A Bayesian Analysis of Technological Intelligence in Land and Oceans

Current research indicates that (sub)surface ocean worlds essentially devoid of subaerial landmasses (e.g., continents) are common in the Milky Way, and that these worlds could host habitable conditions, thence raising the possibility that life and technological intelligence (TI) may arise in such aquatic settings. It is known, however, that TI on Earth (i.e., humans) arose on land. Motivated by these considerations, we present a Bayesian framework to assess the prospects for the emergence of TIs in land- and ocean-based habitats (LBHs and OBHs). If all factors are equally conducive for TIs to arise in LBHs and OBHs, we demonstrate that the evolution of TIs in LBHs (which includes humans) might have very low odds of roughly $1$-in-$10^3$ to $1$-in-$10^4$, thus outwardly contradicting the Copernican Principle. Hence, we elucidate three avenues whereby the Copernican Principle can be preserved: (i) the emergence rate of TIs is much lower in OBHs, (ii) the habitability interval for TIs is much shorter in OBHs, and (iii) only a small fraction of worlds with OBHs comprise appropriate conditions for effectuating TIs. We also briefly discuss methods for empirically falsifying our predictions, and comment on the feasibility of supporting TIs in aerial environments.


INTRODUCTION
It is a well-known fact that liquid water (or "water" for short) is a critical prerequisite for life-as-we-know-it because it exhibits many desirable properties as a solvent (Pohorille & Pratt 2012;Ball 2017;Schulze-Makuch & Irwin 2018). It is not surprising, therefore, that the "follow the water" strategy is widely pursued in astrobiology (Hubbard et al. 2002;Mottl et al. 2007;Westall & Brack 2018); this approach is manifested, for instance, in the concept of the habitable zone (HZ) (Dole 1964;Kasting et al. 1993;Kopparapu et al. 2013Kopparapu et al. , 2014. 1 If we contemplate the Solar system, there are many worlds that host(ed) extensive bodies of liquid water. The majority of them can be termed "ocean worlds" (or "water worlds") due to the fact that they lack subaerial landmasses (notably continents). Earth itself appears to have been mostly devoid of subaerial landmasses for a fraction of its history as per several analyses (Hawkesworth et al. 2017). In this context, some theoretical models and empirical geochemical constraints suggest that continents may not have emerged for most Corresponding author: Manasvi Lingam mlingam@fit.edu of the Archean (Flament et al. 2008;Bindeman et al. 2018;Johnson & Wing 2020), making the Earth effectively (although not completely) an ocean world during this interval of nearly 2 Gyr since its formation. In our Solar system, the vast majority of objects with liquid water may actually consist of subsurface oceans underneath icy crusts, as opposed to containing oceans on the surface. The quintessential examples in this category are Enceladus and Europa, and several other worlds (e.g., Titan) are also confirmed to host subsurface oceans (Nimmo & Pappalardo 2016;Lunine 2017;Hendrix et al. 2019). Hence, substantial attention has been devoted to gauging the habitability (via modeling and experiments) of the subsurface ocean worlds discovered in our Solar system (Hand et al. 2020;Taubner et al. 2020;Cable et al. 2021;MacKenzie et al. 2021;Glass et al. 2022). The physicochemical prerequisites for habitability of planetary bodies, which is an inherently multifaceted paradigm, are reviewed in Lammer et al. (2009); Kasting (2010); Cockell et al. (2016Cockell et al. ( , 2022; Shields et al. (2016); Lingam & Loeb (2019a); Kane (2021).
Looking beyond the Solar system, the discovery of debris disks (comprising analogs of the Kuiper belt) and exocomets (Matthews et al. 2014;Hughes et al. 2018;Rappaport et al. 2018;Strøm et al. 2020;Rebollido et al. 2020), in a sizeable fraction of planetary systems (Montesinos et al. 2016;Sibthorpe et al. 2018), supports the surmise that small icy bodies -which could host subsurface oceans of liquid water in principle -are prevalent in the Milky Way. Changing tack, a combination of exoplanet observations and modeling has demonstrated that many of them are likely to be ocean worlds -building on early proposals by Kuchner (2003) and Léger et al. (2004) -with only oceans and no landmasses on the surface (Zeng et al. 2019(Zeng et al. , 2021Venturini et al. 2020;Mousis et al. 2020;Luque & Pallé 2022;Neil et al. 2022).
Some of the planets of the famous TRAPPIST-1 system detected in 2016-17 (Gillon et al. 2017) might belong to this group, and host water fractions of 10% (Grimm et al. 2018;Agol et al. 2021;Acuña et al. 2021); on the other hand, Earth's oceans merely add up to ∼ 0.02% of its mass. The surficial habitability of ocean worlds has been explored in numerous publications (e.g., Goldblatt 2015;Kitzmann et al. 2015;Noack et al. 2016;Kite & Ford 2018;Lingam & Loeb 2021a;Madhusudhan et al. 2021;Syverson et al. 2021). While the existence of liquid water is a given for these worlds (by their formulation), the prospects for maintaining stable climate, nutrient supply, and water-rock interactions, inter alia, on geological timescales are less clear.
Yet, it is an incontrovertible datum that humans evolved on land-based habitats, and not in aquatic environments even though the latter are anticipated to be commonplace in the Milky Way. 2 Our emphasis on humans is not just mere anthropocentrism, but is instead a reflection of the canonical received notion that no other known species on Earth has (a) so radically transformed the biosphere in such a short timescale, even leading to the coinage of a potential new epoch, the Anthropocene (Ellis 2011;Lewis & Maslin 2015;Zalasiewicz et al. 2015;Waters et al. 2016); and (b) generated signatures of its technology (technosignatures) that are detectable across significant (e.g., interstellar) distances (Tarter 2001;Socas-Navarro et al. 2021).
The preceding paragraphs raise the question: What is the probability of the emergence of technological intelligence (e.g., humans) in land-and ocean-based habitats? Earth is composed of both types of environments, but ocean worlds only possess the latter. This topic has an unexpectedly long history. Alfred Russel Wallace, who is renowned as the co-discoverer of the theory of natural selection (along with Charles Darwin), contended over a century ago that worlds with both continents and oceans are apposite for the evolution of complex animal-like lifeforms (Wallace 1903, Chapter 12). In recent times, by performing mathematical analyses, Simpson (2017) and Lingam & Loeb (2019b) posited that the concomitant existence of oceans and continents on Earth was pivotal for the genesis of technological intelligence.
2 In a similar vein, other seemingly unusual circumstances linked to humans include the presence of a large moon (Ward & Brownlee 2000;Benn 2001); the location of Jupiter in the Solar system (Ward & Brownlee 2000;Horner & Jones 2008); orbit around a Gtype star (Haqq-Misra et al. 2018;Kipping 2021); and existence in the current cosmic epoch (Loeb et al. 2016;Kipping 2021).
In contrast, a few publications have postulated the opposite stance either implicitly or explicitly, to wit, that it is feasible to have technological intelligences emerge on ocean worlds, which consist of surface or subsurface oceans. As briefly reviewed hereafter in Section 4.1, several marine animals evince multiple attributes of complex (higher-order) cognition. Clements (2018) conjectured, in connection with the Fermi paradox (Cirkovic 2018;Forgan 2019), that the majority of such intelligent organisms may be sealed in subsurface ocean worlds. It must be recognized, however, that in this case, the evolution of humans in a land-based environment would be rendered anomalous to a certain degree.
Motivated by the previous exposition, we carry out a quantitative (viz., Bayesian) analysis of the emergence of technological intelligence in land-and ocean-based habitats, taking our cue from Bayesian approaches in astrobiology that have sought to address a diverse array of unknowns (e.g., Waltham 2011Waltham , 2017Spiegel & Turner 2012;Lacki 2016;Simpson 2017;Catling et al. 2018;Whitmire 2019;Lorenz 2019;Balbi & Grimaldi 2020;Kipping 2020Kipping , 2021Snyder-Beattie et al. 2021;Lineweaver 2022). The structure of the paper is constructed based on the following line of reasoning.
