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The Fermi Paradox, Expanded

via Flickr user Chris Radcliff

In a casual conversation in 1950, among a number of eminent physicists of the time, Enrico Fermi asked why we haven’t found evidence of extraterrestrial life. After all, with so many billions of stars out there in the vastness of space, and an even greater number of planets, even if the chances of a planet producing intelligent life that is capable of interstellar communication and travel are absolutely minuscule, there should still be at least some signs of other civilizations in the universe. This disconnect between the idea that we should be seeing signs of life in the universe, and the fact that we are not, has been called The Fermi Paradox.

In 1961, astronomer Frank Drake formalized this idea into an equation, known as the Drake equation:


There are some very good websites that examine the math in detail, and even let you plug in your own numbers, but the gist is as follows. There are around 100 billion stars in our galaxy. We don’t know for sure, but scientists “guesstimate” that the average number of planets per star may be anywhere from one-half (i.e., one planet for every two stars) to as many as two or three. But of course only a fraction of those planets will be habitable.

Multiply those factors together and you get an estimate of how many total habitable planets are out there. The Drake equation itself goes about coming up with a “number of potential planets” a little differently, using R* as the rate of star formation, fp as the fraction of stars that form planets, ne as the number of habitable planets around those stars, and L as the length of time a civilization might stick around on those planets. However, those mathematical details aren’t particularly important: for now, you can just start by imagining the total number of habitable planets that exist in the galaxy.

From there, to get the number of civilizations that we should be able to detect in the galaxy, you just start whittling that number down based on all the different ways things can go wrong that will stop a civilization from developing on a planet.

Via Flickr user European Space Agency

First, toss out any planets that don’t develop life. This requires you to speculate about how likely you think life is to develop on a planet that could develop life. That’s fl. If you think life is just bound to spring up anywhere it has a chance, then multiply by a fraction close to 1. If you think life is a freak accident that is very unlikely, then multiply by a fraction close to 0.

Of course, life may never evolve intelligence. So now you multiply your number of remaining planets by the chances that life will produce intelligence: that’s fi.

Finally, even intelligent life might not produce anything that we can detect with our current technology. So we need to multiply our number by the fraction of the intelligent life out there that actually does stuff that we could notice: sending out radio signals, altering the

surface of their planet so drastically that we can tell there is something unnatural about their atmosphere or energy emissions, or building a Death Star or Dyson Sphere that we can see all the way from Earth. That is fc.

The number that you are left with, after all of those failure scenarios are shaved away, is the number of alien civilizations that we should see evidence of.

Of course, the reality is that we don’t see evidence of alien civilizations. That final number that we get from the result of the equation--the only number, apart from the number of stars in the galaxy, that we can actually measure with certainty--is currently zero. Why? Which of the “ways things can go wrong” is to blame for the silence in the universe?

An Equation for the New Millennium: Anyone At Home?

The speculation of different scenarios began in earnest in June 1975, when astronomer Michael Hart published An Explanation for the Absence of Extraterrestrials on Earth in the Quarterly Journal of the Royal Astronomical Society. He posited a number of hypotheses that remain popular to this day, including “Earth Zoo” (i.e., we don’t see alien civilizations because they are watching us and waiting to reveal themselves once we have passed some kind of technological or moral threshold) and the “Self-Destruction Hypothesis” (i.e., most civilizations end up destroying themselves before they get very far into the space exploration phase).

But in the four decades since that paper was published, there has been an explosion of new  scenarios proposed for why nobody else in the universe seems to be at home. There have been infographics and extensive lists. There have been speculations based on weird physics and extended think-pieces about the way civilizations may develop over time. There has even been a book dedicated to detailing 50 different explanations for our lack of contact with aliens.

Yet somehow nobody has yet updated the Drake Equation to take into account this rich new spectrum of ideas. The problem isn’t that the Drake Equation is wrong. Rather, it simply isn’t detailed enough to cover the wide wild world of wacky speculations that have sprung up in the last few decades for why we haven’t made alien contact.

It’s time to fix this. I present to you: an updated Drake Equation for the new millennium.

