Content uploaded by John-Oliver Engler
Author content
All content in this area was uploaded by John-Oliver Engler on Nov 16, 2018
Content may be subject to copyright.
‘Where is everybody?’ An empirical appraisal of
occurrence, prevalence and sustainability of
technological species in the Universe
John-Oliver Engler∗and Henrik von Wehrden
Faculty of Sustainability, Leuphana University of L¨uneburg, Germany
November 16, 20185
Abstract
We use recent results from astrobiology, particularly the A-form of the
Drake equation and combine it with data on the evolution of life on Earth
to obtain a new assessment of the prevalence of technological species in our
Universe. A species is technological if it is, in theory, capable of interstellar10
communication. We find that between seven and 300 technological species
have likely arisen in the Milky Way until today, the current state of which
however unknown. Assuming that we are currently alone in our galaxy, we
estimate that we would need to wait for roughly 26 million years for a 50%
chance of another technological species to arise. By relating our results to15
the much-debated Fermi-Hart paradox, we discuss if and to what extent our
results may help quantify the chances of humanity to manage the transition
to a long-term sustainable path of existence.
Keywords: Drake equation; extraterrestrial intelligence; future of humanity; SETI;
∗Corresponding author: Quantitative Methods of Sustainability Science Group, Leuphana Univer-
sity, L¨uneburg, Germany, phone: (+49) 04131/677 2804, email: engler@leuphana.de
1
sustainability
Running title: Where is everybody?5
2
1 Introduction
Whether and how abundant life on other planets exists and what its future might
look like, including our own, are some of the core questions of astrobiology (Sullivan
and Baross 2007; Hubbart 2008). Even though astrobiology is a rather young field, it
is considered likely that humans have been wondering about the existence of other5
living beings in the Universe for millennia (Dick 1982; Crowe 1986). Indeed, the
idea of humanity being alone seems improbable to many scientists and laypersons
alike, and this mindset is maybe best subsumed in the famous question ‘Where is
everybody?’, often attributed to Enrico Fermi, but arguably erroneously so (Finney
and Jones 1985; Gray 2015). In the quest to quantify the number of currently10
existing technological extraterrestrial species1N, the Drake equation (Drake 1965;
Drake and Sobel 1991) has been one of astrobiology’s work horses. In its original
form, it can be written as
N=NAst ·fbt · hLi(1)
where NAst is the number of potentially habitable worlds, i.e. the ‘astrophysical
factor’, fbt is the fraction of such planets that actually develop technological life, i.e.15
the ‘biotechnical factor’ (Frank and Sullivan 2016: 360), and hLiis the mean length
of time over which such technological species release detectable signals.
The Drake equation however, even though very simple in terms of its mathe-
matical structure, has proven hard to evaluate, because a number of its parameters
seem to evade any conclusive value assignment. In particular, while the astrophysi-
cal factors of the equation have been determined ever more precisely in recent years
(Cassan et al. 2012; Petigura et al. 2013), the biotechnical factor fbt, which is es-
sentially a product of probabilities, has remained somewhat arbitrary. Recently,
there have been considerable efforts to provide numerical estimates of the number5
of technological species, or single components of the biophysical factor in the Drake
equation, based on statistical modeling or Monte Carlo simulation (e.g., Forgan and
1The term ‘technological species’ implies technological capability of a species to communicate
across interstellar distances (e.g., Maccone 2010).
3
Rice 2010; Maccone 2010; Glade, Ballet and Bastien 2012; Rossmo 2017; Ramirez
et al. 2018). Notably, Frank and Sullivan (2016) derived most pessimistic lower
boundaries of fbt by reformulating the Drake equation without hLi. In particular,10
they advocate that there was ‘basically no theory to guide any estimates’ for fbt
(ibid.: 360). However, we argue that there are principles from statistics and sta-
tistical physics, which can be used to obtain estimates for fbt and in turn for the
number of technological species that have ever arisen in the Universe. Frank and
Sullivan (2016) refer to this number as A.15
Here, we use Frank’s and Sullivan’s (2016) time-independent version of the Drake
equation and provide estimates for fbt to obtain most likely ranges of Aon different
scales of interest (Milky Way, galaxy cluster, super cluster, observable Universe).