We begin with clarifying some central terms employed throughout the paper and discussing the prevalence of worlds with LBHs and OBHs in Section 2, thereby establishing the foundation(s) for the Bayesian analysis in Section 3, which is mathematically (albeit not physically) equivalent to the formalism in Kipping (2021); in this section, we also demonstrate how technological intelligences in land-based habitats may be anomalous. In Section 4, we qualitatively and quantitatively describe avenues whereby technological intelligences in land-based habitats could be rendered non-anomalous. Lastly, our salient findings are summarized in Section 5.

BASIC CHARACTERISTICS OF THE MODEL
We will introduce a number of definitions and heuristics that are vital for our subsequent mathematical analysis. The reader may, instead, proceed directly to Section 3 for the statistical treatment.

Model definitions
To begin with, the classification that we shall tackle is the demarcation of land-and ocean-based habitats, because it is central to this work.
Land-based habitats (LBHs): In land-based habitats, we include all terrestrial environments that can exist on worlds with landmasses, but not on ocean worlds. In other words, this category encompasses not just subaerial settings like continents and volcanic islands (and the water bodies ensconced amid them), but also subterranean environments (typically) within the continental crust; the latter on Earth host the thriving deep biosphere (Edwards et al. 2012;Magnabosco et al. 2018). A clarification worth underscoring is that organisms in land-based habitats would still require access to water, which is the solvent for life-as-we-know-it. 3 Moreover, in the limit of the land fraction approaching unity, the world is predicted to be covered by arid deserts with minimal biological productivity (Wallace 1903;Lingam & Loeb 2019b;Höning & Spohn 2022).
Ocean-based habitats (OBHs): By ocean-based habitats, we cover all environments that can theoretically exist on ocean worlds, as well as those harboring a mixture of oceans and landmasses (i.e., akin to Earth). Therefore, as indicated by the terminology, OBHs necessitate the presence of oceans in some form. This category includes putative environments on the seafloor (e.g., submarine hydrothermal vents) and underneath it (i.e., in the oceanic crust), 4 both of which feature diverse ecosystems on Earth (Whitman et al. 1998;Orcutt et al. 2011;Orsi 2018) in addition to the oceans themselves. The oceans can either occur on the surface or underneath an icy crust or ice-rock mixture (Vazan et al. 2022); the second case of this trio would resemble certain icy worlds (e.g., Enceladus) in our Solar system. At first glimpse, these two eclectic categories appear to span the range of possible habitable worlds (for life-as-we-know-it) along with the myriad environments inherent to these worlds. It should be appreciated that OBHs and LBHs, although by their formulation cannot overlap, may nonetheless coexist in the same world, as is the case for Earth. A handful of other noteworthy subtleties warrant highlighting and elucidating.
1. It is natural to wonder in which category amphibious organisms, which are quite widespread on Earth, should be assigned; as suggested by their nomenclature, the life cycles of these lifeforms may involve both LBHs and OBHs. By virtue of the manner in which the two classes were delineated, LBHs are automatically excluded from ocean worlds, which are devoid of landmasses altogether. If certain essential components of the life cycle (e.g., reproduction) of a particular species entail LBHs, it may be grouped in that category since LBHs still permit localized water bodies in which organisms might complete parts of their life cycle. In contrast, by simple tautology, OBHs are sans land environments. By the same token, habitats that lie at the interface of 3 Alternative biochemistries may be viable (Firsoff 1963;Bains 2004;Benner et al. 2004;Schulze-Makuch & Irwin 2018), but remain empirically unsubstantiated to this date. Hence, we err on the side of caution and restrict ourselves to lifeforms predicated on the biochemistry of Earth (viz., carbon and water). 4 If the oceans (or overlying icy crusts) are deep and/or the parent worlds are large, the formation of high-pressure ices could prevent the actualization of some of these environments (Noack et al. 2016;Journaux et al. 2020;Nixon & Madhusudhan 2021).
landmasses and oceans are readily conceivable. We can seek to classify such habitats as either LBHs or OBHs on the basis of whether the underlying crust is continental or oceanic. If this distinction is not clear-cut, then we may categorize the environments based on which component (land or water) is more prominent in terms of area, volume, or some other salient characteristic.
2. Aerial habitats are conspicuous by their absence hitherto. It is well-established that microbes survive in Earth's upper atmosphere (Smith 2013;DasSarma & DasSarma 2018), and that the likes of Venus (Morowitz & Sagan 1967;Limaye et al. 2021), Jupiter and other gas giants (Shapley 1967;Sagan & Salpeter 1976), and brown dwarfs (Shapley 1967;Yates et al. 2017;Lingam & Loeb 2019c) might be capable of harboring aerial biospheres in principle. To the best of our knowledge, however, we are not cognizant of any organisms that complete their entire life cycle exclusively in Earth's atmosphere. More importantly, the subject of this study is technological intelligence (TI), as described below.
We outline some feasible reasons in the Appendix as to why TI seems unlikely to transpire in aerial habitats. 5 3. Although we have allowed for the possibility of subterranean and subseafloor habitats, respectively, within the continental and oceanic crust, we will discount such settings hereafter. The chief rationale is that the pores, cracks, and spaces in the rocks are conducive to the existence of microbes, but are anticipated to be inadequate for macroscopic organisms. As remarked in the preceding paragraph, we are interested in TI, and it is worth emphasizing that a general correlation between high cognition, 6 brain size, and body size is documented on Earth (Jerison 1973;Armstrong 1983;Herculano-Houzel 2016). In consequence, if the aforementioned environments can merely host microscopic (or mesoscopic) lifeforms, it is plausible that TI (needing high cognitive skills) would be untenable. Furthermore, these habitats are often severely energy-limited and/or nutrient-limited (Hoehler & Jørgensen 2013;Lever et al. 2015;Magnabosco et al. 2018;Bradley et al. 2020), thereby posing crucial issues for supporting TIs aside from the above constraint of available space. In the same vein, while ice might be an appropriate medium for engendering the origin of life (Trinks et al. 2005;Attwater et al. 2013) and/or hosting small extremophiles (Price 2007;Martin & McMinn 2018), it does not appear suitable a priori for hosting TIs, which are presumably macroscopic, because of the limited space, energy, and nutrients. Hence, ice-based habitats are excluded from our analysis of TIs.
Next, we unpack a vital aspect of the central theme of this paper, to wit, exploring the prospects of the emergence of lifeforms that belong to the same reference class as humans. Under what conditions, however, can organisms be placed in the same reference class as humans?
In grappling with this question, we encounter a cognate fundamental question: What are the core differences between humans and nonhuman animals? Are they "one of degree and not of kind ", as succinctly posited by Darwin (1871, pg. 101)? This subject has, unsurprisingly, attracted intense debate since at least the 19th century. Numerous publications contend that humans and nonhuman animals may be separated by a discontinuity or a profound gap in some respects (Penn et al. 2008;Corballis 2011;Suddendorf 2013;Tomasello 2014;Berwick & Chomsky 2016;Heyes 2018;Kershenbaum 2020), while others favor the opposite stance vis-à-vis select traits or even on the whole (Griffin 2001;Roth & Dicke 2005;Bekoff & Pierce 2009;Whitehead & Rendell 2015;De Waal 2016Andrews 2020). When viewed in totality, the overall trend might be gradually shifting toward the latter camp, which builds upon the philosophy espoused by Darwin (Richerson et al. 2021).
