## Applying statistical thinking to the search for extraterrestrial intelligence

Thomas Basbøll writes:

A statistical question has been bugging me lately. I recently heard that Yuti Milner has donated 100 millions dollars to 10-year search for extraterrestrial intelligence.

I’m not very practiced in working out probability functions but I thought maybe you or your readers would find it easy and fun to do this. Here’s my sense of the problem:

Suppose there are 1 million civilizations in the Galaxy. Suppose they are all sending us a strong, unambiguous signal. Suppose we listen continuously in all directions and suppose we’re right about what frequencies to listen to. What are the odds of detecting a signal within ten years?

As far as I can tell, this question is impossible to answer if we don’t know when they started sending.

Suppose they all *just* started sending a signal. On this view, we’ll probably not detect the fist signal for 300 years. (Carl Sagan calculated the average distance between 1 million galactic civilisations to be 300 ly.) So if we’re hoping there’s some chance of detection within the next 10 years, we’re assuming that some of the 1 million signals left their source long ago.

Now, suppose one of them is 10,000 ly away and started signalling 100,000 years ago. In order to be detectable today the beacon would have to transmit for at least 90,000 years. If it transmitted for a “mere” 25,000 years we’d miss it.

For each civilisation there is uncertainty about the start time *and* the duration of the signal (two important uncertainties).

If the range of start-time uncertainty is 10 billion years (from five billion years ago to five billion years from now) and the duration can be from 1000 to 100,000 years. And we now assign a random distribution over 1 million sources to distances between 300 and 100,000 light years away. That is from each of one million points, between 300 and 100,000 light years away, starting sometime from 5 billion years ago to five billion years from now, a signal lasting between 1000 and 100,000 years is directed at us. What are the odds that a signal is hitting us right now (or during the 10-year ”now” of the Breakthough Listen project).

My sense is that they are very, very low. But am I right about that?

I realize this is a somewhat esoteric topic, but I’d be interested in seeing how this problem can be modelled, and how the parameters can be changed to improved the odds. As far as I can tell, actually, SETI promoters explicitly ”neglect time” in their models, imagining that each signal has been transmitting since the birth of the galaxy and will continue to transmit forever. On that view, of course, there are one million signals actually hitting us right now to find. And the ”cosmic haystack” is just the 200 billion stars in the galaxy. But this assumption is so unrealistic that I’d like to see if the haystack can’t be modelled more usefully.

My reply: I have no idea but perhaps some of the commenters will have thought about this one. My quick thought is that, given that we haven’t heard any such signals so far, it doesn’t seem likely that we’ll hear any soon. But maybe that misses the point that any signals will be so weak that they’d need lots of instrumentation to be detected and lots of computing power to resolve.

The other thing that strikes me is how little we hear about this nowadays. It seems to me that a few decades ago there was a lot more talk about extraterrestrial aliens. Perhaps one reason for the decline in interest in the topic is that we haven’t heard any signals; another reason is that we have an alien intelligence among us now—computers—so there’s less interest in a hypothetical alien intelligence that might not even exist.

1. Sarnese says:

“I realize this is a somewhat esoteric topic…”

Indeed

What would you (or anyone) do differently in your Earthly life if you now detected an intelligent signal from a far distant galaxy? Of what value is such information?

Why devote scarce resources (e.g., SETI) to such ethereal questions, in face of all the other problems & objects of scientific inquiry facing us today?

• Andrew says:

Sarnese:

I don’t disagree with you, but maybe you should be then spending your effort writing comments on sports and celebrity websites. Why devote scarce resources to basketball, reports on movie stars’ lifestyles, etc., in the face of all the other problems etc?

• Alexia says:

There’s a huge value as opposed to what you are implying. If it was proven without a doubt that a extraterrestrial life existed and we knew their location, however how far from them we are, it would mean that we are not alone. This would completely change the direction of our society and our perspective. We would start pushing a lot more toward space exploration. If people knew of this, they would start to think about how to reach them. It would probably takes hundreds if not more years to get to them, knowing that they are there, but our society would at least have the drive to get out there and stop thinking that Earth is the center of the universe.

It’s kind of like how astronauts who see the earth from the outside mention how this simple experience change their whole perspective completely.

• Phil says:

Yes to both Andrew and Alexia.

