On the Likelihood of Observing Extragalactic Civilizations: Predictions from the Self-Indication Assumption

S. Jay Olson∗ Department of Physics, Boise State University, Boise, Idaho 83725, USA (Dated: February 20, 2020) Ambitious civilizations that expand for resources at an intergalactic scale could be observable from a cosmological distance, but how likely is one to be visible to us? The question comes down to estimating the appearance rate of such things in the cosmos — a radically uncertain quantity. Despite this prior uncertainty, anthropic considerations give rise to Bayesian updates, and thus predictions. The Self-Sampling Assumption (SSA), a school of anthropic probability, has previously been used for this purpose. Here, we derive predictions from the alternative school, the Self-Indication As- sumption (SIA), and point out its features. SIA favors a higher appearance rate of expansionistic life, but our existence at the present cosmic time means that such life cannot be too common (else our galaxy would long ago have been overrun). This combination squeezes our vast prior uncertainty into a few orders of magnitude. Details of the background cosmology fall out, and we are left with some stark conclusions. E.g. if the limits to technology allow a civilization to expand at speed v, the probability of at least one expanding cosmological civilization being visible on our past light cone v3 is 1 − c3 . We also show how the SIA estimate can be updated from the results of a hypothetical full-sky survey that detects “n” expanding civilizations (for n ≥ 0), and calculate the implied ﬁnal extent of life in the universe.

I. INTRODUCTION appearance rate. If ambitious life is sufficiently rare, the universe on a large scale will hardly notice — although One of the grand mysteries of the cosmos is the role such civilizations may become enormous, the cosmic ac- of intelligent life. Is it a freak occurrence, rare and fleet- celeration will ensure they remain bounded and isolated ing [1]? Or is life destined to inherit and transform the in an otherwise sterile universe. A large appearance rate universe on the largest scale [2]? means that the universe will quickly become completely To have an opinion on the matter is to have an opinion saturated with ambitious life. on the enabling factors — the limits to practical technol- Despite many decades of searches (from nearby ogy, and the appearance rate of ambitious life. Severe stars [7] to as far as nearby galaxies [8, 9]), no signatures bounds on either mean that life will forever be insignifi- of extraterrestrial intelligence have been demonstrated. cant1. But the opposite case is quite possible. Searches at deep cosmological distances may be forth- It is not difficult to take the optimist position on tech- coming [10], but until then, we are left with anthropic nology. A minimal set of technologies required for this reasoning to estimate the appearance rate — arguments position are high-speed spacecraft that can travel be- that rely on the properties of our own existence [11]. Two tween galaxies [3], with the ability to self-replicate from pieces of anthropic information are particularly impor- available resources [4]. Current human technology is al- tant — we have arrived at cosmic time t0 ≈ 13.8 Gyr, ready developing 0.2c interstellar spacecraft on a realis- and we are apparently not within the domain of an am- tic budget [5], and initial studies suggest that the tech- bitious civilization that is maximizing use of resources. nology gap between interstellar and intergalactic space There are two popular schools of anthropic probabil- travel is slim [6] — the major difference is simply the ity [11]. One is known as the Self-Sampling Assumption travel time. Self-replicating technology is a greater chal- (SSA) — it draws conclusions about the universe by rea- lenge from our present position, but we are surrounded soning as though our existence is a random draw from by numerous species of robust “self-replicating aircraft” a “reference class” of similar life. It does not care how that show the basic principle at work. often civilizations like ours actually occur, but it favors arXiv:2002.08194v1 [astro-ph.CO] 18 Feb 2020 The optimist position on technology implies that ex- conditions that make us more typical within the set of panding cosmological civilizations [2] are possible. Am- those that do occur. We have previously applied SSA bitious life, seeking to maximize access to resources, reasoning to the problem of estimating the appearance can embark on intergalactic expansion spanning billions rate (and observability) of expanding cosmological civi- of light-years, for nearly zero cost (due to use of self- lizations [12–14]. replication). The more difficult question is that of the The other school is known as the Self-Indication As- sumption (SIA). Rather than favoring our typicality within a reference class, SIA favors conditions that are ∗ [email protected] more likely, in an absolute sense, to have produced us. 1 “Insignificant” in the sense that a physical description of the SSA and SIA make different predictions, and the question universe could be an excellent approximation without accounting of which is appropriate for cosmology has been debated for the activities of life. for decades [15–17]. 2