In lieu of an in-depth discussion of this intricate and wide-ranging topic, it suffices to state that we will consider organisms occupying a socio-cognitive niche broadly analogous to that attributed to humans as belonging to the same reference class. This niche is endowed with components such as cultural transmission, language, and theory of mind (Pinker 2010;Boyd et al. 2011;Whiten & Erdal 2012;Laland 2017), inter alia, and is predicated on a high level of technology in conjunction with the manifold facets of intelligence; or equivalently technological intelligence (TI). Therefore, we will designate the biological lifeforms drawn from this reference class as TIs, or sometimes as extraterrestrial technological intelligences (ETIs). While technology on the one hand and intelligence/cognition on the other are manifestly not independent -in fact, they are deeply intertwined insofar as humans are concerned (Engels 1950(Engels [1876; Washburn 1959; Stout & Chaminade 2012; Osiurak & Reynaud 2020) -the above focus on TI renders the connections with technosignatures more apparent.
Before moving on, we underscore that concepts such as "technological intelligence" and "technology" are subtle and exhibit a certain degree of ambiguity. Hence, it is conceivable that TIs in OBHs are endowed with characteristics that might place them in the same reference class as humans in some, but not in all, important respects. As per the Ad Hoc Committee on SETI Nomenclature, (technological) "intelligence" may be understood as (Wright et al. 2018): In the acronyms SETI and ETI, the quality of being able to deliberately engineer technology which might be detectable using astronomical observation techniques.
And "technology" was defined by the aforementioned committee to be (Wright et al. 2018): The physical manifestations of deliberate engineering. That which produces a technosignature.
Due to the complexity of these concepts, a detailed treatment lies beyond the scope of this paper.

Model set-up
Although the quantitative analysis is pursued primarily in Section 3, we will perform a couple of simple estimates herein that are employed later.
In the ensuing calculations, the labels 'L' and 'O' signify LBHs and OBHs, respectively. Our goal is to gauge the potential number of worlds in the Milky Way with LBHs and OBHs that possess suitable conditions for the genesis and sustenance of TIs over geological timescales ( 1 Gyr); these quantities are denoted by N L and N O , respectively. In order to carry out these rough calculations, we will resort to a heuristic approach loosely reminiscent of the Drake equation (Drake 1965;Shklovskii & Sagan 1966). Similar approaches have been adopted for addressing the origin of life (Scharf & Cronin 2016), biosignatures (Seager 2018), and technosignatures (Lingam & Loeb 2019d;Wright et al. 2022).
Let us begin with estimating N L , because N O will be constructed similarly. Along the lines of the preceding publications, we will express N L as where N is the total number of main-sequence stars in the Milky Way, n L is the mean number of worlds per main-sequence star that can host LBHs in principle, and f L is the fraction of such worlds that actually evince conditions appropriate for TIs, i.e., habitable in this sense. The factor f L encompasses multiple desiderata from habitability (aside from liquid water), abiogenesis, and TI. Likewise, the equation for N O is as follows: where n O and f O are the oceanic counterparts of n L and f L . We define the ratio of these two quantities by ξ, as it plays a major role later, and it simplifies to Although n L and n O are unknown, it is still possible to constrain them (to an extent) because these variables fall under the purview of (exo)planetary science.
Turning our attention to n L , the worlds in question must be rocky and situated in the HZ (introduced in Section 1). The latter restriction follows from the fact that even surficial LBHs (see point #1 in Section 2.1) must have liquid water to permit habitability. The number of rocky (planet-sized) worlds in the HZ per star (η ⊕ ) is not yet precisely determined. We will work with η ⊕ ∼ 0.1 (see Kaltenegger 2017), which could be slightly on the conservative side (Dressing & Charbonneau 2015;Zink & Hansen 2019;Bryson et al. 2021). Next, we must specify what fraction of these worlds may have a mixture of landmasses and oceans on the surface. Worlds devoid of surface water are excluded due to habitability issues and worlds sans land (i.e., ocean worlds) are excluded by definition in the context of estimating n L .
Both theoretical estimates (Lingam & Loeb 2021b, pg. 438) and state-of-the-art simulations of exoplanets around low-mass stars (Kimura & Ikoma 2022) indicate that the above fraction is 10% (cf. Tian & Ida 2015). By combining the two factors, we end up with n L ∼ 0.1 × η ⊕ ∼ 0.01. The definition of n L delineated below (1) emphasizes that this estimate is merely in principle, and not in actuality. Hence, our calculation does not imply that 1% of all stars necessarily host rocky worlds with LBHs, and only suggests that they may do so. The rest of the uncertainty is, in essence, folded into the variable f L ; likewise, the corresponding uncertainty for OBHs is incorporated in f O . Now, we shall tackle n O , where we must divide the calculation into two segments to account for surface and subsurface oceans. In the case of surface oceans, the analysis is similar to the previous paragraphs, which leads us to ∼ 0.35 × η ⊕ , with the fraction of 0.35 drawn from the numerical simulations by Kimura & Ikoma (2022); also refer to the model by Tian & Ida (2015). When it comes to subsurface oceans, however, the value of n O is much enhanced through two avenues. First, icy worlds with subsurface oceans are ostensibly common in the outer regions of planetary systems beyond the snow line. Second, a substantial number of icy planetesimals are ejected and comprise a free-floating population.
Tentative constraints on the number density of freefloating icy worlds can be derived by extrapolating microlensing studies to a certain size threshold (Strigari et al. 2012;Dai & Guerras 2018); the recent discovery of interstellar planetesimals has furnished additional data (Moro-Martín 2022; Jewitt & Seligman 2022). With regard to icy worlds that are gravitationally bound to stars, their number is sensitive to planetary system architecture, stellar spectral type, and so forth, thereby requiring a statistical (population) study. Based on the available data, Lingam & Loeb (2019e) proposed that n O ∼ 100 for subsurface ocean worlds, which is compatible with the analysis of Mojzsis (2021). Both these publications allow for the possibility of n O ∼ 1000. We reiterate that n O denotes the number of worlds per mainsequence star that could support OHBs in principle.
After synthesizing the above data, and plugging them into (3), we duly end up with owing to which we adopt the fiducial value of ξ ∼ 10 −4 henceforth, unless stated otherwise. This choice is obtained after specifying f L ∼ f O in (4). We revisit this vital assumption in Section 4.3, since it merely constitutes the default position whose validity is not assured.
If the chosen value of ξ ∼ 10 −4 is approximately correct, the potential number of worlds with OBHs (conducive to TIs) may outnumber those with LBHs by orders of magnitude, making the emergence of TIs in the latter conceivably anomalous, as discussed subsequently.

MATHEMATICAL FRAMEWORK AND IMPLICATIONS
With the various pieces assembled, we are equipped to expound our Bayesian approach. This formalism can be generalized, in principle, to a generic class of problems wherein some event/datum is observed in apparently unusual conditions associated with some reference class. However, as our current thrust is on TIs in LBHs and OBHs, we will tailor our exposition accordingly.
To recap from Section 2.2, the labels 'L' and 'O' stand for LBHs and OBHs, respectively. The variable ξ embodies the ratio of the potential number of worlds with LBHs and OBHs with settings appropriate for TIs, and was estimated in (4). We are chiefly interested in calculating P (L|TI) and P (O|TI). The former roughly represents the probability of hosting TI (in the same reference class as humans) on LBHs, while the latter is the analogous probability for OBHs. To put it more precisely, each of these quantities embodies the probability that a randomly picked habitat belongs to the L or O category, given the condition that it hosts a TI.