We argue that it is possible to use the available data on the evolution of life on
Earth to provide our estimates, based on three assumptions: (1) the Principle of20
Insufficient Reason; (2) ergodicity of evolution; (3) the Copernican principle. We
argue that these assumptions remedy the problem ‘no theory problem’ in estimating
the biophysical factor. Moreover, we show that our argument can be used to derive
estimates for the birth rate of technological species to answer the question of how
long we would have to wait for another technological species to occur, should we
currently be the only one existing. Finally, we discuss to what extent our results can
be used to guide and assess the long-term future prospects of humanity with regard
to its current quest for a sustainability transition. This ‘astrobiological perspective5
on sustainability’ (cf. Frank and Sullivan 2014; Frank et al. 2018) implies that we
understand sustainability in a rather simplistic sense of ‘longevity of the human
species’ (Gott 1993: 316). Hence, in this paper, sustainability means existing long
enough to matter on an astrophysical time scale, i.e. for time periods in the order
of at least 107to 109years.10
The paper proceeds as follows. Section 2 describes the model and explains our
assumptions necessary to carry out our analyses, the results of which we present in
Section 3. In Section 4, we discuss our results, particularly in the context of what
they could mean for our own future as a technological species and with regard to
4
the role of parameter uncertainties. Section 5 concludes.15
2 Methods and data
2.1 Model
We re-visit the ’A-form of the Drake equation’ proposed by Frank and Sullivan
(2016). The A-form is a time-independent re-formulation of the Drake equation
(Drake 1965), which gives an estimate of the number of technological species to ever20
have evolved in all of the currently observable Universe, or, depending on the choice
of parameters, some fraction thereof such as our own galaxy. It reads (cf. Frank and
Sullivan 2016)
A= [N∗fpnp] [flfift] = NAst ·fbt (2)
where N∗is the total number of stars in the region of interest, fpis the fraction of
those stars that host a planetary system, and npis the average number of planets in5
the habitable zone of a star hosting a planetary system. The product of these three
factors thus represents the total number of potentially habitable planets in a given
area of interest NAst. Moreover, flis the fraction of these habitable zone planets
that develop life, the fraction fiof which intelligent. Lastly, ftis the fraction of
intelligent life that develops technology. Hence, the product of all factors fbt is the10
bio-technical probability that life on a given habitable-zone planet evolves to the
stage of a technological species, and NAst ·fbt is the total number of technological
species to have ever arisen anywhere in a specific region of interest in the observable
Universe until now.
2.2 Assumptions15
Frank and Sullivan (2016) argue that, while there are good estimates and measure-
ments of the factors that constitute NAst, it is not possible to give a good estimate
of fbt, the probability that a given habitable zone planet develops life that is capable
5
to develop technology. Here, we posit that an estimate for fbt can be made under
the assumptions laid out in the following.20
2.2.1 Principle of Insufficient Reason
The first assumption that we make is that we apply the Principle of Insufficient
Reason2(Keynes 1921) to determine fl. The principle is a cornerstone in philosophy
of science and states that ‘if we are ignorant of the ways an event can occur (and
therefore have no reason to believe that one way will occur preferentially compared5
to the other), the event will occur equally likely in any way’ (Weisstein 2018).
Hence, if we know what could potentially happen, but do not have any probabilistic
knowledge about these nknown potential outcomes {Oi}n
i=1, there is no sufficient
reason to assume anything else than pi=1
naccording to the Principle of Insufficient
Reason. For any habitable zone planet, there are exactly two possible outcomes:10
either life develops or it does not, and there is no reason why one of the two outcomes
should a priori be considered more probable, provided that we do not know anything
other than the planet being in the habitable zone of its star. By application of the
Principle of Insufficient Reason, we may thus assume fl=1
2. Interestingly, the same
parameter estimate has surfaced before without explicit reference to the underlying15
principle (e.g., in Maccone 2010).
2.2.2 Ergodicity
Our second assumption is the hypothesis that evolutionary dynamics is ergodic in
the sense that Earth is a representative sample for the evolution of life under favor-
able conditions. The question of whether evolutionary dynamics may be considered20
ergodic has received notable attention recently (de Vladar and Barton 2011; McLeish
2015). Here, ergodocity does not imply that if we were to re-run Earth’s history,
say, 1000 times, the result would always be human life. On the contrary, the result
2The principle seems to have been implicitly assumed by Jakob Bernoulli and Pierre-Simon de
Laplace (Laplace 1820; Hacking 1971), and was later reintroduced by economist John Maynard
Keynes as ‘the principle of indifference’.
6
could be quite different each time. In fact, for any fl<1, there might be outcomes
with no life at all. Instead, we mean ergodicity to imply that we can generalize5
insights from evolution on Earth to the ensemble of habitable zone planets (HZPs)
elsewhere in the galaxy or even the observable Universe, i.e. we hypothesize that
hfbtiEarth =fbt HZP (3)
Clearly, our hypothesis is a stretch of concept as the term on the left-hand side
of equation (3) represents a time average, which will hold only to the extent that
the reader is willing to believe that our calculations represent long-term averages10
of fiand ft. Moreover, there are path dependencies in evolution that we cannot
cope with here. On the other hand, many processes and feedbacks involved in
evolutionary dynamics solely rely on physical and chemical laws and constraints,
which are universal across the Universe. It may thus be said that, at the very least,
our contribution is to make an educated guess on the prevalence of technological15
species in our galaxy, based on our knowledge about the evolution of life on Earth.