Resources to search for extraterrestrial intelligence (or to search for anything else) are only scarce if you think other things are more important. To amplify Andrew’s point: Worldwide, about \$145 billion is spent on sports each year. Over \$20 billion is spent on chewing gum.

As to Alexia’s point: in addition to the philosophizing and soul-searching that would be prompted by discovering extraterrestrial intelligence, there’s also just the spirit of scientific inquiry in general. We can afford to satisfy our curiosity about things, especially if we are willing to spend money that could otherwise be spent saving people’s lives or installing solar panels or paying the salary of a sure-handed middle infielder with decent power to left field. We may not be willing to skip the last of these, but we are happy to skip the others.

• I have arrived that conclusion that any arguments that justify looking for ETI would also justify “satisfying our curiosity” about ESP. From day to day, I go back and forth between thinking that counts in favor of ESP research or against SETI. But I have not been able to get one of these projects to seem more or less rational or scientific or worthwhile than they other.

• mark k says:

Honestly I’m not sure how it would “completely change” anything except exobiology, where it provides the first bit of empirical data about how likely intelligence is to evolve. This is rather begging the question. It will change the world because it’s so important it’s world changing and we’ll have to respond.

IMHO scientific types already believe overwhelmingly it is quite possible intelligence exists elsewhere so this is not going to be a Copernicus style rethinking of our place in the world.
A lot of press for a few years. Tons of TED Talks saying it’s revolutionary and attaching it to already existing conclusions. Beyond that, the people who think this is revolutionary and we have an imperative to start a 500 year research program to deliver a post card that will arrive in a 1000 years already strongly support space travel.

Exception would be if the traffic was from some SF like galactic empire, eavesdropping would be cool.

• Thomas says:

I agree with you, Mark. In Copernicus’s time, the idea that the Earth moves was not just exotic but heretical. Today, established science, and much religion, is completely open to the existence of alien life. And the religions that would be shocked aren’t central to our culture and have no power to suppress a discovery. We’ll probably discover an alien bacterium before we discover intelligent beings. This won’t be much more exciting (to most people) than the discovery of a unknown species of fish in the deep, deep ocean. We’ll probably discover an “ancient” (i.e., long dead) alien civilization before we discover a living one. Or the remains of a “primitive” alien society that didn’t get any further. This will fascinate us not much more than archeology in general.

The only real paradigm shift in this area would be the (very unlikely) possibility that we discover the aliens who made us, i.e., who “seeded” this planet with the DNA that evolved into what we are. That our existence is their project, that we are some part of their “purpose”, would turn a great many scientific orthodoxies on their head. I’ve always thought it would be funny (in a scary way) if they came back and actually identified the followers of some particular religion as “the chosen people” (who got it “right”), killed everyone else, and turned off the “aging switch” in the genome. Now THAT would change the game.

• Ian Fellows says:

I can’t tell if this is sarcasm or not :(

2. I think the reason we don’t hear this as much anymore is how we frame our thinking about the Fermi paradox has advanced one funeral at a time. And the older champions are no longer with us, and the newer generation sort of accepts the (never certain but likeliest) conclusion: we are first in our galaxy.

I’d put it this way. The old framing is the 1961 Drake equation. Number of civilizations = prob of star formation * blah * blah blah blah. eg
http://www.space.com/25219-drake-equation.html

First, you can’t know these probabilities, their variance is so high the end number is useless. So you argue and make them up. Second, and far worse, this framing has a hidden assumption that is really dumb (in 2016). No civilization ever expands. Ever. Ever. Robotic replicating neumann probes? Nope. So in 1975 Michael Hart published a paper saying civilizations could expand. And that was pretty much it. Except for all the funerals, which are now mostly done.

Like calculating the number of birthdays in a room with n people, a useful trick for simplifying is to calculate odds of nobody having same birthday. Robin Hanson in 1998 had the brilliant idea to apply this frame to the Fermi Paradox. This is called the Great Filter, what are the odds nobody expands? Suddenly the question is (while still super hard) at least more far more tractable. Note the precisness of the language. It’s not that everyone expands. Rather, it requires nobody expands, which is a far more strict criteria. Here’s hanson.
http://mason.gmu.edu/~rhanson/greatfilter.html

So what you still often see is the question you got asked. Note it is done in Drake equation style. This is really out of date, and if you see this Drake framing, it’s unfortunate. But like much science, the old stuff is amazingly sticky. So hard to wash the obsolete frames out.