As per the well-known Bayes's theorem (Jeffreys 1973;Jaynes 2003), P (L|TI) can be expressed as where P (TI|L) is the probability of the emergence of TI, given the condition that it unfolds in LBHs (namely, on worlds containing LBHs); P (L) denotes the probability of selecting a world with LBHs; and P (TI) is the probability of technological intelligence that will be defined shortly. Likewise, the formula for P (O|TI) is derivable by replacing L with O in (5), thereby yielding Computing the probabilities P (L) and P (O) is straightforward because this problem maps directly to the classic problem of drawing black and red balls from an urn. In consequence, these probabilities are given by from which we notice that P (L) + P (O) = 1. This identity is expected because there are only two categories of habitats for TI in our treatment; note that aerial habitats are excluded, as adumbrated in Section 2.1. It is worth recalling that habitable worlds could consist of both LBHs and OBHs (e.g., Earth) or just OBHs (ocean worlds), as per our conceptualization in Section 2.1. Now, we consider the conditional probability P (TI|L). If the origination of TI is encapsulated by a Poisson process (e.g., Carter 1983;Spiegel & Turner 2012;Scharf & Cronin 2016), we can introduce a uniform rate parameter λ L for the emergence of TI, and a "habitability interval" t L , which is the time over which TI could arise; both these parameters may be visualized as ensemble averages. Since P (TI|L) is the probability that at least one successful instantiation of TI has transpired in the habitability interval, for Poisson statistics we have In a similar vein, we can write down the equation for the conditional probability P (TI|O) as follows: where λ O and t O are the associated rate parameter and habitability interval for TI in OHBs, respectively. Lastly, for computing P (TI), we will utilize the law of total probability (Gut 2005, pg. 17), which leads to P (TI) = P (TI|L)P (L) + P (TI|O)P (O).
(13) The two equations are formally equivalent to those derived in Kipping (2021), who investigated the prospects for TIs on planets around M-dwarfs versus FGK stars. This exact correspondence is readily explainable from a mathematical standpoint because our work and Kipping (2021) both entail two categories of habitable worlds (albeit of different types) and explore the feasibility of the emergence of TI on such worlds. Of this duo, owing to the simple fact that human beings dwell on LBHs, the former is of more relevance and interest to us. We will, therefore, focus on (12) for the remainder of this section. It is apparent from (12) that there are five unknowns, of which we have tackled ξ in Section 2.2, thence leaving us with four parameters. Of this quartet, we will now delve into the habitability intervals below.
As elucidated in Section 2.2, LBHs are linked with rocky worlds in the HZ. An upper bound on t L is consequently set by the amount of time that an object spends in the HZ. As per numerical models, the continuous HZ lifetime ranges from ∼ 6.8 Gyr for 1 M stars to ∼ 42 Gyr for 0.2 M stars (Rushby et al. 2013, Table 5). However, it must be recognized that the habitability interval could be lower in actuality due to the negative effects of various physical processes. For instance, multispecies magnetohydrodynamic simulations have demonstrated that M-dwarf exoplanets with surface pressures of 1 bar are susceptible to complete atmospheric depletion on timescales of 1 Gyr because of substantial nonthermal escape rates (Garcia-Sage et al. 2017;Dong et al. 2017Dong et al. , 2018Dong et al. , 2019Dong et al. , 2020Airapetian et al. 2020).
Aside from the putative drawback of atmospheric retention, M-dwarf exoplanets are plausibly beset by a bevy of challenges such as tidal locking, prolonged premain-sequence phase with high irradiation, insufficient photon fluxes for prebiotic chemistry and photosynthesis, ozone depletion by regular stellar proton events, and frequency of (super)flares, to name a few (Tarter et al. 2007;Shields et al. 2016;Lingam & Loeb 2019a;Airapetian et al. 2020). 7 The primary rationale for singling out M-dwarf exoplanets stems from the datum that M-dwarfs are the most common (∼ 75%) and long-lived stars in the Milky Way (Tarter et al. 2007). Therefore, on account of all the earlier reasons, we adopt a somewhat conservative value of t L ∼ 10 Gyr in lieu of the suitable mean continuous HZ lifetime, which would be a few times higher than our current choice for t L .
Next, we turn our gaze toward t O . As suggested in Section 2.2, the vast majority of worlds with OBHs might be those with subsurface oceans based on extrapolation of known data. In estimating their abundance, we imposed a size cutoff roughly equal to the Moon (or Europa), motivated by the prediction that such worlds may retain liquid oceans on geological timescales of ∼ 1 Gyr (Spohn & Schubert 2003;Hussmann et al. 2006;Mojzsis 2021). It is conceivable, however, that the habitability interval for TIs is lower than this theoretical bound, and we will address this hypothesis further in Section 4.2. At present, we work with the premise of t O ∼ 1 Gyr to explore the ramifications. We are finally left with only two parameters, namely, the rate parameters λ L and λ O . We will study the impact of varying rates in Section 4.1, but we will regularly employ λ O ≈ λ L ≡ λ and seek to understand how P (L|TI) behaves as a function of λ. Before doing so, we note that TI on Earth -either genus Homo in general or Homo sapiens in particular -emerged on an LBH in Africa roughly 4.4 Gyr after the Earth first transitioned to certain habitable conditions such as water oceans and moderate temperatures (Wilde et al. 2001;Valley et al. 2002;Harrison 2020). Instead, if we presume that truly continuous habitable conditions were established only after an initial period of heavy bombardment, we may select a timescale of ∼ 4 Gyr (Nisbet & Sleep 2001).
Thus, if we appeal to the so-called Principle of Mediocrity, also dubbed the Copernican Principle (e.g., Darling 2001; Scharf 2014), we may tentatively suppose that λ L ∼ 1/(4 Gyr) ∼ 0.25 Gyr −1 , which displays excellent agreement with the Bayesian analysis of Kipping (2021) that resulted in a median value of λ L ∼ 0.26 Gyr −1 . Hence, if a fiducial estimate for λ L is needed, we will accordingly adopt the latter value, although we emphasize that this rate is not tightly constrained.
On invoking the above simplifications, it is easy to verify that (12) is transformed into and before plotting this probability as a function of λ, it is instructive to evaluate two extreme cases. First, in the limit wherein λ → 0 (i.e., the emergence of TI is exceptionally hard), we determine that (14) becomes and taking the opposite limit of λ → ∞ (viz., the genesis of TI is virtually guaranteed), we arrive at On inspecting (15) and (16) and recalling that these two expressions act as bounds, it follows that 10 −4 P (L|TI) 10 −3 , which is borne out by Figure 1. Therefore, as the probability is always several orders of magnitude smaller than unity, we are led to the conclusion that the occurrence of humans (classified as TI) in LBHs is rendered highly atypical. To put it differently, we would crudely expect the majority of TIs to dwell in OBHs.
If the preceding analysis is correct, then humanity's existence (in LBHs) would be apparently anomalous to a significant extent. This statement runs counter to the Principle of Mediocrity at first glimpse, which loosely posits that humankind is typical (viz., a random sample from an appropriate set) and that we are not special or privileged. We caution that there are manifold issues and subtleties associated with applying the Principle of Mediocrity tout court, to wit, without taking the situation and context into proper consideration (Crick 1981;Mash 1993;Kukla 2010;Ćirković & Balbi 2020). Hence, it is not impossible that humans are indeed unusual in this particular respect (of originating in LBHs), while perhaps being typical in other ways. To put it more succinctly, humans might be representative of some reference classes and not of certain other reference classes. Thus, the basic concept of typicality is deeply intertwined with the choice of reference class.

COPERNICAN ALTERNATIVES
As the prior two paragraphs suggest, the ansätzen we have chosen seem to collectively violate the Copernican Principle, which is often implicitly taken to hold true; this stance is potentially problematic, as indicated earlier. If we want to preserve the naïve version of the Copernican Principle, we must seek out tenable alternatives. In keeping with this theme, we shall refer to these hypotheses as "Copernican alternatives".
