I’m not sure what is more profound – the idea of potentially thousands of extraterrestrial civilizations in our galaxy, or the idea that this is the 50th post from the Parallax Machine. One thing is certain – the equation for the extraterrestrials is more interesting. So let’s plow forward with that:

N = R_{*} × f_{p} × n_{e} × f_{l} × f_{i} × f_{c} × L

In this equation,

- N is the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy
- R
_{*}is the rate at which new stars are created in our galaxy - f
_{p}is the fraction of stars that have planets - n
_{e}is the average number of planets per star that might support life - f
_{l}is the fraction of life-supporting planets that actually develop life - f
_{i}is the fraction of developed life that becomes intelligent - f
_{c}is the the fraction of intelligent life that sends signals into space - L is how long a signal-sending civilization survives and sends those signals

So far, we have estimated R_{*} = 2 per year, f_{p} = 0.99, n_{e} = 0.35, f_{l} = 0.75, f_{i} = 0.75, and f_{c} = 0.9. Now we address the final piece of the puzzle: L, the number of years that a civilization sends signals into space.

L is probably the toughest factor to evaluate in the Drake equation. R_{*}, f_{p}, and n_{e} were based on a considerable number of observations, and then some logic to extrapolate them to the entire galaxy. f_{l}, f_{i}, and f_{c} were based on what we know about the origins and evolution of life on our own world, and then some more extrapolation logic. But for L, we don’t even have a data point yet to begin with. We know how long we’ve been broadcasting signals into space so far, but we don’t know how long we will be doing that into the future. So maybe if we work backwards from the extreme…

We know that in a vacuum, and based solely on the slow expansion of the Sun, Earth would probably remain habitable for up to another billion years or so, at which point the cascading effects of increased solar radiation would trigger a domino effect, with plants dying off first, and then the rest of the food chain not long after. We would effectively have exited the Goldilocks zone for good at that point. So there’s a reasonable upper limit on L: about a billion years.

Then again, there have been several mass extinctions on our world, dating back to the Cambrian explosion. They were spaced apart by 69 million, 124 million, 51 million, and 134 million years, respectively, with the last one wiping out the dinosaurs 66 million years ago, compliments of an angry rock from space. If we take the average of the intervals between major mass extinction events, we get about 95 million years. We’ve eaten up 66 million of that, meaning that on average, we should expect something to go very wrong again in another 29 million years. It’s not clear that we would die out completely from such an event, but just for argument’s sake, let’s say we do. So there’s another possible value of L: about 29 million years.

Statistically speaking, there is a small chance that something could wipe us out in the next few years. Perhaps a rogue asteroid we missed, or a sudden burst of gamma rays from deep space that we didn’t see coming. A departure that immediate, however, would be more likely to result from our own actions. For example, on Earth, our understanding of electromagnetism was closely linked to our subsequent understanding of relativity and quantum mechanics, which eventually led to the invention of nuclear weapons. So the threats come along right on the heels of the advancements, and the lower limit on L would seem to be about 100 years – at least for us. I think it’s reasonable to assume that if there are other civilizations out there with similar technology, they would also last a similar number of years before exiting stage right.

Or maybe there’s some middle ground number – say we’re halfway through our wonderful ride on Earth as the dominant species, and then take our own bow in another 200,000 years. So there’s another possible value of L. That gives us a pretty nice spread of numbers to try out in the Drake equation: 1 billion, 29 million, 200,000, and 100 years. Plugging those numbers in, we get N = 351 million, 10 million, 70,000, or 35 active, communicative civilizations, respectively. So, a couple of really big numbers, another pretty big number, and 35. To give these numbers any meaning, we need to consider how big the Milky Way galaxy is.

