Introduction
Fermi's Paradox remains insoluble to humankind. The lack of observational data for extraterrestrial intelligences (ETIs), known commonly as Fact A (Hart Reference Hart1975), must be reconciled with our understanding of our own civilization, which we might assume is not rare or unique thanks to the Copernican Principle of Mediocrity. Brin (Reference Brin1983) and Cirkovic (Reference Cirkovic2009) review the Paradox in detail.
One particular solution to the Paradox is referred to as the Zoo hypothesis (Ball Reference Ball1973). In this scenario, humanity is deliberately kept out of the Galactic conversation for one or more reasons, ranging from our own primitive nature and a desire to protect the Earth as a nature reserve, or perhaps a recognition that contacting less developed civilizations has a deleterious effect on their development. The related Interdict Solution also proscribes ETIs from making contact or revealing themselves to us for both our sake and theirs (Fogg Reference Fogg1987).
However, this solution (and many others like it) demand a uniformity of motive amongst ETIs. An interdict placed on Earth can be utterly broken by a single message or spacecraft. Social norms, especially those cultivated between civilizations that evolved independently of each other, require policing.
The development and policing of social norms requires, at the very least, causal contact between civilizations and the existence of a ‘Galactic Club’ to agree on these norms, as well as jurisprudence to deal with their violation (cf. Freitas Reference Freitas1977). Hair (Reference Hair2011) argued that in a simple model of civilization arrival, if the distribution of individual arrival times is Gaussian, then the time between the appearance of the first and second civilizations in the Milky Way, IAT1, follows an inverse exponential distribution (Snyder & Miller Reference Snyder and Miller1991). This inter-arrival time can therefore be very large, meaning the first civilization to arise is able to influence the others greatly, and thereby facilitate the setup of social norms and uniformity of motive across the entire Galaxy.
Forgan (Reference Forgan2011) argued against this model, noting that space–time separation is the critical variable for cultural connectivity, and hence the spatial distribution of civilizations is likely to break this hegemony. Note that this definition of cultural connection demands that a civilization begins receiving transmissions from other civilizations before it becomes technologically advanced enough to detect them, and hence cannot develop its own customs regarding other civilizations without being influenced by previously established norms.
However, the extent of Forgan (Reference Forgan2011)’s work was to suggest that for a plausible set of civilization properties, the number of culturally connected civilization groups (CCGs) in the Milky Way N group > 1. The next logical step is to investigate the behaviour of N group as a function of the properties of ETIs, and identify regimes where a single Galactic Club might be established, and where multiple, smaller Galactic Cliques are established.
In this work, we investigate a toy model for the emergence of intelligent civilizations in the Milky Way. By measuring the space–time separations of civilization pairs, we establish groups of civilizations that are culturally connected. By doing this we can investigate the conditions required for the establishment of uniformity of motive amongst a Galactic population of intelligent species.
In the ‘methods’ section, we describe the simulation techniques we adopt to model the causal and cultural connections between civilizations; in the ‘Results and discussion’ section, we describe the resulting groups established, and the likelihood that the Galaxy contains a single Club, or multiple Cliques; and we summarize the work in the ‘Conclusion’ section.
Method
We carry out Monte Carlo Realization simulations of civilization emergence (and extinction), using a simple toy model. We place civilizations in a Galactic Habitable Zone (GHZ) similar to that of Lineweaver et al. (Reference Lineweaver, Fenner and Gibson2004) and Gowanlock et al. (Reference Gowanlock, Patton and McConnell2011). The field of Galactic Habitability is struggling to achieve consensus on the true GHZ, and it is clear that it will depend sensitively on the stellar kinematics as well as the hierarchical merging history of the Milky Way (Forgan et al. Reference Forgan, Dayal, Cockell and Libeskind2015; Vukotić et al. Reference Vukotić, Steinhauser, Martinez-Aviles, Ćirković, Micic and Schindler2016). We will return to the assumptions made regarding spatial distribution in the Discussion section.
Our GHZ extends from 6 to 10 kpc, with an exponentially decreasing surface density of stars with radius:
$$\Sigma _{^\ast} (r) \propto {\rm e}^{ - R/R_{\rm s}}. $$
The scale length R s = 3 kpc. For simplicity, we do not model the vertical stratification of the Galactic disc, and assume that stars are evenly distributed in the z-axis between −1 and 1 kpc.
Civilizations are assigned an arrival time, which is sampled from a Gaussian distribution with mean and variance (μarrive,
${\rm \sigma} _{{\rm arrive}}^2 $
). This parametrization reflects the observation that the factors which govern the emergence of a civilization satisfy the conditions for the application of the Central Limit Theorem, which has been demonstrated by more detailed MCR modelling (Forgan Reference Forgan2009; Forgan & Rice Reference Forgan and Rice2010). Rather than attempt to constrain the parameters, we instead explore a larger parameter space, presumably larger than the space bounded by factors such as the star formation history and age-metallicity relation of the Milky Way (Rocha-Pinto et al.
