Different is More: The Value ofFinding an Inhabited Planet that is

Far From Earth2.0Adrian Lenardic

∗

Johnny Seales

Rice University

January 9, 2019

Abstract

The search for an inhabited planet, other than our own, is a driver of planetary exploration in our solarsystem and beyond. Using information from our own planet to inform search strategies allows for a targetedsearch. It is, however, worth considering some span in the strategy and in a priori expectation. An inhabited,Earth-like planet is one that would be similar to Earth in ways that extend beyond having biota. To facilitateanalysis, we employ a metric akin to the Earth-similarity index of Schulze-Makuch et al. [2011]. The metricextends from zero, for an inhabited planet that is like Earth in all other regards (i.e., zero differences), towardend-member values for planets that differ from Earth but maintain life potential. The analysis shows howfinding inhabited planets that do not share all other Earth characteristics could improve our ability to assessgalactic life potential without a large increase in time-commitment costs. Search strategies that acknowledgethe possibility of such planets can also minimize the potential of exploration losses (e.g., searching for longdurations to reach conclusions that are search strategy biased). Discovering such planets could additionallyprovide a test of the Gaia hypothesis - a test that has proved difficult using only the Earth as a laboratory.Lastly, we discuss how an Earth2.0 narrative that has been presented to the public as a search strategy comeswith nostalgia-laden philosophical baggage that does not best serve exploration.

Keywords: Exoplanets, Life Potential, SearchStrategies

Introduction

The idea of a second Earth has a long history[Couprie, 2011]. Recently, NASA has enteredinto second Earth thinking: 1) “This discoverygives us a hint that finding a Second Earth isnot a matter of if but when.” - Thomas Zur-buchen, Assoc. Admin., Science Mission Di-rectorate at Nasa, 2017; 2) “This exciting resultbrings us one step closer to finding an Earth2.0.” - John Grunsfeld, Assoc. Admin., Sci-ence Mission Directorate at Nasa, 2015. Thequotes come from press conferences that an-

∗ajns@rice.edu

nounced discoveries regarding planets orbitingstars other than our own (exoplanets). A mo-tivator behind these statements is the searchfor life beyond Earth and placing observationalconstraints on the probability of life in ourgalaxy.

Debates about life beyond Earth have a longhistory. An even-handed referencing wouldtake pages. Interested readers can easily trackdown a multitude of books, articles, blogs,and the like. As a starting point, two booksthat encapsulate competing views are Wardand Brownlee [2000] and Kasting [2010]. End-member views regarding galactic life potentialare “rare-Earth” and “plenitude” (i.e. life re-quires specific environmental conditions, of thekind that exist on Earth, versus the idea that life

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can thrive in a range of conditions that mightexist across planets and/or moons within ourgalaxy). To be clear (and avoid strawmen):1) Rare does not mean singular (a rare-Earthview does not exclude life beyond Earth - itposits that in order for a planet to have life,particularly complex life, it must share certainessential features with the Earth, beyond hav-ing life, that make the Earth the planet it is and,it argues, that the combination of such featuresis rare for planets in our galaxy); 2) Plentitudedoes not mean all things are possible (a plen-titude view acknowledges that there will begalactic bodies with conditions that do not al-low for life); 3) Nature need not care aboutend-members (as an example: conditions thatmake the Earth the Earth, beyond having life,may not be rare in the galaxy such that thereare many planets that are essentially analogousto Earth; life may only exist on such planetswhich would not be in line with a plentitudeend-member view and, although it would notsupport the idea that Earth conditions are rare,it would confirm one aspect of the rare-Earthargument, i.e., Earth conditions are needed forlife).

We are now at the stage of exoplanet researchwhere missions are being designed with thegoal of detecting remote signatures of plane-tary life [e.g., Schwieterman et al., 2018]. Thisis a new phase of exploration into galactic lifepotential. It generates a level of excitement thatmotivated the press release statements quotedin the first paragraph. It brings with it the po-tential that observational data can be broughtto bear on long-standing debates about galacticlife. It also brings with it an equally old ques-tion related to any exploration: how will wechoose to look? This is a decision problem. It isa decision problem under uncertainty. Any ex-ploration comes with risk. Uncertainty adds tothat risk. Acknowledging uncertainty and riskdoes not damp excitement. However, the factthat a particular search strategy is gaining trac-tion, one that is centered around Earth analogs,without being weighed against alternates inlight of uncertainty and risk, does motivate thestep back and rethink that is the core of this

paper (note added in revision: over the timethat this paper was in review we became awarethat we are not the first to suggest a rethink re-garding search strategy [Bean et al., 2017; Kiteet al., 2018; Lingam and Loeb, 2018a]).

A search strategy can be centered on plan-ets that share a high number of Earth at-tributes, with the thought that this maximizesour chances of finding signs of life. Our cen-tral thesis is that a search strategy that allowsfor deviations from Earth analogs can bringmore information and less risk at moderatelyhigher cost. Fleshing this statement out formsthe bulk of this paper.

There is an added reason why we argue fora break from an Earth centered view. Wantingto know if life exists beyond Earth, and whatthat implies for life potential across our galaxy,is not driven by scientific motivations alone.The humanistic implications of the search, andthe humanistic/cultural factors that feed into it,should be acknowledged. More specifically, thedesire to find a planet like our own is drivenby factors that extend well beyond pure sci-entific curiosity [Messeri, 2016]. Our intentis not to argue that humanistic/cultural as-pects be removed from the discussion. Rather,we want to layout how finding inhabited plan-ets that do not look like home to us couldcarry broader scientific and humanistic impli-cations than finding an Earth2.0. The humanis-tic/philosophical implications are discussed inthe final discussion section.