2.2.3 Copernican principle
Our third assumption required to find a reasonable estimate for fbt is that Earth is,
statistically speaking, a ‘normal planet’. As Gott (1993) pointed out, our assumption
is in accordance with the Copernican principle of contesting the believe of humanity
being ‘privileged’ in the Universe. Hence, we do not advocate the ‘Rare Earth
hypothesis’ here (Ward and Brownlee 2000), which we think is in line with ever
more discoveries of Earth-sized HZPs recently (Queloz et al. 2009; Batalha et al.
2011; Quintana et al. 2014).5
As made explicit above, we assume fl=1
2by the Principle of Insufficient Reason.
As to the other ingredients of fbt, we point out the nested structure of the constituent
factors (cf. Glade, Ballet and Bastien 2012), i.e.
fbt =ftfifl=P(technology|intelligence)P(intelligence|life)P(life|HZP) (4)
7
and, since we assume fl=1
2, we may simplify
fbt =P(technology|intelligence)P(intelligence|life)1
2
=1
2P(technology|life) (5)
Hence, because we know that the number of technological species on Earth ntis10
equal to one, we may conclude from equation (5) that it suffices to consider estimates
for the number nsof species that have ever evolved on Earth to be able to calculate
an estimate for fbt.
2.3 Data
Estimates for nshave ranged from anywhere between 17 million to 4 billion, with
more recent estimates stabilizing in the order of 108to 109(Table 1). In light
of recent estimates of the number of species currently living on our planet (Mora
et al. 2011), the lower boundaries of Simpson (1952) and Cailleux (1954) seem5
unrealistically low. Thus, the smallest defensible lower boundary value seems to be
Iberall’s 100 million (Iberall 1989).
Table 1: Ranges of estimates of number of species to ever have existed on Earth.
Estimated interval [million species] Source
[50,4000] Simpson (1952)
[17,860] Cailleux (1954)
[100,250] Iberall (1989)
[250,750] Benton (2011)
3 Results
We present our results regarding the prevalence of technological species in the Uni-
verse (Section 3.1) and the time it would take until the next technological species10
would arise under the assumption that humanity is currently alone in the different
possible spheres of interest (Section 3.2).
8
3.1 Prevalence of technological species
We start from equation (2) and apply our assumptions 2.2.1-2.2.3 to obtain
A=NAst ·fbt =NAstfl
nt
ns
(6)
Note that the inverse relationship A∝nsis in agreement with our general statistical
argument, because a larger value of nswould imply a lower value of P(technology|life)
in equation (5), and therefore a lower value for fbt. Hence, discovering ever more5
species on Earth, still living or already extinct, would decrease the probability of
evolution of technological species elsewhere in the Universe, simply because such
discoveries would make our own existence empirically less likely.3Combining all
ingredients, it follows for the range of the probability fbt that evolution on a life-
bearing HZP develops a technological species10
5·10−9≥fbt ≥1.25 ·10−10.(7)
Lastly, we multiply by the number NAst as taken from Frank and Sullivan (2016),
who refer to Fukugita and Peebles (2004), to obtain the number of technological
species on different scales of interest (Table 2). We find that, as an absolute mini-
mum, at least 7 technological species have likely arisen in the history of our galaxy
until today, while a number of up to 300 is likely under the most optimistic plausible15
parameter values. Our estimated range for Ais notably narrower than what Mac-
cone (2010) estimates for the number of civilizations currently living in the Milky
Way (7453 ≥A≥0). The difference is due to the large value of 0.2 that Maccone
assumes for fiand ft, which leads to a considerably larger value of fbt = 0.02 than
the range that we have provided above. For the observable Universe, our estimates
mean that at least 500 billion technological species have likely arisen to this day.5
However, these numbers do not imply anything about the existence of extraterres-
trial technological species right now, or that communication with them would be
3Consider instead the opposite finding, i.e. a very low value of ns. In this case, we would have to
conclude that it does not take too much ‘trial and error’ to evolve a technological species like us,
so we would conclude that P(technology|life) is rather high.
9
likely. For one, technological species may disappear shortly after they have arisen
(Shklovsky and Sagan 1966, Sagan 2015) and even if they were sending signals, a
2017 study by Grimaldi has shown that the chance of us picking up their signals10
would basically be zero, regardless of how many technological species would actually
be transmitting (cf. Grimaldi 2017). A sensitivity analysis of our estimations can
be found in Appendix A.
