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.