Non-Earthness, Planetary Life

Potential, and Search Strategies

Exploration goal(s) determine search strategies.The goal(s) of exoplanet exploration, as relatedto galactic life, can be expressed as a singlequestion or intertwined questions. There isan existence question: ‘does life exist beyondEarth?’ If this is the only motivating question,then the search endeavor could be of the ‘findone and done’ type. We suspect that mostpeople who have dedicated time and thoughtto exoplanet explorations do not subscribe tothis. Thus, there must be a broader goal. We

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would argue that addressing the issue of galac-tic life potential (rare versus plentiful) is thatbroader goal. That introduces the intertwinedquestions of ‘what conditions allow for and/ormaximize life potential (i.e., the probabilitythat life exists on a planet)?’ and ‘what per-centage of planets in our galaxy are inhabited(i.e., what percentage have a biosphere)?’ Forwhat follows we will, unless otherwise noted,assume all of these questions are motivatorsin the collective search for life beyond Earthand, as such, all should be considered whendetermining search strategies.

We now pose an added question: ‘wouldfinding inhabited planets that share manyother Earth attributes or finding inhabited plan-ets that differ significantly from Earth betterhelp us to address the question of galactic lifepotential and should this consideration feedinto search strategies?’ We will argue that itshould be considered. This leads to a practicalissue that needs to be addressed from the start:an overly broad search is not practical. Giventhat, we would like some constraints on howdifferent we think a planet could be from Earthand still maintain life potential. This motivatesthe first sub-section below.

How Different can Different Be andMaintain Life Potential

The term “Earth-like” is often used in a qualita-tive way. A quantitative metric can be definedas per the Earth-similarity index of Schulze-Makuch et al. [2011]. Our interest is morespecific than asking how close a planet is toEarth in terms of the full range of variablesthat come into play. We are interested in thequestion of how different a planet can be fromEarth and still allow for life. We can, for exam-ple, use the Earth-similarity index and define asub-range over which a planet can maintain lifepotential (this can also be applied to moons).Since our interest is on how different a galacticbody can be from the Earth and allow for life,it will be useful to center our metric on zero(i.e., if a planet with life potential is like Earthin all other ways then the value of the metric

is zero). However one defines such a metrica useful next step will be to ask what are theextreme values it can take while maintaining anon-negligible probability for life.

We start with an agreed upon criteria: liferequires energy. The energy sources for a bio-sphere are energy from the star a planet ormoon orbits and internal energy from the decayof radioactive isotopes within its interior, heatretained from formation, and/or tidal heating.

Figure 1a is a schematic of how energysources affect life on Earth. Solar and internalenergy can be used as direct energy sources topower photosynthesis or chemosynthesis. Theenergy sources also drive cycles that influenceenvironmental conditions. If there is a lim-ited range of environmental conditions underwhich a biosphere can exist, this implies thatenergy sources can affect planetary life poten-tial by maintaining livable conditions. For lifeas we know it, the existence of liquid water iscrucial. The classic idea of a "Habitable Zone"ties into delineating conditions required for aplanet to maintain liquid water over time scalesthat allow for life development and evolution[Kasting et al., 1993].

For the Earth, the buffering of environmen-tal conditions is generally considered to relyon hydrological and geophysical/geochemicalcycles. Internal energy drives volcanic andtectonic activity that transfers volatiles (CO2,H2O) between a planet’s surface envelopes(atmosphere, hydrosphere, biosphere) and itsrocky interior (crust, lithosphere, mantle). Vol-canism cycles greenhouse gases into the atmo-sphere. Tectonics creates weatherable topog-raphy and weathering reactions draw green-house gases out of the atmosphere. Weatheringdepends on hydrology. This means that sur-face and deep planet cycles are linked in sofar as discussions of buffering Earth’s climateare concerned [Kump et al, 2000]. Life alsolinks in as it has the ability to effect the cy-cles that maintain environmental conditionssuitable for its own existence [Lovelock andMargulis, 1974]. Over geologic timescales, at-mospheric CO2 content and associated green-house climate forcing is influenced by the bal-

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Figure 1: Figure 1: a) Schematic of how energy sources affect life, directly and indirectly, on Earth. b) Schematic ofpotentially livable planets/moons on which solar energy is not critical to life. c) Schematic of potentiallylivable planets/moons on which internal energy is not critical to life.

ance between volcanic degassing and weather-ing [Berner et al., 1983]. Weathering dependson processes governed partly by surface tem-perature, which allows for the potential that aplanet can buffer/stabilize climate and surfaceconditions in a manner that allows liquid waterto exist over extended time frames [Walker etal., 1981].

The silicate-weathering negative feedback,outlined above, is the currently preferred hy-pothesis for how the Earth’s climate has beenregulated so as not to enter a prolonged hardsnowball state or a runaway greenhouse state.This has cast a significant influence on ideasabout how to search for inhabited planets be-yond our solar system [e.g., Kasting, 2010]. It isworth stressing that, as formulated for Earth cli-mate stabilization, the feedback relies on bothsolar and internal planetary energy. Remov-ing one of the two energy sources thus affectsdirect energy sources for life and also a mecha-nism for maintaining environmental conditionsconducive to life. This stresses how a planet ormoon that lacks one of the two energy sourceswould be distinctly non Earth-like.

The idea that a planetary body can have lifeeven if solar energy is negligible (Figure 1b) isdriving exploration of icy moons within ourown solar system [Schultze-Makuch and Ir-

win, 2001; Wenz, 2017] and has been suggestedfor planets that do not orbit stars [Abbot andSwitzer, 2011]. For planets that do not orbitstars the difficulty of remote life detection isextreme. For planets/moons that do orbit astar there is the potential that life on such bod-ies would not interact with an atmosphere soas to create biosignatures that can be observedremotely [Schwieterman et al., 2018]. How-ever, it is not clear that life would not leavedetectable signatures that are not connectedto atmospheric chemistry [Lingam and Loeb,2018b]. Detectability cannot be ignored but atthis stage we are concerned about limits. Whatis key to our arguments is that an inhabitedplanet that lacks solar energy affecting life di-rectly or indirectly remains a viable possibility.

