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Anthropic Shadow: Observation Selection Effects and Human Extinction Risks

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Anthropic Shadow: Observation Selection Effects and Human Extinction Risks Risk Analysis, Vol. 30, No. 10, 2010 DOI: 10.1111/j.1539-6924.2010.01460.x Anthropic Shadow: Observation Selection Effects and Human Extinction Risks Milan M. Cirkovi´ c,´ 1∗ Anders Sandberg,2 and Nick Bostrom2 We describe a significant practical consequence of taking anthropic biases into account in deriving predictions for rare stochastic catastrophic events. The risks associated with catastrophes such as asteroidal/cometary impacts, supervolcanic episodes, and explosions of supernovae/gamma-ray bursts are based on their observed frequencies. As a result, the fre- quencies of catastrophes that destroy or are otherwise incompatible with the existence of observers are systematically underestimated. We describe the consequences of this anthropic bias for estimation of catastrophic risks, and suggest some directions for future work. KEY WORDS: Anthropic principle; astrobiology; existential risks; global catastrophes; impact hazard; natural hazards; risk management; selection effects; vacuum phase transition 1. INTRODUCTION: EXISTENTIAL RISKS clude global nuclear war, collision of Earth with a AND OBSERVATION SELECTION 10-km sized (or larger) asteroidal or cometary body, EFFECTS intentional or accidental misuse of bio- or nano- technologies, or runaway global warming. Humanity faces a series of major global threats, There are various possible taxonomies of ERs.(7) both in the near- and in the long-term future. For our purposes, the most relevant division is one These are of theoretical interest to anyone who based on the causative agent. Thus we distinguish: is concerned about the future of our species, (1) natural ERs (e.g., cosmic impacts, supervolcan- but they are also of direct relevance to many ism, nonanthropogenic climate change, supernovae, practical and policy decisions we make today. gamma-ray bursts, spontaneous decay of cosmic vac- General awareness of the possibility of global uum state); (2) anthropogenic ERs (e.g., nuclear war, catastrophic events has risen recently, thanks to dis- biological accidents, artificial intelligence, nanotech- coveries in geochemistry, human evolution, astro- − nology risks); and (3) intermediate ERs, ones that physics, and molecular biology.(1 6) In this study, depend on complex interactions between human- we concentrate on the subset of catastrophes called ity and its environment (e.g., new diseases, runaway existential risks (ERs): risks where an adverse out- global warming). In what follows, we focus mainly on come would either annihilate Earth-originating in- ERs of natural origin.(8) telligent life or permanently and drastically cur- Our goal in this article is to study a specific ob- tail its potential.(7) Examples of potential ERs in- servation selection effect that influences estimation 1 Astronomical Observatory of Belgrade, Volgina, Belgrade, of some ER probabilities, threatening to induce an Serbia. anthropic bias into the risk analysis.3 Anthropic bias 2 Future of Humanity Institute, Faculty of Philosophy & James Martin 21st Century School, Oxford University, London, UK. ∗Address correspondence to M. M. Cirkovi´ c,´ Astronomical Ob- 3 For a summary of the vast literature on anthropic principles and servatory of Belgrade, Volgina 7, 11160 Belgrade-74, Serbia; anthropic reasoning in general, see Barrow and Tipler; Balashov; tel: +381-11-3089079; fax: +381-11-2419553; [email protected]. and Bostrom.(56−58) 1495 0272-4332/10/0100-1495$22.00/1 C 2010 Society for Risk Analysis 1496 Cirkovi´ c,´ Sandberg, and Bostrom Fig. 1. A schematic representation of our single-event toy model. P is the apriori probability of a global catastrophe; Q is the probability of human survival given the catastrophe; E is the fact of our present-day existence. can be understood as a form of sampling bias, in a host of biological, chemical, and physical precon- which the sample of observed events is not repre- ditions. In particular, our existence implies that the sentative of the universe of all events, but only rep- evolutionary chain of terrestrial evolution leading to resentative of the set of events compatible with the our emergence was not broken by a terminally catas- existence of suitably positioned observers. We show trophic event. We shall discuss some of the ambigu- that some ER probabilities derived from past records ities related to this condition below. The hypotheses are unreliable due to the presence of observation se- B1,B2, ...,Bn that are of interest to us here are those lection effects. Anthropic bias, we maintain, can lead dealing with the occurrence or nonoccurrence of a to underestimation of the probability of a range of particular type of global catastrophic event in a given catastrophic events. interval of time. For