There is a timescale issue here too. It takes billions of years to evolve complex life (over 4B on Earth). While expanding with replicating probes is timescale of millions for entire galaxy. So….. that’s another way to convince people. First out the gate is a billion years more advanced than second place.

Of course there are subtle variants and arguments you can make. But by and large I think SETI should look much farther out (beyond our galaxy) for waste IR signals from civilizations billions of years old. Not next door.

I wrote about it on my blog a few years back if you want a fuller version of this argument.

If you think this argument is flawed, I’m very interested in your thoughts! Just putting out my two cents on what’s going on.

• I don’t think this framing is necessarily Drake style. This is about detectability of signals given a kind of best-case of existence more than it’s about the existence of civilizations. I mean, if there aren’t any signals out there we won’t detect them. But even if there were lots of signals that were or will be generated over a 10 billion year period, what’s the chance we could detect them in a particular 10 year window?

• Peter Erwin says:

First, you can’t know these probabilities, their variance is so high the end number is useless.

Some of them are unknown, yes. Others (star formation rate, frequency of planets) are fairly well-determined, or becoming so.

• Yes. Correct. Some of these numbers are fairly well known, and getting better. That is very cool and interesting. Should have worded it that way. So for example of the last 4, the first one ne is becoming knowable. But the last three fl, fi, fc. Not expecting any improvement on them, barring SETI success.
ne = The number of planets, per solar system, with an environment suitable for life.
fl = The fraction of suitable planets on which life actually appears.
fi = The fraction of life bearing planets on which intelligent life emerges.
fc = The fraction of civilizations that develop a technology that releases detectable signs of their existence into space.

So suspect we agree, and your point is well taken. But I’d still contend end number useless given the last three. Given what we know today.

• jrkrideau says:

I have never understood why intelligence must originate on an earth-like planet must because we did. Anthropomorphism applied to intelligence?

• Skeletor says:

You’re correct that this is a bit anthropomorphic, but there are some reasonable constraints that we could place on candidate planets based on what we know about chemistry, biology, etc. For example, the elements and molecules that are associated with complex biochemistry would in all likelihood need to be readily available. Similarly, liquid water may also be required for its solvent and freezing properties (lakes freeze from the top down). Other important requirements could be adequate size (so that there is enough gravity to hold on to lighter elements, and an atmosphere), and a magnetic field to protect from cosmic radiation. IMO, these are all reasonable assumptions, and provide a good argument for why we should be looking for earthlike planets (I would include some moons in this category as well).

• Skeletor says:

Coming from the biology side of things, I can’t stress enough how much the Fermi paradox bugs me. There have been a number of fanciful solutions to the paradox that astrobiologists have proposed, but they all assume that highly intelligent life is somehow a given. I agree with the evolutionary biologists who’ve chimed in on the past on the issue, that this is a probably a false assumption.

I’ve actually pointed to your blog post a number of times when debating this topic in the past! You summed it up pretty nicely.

3. Anoneuoid says:

I get ~5 in a million chance the signal from a given civ will be detectable right now, ie about 5 signals out of the million that will be emitted in the 10 billion year interval can be detected. This assumes the start year, distance from earth, and duration of the signal are all uniformly distributed within the bounds described above.

Histogram of Results: https://i.imgsafe.org/2bdc370340.png
R Monte Carlo Code: http://pastebin.com/E5dk34fg

ps. I still don’t know how to post code in these comments and I am scared to experiment because there is no preview available.

4. Anoneuoid says:

Found a bug already! Change the “NcivsInGal” argument to “nCivs” in the first line to get it to work…

5. It seems that over the past 4-5 decades people have increasingly accepted the possibility of extraterrestrial life. The idea doesn’t seem quite as weird or exotic as it once did. (I think back on those Charles Addams cartoons, which captured many an imagination.) At the same time, there’s greater awareness of the extreme difficulty of interstellar communication. Such a level of difficulty starts to bore people after a while. So, without its former weirdness or imagined feasibility, the idea of extraterrestrial contact has fallen down the public priority list.