Our main goal here is to derive the basic predictions of co-moving volume occupied by such a civilization at cos- SIA reasoning, for the appearance rate and observability mic time t, having appeared at cosmic time t0 is that of of expanding cosmological civilizations. We will find the a sphere, given by: SIA approach has several attractive features. It is far less Z t 3 dependent on modeling of the relative appearance rate 3 0 4π 3 1 00 v V (t , t) = v 00 dt (1) of life throughout cosmic time. It is far less dependent 3 t0 a(t ) on one’s prior assumptions about the magnitude of the where a(t) is the cosmic scale factor3. Note that V (t0, t ) appearance rate. The resulting predictions are simple, 0 also represents the volume of space encompassed by our closed-form expressions. And they are somewhat more past light cone back at time t0. optimistic for detection than SSA-based estimates. At a large scale the universe is homogeneous, so the The SIA approach also lends itself well to the next picture is that of spherical domains randomly appearing step. Suppose that in the future, the full sky is surveyed in space and expanding over a cosmic timescale, anal- to great distance, detecting “n” expanding cosmological ogous to the geometry of a cosmological phase transi- civilizations. We show how this information updates our tion [20, 21]. Indeed, it is more than an analogy, if life SIA estimate for the appearance rate. Based on this re- makes changes to the matter and radiation content. In- sult, we can examine the original question above — that telligent life may literally be a way for the universe to of the ultimate role of life in the universe. At late cosmic quickly find and jump to a higher-entropy state, releas- times, how much of the universe will have been saturated ing heat in the process [2]. by ambitious life? For our purposes, we regard the velocity of expansion, We organize this paper in the following way: Section v, as the same constant for all expanding civilizations. II reviews the basics of homogeneous cosmology with ex- The justification is that the difficulty of launching high- panding civilizations. Section III discusses SSA and SIA speed spacecraft explodes in a fairly narrow range of v. in more detail, and how they are applied in the present At v = 0.2c, it is already practical for humanity [5]. But context. Section IV discusses the issue of our prior uncer- v = 1 is strictly impossible for any civilization, no matter tainty — an essential starting-point for Bayesian reason- how advanced, if our present understanding of physics is ing. Section V derives our main result — SIA estimates not completely misleading. Thus any ambitious civiliza- for the appearance rate and observability of expanding tion will likely encounter a very similar “practical speed cosmological civilizations. Section VI shows how esti- limit” for their spacecraft, which is the main factor in mates are updated (with Bayes’ theorem) after a search, their net expansion speed4. Due to this approximately and section VII addresses the question of the end state universal nature of v (whatever its value may actually of life in the cosmos. Section VIII draws a direct com- be), we refer to it as the dominant expansion velocity. parison to previous SSA-based results, and section IX It is one of the two essential parameters in a cosmology contains our concluding remarks. with expanding civilizations. The appearance rate of such civilizations (with units 3 II. EXPANDING COSMOLOGICAL of appearances per Gly of co-moving volume per Gyr of CIVILIZATIONS cosmic time) is denoted by f(t). Our prior assumptions about f(t) are radically uncertain, but there is a simple way to isolate and express most of the uncertainty. We An expanding cosmological civilization is a hypothet- regard f(t) as the product f(t) = αF (t), where F (t) is ical form of ambitious life that has, as an instrumental a dimensionless time dependence (normalized to a maxi- goal, the control of as many resources as possible. It is mum value of unity), roughly mirroring the cosmic rate of difficult to imagine a more general final state of techno- production of Earthlike planets [23], with a lag of several logical activity. In terms of utility, practically any final Gyr to account for the long process of biological evolu- goal can be more fully realized with access to more re- tion [12] (see Figure 1). The parameter α (carrying the sources [18]. In terms of the energetics of life, an ex- units of appearances per Gly3 per Gyr) determines the panding cosmological civilization is a consequence of the overall scale, where most of the uncertainty lies. With a maximum power principle [19]. In terms of stability of large systems, the act of not expanding requires all par- ticipants to agree not to expand, while initiating cosmic expansion requires only a single, isolated decision to number less than 1. 3 launch one spacecraft that is capable of high speed and We assume the following standard cosmology: ΩΛ0 = .692, −5 −1 self-replication. Ωr0 = 9 × 10 ,Ωm0 = 1 − Ωr0 − ΩΛ0, H0 = .069 Gyr , giving t0 = 13.8 Gyr. Conservative assumptions on physics lead to a simple 4 The travel time between galaxies utterly dwarfs any other geometry for such a civilization — expansion in all di- timescale in the process of expansion, e.g. the time required to rections at some fraction of the speed of light, v.2 The reproduce between generations of spacecraft. Thus, if a civilization is ambitious, their net expansion speed will be very close to the speed of their intergalactic spacecraft. See appendix of [22] for a detailed justification based on the spatial distribution of 2 We use units such that c = 1, and velocities are expressed as a galaxies in the universe. 3