Reference Rocha-Pinto, Maciel, Scalo and Flynn2000), and the details of what makes a planet habitable, what keeps it habitable (Raup & Sepkoski Reference Raup and Sepkoski1982; O'Malley-James et al.
Reference O'Malley-James, Greaves, Raven and Cockell2013; Rushby et al.
Reference Rushby, Claire, Osborn and Watson2013), what governs the emergence of life and intelligent life (Carter Reference Carter2008), and the essentially unknown sociological factors that govern a civilization's development and lifetime.
To calculate civilization connectivity, we calculate the space–time separation 4-vector
$$dx_\nu = \left( {c\Delta t,\Delta x,\Delta y,\Delta z} \right),$$
where c is the speed of light, Δt is the difference in arrival time between the two civilizations, and Δx, Δy and Δz are the spatial separations in Cartesian coordinates. We adopt the following convention:
$$\left \vert {dx_\nu} \right \vert ^2 = c^2 \Delta t^2 - (\Delta x^2 + \Delta y^2 + \Delta z^2 ).$$
Hence, for two civilizations to be causally connected, |dx ν |2 must be positive (or equivalently, |dx ν | must be real). Note that this 4-vector represents the strictest constraints on two civilizations being connected and aware. In effect, it demands that a signal transmitted from civilization i reaches civilization i + 1 ’s home planet before civilization i + 1 emerges. We could construct similar 4-vectors for other possibilities, such as crewed or uncrewed spacecraft being sent from i to i + 1. This would require modification of equation (3), replacing c with a variable representing the spacecraft velocity, which special relativity demands must be less than c. We can therefore be confident that if the space–time separation as given by equation (3) is negative, then it must be negative regardless of how a civilization attempts to communicate.
We assign each civilization a lifetime, which is also sampled from a Gaussian defined by its mean and variance
$({\rm \mu} _{{\rm life}}, \,{\rm \sigma} _{{\rm life}}^2 )$
. We therefore demand that a communication window between both civilizations is open, i.e. that both civilizations must be able to communicate before one or the other goes extinct.
We calculate connected groups using the following algorithm:
-
1. Firstly, the set of all civilizations is sorted by arrival time. The first civilization to arrive establishes the first group, and it is identified as that group's ‘leader’.
-
2. We then test all other civilizations against the leader, in ascending arrival time order, for causal connections using equation (3).
-
3. If the space–time separation between the leader and a civilization is positive, the civilization joins the leader's group.
-
4. If a civilization is not connected to the leader, it begins its own group and is established as a leader.
-
5. Once all civilizations are tested, we move to the next civilization that is not connected, and repeat the algorithm until all civilizations belong to a group.
This produces a single realization of the culturally connected groups in the GHZ. We carry out 30 realizations for any given set of parameters (N civ, μarrive, σarrive, μlife, σlife), and use this data to compute mean and standard deviations (SDs) on the resulting statistics, which include the number of groups N group and their maximum extent S group, which is defined as the maximum distance between any two pairs of civilizations in the group.
Results and discussion
Dependence on total number of civilizations
We first begin by fixing all parameters, and carry out a series of realizations for multiple values of N civ. Figure 1 shows how the mean number of causally connected groups (CCGs) varies with increasing N civ for a fixed (μlife, σlife) = (0.1, 10−3) and μarrive = 5000 Myr. Each curve represents a different value of σarrive = (1, 10, 100) Myr.
The mean number of groups identified in the MCR runs as a function of civilization number, for three values of σarrive = 1, 10, 100 Myr. The black dashed line indicates the maximum number of groups N group = N civ. We fix (μlife, σlife) = (0.1, 10−3) and μarrive = 5000 Myr.
We can immediately see that the lowest group counts occur when σarrive is at its minimum value. This is at direct odds with the result of Hair (Reference Hair2011), which prefers a relatively large value of σarrive for hegemony establishment based on the consequently large inter-arrival time between the first and second civilizations. However, we find that for the largest values of σarrive, the number of groups N group is at its maximum (i.e. it is equal to the number of civilizations N civ) until it reaches N civ > 300. In all three cases, the mean spatial extent of each civilization asymptotes to similar values at large N civ (Fig. 2). While the σarrive = 100 Myr sizes are slightly lower than the other two cases, it remains within a single SD.
The mean spatial extent of groups identified in the MCR runs as a function of civilization number, for three values of σarrive = 1, 10, 100 Myr. As in Fig. 1, (μlife, σlife) = (0.1, 10−3) and μarrive = 5000 Myr.
