This paper was published as a GPI working paper in September 2024.
Abstract
There are some possible events that we could not possibly discover in our past. We could not discover an omnicidal catastrophe, an event so destructive that it permanently wiped out life on Earth. Had such a catastrophe occurred, we wouldn’t be here to find out. This space of unobservable histories has been called the anthropic shadow. Several authors claim that the anthropic shadow leads to an ‘observation selection bias’, analogous to survivorship bias, when we use the historical record to estimate catastrophic risks. I argue against this claim.
Introduction
Estimating the probability of catastrophic events is a difficult business. We don’t have much to go on when the catastrophes would be of a novel kind, arising from hypothetical social or technological developments. On the other hand, for some types of catastrophes we have a long geological record to consult, along with other forms of data and the results of scientific modelling. For example, when it comes to asteroid impacts, we can use geological dating techniques and the observed distribution of crater sizes to inform our estimates of future risks.
A curious thing about this historical data, however, is that there are some possible data points that we could not possibly observe. We could not find in the historical data an omnicidal catastrophe, an event so destructive that it permanently wiped out life on Earth. Had such a catastrophe happened, we wouldn’t be here to find out. Ćirković, Sandberg, and Bostrom (2010) call this space of unobservable histories the anthropic shadow.
Some striking claims have been made about the significance of the anthropic shadow. For example, Ćirković et al. claim that, because of the anthropic shadow, a straightforward treatment of the historical record will lead to systematically underestimating the chances of potentially omnicidal events. In the extreme case, they write,
we should have no confidence in historically based probability estimates for events that would certainly extinguish humanity…(1497)
Tegmark and Bostrom (2005a) elaborate this line of thought in an earlier ‘brief communication’ published in Nature:
Given that life on Earth has survived for nearly 4 billion years (4 Gyr), it might be assumed that natural catastrophic events are extremely rare. Unfortunately, this argument is flawed because it fails to take into account an observationselection effect…, whereby observers are precluded from noting anything other than that their own species has survived up to the point when the observation is made. If it takes at least 4.6 Gyr for intelligent observers to arise, then the mere observation that Earth has survived for this duration cannot even give us grounds for rejecting with 99% confidence the hypothesis that the average cosmic neighbourhood is typically sterilized, say, every 1,000 years. The observation-selection effect guarantees that we would find ourselves in a lucky situation, no matter how frequent the sterilization events.
To avoid any straightforward appeal to the historical absence of omnicidal events, Tegmark and Bostrom develop a more complicated method based on modelling the formation times of habitable planets. More recently, Snyder-Beattie, Ord, and Bonsall (2019) estimate the lifespan of the human species and check how robust this estimate is with respect to different evolutionary hypotheses. They reason:
[I]f human existence required a 10 million year (Myr) period of evolution free from asteroid impacts, any human observers will necessarily find in their evolutionary history a period of 10 Myr that is free of asteroid impacts, regardless of the true impact rate. Inferring a rate based on those 10 Myr could therefore be misleading, and methods must to be used to correct for this bias.
In this paper I argue for a deflationary position: the existence of the anthropic shadow is essentially irrelevant to estimating risks. There are several interesting points that come up along the way, but an initial reason for skepticism is easy to state. According to standard forms of Bayesianism or evidentialism, what we ought to think depends on what evidence we actually have. The fact that we could not easily have had different evidence is not important in itself. So, even if we could not easily have had evidence of past omnicidal events, our actual evidence that there were no such events should make us think that the rate of them is low.
The core of this paper, sections 2–4, analyses a stylized example close to the one in Ćirković et al. Section 5 extends my analysis applies to the models used by Tegmark and Bostrom and by Snyder-Beattie et al., while section 6 concludes. As I mentioned, Ćirković et al. focus on potentially omnicidal events. For present concreteness, let us say that a ‘potentially omnicidal event’ is one that has a 10% chance of permanently ending life on Earth. Then, the upshot of my analysis is essentially as follows.
(A) The fact that life has survived so long is evidence that the rate of potentially omnicidal events is low.
(B) Given the fact that life has survived so long, historical frequencies provide evidence for a true rate rather higher than the observed rate.
(C) These two effects cancel out, so that, overall, the historical record provides evidence for a true rate close to the observed rate.
Thus, contrary to claims about the anthropic shadow, the historical record is (in the stated sense) a reliable guide to the rate of potentially omnicidal events.
On my reading, the authors quoted above are too focused on (B). Based on (B), the suggestion is that using the historical rate as an estimate of the true rate may lead to a bad underestimate. However, I argue that (A) is true and undermines this suggestion. Effectively, focusing on (B) neglects the base-rate provided by (A). I must admit, however, that I find the exact position of Ćirković et al. somewhat difficult to decipher. So, while I will try to indicate the specific points at which I disagree with other participants in this literature, the primary aim of this paper is to lay out the true story as clearly as I can, in a way that will forestall any further confusion.
(Just pointing out that previous discussion of this paper on this forum can be found here.)