An inhabited planet that lacks internal en-ergy sources (Figure 1c) would imply that geo-physical/geochemical cycles are not requiredto maintain conditions conducive to life. Hab-itable conditions can be maintained on wa-terworlds (planets with water masses 10-1000times that of Earth) as a result of stochastic vari-ations in formation conditions with no need forgeochemical cycling [Kite and Ford, 2018]. Thepotential that habitable conditions can be main-tained without geo-cycling can extend beyondwaterworlds if life itself maintains conditions

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that allow for its continued existence. This isthe core of Gaia theory [Lovelock and Mar-gulis, 1974; Lovelock, 1979; 1995; Watson andLovelock, 1983]. Over the course of debatingthe theory, different levels of Gaia have beensuggested [Kirchner, 1989; 2003]. Soft Gaiaconsiders life on Earth to have influence onthe geophysical/geochemical cycles that mod-ulate Earth’s surface environment while thestrong form of Gaia considers life to be criticalto modulating surface conditions at livable lev-els [Barlow, 1991; Schneider et al., 2008]. Undera strong Gaia view, life could exist on a planetor moon that has tapped all of its internal en-ergy. Akin to the discussion of the previousparagraph, the key for what follows is that aninhabited planet that lacks internal planetaryenergy affecting life directly or indirectly re-mains a viable possibility.

The scenarios of Figures 1b and 1c are en-ergetic extremes. Between them sits the po-tential of livable planets that differ from theEarth in other ways. Some examples: Planetswithout oceans could allow for habitable con-ditions [Abe et al., 2011]; Planets that are oceanworlds could allow for life [Kaltenegger andSasselov, 2011]; Planets with internal energyprincipally driven by tidal heating (a minorfactor for Earth) could allow for life [Barnes etal., 2009]; Planets without plate tectonics (thegeologic mode of Earth) could allow for condi-tions conducive to life [Lenardic et al., 2016b;Foley and Smye, 2018].

Galactic Potentialities, Cost, Gain, andRisk: Statistical Thought Experiments

In this sub-section, we explore the degree towhich different search strategies can alter ourability to address questions of galactic life. Theanalysis will be in the form of double ‘whatif’ thought experiments. The distribution oflife in the galaxy is unknown but different po-tentialities can be considered (e.g., ‘what if lifepotential is not peaked around Earth’) to eval-uate how different search strategies performunder variable possibility space (e.g., ‘what ifa targeted search strategy is used under this

Figure 2: Future observations, limited by a window ofpotential habitability (θ) and by the searchstrategy employed, are grouped (θi) relativeto Earth (θEarth). Each group has a differenthabitability potential and there is a set of con-ditions that maximize habitability potential(µ). The width of the search window (θSearch)affects how accurately we can predict theseconditions.

potential life probability distribution’). Themathematical details of the experiments can befound in the appendix. Below we lay out theconceptual approach.

We assume that conditions describing agalactic body can be expressed as an index.The difference between the index values forany galactic body and the Earth defines anEarth-difference metric, θ. A more precise defi-nition for θ, in terms of delineating all the phys-ical/chemical factors that could feed into it, isnot required for the analysis that follows. Fig-ure 2 illustrates how θ is used in our thoughtexperiments. The analysis is referenced to ourown planet as θEarth. We assume there is arange of conditions (θmin to θmax) over whichplanetary life is possible. Galactic bodies aregrouped into bins, denoted as θi, each havinga fixed width. Each bin holds an equal numberof objects, an assumption that can be relaxed.Of those objects, some will be inhabited andsome will not. Based on this premise, a prob-ability index, characterizing the life potentialof each set of conditions, is assigned to each

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bin. Effectively, we are assigning a habitabilityindex, akin to that of Barnes et al. [2015], toeach bin. The bin with the highest probabilityindex is defined to be the set of conditions thatmaximizes life potential. The position of thisbin, on the Earth-difference scale, is denotedby µ.

The procedure above allows a large numberof distributions to be generated. As a start-ing point, we choose a normal distribution tomodel the frequency of inhabited planets basedon their specified conditions. We then vary µand create different probability distributions.Here, µ is varied between 0 and 0.5 at an incre-ment of 0.1. Allowing the life potential peakto vary is resonant with Heller and Armstrong[2014] who have argued that Earth conditionsmay not be those that maximize life potential.To be clear, we are not arguing that this is oris not the case. Our stance is that at presentwe do not know. We consider it a possibilityin the same sense that it is possible that Earthconditions do indeed maximize life potential.Effectively we are considering multiple work-ing hypotheses and exploring the implicationsof each for different search strategies.

Variable synthetic distributions, constructedas per above, represent different galactic poten-tials. The number of observations we have todate do not allow for discrimination betweendifferent potentials. For our experiments wewill assume that future observations can beused toward this end and we will ask how dif-ferent search strategies can achieve it. A searchstrategy is defined in terms of a search win-dow centered about θEarth and extending to avalue of θSearch in both directions. The greaterthe extent, the more we are willing to searchfor inhabited, non Earth-like planets. Increas-ing values of θSearch are evaluated for thereability to recover the mean of the inhabiteddistribution, referred to as µtest, and to provideaccurate estimates of galactic life.

Within this framework, we constructed dif-ferent galactic life distribution potentials andconsidered different search strategies for each.For any distribution, we drew from it at ran-dom, subject to a specific search window, ob-

serving what conditions defined each objectand whether they were inhabited or not. Thenumber of observations needed to find a fixednumber of inhabited objects was tracked. Thisnumber can be varied and we will also con-sider search strategy performance if the goalis to only find a single inhabited planet. If thegoal is to provide some constraints on galacticlife distribution then more than a single findwould be required. The minimum number ofobservations needed to potentially constrain adistribution is not a fixed, agreed upon value.As a starting point, we settled on 30 inhab-ited objects - this number is only a ‘rule ofthumb’ for the minimum number of observa-tions needed to potentially constrain a distribu-tion [Hogg and Tanis, 1997]. Once this numberof observations was obtained, the conditionsthat maximize life were estimated for varyingsearch window widths (differences in the esti-mates could then be compared to actual distri-butions to gauge uncertainty as a function ofsearch strategy). This process was performeda number of times, tracking the number of ob-servations and life potential maximizing condi-tions that were arrived at each time. We thenassessed the accuracy and cost of each searchstrategy. Accuracy was defined as the percenterror between the conditions predicted by eachsearch strategy and the true solution. Cost isrelated to the number of observations. Themore observations needed, the greater the cost.Some function could be devised to approxi-mate how this cost translates to total time andresources. Here we assume that the number ofobservations provides a useful starting point inconsidering relative costs (we appreciate thatthe scaling between number of observationsand monetary cost will likely be a non-linear).