In the case where σarrive is set to its lowest value, the minimum number of groups tends to around 3, and asymptotes to this value for N civ > 1000 (where it also approaches the maximum group extent of 20 kpc, corresponding to the diameter of the GHZ edge). Given that the 1σ uncertainty on N group is around 1, this result contains the Galactic Club scenario within the 3σ confidence interval. We can therefore predict that for this GHZ configuration, civilization populations emerging within a relatively narrow time interval have the best odds for establishing the Galactic Club (given a typical civilization lifetime of 0.1 Myr).
Such coordination of arrival time seems a priori unlikely – indeed, it most likely demands that a global regulation mechanism exists to ‘synchronize the biological clocks’ of planets separated by enormous distances (Annis Reference Annis1999; Vukotic & Cirkovic, Reference Vukotic and Cirkovic2007). Proposed regulation mechanisms, such as gamma ray bursts, would still fail to synchronize the entire GHZ, as their ability to sterilize planets extends no more than a few kpc, and their efficacy even at these distances remains a source of debate (Thomas Reference Thomas2009; Martin et al. Reference Martin, Cardenas, Guimarais, Peñate, Horvath and Galante2010, and references within).
Dependence on civilization lifetime parameters
As we have established that N group can become small for N civ > 500, we now fix N civ = 500 and explore the effects of the civilization lifetime parameters (μlife, σlife). Figure 3 shows how the mean group number depends on these parameters (with each plot showing a different value of σarrive). Again, we can see that hegemony establishment (N group = 1) is easier if σarrive is lower. The group number is only weakly dependent on σlife (except for very high σarrive).
The mean number of groups as a function of μlife and σlife. The mean arrival time μarrive is held fixed, with each plot denoting a different value of σarrive. μarrive is fixed at 5000 Myr.
In all cases, the mean civilization lifetime μlife must exceed around 250 000 years for hegemony to be established. Note that this lifetime is measured from when a civilization is sufficiently technologically advanced to begin communication. The earliest fossil records of homo sapiens date to approximately 190 000 years ago (McDougall et al. Reference McDougall, Brown and Fleagle2005). If human civilization is indeed subject to the Principle of Mediocrity, then we should expect our total lifetime (from the emergence of anatomically modern humans to now, and from now until the end of our civilization) to be close to the mean. The results of this toy model suggests that for hegemony establishment to proceed and form a Galactic Club, our species has likely only persisted for approximately half its lifespan.
Note that if we wished a single civilization to be exceptionally long-lived near the beginning of the simulation (a low mean lifetime with a high SD), then this would still result in a reasonably large number of groups. This underlines that space–time separation is the principal factor, and that the Galaxy is sufficiently large that cliques can be established at large spatial separations even from ancient long-lived civilizations.
Discussion
We should be clear that this work makes no predictions on the number of intelligent civilizations in the Milky Way. It cannot even predict if ETIs exist at all. It is merely a controlled numerical experiment that tests the ability of civilizations to influence each other if they exist, depending on the details of when and where civilizations might emerge.
We have progressed beyond the original assertion of Forgan (Reference Forgan2011), that typically the number of culturally connected groups is >1. Our GHZ model of civilization emergence predicts that initially, there will be significant opportunity for cultural variance across space and time, and as such uniformity of motive is not present.
To reach this conclusion, we have assumed an annular GHZ for civilization emergence. We have assumed the rather wide annular range of 6–10 kpc based on Gowanlock et al. (Reference Gowanlock, Patton and McConnell2011), which remains the most high-resolution study of galactic habitability, if somewhat constrained by demanding azimuthal symmetry (Forgan et al. Reference Forgan, Dayal, Cockell and Libeskind2015). This is actually a restricted GHZ – Gowanlock found that habitable planetary systems were possible from as little as 2.5 kpc from the Galactic Centre. Populating this region with civilizations will result in much smaller spatial separations due to the high surface density of stars, which may reduce the number of cliques. However, the maximum spatial separation is a function of the outer radius of the GHZ:
$$dx_{{\rm max}} = 2R_{{\rm outer}}. $$
If N civ remains small, the outer edge will be poorly populated, reducing the maximum separation below this value (we can infer this by studying the mean group size curves in Fig. 2 for N civ < 100). This would increase the probability of a single Club forming, but only in this limit. If N civ is sufficiently large, populating the interior with more civilizations cannot allow a Galactic Club to form, as a small fraction will reside at the distant fringes of 10 kpc, and the number of culturally connected groups will in general be >1. This is true as long as R outer is relatively large. Given that we exist at R ≈ 8 kpc, we can be reasonably confident that this is the case.
We also assumed that stellar motions are negligible in this analysis, which is clearly not the case even in a relatively restricted GHZ (Vukotić et al. Reference Vukotić, Steinhauser, Martinez-Aviles, Ćirković, Micic and Schindler2016). While the speed of light in vacuo remains constant in all reference frames, the distance between stars can be reduced by proper motions, resulting in reduced light travel times and greater probability of civilization connectivity (with the converse being true for stars receding from each other). Once cliques have been established, the spatial extent of the clique will evolve according to local stellar dynamics. It is likely that initially separate cliques will be able to diffuse into each other. Given that cliques are somewhat intermixed even at inception (which we can see from the large group extents established in Fig. 2), it is unclear what further effects this may cause.