Table 2: Ranges of estimates of number of technological species to ever have arisen
on different astronomic scales.
Scale No. of galaxies NAst Estimated range of A
galaxy 1 6 ·1010 [7,300]
galaxy cluster 300 2 ·1013 [2,500,100,000]
supercluster 3000 2 ·1014 [25,000,1,000,000]
observable Universe 7 ·1010 4·1021 5·1011,2·1013
3.2 How long until the next technological species?
It is well possible that mankind is currently the only technological species in the15
Milky Way galaxy. If this were the case, how long would we have to wait for the
occurrence of another technological species in our galaxy? Recent findings suggest
that the oldest known system of terrestrial-sized planets is about T= 11.2·109
years old (Campante et al. 2015), which is therefore the best possible guess as to
how long evolution may already be at work elsewhere in the cosmos and therefore
in our galaxy. We combine this number with our results for Afrom Table 2 to give
something like the ‘rate of occurrence’ or ‘birth rate’ λof technological species in a5
given sphere of interest, i.e. λ=A
T. Results can be found in Table 3.
Table 3: Ranges of estimates for the birth rate λof technological species on different
astronomic scales.
Scale No. of galaxies NAst Estimated range of λ
galaxy 1 6 ·1010 6.7·10−10,2.7·10−8
galaxy cluster 300 2 ·1013 2.2·10−7,8.9·10−6
supercluster 3000 2 ·1014 2.2·10−6,8.9·10−5
observable Universe 7 ·1010 4·1021 [44,1785]
10
Processes that have a known rate of occurrence may however be modeled by
the Poisson distribution as discussed by Glade, Ballet and Bastien (2012).4The
probability of nevents in the time period twith known rate of occurrence λcan be
shown to follow10
Pn(t) = e−λt(λt)n
n!.(8)
Hence, the probability of at least one event in the time period tis
Pn≥1(t) =
∞
X
n=1
e−λt(λt)n
n!= 1 −P0(t)
= 1 −e−λt ,(9)
and the expected waiting time to the next occurrence of a technological extraterres-
trial species as a function of probability Pn≥1=αbecomes
t(α) = −1
λln(1 −α) (10)
In words, if we were alone in our galaxy today, we would have to wait approximately
t= 26 million (1 billion) years for a α= 50% chance that another technological
species has arisen in our galaxy depending on whether the lowest or highest de-5
fensible estimate of nsis assumed in calculations (2.7·10−8≤λ≤6.7·10−10, cf.
Table 3). For α= 90%, these waiting times would be t= 86 million (3.4 billion).
The ‘pessimistic’ scenario therefore encompasses waiting times much longer than
Earth’s remaining window of habitability, which is determined by the life cycle of
the Sun. Figure 1 illustrates the cumulative probability distributions for the re-10
spective spheres of interest, as well as the ranges that result from optimistic and
pessimistic assumptions on rate of occurrence λ, i.e. we plot equation (9) for the
possible extreme values of λ.
Quite strikingly, under the same assumptions, one could expect between 44 and
1785 technological species to arise every year in the currently observable Universe15
4The underlying assumptions are (cf. Glade, Ballet and Bastien 2012): (1) There exists a time t0at
which no technological species is present; (2) Appearances of technological species are independent
from each other; (3) The number of technological species in a time interval does not depend on
the sampling date.
11
1e+01 1e+03 1e+05 1e+07 1e+09
0.0
0.2
0.4
0.6
0.8
1.0
t [years]
Pn≥1(t)
Milky Way
galaxy cluster
supercluster
Figure 1: Plots of equation (9) for the different values of λthat result from possible
optimistic and pessimistic assumptions, based on the available data on evolution of
life on Earth.
(Table 3). Therefore, if the evolution of life on Earth is taken as a representative
‘blueprint’ for the evolution of life in extraterrestrial habitable worlds, it is close to
impossible that humanity is the only technological species currently in the Universe,
let alone the only one to ever arise. In fact, this is an even stronger conclusion
than Frank and Sullivan’s (2016), who estimated maximum lower boundaries for fbt
20
assuming that humanity has indeed been the only technological species to ever arise
in the Universe.
4 Discussion
Our results have implications for the future of humanity as well as potential exis-
tential threats and provide stimulation for further philosophical reflections on our5
role and responsibilities as technological species in the Universe, which we discuss in
the following. We also briefly discuss the robustness of our estimates to parameter
uncertainties.