Because the final probabilities, (12) and (13), are equivalent to those in Kipping (2021), the Copernican alternatives that can be constructed are likewise equivalent, owing to which our discussion will largely mirror this reference. In general, we highlight that similar hypotheses may come into play as long as we are dealing with the emergence of life or TI in two generic categories that are, in essence, mutually exclusive and complementary. A necessary, although not strictly sufficient, criterion for Copernican alternatives is that P (L|TI) P (O|TI), thereby ensuring that the probability of TI linked with LBHs is higher than, or comparable to, that in OBHs. By employing (12) and (13), this condition converts into and we shall draw on this criterion hereafter. It is straightforward to extend this criterion to encompass a desired confidence level by introducing a prefactor (greater than unity) on the RHS. At the outset, we emphasize that the trio of Copernican alternatives put forward are not, perforce, wholly independent of each other. Indeed, multiple processes and their effects may suppress the prospects for TIs in OBHs in tandem; these mechanisms could, in turn, overlap with more than one alternative. To offer a specific example, let us turn our attention to the wide-ranging domain of abiogenesis (Fry 2000;Ruiz-Mirazo et al. 2014;Luisi 2016;Sutherland 2017;Preiner et al. 2020), and which sites (i.e., microenvironments) would be actually crucial or even imperative for facilitating the origin(s) of life (Stüeken et al. 2013;Camprubí et al. 2019;Sasselov et al. 2020;Deamer et al. 2022).
If, for instance, LBHs such as hot springs (Damer & Deamer 2020) or beaches and lagoons (Robertson & Miller 1995;Lathe 2004) or arid intermountain valleys (Benner et al. 2012) are ineluctable for successful abiogenesis, this scenario would effectively disqualify OBHs, whereas including submarine alkaline hydrothermal vents -widely, albeit by no means universally, perceived as promising environments for the origin of life (Martin et al. 2008;Russell et al. 2014;Sojo et al. 2016;Russell 2021) -allow OBHs to instantiate the origin of life. The former case corresponds to f O → 0, and can have a bearing on both the characteristic emergence rate and habitability interval of TIs in OBHs.
By the same token, the trio of Copernican alternatives is not exhaustive. To single out a possible explanation, only TIs in LBHs may find themselves contemplating the question of the rate of occurrence of TIs in various habitats, and whether the Copernican Principle is violated in LBHs. In this example, however, it would be necessary to justify why most or all TIs in OBHs do not find themselves engaging with this question.

Emergence rate of technological intelligence in
OBHs is suppressed The first Copernican alternative we tackle entails subscribing to the notion that TI is much harder to engender in OBHs than in LBHs. This premise was intimated in Wallace (1903, Chapter 12), and postulated in the Bayesian treatment by Simpson (2017). If this conjecture is correct, the water-to-land transition of vertebrates constitutes one of the major evolutionary breakthroughs in Earth's history (Knoll & Bambach 2000).
However, despite these attributes, it may be contended that none of the species dwelling in OBHs on Earth have evolved a level of TI exactly commensurate with that of humans, whereby the biosphere is shaped profoundly by their goal-directed actions. We will briefly describe some ostensibly plausible reasons that may hinder the emergence of TIs belonging to the same reference class as humans (refer to Section 2.1) in OBHs, before embarking on a quantitative analysis of the criterion presented in (17). Before doing so, we highlight that potentially 11 out of 13 high-performance innovations after the Ordovician transpired first (or only) in LBHs (Vermeij 2017), and the majority of plant and animal biodiversity is documented in LBHs (consult Román-Palacios et al. 2022 and the references therein).
The density and viscosity of liquid water are ∼ 800 and ∼ 50 times higher than that of air (for a 1 bar atmosphere), respectively. This fundamental datum suggests that the activity of organisms, broadly speaking, in OBHs may be limited by the medium of water relative to those in LBHs, which are typically expected to move in air (Denny 1993;Kershenbaum 2020). For starters, the drag force experienced by an organism is where C D is the drag coefficient, A org is the crosssectional area of the organism, ρ f is the fluid density, and v is the organismal velocity measured in the frame of the fluid. As long as the Reynolds number is of order unity and higher (Faber 1995, Section 7.8), 8 it follows that F D ∝ ρ f and by extension, the power needed to overcome the drag scales linearly with ρ f . Therefore, ceteris paribus, an organism moving through water is anticipated to consume ∼ 800 times more energy than in air to offset the effect of drag. Due to the higher power requirements, it is conceivable that putative budding TIs may be able to only traverse limited distances during their emergence, as doing otherwise would expend significant amounts of energy. These potential limitations on the home range (defined succinctly in Burt 1943) could have several consequences with respect to modulating intelligence. For instance, there is some evidence, albeit equivocal in nature, that home range correlates positively with certain aspects of cognitive capacity (Deaner et al. 2000;De Waal & Tyack 2003); this correlation might be explainable by the necessity of possessing high cognition to handle the demands of navigating and utilizing a sizeable home range (van Horik & Emery 2011; see also Rosati 2017).
Aside from the power constraint, we remark that swimming (intrinsically linked with OBHs) confers lower speeds in general compared to some modes of locomotion permitted in LBHs (Hirt et al. 2017). A simple scaling model developed by Bejan & Marden (2006), which has subsequently been refined by later publications, determined that the ratio of optimal flying and running speeds on the one hand to swimming speeds on the other is (ρ org /ρ a ) 1/3 , where ρ org is the organism density and ρ a is the air density. After substituting the appropriate values (when ρ org is close to that of water), the former duo (for Earth-like atmospheres) are about an order of magnitude higher than the swimming speeds.
One of the subtle, yet crucial, divergences between land and water concerns the scope for information gathering via sensory organs. This topic was reviewed in Martens et al. (2015) and Andersen et al. (2016), and its role was explicitly articulated in an astrobiological context by Kershenbaum (2020) and Lingam & Loeb (2021b, Chapter 7.7.2). We shall first assess vision (with the proviso that the ambient radiation in a select wavelength range is sufficient for sensing purposes). The intensity I at distance d from the source is modeled as where I 0 is the intensity at the source's location, and α is the attenuation coefficient. The attenuation coefficients in water and air are, respectively, ∼ 10 −5 m −1 and ∼ 10 −1 m −1 at 600 nm; even at other similar wavelengths (Denny 1993, Figure 11.13), the discrepancy is 2-3 orders of magnitude. In turn, the optical visibility range of ∼ 80 m in pure water (Martens et al. 2015) is over three orders of magnitude smaller than in clear air. 9 The decreased visibility in water may have vital ramifications for the reification of high intelligence and TI, or lack thereof to be precise. The enhanced visual range on land could permit the evolution of more intricate predation strategies (relative to those in water) and concomitantly favor the emergence of complex responses from the prey, thereby possibly initiating a so-called evolutionary arms race. It has been theorized that the emergence of planning -an important facet associated with higher-order cognition -was facilitated by the waterto-land transition of vertebrates (MacIver et al. 2017;Mugan & MacIver 2020;MacIver & Finlay 2022). In the absence of LBHs, the evolution of this characteristic might not transpire at the same frequency. Before proceeding ahead, we reiterate that our exposition is not exhaustive. Subtle or prominent variations in the sensory modalities and Umwelten of "complex multicellularity" (Knoll 2011) dwelling in LBHs and OBHs, which are indirectly explored in Von Uexküll (2010) and Yong (2022), may translate to striking divergences in the probability of emergence of TIs in these environments.
If we focus on TI specifically, lifeforms in OBHs could be stymied by sparse access to raw materials and free energy sources to construct technology. With regard to the latter, to pick a potentially anthropocentric example, the development of fire control (by humans) was so pivotal that it has been postulated as part of one of the "energy expansions" in the evolutionary history of Earth (Judson 2017; see also Bowman et al. 2009;Scott 2018;Pyne 2019). 10 From the narrower standpoint of human technology, fire patently offers numerous benefits (e.g., smelting of iron), but its relevance does not end there. Fire is believed to have contributed profoundly to hominin evolution in multiple ways: detoxifying food and boosting nutrient yield, constructing novel tools, keeping predators at bay, social bonding near the hearth, and expanding into new and otherwise inhospitable environments (Bowman et al. 2009;Wrangham 2009Wrangham , 2017Smil 2008Smil , 2010Smil , 2017Scott 2018;Pyne 2019).