• The difficulty of getting to other parts of the galaxy and/or communication with those parts is still underestimated. I mean, people have a sense “oh that’s hard” but not like “oh by the way it would take more energy than the whole earth’s power system generates in a year…” or whatever.

6. anon says:

Some people say with a straight face that probability dictates the existence of extraterrestrial life is close to certain. It’s always some sort of many independent chances plus the universe is big argument.

7. After sending this to Andrew, I came up with a simpler thought experiment. Suppose there were only one other star in the universe (say, about 100 light years away) and that the probability of a signal from it was exactly 1. That way the Drake probabilities would be reduced significantly. We’d know exactly where to look. The question is remains: When and for how long? And even in this very best of cases, the chance that we’d be listening at the right time is almost zero unless they send for billions of years and we listen for billions of years. Even a thousand-year listening project looking for a thousand-year beacon would have almost no chance of succeeding.

8. Realist Writer says:

“… another reason is that we have an alien intelligence among us now—computers—so there’s less interest in a hypothetical alien intelligence that might not even exist.”

You may like “A Primer in Gont Poetics” (https://github.com/NaNoGenMo/2016/issues/144), a computer-generated “novel” (where novel is defined as a file containing 50,000 words or more). Supposedly, it’s a book about the poetry of an alien lifeforms, but it’s really commentary on “black box” machine learning algorithms. Here’s a synopsis –

“The idea was to generate an exegesis of alien poetry, inspired by the messages we send as attempts to communicate with alien life. I was struck by the gap which separates the scientific parts of these messages (basic mathematics and fundamental physics) with the cultural parts (the Voyager Golden Record begins with a recording of Bach’s Brandenburg Concerto No. 2).

When we learn a human language, we start from very human concepts (“how are you?”, “I have three brothers and one dog”). In contrast, communicating with aliens may mean building everything up from the hyperfine transition lines of a hydrogen atom. This means a very different experience of culture. Is it even possible to communicate across such a gap?

Of course, by alien here, I really mean computer. Modern machine learning techniques for language tasks are the equivalent of the old trope of aliens learning to speak English by watching old TV broadcasts. Can they really understand us that way? Or is the cultural gap too vast?”

9. Peter Erwin says:

This looks like a recent attempt at addressing the question in some fashion:

Horvat, Nakic, and Otocan, “Impact of technological synchronicity on prospects for CETI”, 2011, Acta Astronautica
https://arxiv.org/abs/1112.0423

e.g., “If SETI projects rely on a fortuitous detection of leaked interstellar signals (so called “eavesdropping”) then with minimum prior assumptions N ≥138−4991 Earth-like civilizations have to exist at this moment in the Galaxy for the technological usage synchronicity probability p ≥ 0.95 in the next 20 years.”

10. Peter Erwin says:

A minor nitpick or two:

If the range of start-time uncertainty is 10 billion years (from five billion years ago to five billion years from now) and the duration can be from 1000 to 100,000 years. And we now assign a random distribution over 1 million sources to distances between 300 and 100,000 light years away. That is from each of one million points, between 300 and 100,000 light years away, starting sometime from 5 billion years ago to five billion years from now…

So the initial postulate ends up being: “there will be a total of 1 million civilizations appearing in the galaxy between -5 and +5 billion years from now”. Since we’re assuming uniform distributions, you can immediately eliminate half them (the ones that appear in the future), since we obviously cannot receive any signals they might send.

The real issues are: “how many civilizations have appeared in the galaxy up until now?” — since it’s only from these that we might receive a signal — and “how should their start times be distributed over the past history of the galaxy?”

Also, “we now assign a random distribution over 1 million sources to distances between 300 and 100,000 light years away” obviously violates the earlier statement that “Carl Sagan calculated the average distance between 1 million galactic civilisations to be 300 ly”.

• Thomas says:

The reason to keep the future civilizations is that the odds would improve the longer we listen. If we listen for a billion years for 1000-year signals from up 100,000 light years away there’s a chance we’d find them. Or if we wait another 1000 years and then listen for a hundred years. Etc. In that sense it’s part of the probability space.

I also think you misunderstood that last point. Sagan meant that the closest civilization would probably be 300 ly away from us. The furthest one away would still be at the other end of the galaxy, i.e., about 100,000 ly away.