III. SELF-SAMPLING AND SELF-INDICATION ASSUMPTIONS

The two most common schools of anthropic probability are known as the Self-Sampling Assumption (SSA) and the Self-Indication Assumption (SIA) [11]. In this section, we give a quick review of the reasoning of each in the present context. In SSA, we describe a “reference class” of civilizations that are analogous to humanity, and favor theories of the universe that make humanity more typical within the reference class. Essentially, we are viewing humanity as a random draw from a set of civilizations, and updating our understanding of the universe based on the properties of our draw. FIG. 1: A model for the cosmic time-dependence of the There are multiple ways to arrive at the predictions of appearance rate of advanced life, F (t), normalized to a SIA — here, we use a version called Full Non-Indexical maximum value of unity. The full appearance rate of Conditioning (FNC) [24], which agrees with SIA in the ambitious expanding civilizations is given by limit of observers who carry a significant amount of in- f(t) = αF (t), where α has units of appearances per formation5. Effectively, SIA favors theories that make it Gly3 per Gyr. This model for F (t) is effectively a more likely according to physical law that we should exist model of the planet formation rate of the cosmos, with here, in exactly our conditions. It works by saying the a lag of several Gyr to account for the evolution of conditions most likely to have produced us, are also the intelligent life. conditions that produce many others like us. It makes no appeal to a reference class. model for the background cosmology and F (t) fixed, we A good way to see the distinction is to consider the regard a scenario of expanding cosmological civilizations meaning of the probabilities appearing in a Bayesian as the pair of parameters {v, α}. While v is modestly application of SSA and SIA. The likelihood function, uncertain, almost the entire subject of this paper boils P (anthropic information | theory n) would, in SSA, rep- down to finding an estimate for α. resent the probability that a randomly selected member of the reference class sees anthropic information, accord- It is now convenient to define s(t0) = R t0 ing to theory n. In SIA, this quantity represents the prob- 0 F (t) V (t, t0) dt. For the standard cosmology and the appearance rate function in Figure 1, ability that an observer who sees anthropic information 3 should appear at all, according to theory n. The alter- s(t0) ≈ 1268 Gly Gyr. The fraction of the universe that remains unsaturated by expanding life at the native (complement of anthropic information) in SSA is present cosmic time is given by g(t ): that a different member of the reference class is selected. 0 The alternative in SIA is that the observer who sees an- 3 −αv s(t0) gα(t0) = e . (2) thropic information does not exist. In the present context, the anthropic information is The (average) expected number of expanding cosmologi- humanity’s cosmic time of arrival, t , while theory n is cal civilizations that are present/visible on our past light 0 the value of the appearance rate, α. cone is E (n): α The SSA approach we have previously used is to pre- 3 Eα(n) = α(1 − v )s(t0), (3) scribe a reference class of human-stage civilizations that and the probability that there is at least one on our past appear in galaxies that have not been saturated by am- light cone is then: bitious life [12]. Then we can describe a cosmic time-of- arrival (TOA) distribution of such civilizations according 3 −α(1−v )s(t0) pα(n ≥ 1) = 1 − e . (4) to: 3 The recurring factor of (1 − v ) expresses the fact that F (t)gα(t) p (t|α) = . (5) we count civilizations that have appeared within our past TOA R ∞ 0 0 0 0 F (t )gα(t )dt light cone, but not within our “past saturation cone” (which expands into our past with speed v), since our position in space has apparently not been overtaken and saturated by an expanding civilization. 5 Predictions of FNC have been shown to differ from other pre- As a practical matter, if one can see only a fraction of sentations of SIA when “observers” are extremely simple beings, who carry only a few bits of information [25]. We will not con- the sky (due to the Zone of Avoidance or simply due to sider this possibility, and the results we obtain here can also incomplete galaxy surveys), multiply s(t0) in the expres- be obtained using the older technique of modifying the prior to sions for Eα(n) and pα(n ≥ 1) by the fraction of the sky cancel the reference class. For this reason we use FNC and SIA that is visible. interchangeably here. 4