Subsurface ocean worlds seemingly comprise the most common repositories of OBHs, as outlined in Section 2.2. Hence, in many (and perhaps most) OBHs, it is plausible that fire could be absent if one or more of the fuel, oxidant, or heat source is unavailable, thereupon posing major hurdles to reifying TI. With that being said, if we specialize to Earth, the temperature of certain submarine hydrothermal vents can reach > 400 • C (Haase et al. 2007;Koschinsky et al. 2008) and the melts of submarine volcanoes possess initial temperatures well above 1000 • C (Kelley et al. 2002, pg. 390), thus constituting plausible energy sources that may be harnessed in lieu of fire. Analogs of fire (vis-à-vis providing substantial sources of free energy and temperature) could exist in OBHs if strong oxidants and reductants are colocated, although no such concrete alternatives have been identified so far. Lastly, with respect to raw materials for creating technologies, extracting them from the ocean subseafloor (under high pressures) and transporting them against the drag might entail unforeseen challenges.
Hitherto, we have delineated several mechanisms that may be responsible for suppressing the emergence of TI in OBHs. Now, we will compute the quantitative outcomes of (17). Our goal here is to determine the constraint(s) on λ O while holding all parameters aside from If we take the limit of λ L → ∞ (i.e., TI is common in LBHs) and ξ 1, we obtain the analytical expression On the other hand, taking the opposite limit of λ L → 0 (i.e., TI is rare in LBHs) and ξ 1, we arrive at Between (21) and (22), the smaller of the duo is the latter because we relied on the condition λ L t L 1. In other words, we have derived an upper bound on the ratio of the rate parameters that is given by where the last equality has followed after substituting the fiducial values for the parameters on the RHS. Hence, if the rate of the emergence of TIs in OBHs is at least three orders of magnitude smaller than the corresponding rate in LBHs, this explanation could serve as a viable Copernican alternative. We have plotted the ratio λ O /λ L as a function of λ L , which is calculated from (20, in Figure 2 and it is observed that the above trends manifest along expected lines.

Habitability interval in OBHs is transient
In the second Copernican alternative, we will specify λ O ≈ λ L in the same vein as Section 3 and counter to that of Section 4.1. Instead, the hypothesis we investigate is that the habitability interval for TI in OBHs (which is encapsulated by t O ) is suppressed by orders of magnitude with respect to LBHs. Before tackling the mathematical aspects, we outline a couple of credible routes that may engender this scenario.
It is plausible and perhaps likely that TIs are predicated on metabolic pathways that are highly exergonic, and yield ample energy to carry out essential functions such as growth, maintenance, and reproduction. If this reasonable premise is correct, it automatically follows that the substrates involved in these pathways must be available in sufficient abundances, among other prerequisites for the existence of TIs. As a corollary, in the event that OBHs permit such metabolisms to operate only for transient periods of time on the whole, this trend would lower the prospects for TIs in OBHs and therefore act as a tenable Copernican alternative.
Let us consider a widely studied example in our Solar system: Enceladus. A combination of theoretical models, laboratory experiments, and observational data from the Cassini mission appear to support the conclusion that the timescale for serpentinization on Enceladus is ∼ 100 Myr (Zandanel et al. 2021;Daval et al. 2022). Of the noteworthy byproducts of serpentinization, which has been posited as "life's mother engine" (Russell et al. 2013), molecular hydrogen (H 2 ) stands out since it can be employed in ancient chemoautotrophic pathways such as hydrogenotrophic methanogenesis and acetogenesis (Cockell 2020). Hence, if the availability of H 2 were to be temporally curtailed in general (more so than in Enceladus), then the probability of the emergence of life and possibly TIs in OBHs may be diminished.
Second, let us contemplate one of the most potent oxidizing agents in metabolic pathways on Earth: molecular oxygen (O 2 ). In worlds with subsurface oceans, which are anticipated to constitute the dominant repositories of OBHs (refer to Section 2.2), O 2 levels are modulated by the delivery of oxidants from the surface and by the radiolysis of water, among other channels (e.g., Chyba & Hand 2001;Chyba & Phillips 2001;Hand et al. 2007;Bouquet et al. 2017;Russell et al. 2017;Lingam & Loeb 2019e;Ray et al. 2021); aside from the sources, the magnitude(s) of the sinks must be taken into account in gauging the O 2 abundance. If the dissolved oxygen attains high-enough concentrations, it is plausible that OBHs in subsurface ocean worlds could support TIs, by virtue of the fact that aerobic metabolisms can yield approximately an order of magnitude more energy than anaerobic metabolisms for the same food intake (Catling et al. 2005;McCollom 2007;Koch & Britton 2008).
At this stage, a brief digression is warranted. The preceding exposition may suggest at first glimpse that once the O 2 levels exceed a certain threshold, the advent of TIs would be facilitated. In actuality, the existence of such a threshold is hard to establish, if the Earth's record is anything to go by. The hypothesis that the evolution of animals (to which humans as TI belong) is directly linked to the rise in Earth's atmospheric O 2 has a long history (Nursall 1959;Cloud Jr. 1968;Runnegar 1982), but this posited causality has been called into question by recent empirical evidence (Cole et al. 2020;Lyons et al. 2021;Mills et al. 2022;Sperling et al. 2022); in particular, some animals are documented to readily survive under low-oxygen (e.g., Demospongiae) or completely anoxic (e.g., Henneguya salminicola) conditions (Danovaro et al. 2010;Mills et al. 2014;Yahalomi et al. 2020). Notwithstanding this caveat, it is still conceivable that the evolution of the forerunners of TIs (e.g., complex multicellular lifeforms that are macroscopic and motile) might necessitate high O 2 concentrations (Mills et al. 2023); the latter could also promote higher biodiversity and complex food webs (Levin & Gage 1998;Sperling et al. 2013;Knoll & Sperling 2014).
Circling back to the original theme, if worlds with OBHs accrue substantial O 2 levels only after a lengthy duration (labeled by t oxy ), this path might translate to a truncated habitability window for the emergence of TIs. The timescale for oceanic oxygenation could be 1 Gyr (Greenberg 2010;Lingam & Loeb 2021b), consequently narrowing the habitability window in principle. To illustrate how this sequence of events may occur, we must recognize that the depth of the subsurface ocean can decrease over time as the icy crust thickens with a decline in the internal heat budget, eventually freezing over; the timescale is denoted by t freeze . The habitability interval would thus be ∼ (t freeze − t oxy ) in this context, which ought to become small if t oxy ≈ t freeze is valid or even zero if t oxy ≥ t freeze . To sum up the previous paragraphs, temporal availability of reducing and oxidizing agents represents a potential method of decreasing t O .