12
4.1 The future of humanity
It is sometimes claimed that if only one technological species had existed long enough
to master interstellar travel, they would have likely colonized the entire galaxy within
a few million years (Hart 1975; Hanson 1998; Bostrom 2008). The absence of ev-
idence for extraterrestrial existence thus far is referred to as ‘Fermi-Hart paradox’5
(Hart 1975; Tipler 1980). While many different solutions to the paradox have been
proposed, only a few of these allow conclusions with regard to humanity’s sustain-
ability. Here, we define sustainability in a rather rudimentary way as long-enough
survival of the human race to matter on an astrophysical time scale. At the very
least, this would imply a longevity in the order of at least 107to 109years. One of10
the proposed solutions to the Fermi-Hart Paradox is that there is a ‘Great Filter’
in one or several of the steps required for a species to complete before eventually
evolving to the point of being technically capable of colonizing the galaxy. The
Great Filter argument posits that at least one of the evolutionary steps to becoming
space colonizers must be highly improbable, and that this Filter may be behind us,15
still ahead of us, or both (Bostrom 2008). If it were still ahead of us, it would be
likely, according to Great Filter Theory, that other civilizations had reached at least
our level of technical and intellectual sophistication, but failed to take the last step
and ultimately became extinct. If we, for the moment, accepted this argument, our
results would imply that our chances of taking this last step and establish some-20
thing like a long-term sustainable existence for humanity (in the sense of eventually
evolving to a space colonizing form of existence) were, at the very best, 12.5% (i.e.
one out of eight, cf. Table 2), but possibly as low as 0.3% (i.e. one out of 301), which
seems to fit to the somewhat gloomy prediction by Gott (1993), who estimated
the remaining lifetime of humanity to lie within 5,100 and 7.8·106years with 95%
confidence, based on statistical implications of the Copernican principle.
13
4.2 Where is everybody?5
Despite its popularity, the Fermi-Hart paradox is neither a paradox (Gray 2015)
nor tenable from the point of view of propositional logic (Freitas 1985). First and
foremost, technological species developing the capabilities needed to colonize other
planets and stellar systems may not necessarily colonize the entire galaxy. In a
percolation model of galactic colonization, each colony may choose to spread further10
with some probability pand the entire galaxy will only be colonized at some point
if pis larger than some critical probability pc(Landis 1998). However, even if
p≈pc, there may be large ‘unoccupied’ parts of the galaxy. It thus is perfectly
possible that we are living in such an empty part of the Milky Way. Moreover,
even p>pcwould not necessarily imply that we could notice any difference, either15
because we could still by chance (or by deliberation) have ended up in a pocket of
galactic emptiness or simply because chances are that we would not have noticed
possible evidence for the existence of technological extraterrestrial life, even it were
there (Freitas 1983). In addition, even if extraterrestrial technical species were
abundant in our galaxy and making concentrated efforts to communicate, the mean20
number of detectable emitters would likely be less than one, for reasons of space-time
geometry and limited signal longevity5(Grimaldi 2017), and transmissions detected
by us today may come from long-extinct extraterrestrial civilizations (Grimaldi et
al. 2018). The percolation argument is generalizable to the situation of intergalactic
colonization, so resorting to intergalactic colonization would not be of any help to ET
enthusiasts. Most fundamentally though, the Fermi-Hart paradox can be formally5
refuted as a logical fallacy (Freitas 1985), so use of the Fermi-Hart paradox as one
of its main premises might debunk Great Filter theory as having feet of clay.
Albeit understandable, the focus of the discussion about technological species
like our own in extraterrestrial worlds seems to entail that one simple fact is often
5Grimaldi considers a statistical model of the domain covered by hypothetical extraterrestrial
signals assuming that signal emitters are independent. He uses his model to derive a probability
that Earth is within such a domain, and shows that even in case of moderately large detection
probabilities of about 50% and a signal longevity of 1,000 years, the expected number of detectable
signals remains below one. In Grimaldi’s words, ‘this is perhaps the most compelling argument
that the so-called Fermi paradox is, actually, not a paradox.’ (Grimaldi 2017: 6)
14
overlooked: we should expect non-technological life to be a common thing in our10
galaxy, even if flwere considerably lower than 0.5, just because of the sheer number
of 60 billion potentially habitable planets in our own cosmic ‘backyard’ that is the
Milky Way. Even intelligent life forming some kind of ‘intelligent civilization like the
first, historic human civilizations on Earth’ (Maccone 2010: 1367) should be a rela-
tively abundant thing, given the range of estimates for fifrom 0.01 (Drake and Sobel15
1991) to 0.2 (Maccone 2010) that have been advocated in the literature. Whichever
factor of these one chooses, the number of non-technical intelligent civilizations to
ever arise in our galaxy would be in the order of 108to 109.
4.3 Birth rate of technological species
The ‘birth rate’ of technological species in the Universe has been a matter of spec-
ulation and educated guesses (Carter 1983; Gott 1993), and has served as central
yet largely undetermined parameter in SETI-related research (Grimaldi et al. 2018).
