to a different answer.
My understanding of the steps of the anthropic shadow argument (possibly flawed or incomplete) is something like this:
You are an observer -> We should expect observers to underestimate the frequency of catastrophic events on average, if they use the frequency of catastrophic events in their past -> You should revise your estimate of the frequency of catastrophic events upwards
But in the coin/tile case you could make an exactly analogous argument:
You see a blue tile -> We should expect people who see a blue tile to underestimate the frequency of heads on average, if they use the frequency of heads in their past -> You should revise your estimate of the frequency of heads upwards.
But in the coin/tile case, this argument is wrong, even though it appears intuitively plausible. If you do the full bayesian analysis, that argument leads you to the wrong answer. Why should we trust the argument of identical structure in the anthropic case?
This is a good thing to flag. I actually agree re: anthropic reasoning (though frankly I always feel a bit unsettled by its fundamentally unscientific nature).
My main claim re: AI—as I saw it—was that the contours of the AI risk claim matched quite closely to messianic prophesies, just in modern secular clothing (I'll note that people both agreed and disagreed with me on this point and interested people should read my short post and the comments). I still stand by that fwiw—I think it's at minimum an exceptional coincidence.
One underrated response that I have been thinking about was by Jason Wagner, who paraphrased one reading of my claim as:
"AI might or might not be a real worry, but it's suspicious that people are ramming it into the Christian-influenced narrative format of the messianic prophecy. Maybe people are misinterpreting the true AI risk in order to fit it into this classic narrative format; I should think twice about anthropomorphizing the danger and instead try to see this as a more abstract technological/economic trend."
In this reading AI risk is real, no one has a great sense of how to explain it because much of its nature is unknown and simply weird, and so we fall back on narratives that we understand—so Christian-ish messiah-type stories.
Hey Ryan,
I think I agree with the religious comparison- they do seem similar to me and I liked that part of your post. I just think failed apocalyptic predictions don't give that much evidence that we can discount future apocalyptic predictions.
Religious apocalypses are maybe a little different because I think (but don't know) that most people who predict the end of the world via God are claiming that all possible worlds end, not just predicting an event that will normally occur.
I mostly think anthropic reasoning is good (but there is a voice in my head telling me I'm crazy whenever I try to apply it).
I'll re-word my comment to clarify the part re: "the dangers of anthropic reasoning". I always forget if "anthropic" gets applied to not conditioning on existence and making claims, or the claim that we need to condition on existence when making claims.
Cross-post from Cold Button Issues.
Is the world at risk of ending soon? One answer is no and people predicting a proximate apocalypse will make a fool out of themselves, just like everybody who predicted this in the past. Ryan Briggs just offered a version of this argument. Briggs pointed out that lots of people have predicted a total upheaval of the world, or its end at the hands of super-beings (gods) and as far as we know those predictions have always failed.
Not everyone finds this style of argument convincing.
One response to Briggs is that contemporary arguments for apocalypses or existential risk are just much more sophisticated and likely to be correct than older arguments. Or perhaps philosophers and scientists are better at predicting the end of the world than pastors and theologians. Maybe.
Objectors can also zero in on a particular world-ending threat, normally artificial intelligence but sometimes something else, and explain that we have very specific reasons to be afraid of this type of apocalypse. Another rebuttal is that the accuracy of religious apocalyptic predictions tells us nothing about the accuracy of secular apocalyptic predictions.
But I think a better response to people bringing up failed apocalyptic predictions is that we must live in a world where the world didn’t end- otherwise we wouldn’t be around to observe it. We are doomed to under-estimate the risk of the world ending because whoever is making these estimations have to exist in order to make them.
Ćirković, Sanderg, and Bostrom call this anthropic shadow. They point out that we can’t use history to estimate every type of existential risk because our existence is predicated on them not happening. They suggest that we are likely underestimating all kinds of existential risks including death by asteroids, supervolanoes, and gamma ray bursts. We can only notice that doomsday preachers are wrong, when we survive doomsday because it doesn’t happen. For all we know, doomsday preachers may be great at their job.
One response and the one recommended by Ćirković, Sanderg, and Bostrom is to take this challenge seriously and invest more in research to try to gauge how at risk is the world from various threats
Maybe we could also try to prioritize interventions that might keep humanity alive through various types of disasters- interplanetary expansion perhaps.
A less optimistic implication is that the far future may be far emptier than we think. Maybe we should eat and drink and be merry- or more altruistically focus on helping people today.
(I have not read the relevant papers)
My own take is that anthropic shadow seems to be a pretty weak argument for things like asteroids or supervolcanoes or (arguably) nukes in the world we live in, because our current scientific understanding of near-misses for total extinction is that there weren't that many (any?) of them.
I think the anthropics argument can however be mostly rescued by: "Of observers that otherwise naively seem very similar to us, if they lived in an environment with much higher background risk of asteroids/supervolcanoes/etc, their observations would not seem very different from that of our ancestors." Thus, we cannot use past examples of failed apocalypses as strong Bayesian evidence for future categories of apocalypses, as we are anthropically selected to come from the sample of people who have not been correct in determinations of past high risk.
EDIT: Rereading this argument, I'm worried that it's "too clever."
related notes by Ben Garfinkel (though not focused on anthropics specifically).