For the initial suites of experiments, the prob-ability of life amongst galactic bodies at thedistribution peak was set to 20%. The proba-bility then dropped toward zero as conditionsmoved away from the peak toward the most ex-treme cases that maintained life potential (Fig-ure 2). This equated to assuming that roughly5% of galactic objects that reside within thewindow of planetary conditions that allow for

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Figure 3: a) A cost-benefit relationship based on search window width (color of dot) and how different the conditionscan be from Earth and allow for life (larger dots are further from Earth-like). b) Accuracy is assessinghow prevalent life is within the galaxy (Pgalaxy) versus search window width for different potential galacticdistributions (µtest).

life would be inhabited. That number can andwill be varied extending to 25% and less than1%.

The first scenario considered was one underwhich the conditions that maximize life poten-tial are centered on Earth conditions. In thiscase, a focused search strategy (i.e. a narrowsearch window) is ideal for finding a mini-mum number of inhabited planets in a costefficient way (Figure 3a). It can under predicthow prevalent life is in the galaxy by about athird (Figure 3b). Doubling the search windowcan bring the estimate of galactic life downto the lowest possible error at approximatelytwice the cost of a narrow search.

If the conditions maximizing life potentialare different from Earth then the accuracy andefficiency of different search windows changes(Figure 3). The changes for some search win-dows are large while for others they are rela-tively mild (i.e., different strategies have dif-ferent levels of robustness). When the optimalconditions are similar to Earth (µtest = 0.1),the error of the narrowest search strategy inestimating galactic life is not significantly in-

creased (Figure 3b) and cost remains low (Fig-ure 3a). The gains associated with moving toan intermediate search window are similar tothe Earth centered case (Figure 3b).

If conditions that maximize life potentialdeviate further from Earth (µtest = 0.3) thenchanges in the cost-benefit relationships, forvariable search strategies, can become signif-icant. For the narrowest window, accuracycontinued to decrease while cost, in terms ofnumber of observations, increased relativelyrapidly. The cost of a narrow search exceededthat of an intermediate search as µtest exceeded0.3. For those cases, a narrow search windowleads to significant bias. As a result, a lot ofobservations (and time) are required and theprediction they lead to regarding galactic lifepotential is in significant error. This is a dan-gerous combination. For µtest = 0.3, goingfrom a narrow to an intermediate search canlower the error in assessing galactic life poten-tial from over 70% to under 10% with closeto zero increase in cost. For µtest > 0.3, goingto an intermediate search can lower both errorand cost.

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Figure 4: Results from experiments, as per Figure 3, that vary the total percentage of inhabited galactic bodies.

Thus far, we have focused on the contrastbetween narrow and intermediate search strate-gies. Extending the search to observe every-thing that we think is capable of harboringlife increases accuracy over all potentialities.This comes with increased cost. Over mostof the potentiality space we have explored theincreased cost in going from an intermediateto a wide search does not come with a signifi-cant increase in accuracy. For the most extremecases tested, there is a significant increase inaccuracy. For those cases, the accuracy increasefor a wide relative to an intermediate searchis a factor of 4 with a factor of 1.25 increasein cost. In short, the principal gain in goingfrom an intermediate to a wide search is thatthe risk, in terms of misrepresenting galacticlife, for a “worst-case” situation is minimized.

The absolute number of observations neededto find a fixed number of inhabited planets, forany search strategy, depends on the assumedpercentage of inhabited galactic bodies. Figure4 shows results from experimental suites thatvary that value under the goal of finding 30(Figure 4a) or a single inhabited planet (Figure4b). For the experiments of Figure 4a, the accu-racy in assessing galactic life follows the sametrends as in Figure 3b. The relative difference

between search strategies remains robust fordifferent assumptions as to the total number ofinhabited planets. The exception is that as thetotal number becomes very low the potentialadvantage of a wide search becomes weaker(Figure 4a, lower right corner). If the total num-ber of inhabited planets is very low, then thenumber of planets that must be assessed to findmore than a single inhabited planet becomeslarge under all search strategies. If that is thecase, then we are pushing toward the limit atwhich statistical analysis is not justified.

To this point we have assumed that findinga single inhabited planet is not the sole goalfor explorations of galactic life. Nonetheless, itis useful to consider time commitment towardthe first milestone within the overall search en-deavor. The results of Figure 4b can be viewedin this way. They also have potential utility ifthe total number of inhabited planets in thegalaxy is so low that efforts to determine a‘life potential distribution’ will be effectivelydoomed from the start. If finding a single in-habited planet is the sole goal and/or if it turnsout that a very large number of planets needto be assessed before we find any signs of lifeon one of them, then Figure 4b is pertinentwhile issues of accuracy as per Figure 3b are

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less pertinent. There are some difference be-tween a single planet and multi planet goal,particularly if the total number of inhabitedgalactic bodies is low. However, the main trendwe are highlighting remains robust: a narrowsearch can be more efficient under some galac-tic life potentials but it comes with greater riskwhen evaluated over a broad range of poten-tials that extend beyond the assumption thatEarth conditions maximize life potential.