Given SSA, one assumes that humanity is a random sam- change if the endpoints are extended further than that — ple from this distribution. To get predictions, one speci- a surprising result to be justified below. In any case, the fies an assumption about humanity’s “typicality in time” next section will derive closed-form results that are valid (whether were are at the average time of arrival, a one for any chosen values of αmin and αmax, and then take standard-deviation latecomer, etc.) and finds the corre- the limit that the endpoints of the prior go to αmin → 0 sponding value of α that matches t0 with the assumption. and αmax → ∞. This value of α is then used to get predictions according to equations 3 and 4. The SIA approach we will develop below is more di- V. SIA APPLIED TO EXPANDING rectly Bayesian. The (unnormalized) likelihood of our COSMOLOGICAL CIVILIZATIONS: PREDICTIONS FOR EXTRAGALACTIC SETI appearance here at cosmic time t0 is:

P (t0|α, γ) = γ F (t0) gα(t0). (6) To update our prior, P (α), our cosmic time of arrival Here represents the probability of anthropic informa- is particularly important. If the appearance rate α is too tion that is irrelevant to our problem. That is, we carry high, the universe would long ago have been completely a great deal of information in our memories that depends saturated with expanding life. In other words, high val- on local events that have happened on the Earth, and the ues of α give gα(t0) ≈ 0, so there would be no opportunity probability of their occurrence is the fantastically small for us to arise in an empty (by all appearances) galaxy. number . It will cancel out with the normalization in SIA encodes our anthropic information by expressing Bayes’ theorem. The new parameter γ gives the appear- the likelihood that we should appear at time t0 in an ance rate of human stage civilizations (when multiplied untouched galaxy: by F (t)), and is related to α but carries is own uncer- P (t0|α, γ) = γ F (t0) gα(t0). (8) tainty. It too is destined to fall out of the analysis, through its relationship to α. Very significant to this As discussed in section III, represents the incredibly approach is that the probability for humanity to occur tiny probability of local events playing out for us in exactly the way they have, and γ F (t ) represents the cos- at t0 is proportional to gα(t0), the fraction of the uni- 0 verse that has not been overrun by ambitious life at the mic appearance rate of human stage life in unoccupied present cosmic time. space, at the present cosmic time. However, γ is not in- This Bayesian approach requires us to specify a prior dependent of α, since all expanding civilizations presum- pdf over α. ably went through a stage of technological adolescence, similar to the current state of humanity. This implies γ should be larger than α by some unknown factor. In IV. PRIOR UNCERTAINTY other words, α = q γ, where q represents the fraction of human-stage civilizations that go on to become expand- Before any observations or anthropic considerations ing cosmological civilizations. We expect that the ques- are made, we have essentially no ability to predict α. tion of whether a given human-stage civilization goes on Should α be of order 10, or of order 