N = P*  ・ pL  ・ pc  ・ pi  ・ pt  ・ pk  ・ pb’k  ・ ph  ・

[ pus  ・ (1-pv)  ・ ps  ・ pd + (1-pus)  ・ [ pg ・pd + (1-pg) ・pdd ・p👀 ] ]

Now this looks very complicated, but don’t be intimidated!  It’s actually very simple, and can be understood using this handy flowchart:

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Remember: the original Drake equation is basically a bunch of fractions that represent all the ways that things can go wrong, in other words, the things that can prevent us from detecting alien civilizations. This principle's true with this new, updated Drake Equation. So let’s start by looking at all of the planets in the galaxy (P*), and see

what can go wrong.

Start in the top left corner of the chart.

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Question: Is there life on the planet?

Variable: pL : What is the probability of life on a planet?

Fail Scenario: We won the jackpot. Also called the “Rare Earth Hypothesis” or “Lonely Universe.”

It could just be that the chances of life happening are extremely rare. We are here because it happened at least once, but it was such a bizarre set of circumstances that it has happened very few times in the history of the universe.

Question: Is there complex life?

Variable: pc : What is the probability that life will evolve complexity?

Fail Scenario: Alien Algae. Also called the “Early Filter.”

Recent biological research suggests that cells with a nucleus and mitochondria, capable of producing multicellular life, only happened once on Earth. Moreover, single-celled life hung out for more than two billion years before cellular complexity even happened. Maybe most of the planets that have life will never get beyond the single-celled phase.

Nick Lane discusses this view in the amazing book Power, Sex, Suicide: Mitochondria and the Meaning of Life.

Question: Did intelligence evolve?

Variable: pi : What is the probability that complex life will produce intelligence?

Fail Scenario: Alien Dinosaurs

We take for granted that intelligence is a useful thing for evolution to have produced. In reality, there is no reason to think that most environmental conditions would produce intelligent species. The dinosaurs are a great example of a dominant species that evolved and ruled the planet for over 100 million years without ever developing intelligence. It could be that we will find planets full of happy animal and plant life that simply never had any reason to develop intelligence.

Question: Have they had time to develop technology?

Variable: pt: What is the probability that they have been around long enough for technology to progress to an advanced stage?

Fail Scenario: Late-Start Universe. Also called the “Phase Transition Hypothesis.”

There could be something about the universe that has prevented any intelligence from developing until relatively recently. Although this was speculated as early as Hart’s 1975 paper, recent data and theories have produced evidence that make it more plausible than ever. Some physicists believe that for most of the universe’s existence, galaxies were subject to “gamma ray bursts” that would wipe out any life in vast regions of space before it ever had time to develop intelligence. If the universe has only calmed down enough recently for intelligence to arise, we may simply be among the first species

“out of the gate,” as it were.

From there, make your way to the second column.

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Question: Have they killed themselves off before developing technology we can detect?

Variable: pk :  What is the probability that an intelligent civilization will destroy themselves before they reach out to the stars?

Fail Scenario: The Late Filter. Also called the “Self-Destruction Hypothesis.”

We see how horrible and violent humans are, and we see how much damage we’re doing to the Earth, and we think: maybe everybody sucks and kills themselves off before they get advanced enough to signal long distances or build gigantic space-faring ships? It certainly is a possibility.

Question: Do they even want a highly technological, space-faring civilization?

Variable: pb’k :  What is the probability that an advanced civilization even wants to explore space or build technology that would be detectable by us?

Fail Scenario: Ba’ku People. Also known as the “Contemplation Hypothesis” or “Aliens are Homebodies.”

The film Star Trek: Insurrection features a race of people, the Ba’ku, who have all of the knowledge and experience for advanced technology and starflight, but they just don’t want it. This is a common theme in science fiction, and a kind of counter-balance to the “Late Filter” view: maybe the truly advanced civilizations can’t be detected because they enjoy living in grass huts?

Question: Are they deliberately hiding from the universe?

Variable: ph :  What is the probability that they are technological but deliberately hiding?

Fail Scenario: Scaredy Cat People. Also called “Destroy or be Destroyed” or “Self-Imposed Quarantine.”

Maybe the advanced civilizations out there are so terrified of what might be out in the universe to threaten them, that they deliberately conceal all evidence that they exist?

From here, the flowchart branches into two paths, based on whether or not the aliens know that we (specifically) exist. The probability that they are aware of us (pus) is really anybody’s guess. But if the answer is yes, creative speculators have come up with far more ways that things can go wrong than right.

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Consider, for example, the possible scenarios where aliens know about us and are able to visit us. There is not a single desirable outcome from that point on in the flowchart.