We will now perform our mathematical analysis; before doing so, recall that we have set λ O ≈ λ L ≡ λ. On substituting this expression in (17), and solving for t O as a function of λ, we accordingly obtain Before undertaking the plot, it is instructive to calculate the twin limits of λ → ∞ and λ → 0 after using the relation ξ 1. The former case leads us to and determining the second limit yields  Figure 3. Ratio of the habitability intervals for TIs in OBHs and LBHs as a function of the emergence rate of TIs in LBHs (units of Gyr −1 ) to achieve a resolution roughly compatible with the Copernican principle. The region under the curve depicts the parameter space for this Copernican alternative. The vertical line is an estimate of the median value of the emergence rate, based on the data from Earth. The horizontal dashed line is the fiducial value of this ratio, which is substantially greater than the Copernican alternative. and of these two equations, the latter is the relevant bound because of the built-in ordering of λt L → 0. Thus, after simplifying (26), we arrive at

Ratio of habitability intervals for TIs
after we have utilized the default choice for ξ. The above equation tells us that t O must be lowered by at least four orders of magnitude relative to t L . Since we have chosen t L ∼ 10 Gyr, we would require t O 1 Myr; in contrast, observe that the fiducial value for t O is much higher at ∼ 1 Gyr. Hence, the factor by which t O must be suppressed is undoubtedly significant, and it is unclear as to whether the premise outlined in this subsection is entirely tenable for this reason. We have plotted t O /t L as a function of λ in Figure 3, from which we see that the aforementioned characteristics are all apparent. For example, it is evident that t O /t L must be suppressed by orders of magnitude relative to its standard value. Lastly, we comment on the fact that we held t L fixed and sought to examine the ensuing constraints on t O . In reality, the chief quantity of interest to us is the ratio t O /t L . Therefore, boosting t L could also count as a feasible Copernican alternative, given that it would be analogous to decreasing t O instead. The elevation of t L may arise if LBHs predominantly occur on K-and M-dwarf exoplanets, and the habitability intervals of these worlds are markedly higher than their HZ lifetimes. 11

Fraction of habitable worlds with OBHs is low
For TIs to originate, it is virtually a tautology to say that the worlds in question must have some basic set(s) of conditions that allow for this possibility. This notion of "habitability" in connection with TIs is encapsulated in the factor ξ, specifically in the form of f L and f O , as delineated in Section 2.2. Hence, if we relax the assumption made hitherto, namely that f L ∼ f O , it is easy to enhance ξ and thereby fulfill the criterion in (17). Hence, the third Copernican alternative we evaluate postulates that the majority of worlds with OBHs are outright not suitable for TIs (and their emergence) in any fashion.
As before, it behooves us to identify potential mechanisms that may suppress f O and boost ξ. Although numerous avenues could exist, we will single out a couple of candidates. The first pertains to the access to energy sources and the next two revolve around the abundances of vital nutrients, all of which can be a major hurdle for OBHs in subsurface ocean worlds; recall that this category of worlds is predicted to be particularly common in the Galaxy, as reviewed in Section 2.2.
We have touched on the first theme in both Sections 4.1 and 4.2. In the former, we discussed how certain OBHs may lack energy sources that can be efficiently deployed by TIs, akin to the role(s) played by fire on Earth with regard to humans. In the latter, we commented on the centrality of molecular oxygen for supporting complex life and TIs. It should be recognized in this context that not all ocean worlds are likely to attain high levels of dissolved O 2 if we extrapolate from the Solar system (Ward et al. 2019), and in theory, only a small fraction of them might actually do so. For instance, it is plausible that a sizeable fraction of worlds with (sub)surface oceans lack O 2 concentrations adequate for organisms resembling macroscopic motile animals (Lingam & Loeb 2019b;Glaser et al. 2020;Höning & Spohn 2022).
The second major justifiable impediment is nutrient availability. A bevy of publications have proposed that a subset of worlds with surface (Wordsworth & Pierrehumbert 2013;Lingam & Loeb 2019b;Glaser et al. 2020;Olson et al. 2020) or subsurface (Zolotov 2007;Lingam & Loeb 2018b) oceans may evince a scarcity of dissolved phosphorus (a bioessential element for life-as-we-knowit) in the form of phosphates, while other studies have elucidated avenues that could raise phosphorus concentrations to Earth-like levels or higher (Pasek et al. 2013;Syverson et al. 2021;Brady et al. 2022;Hao et al. 2022;Pasek et al. 2022). Looking beyond phosphorus, many other elements are critical for life-as-we-know-it (Fraústo  Wackett et al. 2004), and even if one or a few of them are scarce, putative complex biospheres might be ruled out. Thus, when viewed cumulatively, the dual restrictions imposed by the need for appropriate energy sources and nutrients can jointly suppress f O to produce the desired outcome.
Third, if worlds with OBHs are widely endowed with substantial H 2 O inventories, manifesting as thick ice layers (for subsurface ocean worlds) and/or deep oceans, the pressures at the ocean floor can become high enough (typically 1 GPa) to drive the formation of highpressure ices (Petrenko & Whitworth 1999). In this scenario, vital water-rock reactions might be suppressed, thereby stymieing access to nutrients, substrates, chemical energy, and miscellaneous sources of disequilibria (Noack et al. 2016;Journaux et al. 2020;Journaux 2022). However, this drawback may be mitigated by recent numerical models, which imply that the slow transport of salts, nutrients, and other substances into the ocean is feasible even when high-pressure ices exist (Choblet et al. 2017;Journaux et al. 2017;Kalousová & Sotin 2018;Hernandez et al. 2022;Ojha et al. 2022).
Returning to (17), we can derive the necessary lower bound for ξ, which duly leads to and we have imposed the previous ordering λ O ≈ λ L ≡ λ because our goal is to determine ξ as a function of λ. Let us first take the limit of λ → ∞, which corresponds to the emergence of TIs being virtually guaranteed -we end up with the simple expression ξ 1. On substituting (4) into ξ 1 and simplifying, we arrive at Now, let us tackle the opposite regime wherein the emergence of TI is extremely hard (λ → 0), which yields where the second inequality follows from inputting the fiducial values for t O and t L motivated in Section 3. After plugging (4) into (30), we arrive at Therefore, upon inspecting (29) and (31), it is apparent that the fraction of habitable worlds (sensu capable of engendering TIs) with OBHs must be suppressed by approximately 3-4 orders of magnitude at the minimum compared to LBHs. Even though we have highlighted some bottlenecks to habitability with respect to TIs in OBHs, this factor is undoubtedly substantial, indicating that the vast majority of worlds (typically with subsurface oceans) comprising viable OBHs must be fully incompatible with the conditions required for TIs. Instead of plotting ξ, we have opted to depict the above ratio f O /f L in Figure 4. This quantity is readily obtained by merging (4) and (28), and we obtain Upon perusing Figure 4, the analytical criteria embodied by (29) and (31) are manifested as anticipated.
In closing, let us recall that the current objective was to boost ξ compared to its fiducial value of ∼ 10 −4 . We have sought mechanisms that suppress f O /f L , and thus raise f L /f O and ξ. On examining (3), however, we notice that ξ can be increased if n L /n O is enhanced. This result is realizable if the number of worlds with the basic potential to host LBHs is higher than expected, or the opposite trend (i.e., lower) is applicable for OBHs. Exoplanet surveys and theoretical models have already shed light on n L /n O , and this quantity will be further resolved with additional data in the future.

CONCLUSION
Humans are an example of technological intelligence (TI), albeit of the specific kind that can profoundly influence the biosphere through their purposeful activities and produce detectable signatures of their technology. It is a well-established fact that TI on Earth arose on land, and not in the oceans, despite the prediction that ocean worlds should be prevalent in the Milky Way. In this paper, we performed a Bayesian analysis of the probability of TIs existing in LBHs and OBHs.
There are four broad outcomes that appear to be consistent with the datum that TI on Earth emerged in a particular LBH; of this quartet, the first seemingly violates the Copernican Principle, while the other trio ostensibly preserve the elementary form of this principle.
1. The existence of TI in LBHs on Earth is a genuine "fluke" with odds ranging from 1-in-10 3 to 1-in-10 4 . To put it another way, one would expect the overwhelming majority of TIs to inhabit OBHs (which does not seem compatible with available data from the Solar system).
2. OBHs have a much lower (ensemble-averaged) rate of emergence of TIs relative to their counterpart for LBHs. To be precise, in case the rate associated with OBHs is at least three orders of magnitude smaller than that of LBHs, the fact that TI dwells in LBHs on Earth is not anomalous.
3. OBHs are endowed with a much more transient interval of habitability for TIs compared to LBHs. If the (ensemble-averaged) habitability timescale for OBHs is more than four orders of magnitude lower than its analog for LBHs, the existence of TI on Earth in LBHs would not be anomalous.