10−10? To reflect to cosmological expansion depends almost entirely on lo- this degree of uncertainty, we follow the reasoning of cal events, so q should be independent of the cosmic time Tegmark [26] and work exclusively with a prior pdf in of arrival. So while α and γ are not independent, we can α, denoted P (α), that assigns equal weight to each order regard α and q as independent parameters, giving: α of magnitude between αmin and αmax. Explicitly, this is P (t |α, q) = F (t ) g (t ). (9) 0 q 0 α 0 1 1 P (α) = . (7) Since our prior assumptions about α and q are indepen- log(αmax/αmin) α dent of one another, and the above likelihood function This kind of uncertainty tends to arise when a large factors, it is simple to marginalize over q, giving: number of modestly uncertain factors contribute to the value of α. This can be seen to occur, for example, in P (t0|α) = α F (t0) gα(t0). (10) an analysis of the Drake equation [27] — the product Invoking Bayes’ theorem, we then get the SIA predic- of seven rough estimates does not result in an “order of tion for α, given that we have arrived at cosmic time magnitude estimate.” It results in uncertainty that is t0: inevitably spread over many orders of magnitude [28]. α g (t ) P (α) Using the above prior, the question shifts to the end- P (α|t ) = α 0 (11) 0 R αmax 0 0 0 α gα0 (t0) P (α ) dα points. How many orders of magnitude should P (α) con- αmin tain? Lacki has considered priors for the prevalence of 3 s(t ) v3 e(αmin+αmax−α)s(t0)v life spanning 10122 orders of magnitude [29], but in our = 0 . (12) α s(t )v3 α s(t )v3 context we only need the prior to stretch from about e max 0 − e min 0 −6 3 αmin = 10 to αmax = 10 (appearances per Glr per So long as our prior is sufficiently spread out (and we Gyr). Predictions from the SIA will not substantially avoid considering tiny values of the expansion speed v — 5 more about this below), this result is well-approximated We can now use this posterior to get SIA predictions by taking the limit that αmin → 0 and αmax → ∞, for the number of visible civilizations, and the probability giving: at least one is visible, by using equations 3 and 4:

3 3 −α s(t0) v P (α|t0) = s(t0) v e . (13)

Z αmax E(n) = Eα(n) P (α|t0) dα (14) αmin 3 ! αmaxs(t0)v 3 1 s(t0)(αmax − αmin)e = 1 − v αmaxs(t0) + − 3 3 (15) v3 eαmaxs(t0)v − eαmins(t0)v 1 → − 1 (16) v3 and

Z αmax p(n ≥ 1) = pα(n ≥ 1) P (α|t0) dα (17) αmin 3 v3 eαmaxs(t0) − eαmins(t0) es(t0)(v −1)(αmax+αmin) = 1 − 3 3 (18) eαmaxs(t0)v − eαmins(t0)v → 1 − v3 (19)

where the arrows in the ﬁnal lines indicate taking the 1.0 limit of αmin → 0 and αmax → ∞.

Since E(n) diverges, one can see that the αmax → 0.8 P(α)

∞ approximation is breaking down for tiny values of v. Pv=.5 (α|t 0)

With smaller v, the posterior puts more weight on higher Pv=.5 (α|t 0)(αmin→0,α max→∞) values of α. At very tiny values of v, it begins telling 0.6 us that the appearance rate for expanding civilizations is greater than the formation rate of planets — a non- 0.4 physical manifestation of allowing αmax → ∞. Reasonable values of v avoid this. Already at v = 0.1, essentially all of the probability weight is well under 0.2 oaihi rbblt Density Probability Logarithmic α = 10 appearances per Gly3 per Gyr, and there is no