Our result of 6.7·10−10yr−1≤λ≤2.7·10−8yr−1is a good improvement over Gott’s5
1993 rough estimate of λ < 0.01yr−1for the Milky Way. More fundamentally, our
birth rate estimates, in particular those for the observable Universe, imply that the
question ‘Are we alone in the Universe?’ reduces to a merely rhetorical phrase.
However, it may well be that we are currently the only ones in our immediate cos-
mic neighborhood, i.e. our galaxy and even the galaxy cluster that the Milky Way10
belongs to, in which case humanity would probably remain alone for far longer than
Earth’s remaining period of habitability. More importantly, it seems safe to con-
clude that the mere ‘birth’ of other technological species in our galaxy would not
be of any practical relevance to us, because the time span between birth and the
ultimate arrival of some transmitted alien signal on Earth could take thousands15
or even ten thousands of years. This simple fact alone seems to destroy any hope
for meaningful interstellar conversations with other intelligent beings, let alone the
other recent findings regarding the issue (Grimaldi 2017; Grimaldi et al. 2018).
15
4.4 Parameter uncertainties
Our understanding of the atmospheric processes that led to the formation of life on20
early Earth is still fragmented (Hanson 1998; Lunine 2006; Ferus et al. 2017). It
may well be possible that future research might prove our assumption of fl=1
2too
optimistic or pessimistic. In any case, we maintain that application of the Principle
of Insufficient Reason to determine flis well justified, at least until we have strong
evidence that suggests to do otherwise. Clearly, the number of species currently
living on Earth and hence also the number of species to ever live on Earth are very5
actively researched topics (Schloss and Handelsman 2004; Locey and Lennon 2016),
and new results might alter our estimates. For example, in the pessimistic scenario
where A= 7.5, an uncertainty of ±20% ≡ ±0.1 in flwould result in an uncertainty
∆A= 1.5, and a ∆ns=±20% ≡8·108would entail an additional uncertainty in
Aof ∆A= 1.5, putting Ain the range between 4 and 10, but still well above zero10
(see Appendix A). Similar results hold for the optimistic scenario of A= 300. Thus,
under reasonable assumptions of parameter uncertainties, it remains very likely that
other technological species have arisen in our galaxy before.
5 Conclusion
We have provided a new empirical assessment of the number of technological species15
in our galaxy and beyond using the A-form of the Drake equation (Frank and Sullivan
2016). Our estimate required data on the number of species that have ever evolved
on Earth as well as three assumptions: Principle of Insufficient Reason, ergodicity
of evolution and the Copernican principle. Our approach enabled us to find an
empirical range for the factor fbt, which is the probability that a given habitable-20
zone planet develops life that advances to the stage of a technological species. We
have found that, between seven and 300 technological species have likely arisen in
our galaxy up until today. However, should we currently be alone in our galaxy, we
would likely have to wait for at least 26 (86) million years for a 50% (90%) chance
16
of another technological species arising in the Milky Way. We have discussed the
potential to use our results to derive a probability that humanity will manage the5
transition to a long-term sustainable path of existence, as well as the limitations
of that approach. The Great Filter Theory may be logically untenable, but its
proponents are certainly right to point out potential existential risks to humanity like
the invention of new weapons technology, artificial intelligence and the destruction
of ecosystems. Indeed, it seems that ‘what now matters most is that we avoid ending10
human history’ (Parfit 2011: 620).
Data accessibility
This paper does not have any data.
Competing interests
We have no competing interests.15
Authors’ contributions
JOE conceived of the study, designed the study, conducted the statistical analyses
and drafted the manuscript. HvW helped interpret the results of the data analysis,
and revised and edited the paper critically for important intellectual content. All
authors gave final approval for publication.5
Funding statement
The authors gratefully acknowledge funding from the State of Lower Saxony (Nieders¨achsisches
Ministerium f¨ur Wissenschaft und Kultur, grant number VWZN3188).
17
A Sensitivity analysis
In order to assess how parameter uncertainty in our revised version of the A-form of
the Drake equation (equation 6) affects our results, we consider the absolute value
of the total differential of A=A(fl, nt, ns)
|dA|=
∂A
∂fl
dfl
+
∂A
∂nt
dnt
+
∂A
∂ns
dns
=
nt
ns
dfl
+
fl
ns
dnt
+
fl
nt
n2
s
dns
NAst
=
nt
ns
dfl
+
fl
nt
n2
s
dns
NAst (11)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
0
1
2
3
4
∆ fl
∆ A
0e+00 2e+08 4e+08 6e+08 8e+08 1e+09
0.0
0.5
1.0
1.5
∆ ns
∆ A
0.00 0.05 0.10 0.15 0.20 0.25 0.30
0
50
100
150
∆ fl
∆ A
0e+00 2e+06 4e+06 6e+06 8e+06 1e+07
0
5
10
15
20
25
30
∆ ns
∆ A
Figure 2: Sensitivity analysis of our estimations for the number of technological
species ever to arise in our galaxy A. The upper two graphs illustrate the sensitivity
of our estimate of Awith respect to uncertainty in fl(left) and ns(right) for the
lower boundary estimate (A= 7), the lower two graphs show the same for the upper
boundary estimate (A= 300).