4. Only a minuscule fraction of worlds with OBHs (with respect to LBHs) feature desiderata conducive to the emergence of TIs. If the fraction of worlds containing OBHs with habitable conditions for TIs is smaller by 3-4 orders of magnitude than the corresponding fraction for LBHs, the presence of TI in LBHs of Earth is not anomalous.
As remarked above, a clear distinction between hypothesis #1 and the remaining three possibilities arises automatically. In consequence, we are naturally propelled toward the question of how to differentiate between these scenarios, and thence falsify or validate them. Let us contemplate the first conjecture once more. If OBHs are not significantly disfavored in some fashion compared to LBHs, then TIs should be far more common in the former. In this context, determining whether a world has surficial landmasses and/or oceans is feasible, in principle, via spectrophotometric observations (Cowan et al. 2009;Fujii et al. 2010Fujii et al. , 2018Lustig-Yaeger et al. 2018;Kuwata et al. 2022). Hence, if future technosignature surveys (reviewed in Wright 2021; Lingam & Loeb 2021b;Socas-Navarro et al. 2021;Haqq-Misra et al. 2022) discover that the majority of signals emanate from ocean worlds (sans LBHs by definition), this trend might assist in confirming hypothesis #1. In contrast, if most technosignatures originate from worlds with LBHs, this result may serve to falsify hypothesis #1 and thereby lend credence to the other outcomes. We caution, however, that the process of falsification and verification is not straightforward as the likes of false positives and negatives must be accurately addressed.
For the sake of argument, let us suppose that we have ruled out hypothesis #1 as described in the prior paragraph. This route would still leave us with the conundrum of determining which of hypotheses #2, #3, and #4 is/are correct. In view of the rather limited scope of surveys as well as the data garnered from them in the near-future, it seems very unlikely these hypotheses can be differentiated from one another. Thus, at least in the upcoming decades, any progress on this front could be restricted to performing careful extrapolations from Earth and/or carrying out theoretical modeling.
In summary, we have tackled the fundamental question of why we -in the specific sense of constituting a TI -find ourselves having evolved in LBHs and not in OBHs, despite the latter being potentially much more common than the former. A Bayesian approach suggests that our emergence in the former setting was indeed deeply unlikely prima facie, unless certain mechanisms act to selectively suppress the prospects for TIs in OBHs relative to LBHs. Future surveys for technosignatures, backed by forthcoming missions seeking biosignatures, may shed welcome empirical light on this question, and enable us to gauge whether TIs in LBHs are actually uncommon (in comparison to OBHs).

APPENDIX
As stated in Section 2.1, the objective of this Appendix is to sketch severe challenges that could confront the emergence of TIs in aerial biospheres, which may explain why atmospheric settings are unsuited for this purpose. We emphasize that this summary is not exhaustive since other drawbacks can be readily identified.
The first hurdle we wish to underscore is the abundance of bioessential elements in the atmosphere. Even if the availability of certain lighter bioessential elements and compounds (e.g., carbon and water) does not comprise a bottleneck (a premise that is, however, not assured), the situation could prove to be completely different when it comes to trace metals; these elements play crucial roles in biological processes (Fraústo Da Silva & Williams 2001;Wackett et al. 2004). For example, molybdenum (Mo) is not only vital for biological functions such as nitrogen fixation (Hille 2002;Williams & Frausto Da Silva 2002;Schwarz et al. 2009) but has also been implicated in the origin of life itself (Schoepp-Cothenet et al. 2012. With regard to the latter, numerous experiments in recent times have demonstrated that metals (e.g., iron, nickel, chromium) in some form can serve as nonenzymatic catalysts for initiating protometabolic networks conceivably at the heart of life's origins (Muchowska et al. 2020;Preiner et al. 2020).
To continue with our focus on molybdenum, it is possible that, by virtue of its high density either in elemental or compound form, it would be liable to sink downward and thence become depleted over time. We have commented on the prospects for an aerial biosphere on Venus in Section 2.1, and the habitable region under consideration appears to have nutrients like phosphorus and sulfur at potentially adequate concentrations to support Earth-based microbes (Milojevic et al. 2021), although significant uncertainties remain due to the paucity of reliable data (Cockell et al. 2021). This optimism must be appropriately counterbalanced by the fact that the abundances of most trace metals are wholly unconstrained. Some of them (e.g., molybdenum) might not occur at desired abundances in the cloud decks of Venus, and perhaps other aerial habitable environments (Lingam & Loeb 2018b).
The second difficulty we wish to foreground has to do with the challenge of staying afloat in the habitable region, i.e., preserving the altitude. The net downward force (weight minus buoyancy) that would be experienced by a hypothetical organism of volume V org is given by where g is the acceleration due to gravity and the two densities were defined in Section 4.1. If the organism is to avoid downward acceleration, which would eventually drive it beyond the habitable environment, the above force must be balanced by the drag delineated in (18). As long as the Reynolds number is not smaller than unity, we end up with the following scaling for the terminal velocity (v t ): v t ∝ ρ org ρ a − 1 1/2 and if we specialize to a Reynolds number of order unity and lower, we arrive at in which L org represents the characteristic length scale of the organism. This equation is derived after invoking the Stokes relationship C D ≈ 24/Re (Faber 1995, Section 7.8) in (18), where Re is the Reynolds number; the parameter L org is manifested through Re. Our goal is to decrease the terminal velocity, as otherwise, the organism would exit the habitable region swiftly and thus lose functionality. Alternatively, this terminal velocity would need to be balanced by convection that is vigorous enough to counterbalance v t . As revealed by (2) and (3), there are two noteworthy avenues whereby the terminal velocity can be lowered. First, this result is effectuated when ρ org ∼ ρ a , implying that the organism would possess a balloon-like structure primarily composed of air, analogous to the "floaters" envisioned by Sagan & Salpeter (1976). In that event, however, the protection conferred against galactic cosmic rays, stellar energetic particles, and micrometeorites could be reduced owing to the relatively thin membrane enclosing air (and internal organs).
In addition, if the organism were to rely upon the aforementioned strategy, the majority of its area may be expected to consist of the balloon-like component. This surmise leads us naturally to the second approach wherein A org is substantially increased, while the volume, mass, and other properties of the organism are held fixed; boosting A org will suppress v t as seen from (2) and (3). Lifeforms in this vein could resemble pancakes or something similar, either with or without the balloon-like structure. However, as we shall describe below, this route of enhancing A org also has some prominent shortcomings associated with it.
An organism at temperature T org will radiate away energy at the rate P org , which is expressed as when we model it as a blackbody. Hence, if A org is significantly increased, it follows that P org will be raised commensurately, thereupon leading to conceivably substantial energy losses. To counter this issue, it would be necessary for the organism to locate, acquire, and process raw materials for metabolism in greater quantities or at higher efficiency (Planinšič & Vollmer 2008), both of which might engender additional barriers to the evolution of complex, motile, and macroscopic multicellular lifeforms. Second, if the cross-sectional area is enlarged, the ratio of this quantity to the volume (denoted by SA:V) is raised by the same amount because the volume is held constant. While increased values of SA:V may be rendered advantageous in some respects, it is simultaneously accompanied by crucial downsides. For example, high SA:V ratios could translate to elevated rates of water loss (Kühsel et al. 2017), which would be a critical issue in arid settings like the clouds of Venus (Hallsworth et al. 2021). Moreover, when the SA:V ratio becomes substantial, it might amplify: (a) the leakage rates of nutrient and useful metabolites, (b) the energy expended to sustain homeostasis, and (c) the costs of maintaining the structures (e.g., cells and tissues) that demarcate the organism (Beardall et al. 2009;Okie 2013); other negative ramifications of high SA:V can be gleaned from Kooijman (2000).