One of the more famous challenges of modern science is the Fermi paradox. This is the apparent contradiction between the likelihood of extraterrestrial civilizations existing elsewhere in the galaxy and the lack of evidence of them. Or, as the physicist Enrico Fermi once asked over lunch at Los Alamos National Laboratory in 1950, “Where is everybody?”

The answer, of course, is that nobody knows. But in 1973, a potential solution was put forward by John Ball, a radio astronomer at MIT. Ball’s suggestion is that the lack of communication can be explained if extraterrestrial civilizations have set us aside, perhaps as part of a wilderness area or a zoo. In this so-called “zoo hypothesis,” aliens must have agreed among themselves to ignore humanity, perhaps to protect us or maybe even to protect themselves.

That raises an interesting set of questions. The galaxy is huge and communication between civilizations is limited by many factors, not least of which is the speed of light. So forging any kind of agreement among alien civilizations would be no mean feat. So how likely is it that extraterrestrials could come to such an understanding?

Today, we get an answer of sorts thanks to the work of Duncan Forgan at the University of St. Andrews in the United Kingdom. Forgan has built a mathematical model of the galaxy that simulates how alien civilizations would need to network to forge a treaty to leave primitives, like us, in the cold.

Forgan begins with a set of simple assumptions. Chief among these is the idea that communication between civilizations is only possible when they overlap for long enough for messages to be passed between them and that these are necessarily limited by the speed of light. He goes on to assume that civilizations evolve only in parts of the galaxy that are suitable for life and that this galactic habitable zone takes the form of two-dimensional annular stretching between six kiloparsecs and 10 kiloparsecs from the galactic center. (The sun sits at about eight kiloparsecs from the center.)

Next, the computer simulates civilizations appearing at random points within the habitable zone and disappearing some time later. It measures the distance between these civilizations and calculates whether communication is possible within their lifetimes or, in other words, whether they are causally connected. If so, then the two civilizations can come to agreement.

The key question here is in what circumstances can all civilizations can come to a single agreement. To find out, Forgan varies the parameters in his model to see how it influences the nature of galactic communication. These parameters include the number of civilizations, the length of time they exist for, and how closely they appear after each other.

The algorithm is then straightforward.

1. First, it sorts the set of all civilizations by arrival time. The first civilization to arrive establishes the first group and is identified as that group’s leader.

2. The computer then tests the causal connection between the leader and all other civilizations in order of arrival time.

3. If a causal connection exists, the civilization joins the leader’s group.

4. If a civilization is not connected to the leader, it begins its own group.

5. Once all civilizations are tested, the model moves to the next civilization that is not connected, and repeats the algorithm until all civilizations belong to a group.

It’s easy to see that when the number of civilizations is small, the possibility that they are all causally connected is also small. Indeed, they can form as many groups as there are civilizations, and this makes the zoo hypothesis untenable.

However, Forgan says that the number of groups can be come small when the number of civilizations increases beyond 500. So next he fixes the number at 500 and varies the lifetime of civilizations to see what happens.

The results make for interesting reading. The model shows that, at the beginning, there is little contact between civilizations and so few if any opportunity for an agreement to emerge.

As time goes on, groups of civilizations come into contact providing an opportunity to come to agreement on how to treat emerging civilizations like our own. But even then, the number of different groups is likely to be more than one. This is because a small fraction of civilizations will always be at the fringes of the galactic habitable zone and so will be less easily connected to the others. “The number of culturally connected groups will in general be greater than 1,” says Forgan.

The lifetimes of the civilizations are important, too. The model suggests that if civilizations last less than a million years, then there is likely to be far more than one galactic group. If all civilizations last much longer than a million years, then a single galactic club can become established, but only if all civilizations appear at nearly the same time.

Of course, Forgan’s model has a number of limitations. For example, it does not account for the way stars move relative to each other. This movement would cause civilizations to diffuse into each other over time and so are perhaps more likely to connect than the model predicts.

Neither does the model take into account the factors that determine how civilizations interact. Forgan suggests the civilizations must greatly differ. “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,” he says.

In other words, the galaxy ought to be culturally diverse. So if the zoo hypothesis is correct, it can only have come about under a small subset of circumstances.

Forgan puts forward some ideas about what these might be. “If the Zoo hypothesis is correct, 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,” he concludes.

The idea of alien civilizations far older and more advanced than our own agreeing by political means sounds reasonable. The imposition of ideas by military means is more worrying.

Ref: arxiv.org/abs/1608.08770: The Galactic Club, or Galactic Cliques? Exploring the Limits of Interstellar Hegemony and the Zoo Hypothesis