Changing Minds

Different ideas about life in our galaxy (e.g.,rare versus plentiful) can be viewed as compet-ing hypotheses or, in a probabilistic framework,different a priori assumptions that have notbeen fully tested (in this case because observa-tions are currently limited). Each end-memberidea is a viable hypothesis. Each is testable.That is, each is a scientific prior. Any scien-tific prior will adjust to new observations and,given a large number of observations, all suchpriors should converge toward the hypothe-sis that is most consistent with observations.In principal, it does not matter what prior as-sumptions a search strategy is based on - theobservations will decide in the end. In prac-tice, we need to consider that the observationswe will make over the next wave of missionswill be discrete in number. Using the Earth-likeness metric of the previous sub-section wecan ask which hypothesis is more responsiveto discrete new observations.

The discussion above relates to search strate-gies. One can imagine that a scientist whoholds to a rare-Earth, or Earth-centered, viewwould opt for a narrow search window on thegrounds that this would be the most efficientstrategy. On the other hand, a scientist whoholds to the view that a wide range of condi-tions can allow for planetary life might argueagainst a narrow search on the grounds that itwill introduce a bias. We can pose the questionof how many discoveries of inhabited planetswould be required to change either scientist’smind if their hypothesis happens to be incor-rect.

Figure 5: The number of discoveries, of inhabited plan-ets, it takes to converge to the attributes thatmaximize inhabitance for different priors andfor different life probability potentials.

The question above may seem highly subjec-tive. However, asking the question of how a pri-ori ideas or beliefs adjust to new observationslends itself to a Bayesian analysis (Appendix),which can provide quantitative insight. For anEarth-centered prior, initial confidence beginstightly peaked around θEarth . A plentitudeprior assigns equal weight across some θ-range.As in our previous analysis, we can draw ob-servations randomly and track the conditionsof the body and whether or not it is inhab-ited. If the body is indeed inhabited, bothend-member priors are updated to reflect this.This is repeated and the number of observa-tions tracked until each scientist’s confidenceis in alignment with the true set of conditionsthat maximize life potential within an equaltolerance. This is quantified using a maximuma posterior (MAP) metric [Robert, 2002]. Thatmetric is defined as the parameter with themaximum posterior probability (further detailscan be found in the appendix).

Figure 5 shows how long it takes each end-member hypothesis to converge for differentpotential galactic life distributions. If galacticconditions are Earth centered, it would not takelong to alter either a priori view. If the con-ditions are different than Earth, it takes moreobservations for both priors to converge to thetrue solution. This increase occurs because our

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first data point is always Earth. That initial dataconstraint is a restatement of our current un-derstanding of life in the galaxy: we have onlyobserved one inhabited body, Earth. If condi-tions maximizing life potential are far differentfrom Earth, then our planet can introduce aninitial bias. A plentitude view adjusts relativelyquickly, regardless of our planets galactic sta-tus. An Earth-centered prior has a slower ad-justment in the face of new observations, i.e., itcomes with a greater resistance. If galactic lifepotential is not Earth centered, then going inwith the assumption that it is, as opposed tothe assumption that a wider range is possible,will lead to ∼6 times more observations beingrequired to remove the shadow of the a prioriassumption.

Discussion

In the previous section we used an Earth-likeness (equivalently a nonEarthness) metricto evaluate the cost, accuracy, and risk associ-ated with different search strategies and themore subjective cost associated with compet-ing a priori hypothesis regarding planetary lifepotential. We employed a generic metric to pro-vide a quantitative measure of the degree ofnonEarthness that maintains life potential. Inthe statistical thought experiments, the resultswere dependent on the value of this metric tovariable degrees - in some scenarios that can-not be observationally ruled out the degree ofdependence was large. An upshot is the sug-gestion that there is value in developing, asa community, a more tightly defined metric.This could provide some nonEarth1.0 balanceto Earth2.0 thinking and discussions. The bal-ance could have scientific and humanistic im-plications. In the following sub-sections, wewade into these discussion topics, not as a finalsay, but as a starting point.

Different is More

What is the value of considering the poten-tial of inhabited, nonEarth-like planets in thesearch for life? What is the value of finding

such a planet? The first question was at thecore of the previous section. A key implica-tion was related to risk minimization, whichwe expand on below. We then move to the sec-ond question. We focus in on Gaia theory andon how exoplanet exploration could provide auseful Gaia test bed that extends beyond Earth.

Search strategies should be able to achievegoals in cost efficient ways that minimize riskin the face of worst-case scenarios. What isthe worst-case scenario for investing resourcesto assess galactic life potential? Is it findingno signs of life beyond Earth? That is a worstcase if one believes that it is a negative con-clusion. If the goal is to reach a conclusionwe can be as confident of as we can be, thenno conclusion is negative if it is the one thatfollows from the preponderance of un-biasedevidence. We would argue that the worst casewould be spending a large amount of time andresources to reach the wrong conclusion. Fig-ure 3 indicates that an overly narrow searchcan open us to that risk.

The above can be viewed as an overly “for-malized” assessment. Exploration depends onpublic interest, which doesn’t fit as easily intoformalized analysis. From that angle, a worst-case scenario could be viewed as one that triespublic patience (although we would argue thatan equally valid worst-case scenario would bemisinforming the public). This could motivatethe idea that we need to find signs of an inhab-ited planet beyond Earth as soon as we can (theopening statements quoted in the introductionreflect that, rightly or wrongly, this has alreadybeen effectively promised to the public). This,in turn, could be used to argue for an Earth-centered search based on the idea that it wouldminimize time commitment. The difficulty isthat we would then be making a time invest-ment decision based on assuming we know theanswer to a critical question before we put theinvestment strategy into practice. This againopens us to risk as a narrow search could comewith a higher time cost if we are wrong interms of our a priori assumption (Figure 4b).