Either they could visit us but they haven’t, and they aren’t keeping an eye on us, which means they just aren’t that into us. Maybe they think we are ugly. Maybe they think we are boring. This is the scenario made popular by Terry Bisson’s science fiction story “They’re Made Out Of Meat.”

Or, perhaps they haven’t visited us but are still watching us, in which case they may either expect good things from us and are waiting for us to pass a test, at which point they will introduce themselves (the “Earth Zoo hypothesis”), or they hate us and are just making sure we don’t get out of hand (the “Whack-a-mole” hypothesis).

Alternatively, it’s possible that they have already visited us and moved on. This is often called “Garden World” or the “Panspermia hypothesis”: the belief that aliens were around at one point, either caused or nurtured life here, and then went on their way, on because they had better things to do with their time.

Finally, there are those who believe that aliens came here and are still here. This is sometimes called the “Here and Hiding” hypothesis or the “Perks of being a wallflower” hypothesis. Some people tie this idea into paranoid theories about government cover-ups.

Once you’ve assumed that aliens know about us and are able to visit us, the only options left are “fail scenarios”: there is no pathway towards making alien contact.

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But luckily, it’s possible that they know about us and have tried signaling us, or that they don’t know about us but they are generally sending signals out into the universe, just as we are.  If either of those situations is true, there is just one more question and possible “fail scenario”:

Question: Can we actually detect and recognize their signals?

Variable: pd : What is the probability that they signaling us in a way that we can detect and recognize?

Fail Scenario: Universe of Babel. Also called “We can’t read the signs.”

It’s possible that these alien life forms are so different from us that we can’t even detect whatever methods they are using to signal. Maybe they have ESP and are thinking at us, and can’t understand why nobody is out in the universe thinking back at them.

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As long as they don’t fail on this point, we should be able to detect aliens who send out signals.

Finally, of course, there is one more way that we could possibly detect alien civilizations, even if they are not sending signals into space: they could be altering their planet on such a large scale, or building large-scale space stations, that we would be able to detect from Earth. In order for us to detect this kind of civilization, there are two more key questions, and key variables, that we need to consider.

Question: Do they have technology that we would be able to detect from a distance?

Variable: pdd :  What is the probability that they have built something so big, or that changes their planet so much, that we’d be able to tell just by looking?

Fail Scenario: Invisible habitats.

These alien civilizations could be incredibly advanced, but simply not have built anything large enough to detect. Perhaps they have evolved to the point where they have uploaded their brains into computers, and are happily exploring their inner lives in vast virtual worlds on their planet? Perhaps they have bodies made up of swarms of microscopic nanobots?

Question: Are we looking in the right places to detect them?

Variable:p👀:  What is the probability that they live in places where we are looking, or where we even can detect them?

Fail Scenario: Unusual locations

If they are highly advanced, they could be living deep in the center of the galaxy where there is so much electromagnetic interference we couldn’t see them, or out on the rim where they are too remote to be detected. Or they might even be living in inside a black hole.

If these last “fail scenarios” are avoided, then we should be able to detect them.

Putting The Equation Together

If you trace your way through the flowchart, you will see that there are actually three alternative pathways that get you from the top left corner to the “success” point of actually detecting alien civilizations.

  1. They know we exist, have tried signaling us, and happen to use electromagnetic signals that we would be able to tell were deliberate signals
  2. They don’t know we exist, but they are sending out general signals to the universe, again using electromagnetic signals that we would be able to recognize
  3. They don’t know we exist and aren’t trying to signal anyone, but they are building gigantic things or making big changes to their planet so that we’d be able to detect them anyway.

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The real punchline, however, is that there are clearly many, many more ways to end up not detecting alien civilizations than there are ways to detect them.

Finally: One thing that this new equation highlights that is often ignored in conversations of the original Drake equation is that there is no reason to think that only one of these “fail” scenarios is true. In fact, there could be aliens in just about every category we’ve looked at. At this very moment, there may be aliens who are trying to communicate with us in ways we can’t detect, as well as aliens happily living in grass huts who don’t want technology, as well as aliens who are watching us and waiting to beat us back if we get too feisty. The universe may be teeming with life that fits every single other explanation for why we aren’t seeing them.

To figure out how many civilizations of each type there are, you just have to plug in the probabilities. So how would you solve the new Drake Equation v2.0?

Editor's Note: This post has been updated to correct an error in the original Fermi Paradox Flowchart.