18
References
Batalha, N.M., W.J. Borucki, S.T. Bryson, L.H. Buchhave, D.A. Caldwell, J. Christensen-
Dalsgaard, D. Giardi et al. (2011), Kepler’s first rocky planet: Kepler-10b, The Astro-
physical Journal, 729:27 (21 pp.)
Benton, M. (2011), Paleontology and the history of life, In: Ruse, M. and J. Travis (eds.),5
Evolution: The First 4 Billion Years, pp. 80–104, Harvard University Press, Cambridge,
MA
Bostrom, N. (2008), Where are they? Why I hope that the search for extraterrestrial life
finds nothing, MIT Technology Review, May/June issue, pp. 72–77
Cailleux, A. (1952), How many species? Evolution 8, 8310
Campante, T.L., T. Barclay, J.J. Swift, D. Huber, V. ZH. Abidekyan, W. Cochran, C.J.
Burke et al. (2015), An ancient extrasolar system with five sub-earth-size planets, The
Astrophysical Journal 799:170 (17pp.)
Carter, B. (1983), The anthropic principle and its implications for biological evolution,
Philosophical Transactions of the Royal Society A 310, 347–36315
Cassan, A., D. Kubas, J.-P. Beaulieu, M. Dominik, K. Horne, J. Greenhill, J. Wambs-
ganss, J. Menzies et al. (2012), One or more bound planets per Milky Way star from
microlensing observations, Nature 481, 167–169.
Crowe, M.J. (1986), The Extraterrestrial Life Debate, 1750–1900, Cambridge University
Press, Cambridge, MA20
de Vladar, H.P. and N.H. Barton (2011), The contribution of statistical physics to evolu-
tionary biology, Trends in Ecology and Evolution 26, 424–432
Dick, S.J. (1982), Plurality of Words: The Extraterrestrial Life Debate from Democritus
to Kant, 1st edition, Cambridge University Press, Cambridge, MA
Drake, F. (1965), The radio search for intelligent extraterrestrial life, In: Mamikunian, G.5
and M.H. Briggs (eds.), Current Aspects of Exobiology, pp. 323–345, Pergamon, New
York, NY
Drake, F. and D. Sobel (1991), Is Anyone Out There? Simon & Schuster, London, UK
19
Ferus, M., F. Pietrucci, A.M. Saitta, A. Kn´ıˇzek, P. Kubelik, O. Ivanek, V. Shestivska
and S. Civiˇs (2016), Formation of nucleobases in a Miller-Urey reducing atmosphere,10
Proceedings of the National Academy of Sciences 114(17), 4306–4311
Finney, B.R. and E.M. Jones (1985), Is anybody home? Introduction; Synopsis of Fermi’s
question, in: Finney, B.R. and E.M. Jones (eds.), Interstellar Migration and the Human
Experience, University of California Press, pp. 298–300
Forgan, D.H. and K. Rice (2010), Numerical testing of the Rare Earth Hypothesis using15
Monte Carlo realization techniques, International Journal of Astrobiology 9, 73–80
Frank, A., J. Carroll-Nellenback, M. Alberti, and A. Kleidon (2018), The Anthropocene
generalized: evolution of exo-civilizations and their planetary feedback, Astrobiology
18(5), 503–518
Frank, A. and W.T. Sullivan (2014), Sustainability and the astrobiological context: Fram-20
ing human futures in a planetary context, Anthropocene 5, 32–41
Frank, A. and W.T. Sullivan (2016), A new empirical constraint on the prevalence of
technological species in the Universe, Astrobiology 16(5), 359–362
Freitas, R.A. (1983), Extraterrestrial intelligence in the solar system: resolving the Fermi
Paradox, Journal of the British Interplanetary Society 36(11), 496–500
Freitas, R.A. (1985), There is no Fermi Paradox, Icarus 62, 518–520
Fukugita, M. and P.J.E. Peebles (2004), The cosmic energy inventory, Astrophysical Jour-5
nal 616, 643–668
Glade, N., P. Ballet and O. Bastien (2012), A stochastic process approach of the Drake
equation parameters, International Journal of Astrobiology 11(2), 103–108
Gott, J.R. III (1993), Implications of the Copernican principle for our future prospects,
Nature 363, 315–31910
Gray, R.H. (2015), The Fermi paradox is neither Fermi’s nor a paradox, Astrobiology 15(3),