In regards to assumptions, all of our resultsrequired assumptions regarding galactic life

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distributions. This, we would argue, does notweaken our conclusions but is an overarchingpoint of the analysis to begin with. The tightera search focuses around an Earth2.0 mode, themore a soft form of rare-Earth is being assumedto be valid (i.e. life potential peaks at Earth).One could argue that models of planetary hab-itability and observations from our solar sys-tem, to date, lend support to this assumption.Fair enough but it remains an assumption. Itmay prove correct but if it is used to justify asearch strategy then the strategy is designed,effectively, to test only one hypothesis. Onecould take an alternate view. Rather than ar-guing for one hypothesis over another (e.g.,life potential peaking near or away from Earth[e.g., Heller and Armstrong, 2014]), we can as-sume that a range of hypothesis remain viableand seek to minimize risk in the face of thevarious potentialities. This is the view we haveargued for. Considering the potential of inhab-ited non-Earth like planets can minimize riskat an increased cost that, in our opinion, is notexcessive (Figures 3 and 4). It also allows forthe potential of discriminating between differ-ent hypotheses regarding galactic life (Figure5).

We now turn to the question of “what isthe value of finding an inhabited planet that isnon Earth like in other regards?” The classicconcept of a “Habitable Zone” assumes thatdelineating planetary conditions that allow forthe potential of life can proceed without con-sidering life’s role [Kasting et al., 1993]. Ineffect, it is assumed that habitability can be de-termined without explicitly considering inhab-itance. This assumption has been challengedand the degree to which removing it from exo-planet discussions could influence our thinkingabout life in our galaxy is significant [Goldblatt,2016]. The difficulty has been and remains thatobservations from this planet can not unravelthe degree to which life influences cycles thatregulate environmental conditions (the Earthhas life and remains geologically active - whichof these is more critical to the Earth being hab-itable is difficult to unravel as life has entwineditself in a range of geophysical/geochemical

cycles [Goldblatt, 2016]).

From an exoplanet perspective, we can pushGaia theory to a limit. If a strong form of Gaiacan operate then planetary regulation could oc-cur without abiotic cycles (Figure 1c). That is,life could do the heavy lifting for maintaininghabitable conditions. The implication is thatalthough planetary internal energy, that drivesvolcanism and tectonics, plays a role for theEarth’s inhabitance it is not critical for plane-tary bodies in general. The internal energy of aplanet will depend on its age and composition.The potential of determining composition andage for exoplanets is actively being discussedwithin the community. Both could be withinreach for next generation observations. If aplanet is found that has low potential of beinggeologically active and shows biosignaturesthis would provide a step toward confirmingGaia (internal energy may still have been cru-cial for the origin of life [Baross and Hoffman,1985] and for maintaining habitable conditionsearly in the planets lifetime but the extensionof habitable conditions past the geologic life-time of the planet would be due to life itself).At present, search strategies are focused onplanets that are likely to be geologically ac-tive with the thought that this is critical forlife [Ward and Brownlee, 2000; Kasting, 2010].That remains an assumption. It is an assump-tion that has the potential to be refuted if asingle strong Gaia1.0 is found (a greater num-ber of Earth2.0’s would be required to confirmthe assumption at a statistical level).

Finding strong Gaia1.0 would dramaticallychange our views about planetary habitability(finding Earth2.0 would be a confirmation ofa prevalent idea). The degree of rethinkingcan be hinted at by posing a question: Is hab-itability a characteristic of a planet, like tem-perature, or is it something that flows throughit, like heat? Stated another way, is it a stateor a process variable? The classic "habitablezone" concept assumes that it can be treatedas a state variable. From that, follows the as-sumption that its limits can be determined soas to effectively make a phase diagram thatdelineates regions that allow for life. On a

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Different is More Lenardic and Seales

strong Gaia the origin and evolution of lifeare dominant for habitability. With that comescontingency and the potential of multiple tem-poral paths leading to variable end states ofinhabitance [Walker et al., 2018]. This is aprocess variable view [Bridgman, 1943] underwhich multiple equilibrium states are possibleand path-dependence cannot be ignored [Dykeand Weaver, 2013; Weaver, 2015; Lenardic etal., 2016]. This brings in layers of potentialityassociated with evolution and historical con-tingency (to be clear, a contingent process isnot the same as a random process [e.g., Bohm,1957]). The approach to planetary life researchwould, as a result, need to move toward onethat is more statistical/probabilistic than it isat present [Walker et al., 2018].

The issue of evolution leads to a final point.Rare-Earth ideas acknowledge that planets dif-ferent from the Earth could have simple (mi-crobial) life but argue that higher life (plantsand animals) requires conditions like that ofEarth [Ward and Brownlee, 2000]. Life can re-spond to environmental changes. Many of thechanges, that are considered critical to the de-velopment of higher life on Earth, are ascribedto internal energy sources driving changes insurface conditions such that if a planet lackedthe geological changes that occurred on Earthit could have microbial life but it would nothave developed higher life [Ward and Brown-lee, 2000; Stern 2016]. The idea that evolutionrequires environmental changes is not agreedupon for the evolution of life on Earth [McKee,2000] and, as such, extending it to planetarybodies in general is an a priori assumption.Exoplanet search strategies have incorporatedthe potential that atmospheric bio-signaturesmight be of the kind that prevailed on earlyEarth, before the rise of complex life, or of thekind associated with higher life [Schwietermanet al., 2018]. Finding signs of higher life ona geologically inactive planet could provide anew layer of evidence that evolution can pro-ceed in an autocatylistic mode with no needfor externally driven environmental changes[Kauffman, 1993; McKee, 2000; Cazzolla Gatti,2011].

Finding signs of life on another planet, be itlike our own or significantly different, wouldbe a major discovery. The implications of thatdiscovery could be further reaching for planetsthat are different. In that sense, different ismore - it could bring more information contentabout life potential in our galaxy.

Narratives

The search for life beyond Earth is no smallundertaking. It can benefit from efforts toengage the public. The engagement is of-ten framed as a narrative. Narratives can gowell beyond public relations. A narrative canframe a problem in a way that favors one deci-sion/conclusion over alternatives that are justas rational as the frame-favored decision [Tver-sky and Kahneman, 1981]. For the issue athand there is a feedback as public opinion caninfluence exploration strategies. Whether it isintended or not, building a narrative around aproblem will influence the way humans thinkabout the problem and, in keeping with thecultural/humanistic connections of this sub-section, ‘what we think changes how we act’[c.f., Gang of Four, Solid Gold, EMI/WarnerBros., 1981]. In short, this encapsulates thevalue of re-framing problems and consideringmultiple frames when addressing problems in-volving uncertainty [Tversky and Kahneman,1986].