0.0 problem with allowing αmax → ∞. In principle, s(t0) 10-5 10-4 0.001 0.010 0.100 could also be made tiny to exacerbate the problem, but Appearance Rate Parameterα(appearances per Gly 3 per Gyr) doing so would require a truly bizarre model of F (t) to alter conclusions for v ≥ 0.1. So long as estimates of v FIG. 2: A prior pdf P (α) over the appearance rate α −5 −1 and s(t0) are not completely shocking, the αmax → ∞ that stretches between αmin = 10 and αmax = 10 , limit is an excellent approximation. This point is illus- along with its anthropic SIA update P (α|t0). Also trated in Figure 2, where a direct comparison to the case depicted is the SIA update of a prior in the limit that −5 −1 of αmin = 10 and αmax = 10 is shown. αmin → 0 and αmax → ∞. There is no visible As noted in section II, it easy to account for the pos- distinction — SIA eﬀectively does not care how spread sibility that a survey covers only a fraction F racSky of out is the prior, beyond the ﬁrst few orders of the sky. The SIA results for such a survey are: magnitude.

1 E(n) = F racSky − 1 (20) v3 1 − v3 p(n ≥ 1) = . (21) 1 3 1 + F racSky − 1 v

Results for values of F racSky equal to 1, 0.8, and 0.35 are shown in Figure 3. These values correspond respectively ance, and the coverage of the Sloan Digital Sky Survey to the full sky, the full sky minus the Zone of Avoid- (DR10) [30]. 6

1.0 1.4

P(α|n=0) 1.2 0.8 P(α|n=1)

1.0 P(α|n=10) P(α|n=100) 0.6 0.8

p(n≥1)(FracSky=1) 0.6 0.4 p(n≥1)(FracSky=0.8) p(n≥1)(FracSky=0.35) 0.4

0.2

0.2 oaihi rbblt Density Probability Logarithmic isaeVisible are Civs n ≥ 1 Probability

0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 10-6 10-5 10-4 0.001 0.010 0.100 1 Dominant Expansion Velocity v Appearance Rate Parameterα(appearances per Gly 3 per Gyr)

FIG. 3: SIA estimated probability (as a function of the FIG. 4: SIA estimate of α after update from a dominant expansion velocity v) that one or more hypothetical full-sky survey that detects n expanding expanding cosmological civilizations are visible on the civilizations, for n = 0 (null result), n = 1, n = 10, and full sky (FracSky = 1), the full sky minus the Zone of n = 100. Avoidance (FracSky = 0.8), and the coverage of the Sloan Digital Sky Survey (FracSky = 0.35). but the greater the value of n, the less uncertainty we have. An observation of n = 1 narrows the uncertainty VI. UPDATES BASED ON SEARCH RESULTS to within two orders of magnitude. An observation of n = 10 would narrow uncertainty to within a single or- The Bayesian framework lends itself to taking the next der of magnitude. Figure 4 shows P (α|n) for several step. Suppose that in the near future, a full-sky galaxy hypothetical values of n. survey has been completed and discovers n cosmological civilizations expanding at speed v. What would that do for our knowledge of α? Such an update would be the VII. THE FINAL EXTENT OF LIFE IN THE final word on SIA estimates for α, until a cosmological COSMOS time has passed, allowing more information to slowly ac- cumulate. After updating our SIA estimate to P (α|n) (from ob- We can perform such an update by noting the appear- serving “n” expanding civs), we are in a position to ad- ance of expanding civilizations is a Poisson process (ap- dress a fundamental question about the ultimate role of pearances are independent events), and thus the proba- life in the universe. bility to observe exactly n is: The fraction of the universe that remains forever un- n touched by life is g (t → ∞), given by: Eα(n) α p(n|α) = e−Eα(n). (22) n! −αv3s(∞) gα(t → ∞) = e (25) Feeding this into Bayes’ theorem to update our earlier R ∞ SIA estimate gives: with s(∞) = 0 F (t) V (t, ∞) dt — a finite quantity in the standard cosmology. With our model for F (t), we p(n|α)P (α|t ) 0 get s(∞) ≈ 207986. P (α|n) = R 0 0 0 . (23) p(n|α )P (α |t0) dα We can then calculate its expected value, based on SIA and an observation of n expanding civilizations at Using the limit of αmin → 0 and αmax → ∞ for P (α|t0), this returns: the current cosmic time, according to: s(t ) Z ∞ 0 n −α s(t0) P (α|n) = (α s(t0)) e . (24) En(g(t → ∞)) = gα(t → ∞) P (α|n) dα (26) n! 0 n+1 Note that this result is independent of v — the act of s(t0) = 3 . (27) performing a definitive search cancels all velocity depen- s(t0) + s(∞) v dence from our knowledge of α, even in the case of a null result, with an observation of n = 0 civilizations. Figure 5 illustrates expected values of g(t → ∞). The The SIA estimate of P (α|t0) begins with uncertainty conclusion is quite consistent for any value of “n.” If spread over about three orders of magnitude (for any pro- ambitious civilizations can expand at a middling to high posed value of v). A null result (n = 0) does not improve fraction of the speed of light, then life will come to sat- this uncertainty (except to eliminate dependence on v), urate most of the cosmos. This remains true even for 7