195–199
Grimaldi, C. (2017), Signal coverage approach to the detection probability of hypothetical
extraterrestrial emitters in the Milky Way, Nature Scientific Reports 7, 46273, DOI:
10.1038/srep4627315
20
Grimaldi, C., G.W. Marcy, N.K. Tellis and F. Drake (2018), Area coverage of expand-
ing E.T. signals in the galaxy: SETI and Drake’s N, preprint available online at
https://arxiv.org/pdf/1802.09399v1.pdf, accessed on 06/08/2018
Hacking, I. (1971), Jacques Bernoulli’s art of conjecturing, British Journal of Philosophical
Science 22, 209–22920
Hanson, R. (1998), The Great Filter – Are we almost past it? retrieved from
http://mason.gmu.edu/ rhanson/greatfilter.html on 03/16/2018
Hart, M.H. (1975), An explanation of the absence of extraterrestrials on Earth, Quarterly
Journal of the Royal Astrophysical Society 16, 128–135
Hubbart, G.S. (2008), What is Astrobiology? retrieved from
https://www.nasa.gov/feature/what-is-astrobiology on 11/13/2018
Iberall, A.S. (1989), How many species? GeoJournal 18(2), 133–1395
Keynes, J.M. (1921), A Treatise on Probability Macmillan, London, UK
Landis, G.A. (1998), The Fermi paradox: an approach based on percolation theory, Jour-
nal of the Bristish Interplanetary Society 51, 163–166
Laplace, P.S. (1820), Th´eorie Analytique des Probabilit´es, Mme Ve Courcier, Paris
Locey, K.J. and J.T. Lennon (2016), Scaling laws predict global microbial diversity, Pro-10
ceedings of the National Academy of Sciences 113(21), 5970–5975
Lunine, J.I. (2006), Physical conditions on the early Earth, Philosophical Transactions of
the Royal Society B 361, 1721–1731
Maccone, C. (2010), The statistical Drake equation, Acta Astronautica 67, 1366–1383
McLeish, T.C.B. (2015), Are there ergodic limits to evolution? Ergodic exploration of15
genome space and convergence, Interface Focus 5: 20150041 (12pp.)
Mora, C., D.P. Tittensor, S. Adl, A.G.B. Simpson and B. Worm (2011), How many species
are there on Earth and in the ocean? PLoS Biology 9(8), e1001127, 8 pp.
Parfit, D. (2011), On What Matters, Volume 2, Oxford University Press, UK
Petigura, E.A., A.W. Howard and G.W. Marcy (2013), Prevalence of Earth-size planets20
21
orbiting Sun-like stars, Proceedings of the National Academy of Sciences USA 110,
19273–19278
Quelhoz, D., F. Bouchy, C. Moutou, A. Hatzes, G. H´ebrard, R. Alonso, M. Auvergne et
al. (2009), The CoRoT-7 planetary system: two orbiting super-Earths, Astronomy and
Astrophysics, 506(1), 303–319
Quintana, E.V., T. Barclay, S.N. Raymond, J.F. Rowe, E. Belmont, D.A. Caldwell, S.B.
Howell et al. (2014), An Earth-sized planet in the habitable zone of a cool star, Science,5
344(6181), 277–280
Rossmo D.K. (2017), Bernoulli, Darwin, and Sagan: the probability of life on other planets,
International Journal of Astrobiology, 16(2), 185–189
Sagan, C. (2015), The Quest for ET Intelligence, Cosmic Search 1(2), available online at
www.bigear.org/vol1no2/sagan.htm, retrieved on 01/31/201810
Schloss, P.D. and J. Handelsman (2004), Status of the microbial census, Microbiology and
Molecular Biology Reviews 68(4), 686–691
Shklovsky, I.S. and C. Sagan (1966), Intelligent Life in the Universe, Holden-Day, San
Francisco, CA
Simpson, G.G. (1952), How many species? Evolution 6(3), 34215
Sullivan, W.T. and J.A. Baross (2007), Planets and Life: The Emerging Science of Astro-
biology, Cambridge University Press, Cambridge, MA
Tipler, F.J. (1980), Extraterrestrial intelligent beings do not exist, Quarterly Journal of
the Royal Astrophysical Society 22, 267–281
Weisstein, E.W. (2018), ‘Principle of Insufficient Reason’, From20
MathWorld – A Wolfram Web Ressource, retrieved from
http://mathworld.wolfram.com/PrincipleofInsufficientReason.html on 09/13/2018
22