While cultural variation is initially large, this does not preclude the later emergence of uniform motive once individual cliques become causally connected to each other, i.e. a uniformity established through political means. The galactopolitical machinations of a set of civilization cliques (and the internecine activities of an individual clique) far exceed the capabilities of this simple toy model. All that we can predict is that if civilization cliques do come into contact, it is likely they will hold significantly different perspectives on the Universe, and the rights and responsibilities of sentient beings and the institutions they construct.
It is also possible for cliques to evolve internally, in isolation from their peers. Cultural norms change with time, and the growth of a clique as new civilizations become culturally connected may enhance the rate of cultural evolution, as new ideas and perspectives begin to percolate through the clique's membership. A clique that initially holds treaties regarding contact in high regard may discard them through changes in their internal make-up, especially if they are subject to strong environmental pressures that impact their way of life.
Despite these factors that are beyond the realms of simple MCR analyses such as this work, we are still able to draw important conclusions on the Zoo Hypothesis. The initial state of the Zoo hypothesis (that is, when cliques initially come into being) is soft – in general, we must assume that the Galaxy is culturally diverse. Subsequent cultural evolution can act to soften the Zoo Hypothesis, just as much as it may act to harden it. For example, a dominant clique may attempt to impose an authoritarian monoculture, or cliques may ‘agree to disagree’ for political expediency.
We have no way of predicting how extraterrestrial cultures will interact. However, we do know that from the multitude of possible outcomes of political negotations, the Zoo hypothesis demands that only a small subset of these outcomes are possible. If the Zoo hypothesis is correct, and it demands a uniformity of motive established via a Galactic monoculture, we should conclude that it is most likely imposed – perhaps against the wishes or interests of the Galactic community – through interactions between a number of cliques, either through political or military means.
Conclusion
In this work, we have investigated the implicit assumptions made to invoke the Zoo hypothesis as a solution to Fermi's Paradox. We achieved this by explored the CCCs present in a toy model of the intelligent civilization population of the Milky Way. We find that for there to be only a single group (a ‘Galactic Club’), the mean civilization lifetime must be extremely long, and the arrival time between civilizations in fact must be relatively short (constrained by a small SD in arrival time, σarrive). This is perhaps an unlikely scenario, as it would require a large number of civilizations to emerge across the Galaxy in a very short time frame. This is also in opposition to previous work which has suggested σarrive needs to be large for a single first civilization to dominate the Milky Way.
This toy model underlines that the Zoo solution to the Fermi Paradox remains ‘soft’, i.e. it demands a uniformity of motive amongst ETIs that only exists when certain conditions are met. Our previous work in this area has suggested that these conditions are unlikely to be met in our Galaxy (Forgan Reference Forgan2011), but did not explore the population of CCGs that would result.
We therefore conclude the following:
-
• If civilizations typically last <1 Myr, then it appears likely that N group > 1, resulting in a set of ‘Galactic Cliques’ rather than a single Galactic Club.
-
• A single long-lived, ancient civilization still fails to knit the entire Galactic community of civilizations into a single Club.
-
• If all civilizations can last much longer than 1 Myr, then a single Galactic Club can be established, but only if all civilizations arrive quite close together in time.
Typically, the Galaxy is composed of ‘Galactic Cliques’. Once established, these cliques may come into causal contact with others, bringing their own established norms to discussions in a scaled-up version of contact between individual civilizations. One clique attempting to place an interdict on contacting ‘primitive’ civilizations is likely to encounter significant problems if another clique disagrees.
This analysis remains insufficient to completely remove the Zoo solution from the list of possible solutions to Fermi's Paradox, but it illustrates the underlying assumptions required to propose it. It may well still be the case that the Earth resides in a region of space occupied by a conservative clique bent on non-contact. However, as our ability to detect unintentional signals from both living and dead civilizations increases (e.g. Stevens et al. Reference Stevens, Forgan and O'Malley-James2015; Wright et al. Reference Wright, Cartier, Zhao, Jontof-Hutter and Ford2015), we should presumably be able to break the deadlock imposed in this scenario. In an extreme case, a neighbouring clique is free to violate non-contact treaties with impunity – if we are a late arrival to a populous Galactic community, then many established cliques may be aware of our presence, and they may not pay attention to local signage forbidding them to reveal themselves.
Acknowledgements
The author gratefully acknowledges support from the ECOGAL project, grant agreement 291227, funded by the European Research Council under ERC-2011-ADG and the STFC grant ST/J001422/1.