1.0 A simpliﬁed approach to using SSA is to set an anthropic bound — a maximum plausible value of α that

0.8 implies opportunities for human-stage life to appear are in rapid decline, due to displacement of galaxies by am- En=0(g(t→∞))

En=1(g(t→∞)) bitious life [14]. This will imply bounds on E(n) and 0.6 En=10 (g(t→∞)) p(n ≥ 1). While this approach is far easier to compute,

En=100(g(t→∞)) it is merely a quick way to rule out high values of α —

0.4 it cannot make a true prediction without a prior over α that will control the result. The SIA approach developed in the previous sections 0.2 answers nearly all of these drawbacks of the SSA. It does not rely on assumptions about humanity’s typicality in ia nauae rcino h Cosmos the of Fraction Unsaturated Final 0.0 0.0 0.2 0.4 0.6 0.8 1.0 time. It does not require a model of F (t) that stretches Dominant Expansion Velocity v into the distant future. It is easy to compute. Life-hostile conditions in the past do not paradoxically imply that life FIG. 5: Expected fraction of the universe remaining is easier to observe in the present. It makes very modest untouched by expansionistic life at late cosmic time demands of our prior assumption about α, requiring only (t → ∞), based on the updated SIA estimate of α after that the prior is sufficiently spread out on a logarithmic observing n = 0, n = 1, n = 10, or n = 100 expanding scale to return closed-form, model-independent results. civilizations at the present cosmic time. If high-v It is not vulnerable to the “reference class problem” of the expansion is practical, the SIA expectation is simply SSA. And it makes true predictions, not merely setting that ambitious life will come to dominate the universe. bounds. It is also more optimistic than SSA-based predictions. If the dominant expansion speed is below about v = 0.8, the case of n = 0 (a null search result) — it is a nearly- then SIA gives odds better than 50% that an expand- 6 unavoidable feature of using the SIA . ing cosmological civilization is visible on our past light cone. To get similar predictions, earlier SSA estimates would require us to assume that humanity has appeared VIII. COMPARISON TO SSA-BASED between one and two standard deviations later than the ESTIMATES average time of arrival [12]. On the other hand, the very fact that SIA predictions The SIA estimate is different in character from the are so model-independent might actually be cause for prior uses of SSA [12–14], offering major advantages and skepticism. What is such model-independence saying? simplifications. It also introduces the well-known con- SIA is so strong that the background cosmology, the rel- ceptual challenges connected to the SIA. ative time dependence F (t) for life, and the endpoints of A drawback of the earlier SSA-based approach is that the prior (αmax and αmax) are falling out of the key pre- it requires a model of F (t) throughout all time, including dictions because they are not important enough to matter. the extreme future, where such models are most uncer- This suggests that invoking SIA is a strong assumption tain. For example, the habitability of class M stars, with indeed. their extreme lifetimes, is controversial, and such con- In fact, this is related to the “Presumptuous Philoso- siderations can heavily influence models for F (t) in the pher” thought experiment, which was designed to show- far future [31]. It also contains a very counter-intuitive case the unreasonable strength of SIA [11, 17]. In Pre- feature that life-hostile conditions at earlier times in the sumptuous Philosopher, SIA so heavily favors conditions universe can increase estimates for α and our probability for plentiful life, that a philosopher is happy to go deeply to observe expanding civilizations7 [32]. The previous into debt, placing bet after bet in favor of life, even in SSA