• Peter Erwin says:

The reason to keep the future civilizations is that the odds would improve the longer we listen.

Sure, that makes sense. But your original question was phrased as: “What are the odds that a signal is hitting us right now (or during the 10-year ”now” of the Breakthough Listen project).” In which case listening for several billion years is not part of the picture. (Your “1 million civilizations appearing over 10 billion years” implies a new civilization appearing every 10,000 years or so, so that’s about the minimum amount of time you’d have to listen in order to start to have “future civilizations” enter the picture.)

I also think you misunderstood that last point. Sagan meant that the closest civilization would probably be 300 ly away from us. The furthest one away would still be at the other end of the galaxy, i.e., about 100,000 ly away.

True; the only problem is that your limits eliminate the possibility of a civilization closer than 300 ly, which is entirely possible in Sagan’s original estimation. (I mentioned these were minor nitpicks…)

As I pointed out in another comment above, the “distances drawn from a uniform sampling” idea isn’t physically/geometrically plausible. Within a thousand light years or so, the probability density of distances would scale with the distance squared; over the larger scale of the whole galaxy (which is highly flattened), it would scale with the distance.

• Thomas says:

I’m not a statistician, but it seems to me that you can’t calculate the odds of a “now” except in a space where, if you extend the “now” from ten to a billion years, all things being equal, the odds would improve. So the space had to be defined to include that into which the “now” could be extended, to calculate our odds in this moment. (Part of the question is: what are the odds that right now is the right time to listen for ten years?)

The thing with the closer civilizations is that there signals also pass us soon after they’ve stopped sending. There will in any case only be very few of them, so keeping them in won’t improve the odds greatly. See my “two star universe” example above.

I’m not sure, but I think your last point introduces a “directional” issue. I we imagine that the listening operation is pointed in all directions, I’m not sure that would be a real problem. But I do see what you’re driving at.

• Peter Erwin says:

So the space had to be defined to include that into which the “now” could be extended, to calculate our odds in this moment.

That doesn’t really make sense to me.

The probability that I’ll see a police car in the street when I wander around tomorrow, for example, doesn’t depend on how many days after tomorrow I spend wandering the streets. How could it?

(Part of the question is: what are the odds that right now is the right time to listen for ten years?)

OK, but that’s not the question you asked. (And it’s not a very practical one: if the “right” time was three billion years ago, we can’t exactly go back then and start listening.)

I think your last point introduces a “directional” issue.

No, it’s just taking geometry into account. The simplest model is that civilizations are uniformly distributed through space — that is, they have a uniform density per cubic light year. That’s not too bad an approximation (for stars, anyway) out to a few hundred or a thousand light years from the Sun. So in that case, the number of civilizations located at a distance d from you is the density rho times the volume of a thin spherical shell of radius d, which can be approximated as rho * (4 pi d^2 dr). This means that the number of civilizations goes as d^2.

For the galaxy as a whole, a somewhat better approach is to pretend it’s a thin sheet, in which case everything is in the same plane. Then the number of civilizations at distance d is proportional to rho * (2 pi r dr), and the number of civilizations goes as d.

In either case, the further the distance, the larger the volume (or area) at that distance, and so the larger the number of civilizations at that distance. To get civilizations whose distribution was uniform with d, you’d have to have some funny distribution where the density of civilizations was higher the closer you got to us…

(If you wanted to get really fancy, you could take into account the fact that the density of stars is not uniform, but increases towards the center of the galaxy, but that’s making things too complicated for an exercise like this.)

• The way I’m thinking about this is: we don’t know when the police cars will leave the station or what their route is. So the more days I go out wandering, the greater much chances of ever seeing one. However we may calculate the odds for tomorrow, we have to make sure our model is scalable, so that if my research project could be extended to ten days or ten weeks or ten years. At some point the odds of a confirmed sighting will be essentially 1. But the behavior of the police cars remains the same throughout the period.

I grant that I didn’t make this totally clear in my mail to Andrew. But I wanted a model that could tell us both what our chances are and how they could be improved. Like I say, it seems to me that the two important variables (given that we don’t know when the signal begins transmitting) is how long we’re listening and how long they’ll continue transmitting. That’s why the probability space has to be extended billions of years into the past and future.