example, one hypothesis may We first present a simple toy model of the effect be “There were at least five impacts of asteroids or in Section 2, which we generalize in Section 3. We de- comets of 10–20 km size during the last 108 years”; velop the argument in more detail in Section 4, and or “There was no supernova explosion closer than 10 consider its relevance to various types of global catas- parsecs from the Sun between 2 × 107 and 5 × 106 trophic risks in Section 5. Finally, in Section 6, we dis- years before present (henceforth B.P.).” cuss how the theory of observation selection effects Consider the simplest case of a single very de- might generally be applied to global catastrophes. structive global catastrophe, such as a Toba-like su- pervolcanic eruption.(9) The evidence that we wish 4 to conditionalize upon in a Bayesian manner is the 2. A TOY MODEL OF ANTHROPIC BIAS fact of our existence at the present epoch. We can The basis of our approach is Bayes’s formula for schematically represent the situation as in Fig. 1: the conditional probability: prior probability of catastrophe is P and the prob- | ability of human survival following the catastrophic | = P (Bi ) P (E Bi ) , event is Q. We shall suppose that the two probabili- P (Bi E) n (1) ties are: (1) constant, (2) adequately normalized, and P (B ) P (E | B ) j j (3) apply to a particular interval of past time. Event j=1 B2 is the occurrence of the catastrophe, event B1 is where P(Bi) is prior probability of hypothesis Bi be- the nonoccurrence of the catastrophe, and by E we ing true, and P(Bi|E) is the conditional probability of denote the evidence of our present existence. hypothesis Bi being true, given evidence E. The evi- The direct application of Bayes’s formula in the dence we will consider is our existence as intelligent form: observers in the present epoch. Our existence entails P(B ) P(E | B ) P(B | E) = 2 2 , 4 2 Some earlier findings related to this section were presented in P(B1) P(E | B1) + P(B2) P(E | B2) Cirkovi´ c.´ (59) (2) Anthropic Shadow: Observation Selection Effects and Human Extinction Risks 1497 yields the posterior probability as: Overconfidence becomes very large for very de- PQ PQ structive events. As a consequence, we should have no P(B | E) = = . confidence in historically based probability estimates 2 (1 − P) · 1 + PQ 1 − P + PQ for events that would certainly extinguish humanity (3) (Q = 0). While this conclusion may seem obvious, We can define an overconfidence parameter as: it is not widely appreciated. For instance, as we dis- cuss below, a well-known argument of Hut and Rees P (apriori) η ≡ , (4) dealing with the hypothetical risk to the stability of P (a posteriori) quantum vacuum due to the high-energy physics ex- which in this special case becomes: periments is partially misleading because it fails to take into account the anthropic bias.(10) P 1 − P + PQ η = = . The same reasoning applies to those extremely | (5) P (B2 E) Q rare, but still definitely possible, physical disasters As η moves beyond 1, our inferences from the like various strange astronomical occurrences lead- past become increasingly unreliable, and we under- ing to the Earth becoming an unbound planet due to estimate the probabilities of future catastrophes. For close passage of a normal star (see e.g., Laughlin and instance, suppose Q = 0.1 and P = 0.5, correspond- Adams for estimates how probable it is in the remain- (11) ing to a fair-coin-toss chance that a Toba-scale event ing lifetime of the solar system ), or even more ex- occurs once per 1 million (106) years (Myr) of human otic objects, like a neutron star or a black hole. The evolution, and that the probability of human survival conclusion that the irreversible destruction of Earth following such an event is 0.1. The resulting value in an encounter of the solar system with a passing of the overconfidence parameter is η = 5.5, indicat- star or a black hole is extremely improbable cannot ing that the actual probability of such an event is 5.5 be obtained solely from the inference from the past times our initial estimate. Values of overconfidence history of our planetary system. In this case, how- as a function of severity (as measured by the extinc- ever, admission of additional information, based on tion probability 1 − Q) are shown in Fig. 2. our understanding of the solar neighborhood in the Note that Milky Way and the mass function of stellar objects, for instance, could render the conclusion that we are lim η =∞. (6) Q→0 safe from this particular risk rather bias-free and per- suasive. On the other hand, the amount of additional admissible information is highly uneven when we are dealing with a wide spectrum of possible global haz- ards. 3. GENERALIZING THE MODEL How to generalize this to a series of possible catastrophic events? We shall briefly sketch one pos- sible approach here. We face a situation like the one shown in Fig.
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