approach has been criticized for a reliance on the the face of strong experimental evidence piling up against idea of “typicality in time.” [33] The results of the SSA him. Invoking SIA, in the Presumptuous Philosopher approach also tend to be inconvenient to compute. scenario, is actually stronger than observation. In the present case, the strength of SIA manifests in a slightly different way. SIA does not blindly favor “more 6 Unlike the previous sections, this result depends on our model life” — it favors more life with exactly our anthropic for F (t) into the cosmic future (through s(∞)). So although our information. Conditions that are too favorable for ex- conclusion is nearly independent of n, it is more vulnerable to pansionistic life must be ruled out, because SIA favors major modeling changes. conditions for us to appear at the present cosmic time, in 7 This can be understood as analogous to the Doomsday Argu- ment. Assuming more life-hostile conditions at substantially ear- an empty galaxy — too many expanding civilizations di- lier times in the universe means that we are closer to the earliest minish the opportunity for that to occur. The strength of possible civilization, and this makes “Doomsday” (the appear- SIA is not manifesting in enormous estimates for life (the ance of expanding civilizations) more probable, to compensate. predicted values of α are, after all, rather tiny) — it is 8 manifesting in a very specific pdf, P (α|t0), no matter how conservatively spread out one’s prior assumptions about conservatively spread out our prior may be. The amount the magnitude of the appearance rate — take for example of information gained by invoking SIA is enormous8. Our Lacki’s 10122 orders of magnitude [29] — the SIA poste- model could result in a presumptuous philosopher, if he rior always narrows the uncertainty down to about three is placing bets about α to occur within a few specific orders of magnitude. orders of magnitude. If one is convinced of the SIA, it difficult to avoid these conclusions. It could be the case that expanding civilizations have very little impact on their occupied galax- IX. CONCLUSIONS ies, making them invisible from a cosmological distance. This would be difficult to square with the maximum To those familiar with SSA vs. SIA debates, it may not power principle [19], and the fact that Dyson swarms are be surprising that an anthropic SIA model of extragalac- not a particularly exotic or difficult technology [10, 35]. tic civilizations has two prominent features: Increased It could be that some expanding civilizations will de- simplicity, and surprisingly high certainty. These are ex- liberately adopt a strategy of “stealth expansion” until actly the lessons of the SIA in two of the most famous late cosmic times, to avoid influencing potential competi- anthropic thought experiments — the Doomsday Argu- tors [22]. Or it could be that intergalactic expansion is ment and the Presumptuous Philosopher [11]. physically impossible. None of these is a particularly Their presence here is stark. For dominant expansion compelling escape. In our opinion, the weakest link is velocity v (whose value is a technological question), the the use of the SIA itself — it would not be a huge sur- “bottom line” is that the expected number of expanding prise to learn that SSA or some other approach is more cosmological civilizations that should be visible on our appropriate for cosmology. 1 ACKNOWLEDGMENTS past light cone is v3 − 1, and the probability for us to see at least one is 1 − v3 — this is true for any reasonable standard model cosmology, and any reasonable model for I am grateful to Toby Ord, who asked me how the Self- the relative appearance rate, F (t). And no matter how Indication Assumption would change earlier conclusions.

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