An Earth2.0 narrative that has been used toframe exoplanet exploration reinforces the ideathat Earth conditions are the ideal ones forhabitability (a variant of a rare-Earth narrative[Ward and Brownlee, 2000]). We would arguethat we do not have the observations neededto discriminate between different assumptionsregarding galactic life potential at this stageof our exploration and it is not in the bestinterest of the search to send messages, explicitor implicit, that we do. An Earth2.0 narrative,as it is being presented to the public, walksthe line of promising specific returns and thedangers of that for science, in the public realm,should be kept in mind [e.g. Riordan et al.,2015].

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Different is More Lenardic and Seales

Beyond sending messages that do notaccurately reflect the state of our knowledge,an Earth2.0 narrative comes with philosophicaland cultural baggage that may not bestserve its intended purpose. An Earth2.0narrative is nostalgia heavy. There have beenmany words put forward in the service ofan Earth2.0 narrative but images, arguably,can give a better sense of the messages thisnarrative carries. Artwork depicting travelposters to exoplanets with white picketfences [https://exoplanets.nasa.gov/alien-worlds/exoplanet-travel-bureau/] invoke asense of the familiar - a sense of home (note:only a sense of home for those who grew upculturally and economically in places thathad white picket fences to begin with). Thedesire for a place just like home is fed bynostalgia and a desire for an ideal [Messeri,2016] - an ideal that may never have existed.The potentially false narrative of an ideal pasthas been taken up in artistic works (e.g., somemovie examples: Plaesantville, Midnight inParis, Trainspotting 2) and in historical studies[e.g., Webb, 2017]. We mention these worksto point out that, to a portion of humanity,a nostalgia filled narrative may not have theeffects hoped for.

We are not implying that the cultural valueof nostalgia in general, or specifically for devel-oping public narratives, can be broken downto 1’s and 0’s. It is not as simple as it’s alwaysgood or always bad. It depends on context[e.g. Bonnett, 2010]. Within the context ofspace exploration, a narrative built on findinga second Earth is intertwined with the idea offinding a second home [Messeri, 2016]. Homeis something we know, something comfortable,and ideas of home can lead to thoughts of "bet-ter times". This can send the message thatour goals are to recapture something. It in-vokes a sense of looking toward the past, whichruns counter to the idea of exploration. Whenpushed to limits, such nostalgic messages areassociated with populist movements. Fromour perspective, this also runs counter to theidea of space exploration, which is a globalendeavor (i.e., an internationalist as opposed

to a national endeavor).An alternate narrative, as compared to

searching for an Earth2.0, is one of galacticdiversity in terms of livable and living planets.In this alternative narrative, the future becomesmore prominent with all the lack of certainty,immediate comfort and familiarity that a fu-ture holds. Planets with life beyond Earth maybe something foreign to us. They may be un-comfortable for us to live on at first. To knowthem we need to find them, as opposed to start-ing our exploration on the premise we alreadyknow them (we are not the first to remark onthe dangers of assuming we know the answerbefore hand when it comes to planetary explo-ration [Moore et al., 2017; Tasker et al., 2017]).The alternate framework we are proposing willalso not resonate across all of humanity as apublic engagement narrative but which of thetwo, diversity of living planets versus findinga second Earth, better represents the sense ofexploration that got us, as human beings, tobegin exploring space in the first place?

Appendix: Methods

Statistical Cost-Benefit-Risk Analysis

We used a statistical analysis to address ourmotivating question: How does search windowwidth affect the cost-benefit relationship basedon the conditions that maximize life potential?In the analysis, we tested three search win-dow widths - narrow, intermediate and wide,which are defined by the θSearch values 0.2, 0.6and 1.0, respectively. For each search windowwe tested six different life distributions, eachhaving increasingly nonEarth-like life potentialmaximizing means (µtest), ranging from 0.0 to0.5. For each combination of θSearch and µtest,we conducted 100 trials that randomly sam-pled a synthetic data set, characterized by theconditional probability P(I|Θ), the probabilitythat an object is inhabited given a specific setof conditions. We assumed that each subset ofconditions, broken up into discrete intervals(θi), 0.1 units in width, were equally likely torepresent any observable object. Within each θi

13

Different is More Lenardic and Seales

interval, some of the objects were inhabited andsome were not. The percentage of inhabitedbodies in each θi interval was approximatedas the probability for that bin given a normaldistribution defined by µtest and a standarddeviation (σ) of 0.2, which we held constant.

For each combination of θSearch and µtest, aset of trials were performed to estimate thesample statistics. In each trial, we used a uni-form random number generator to determinethe bin from which an observation would bedrawn (subject to limits imposed by the searchwindow). Then, we did a second random draw,from that bin, and tracked whether the observa-tion was of an inhabited or uninhabited object(the greater the habitability probability fromthat bin, the greater the chances that an inhab-ited object would be observed). During theduration of the trial, we tracked the total num-ber of observations, the conditions that definedeach observed object, how many objects wereaccumulated in each interval θi and whetheror not each object was inhabited. Once 30 in-habited objects were observed, we calculatedthe mean x̄ and standard deviation (s) of thesample. Following the 100 different, random-ized trials, we calculated the means µx, µs, µni

and µnθiof the sampled statistics. In this paper,

we refer to µx as the observed mean, µs as ob-served standard deviation, µni as the numberof observed inhabited objects in the interval θiand µnθi

as the total number of observations inthe interval θi.

Using the results of the statistical analysis,we calculated the percent error between thetrue (Pgalaxy) and predicted number of inhab-ited galactic objects (P∗galaxy) for each combina-tion of Search and test. The statistical analysisresults tell us the average ratio between thenumber of inhabited objects and total observedobjects is defined as

µni

µnθi

(1)

for each θi. Equation 1 can be scaled to theentire population by the relation

µni

µnθi

=NiNθi

(2)

where Ni is the total number of inhabited ob-jects in the interval and Nθi is the total numberof objects in the interval. Using our mean ofthe distribution of the means (µx̄ and µs), wecan approximate the probability distribution oflife conditions as

P(I|Θ) = N(µx̄, µs) (3)

Furthermore, for each interval, we know that

P(I|θi) =Ni

Pgalaxy, (4)

where Pgalaxy is the number of objects in thegalaxy that are inhabited. Combining equa-tions 1, 2 and 4, we arrive at our estimate ofthe galactic population

P∗galaxy =Nθi ni

µnθiP(I|θi)

. (5)

Following the same procedure, except usingµtest and σ rather than µx̄ and µs in equation 3,the true galactic population is

Pgalaxy =Nθi ni

µnθiP(I|θi)

(6)

where ni is the true number of bodiespresent in the interval i if a representative sam-ple were taken of size µnθi

. That is

ni = µnθiP(I|θi). (7)

Substituting equation 7 into 6 we get

Pgalaxy = Nθi . (8)

This relationship is a result two main as-sumptions: (1) that every object is equallylikely to be characterized by any set of con-ditions θi, and (2) the proportion of objects thatare inhabited within a given interval i is rep-resented as the probability of that interval forthe normal distribution characterized by µtestand σ. To obtain the percent error (ε), we usethe relation

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Different is More Lenardic and Seales

ε =

∣∣∣∣∣Pgalaxy − P∗galaxy

Pgalaxy

∣∣∣∣∣ , (9)

which, after combining with equations 5 and8, simplifies to

ε =

∣∣∣∣∣1− µni

µnθiP(I|θI)

∣∣∣∣∣ . (10)

Changing Minds

Bayesian inference provides a framework toevaluate how new data can alter a priori as-sumptions that define different end-membersearch strategies. Assumptions regarding ourcurrent state of knowledge are used to assignprobabilities to a particular set of beliefs knownas the prior, P(θ), where θ is a discrete vec-tor representing parameters. As new data (D)are discovered, the chances of them occurring,given that a particular parameter is correct,is then computed to produce the likelihoodfunction, P(D|θ). The likelihood is telling usthe probability of getting the data given theset of conditions. The prior and likelihoodfunction are then combined to produce ourupdated knowledge, known as the posteriorP(θ|D), which is interpreted as the probabilitythat parameter θ is correct, given the observeddata set D. These three components are relatedby

P(θ|D) ∝ P(D|θ)P(θ) (11)

In our analysis, θ represents how Earth-likea body is and D represents the number ofsuch galactic bodies that are inhabited. Earth-likeness is a sliding parameter scale normal-ized to Earth at a value of zero and extendingto negative and positive infinity. We consider afinite range between some assumed minimumand maximum value, θmin and θmax (θmin andθmax are assigned normalized values of -1.0 and1.0, respectively, for the most extreme versionof a plentitude hypothesis). We consider dif-fering values of Earth-likeness at intervals of0.1, totaling 21 different types of Earth-likenessbins.

We use different priors to represent compet-ing hypotheses for the range of earth-likenessan inhabited planet can have. One prior as-signs a high probability around zero in θ-spaceand much lower values everywhere else. It isrepresented as a normal distribution with amean value of zero and variance of 0.1. Thesecond prior assumes that all earth-likenesses,within our finite range of consideration, areequally probable to be inhabited.

Discoveries of future hypothetically inhab-ited planets are used to produce the likelihoodfunction. It is assumed that the Earth-likenessof each new discovery can be categorized. Us-ing this data, the standard Gaussian functionalform is used to derive the likelihood function,

P(D|θ) =N

∏i=1

1√2πσ

exp

[− (θ − Di)

2

2σ2i

]P(θ)

(12)

where we assume each new data point isindependent of any other, potentially a limitingassumption as the sampling may be highlyselective. This allows for the multiplication ofthe prior and likelihood function to producethe posterior. The posterior is then normalizedsuch that the sum of probabilities from all binsequal one.

A plentitude hypothesis uses an uninforma-tive prior, which allows the data to directlyinfluence the posterior distribution. The poste-rior is computed by calculating the likelihoodfunction and normalizing the sum of proba-bilities to one. On the other hand, an Earth-centered prior is normally distributed and ismultiplied with the likelihood function produc-ing a posterior that is also normally distributed.The mean and variance of this posterior is com-puted as

15

Different is More Lenardic and Seales

a =1

σ2prior

, (13)

b =nσ2 , (14)

µpost =aµprior + bx̄

a + b, (15)

σ2post =

1a + b

(16)

where σ, x̄ and n are the known uncertaintyof the likelihood, the mean value of the dataand number of data points, respectively. Oncethe probabilities have been computed, theymust be normalized to sum together to one.

To gauge the convergence of a given priorwe use the maximum a posteriori (MAP), de-fined as the parameter, which has a maximumposterior probability [Robert, 2002]. The MAPis used to calculate the convergence of end-member priors to a final solution. The numberof discoveries it takes for the MAP to equal theassumed mean of θ, given random draws froman assumed data set, defines the “convergencemetric” plotted in Figure 5.

To test the convergence of each prior, we as-sume a normally distributed subset of 1,000inhabited planets (other values can be tested- our initial interest is a relative comparisonbetween two end-member priors and, as such,absolute numbers for convergence are not par-ticularly meaningful as they are overly depen-dent on the assumed number of inhabited bod-ies). The mean of different potential galacticdistributions (µtest) is varied between 0 and 1 inθ-space with a standard deviation of 0.3. Plan-ets are drawn at random, following Earth asthe initial data point, and the number of drawsit takes to converge to a solution is tracked.The process is repeated for each µtest and eachprior 150 times and the average number ofdraws, from the subset of 150, is reported asthe convergence metric for each prior undereach variable galactic life potential (Figure 5).

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