The Milky Way is composed of several spiral arms of stars emanating from a massive bulging center. But for the purposes of computing its total volume, we can simplify things by treating it like a disk, 100,000 light years in diameter and 1000 light years thick. When we do that, we compute a total volume of 7.9 trillion cubic light years. As another very rough approximation, we can then divide that volume by the number of star systems with active, communicative civilizations, to figure out how far apart they might be:

L (years) | N (civilizations) | Volume per civilization (cubic light years) | Distance from one civilization to the next (light years) |

100 | 35 | 226 billion | 16,952 |

200,000 | 70,000 | 113 million | 379 |

29 million | 10 million | 790,000 | 31.7 |

1 billion | 351 million | 22,507 | 5.35 |

It bears repeating – these are rough approximations. But we’re just trying to get a general sense here of what certain orders of magnitude of L mean. If all communicating civilizations lasted for as long as their planets could support them, we would expect the nearest one to be a little over 5 light years away. The nearest star to our Sun is around 4 light years away. So in this scenario, the galaxy would be jam-packed with communicating civilizations, and our own signals would have reached our nearest neighbors only a few years after we first started transmitting them. If civilizations are limited more by cataclysmic events like collisions with asteroids, then we’d expect the nearest one to be about 32 light years away – still not all that far in the grand scheme of things, and still close enough that our signals would have reached them by now.

Going for a moment to the extreme case of L=100, the nearest civilization would be nearly 17,000 light years away. If we were to receive a signal tomorrow from that civilization, it would have been transmitted during our last Ice Age, and our Earth may look very different by the time they receive anything we’ve transmitted since the early 20th century. But, if L=100, that also means that civilization stopped transmitting during that same Ice Age, and by the time our signals hit their world, they would no longer be around to receive them (and neither would we). L=100 can therefore be considered the “hopeless” portion of the table.

There are other factors at work here that we haven’t considered. First, what if a civilization arises, begins to communicate, and then perishes, but it’s eventually replaced by another advanced civilization on the same planet? That would bump some of these numbers up a bit. Second, what if a civilization colonizes other systems during its lifetime? We know that, at least for ourselves, that will take longer than 100 years from our first signal. As far as we know, there is no way to travel faster than light, so even if we had the technology and the will to colonize the nearest star system, it would be a multi-decade endeavor at best between initial planning, multiple journeys, and multi-year communication delays back and forth with Earth. In other words, if L=100, then civilizations typically don’t last long enough to colonize other systems. But if L=500 – maybe that changes dramatically? Then you’d have a domino effect.

To date, and to general knowledge, we have not detected signals from another civilization. I am learning this along with you as I go, so I’m not entirely sure how to interpret that, even so far as how it effects the possible range of L. To my naive mind, this seems to suggest that either L is not in the millions or billions, or that I was too optimistic with the other factors in the equation. On the other end of the spectrum, if L=100, there isn’t much to be gained by pursuing the matter – it would mean civilizations snuff themselves out almost immediately after they are capable, and no one lasts long enough to communicate, so if there is intelligent life elsewhere, we will never know.

But assuming the values I assigned to the other factors in the equation are somewhat reasonable, what would cause a typical value of L to be in that vast wasteland between a 100 and 29 million years? Here’s another thought – maybe there is a trigger point? Species that figure out how to get sufficiently past our current adolescent stage of civilization don’t get wiped out until an asteroid comes along? So a civilization either lasts a few hundred years or tens of millions, with not much middle ground in between? In that event, looking at the table, for the majority of the potential percent mixes of those two cases, the total number of civilizations would be dominated by the more successful ones. So let’s say 10% of all civilizations figure out how to get past the phase we’re in right now, and then they last on that world until the typical extinction event comes along. That would mean a million active and communicative civilizations in the galaxy at this instant, with the closest one 100 light years away.

In the next and final post in this series, we will take a look at what’s been done to date to detect extraterrestrial civilizations, and how that meshes with the previous paragraph, as well as with the idea that we haven’t found one yet. To be complete, we’ll also consider the idea that we *have* detected one or more, but it’s been covered up. And we’ll finish with what it all means for us. For now, picture a million species like (or unlike) our own, scattered across the galaxy, and asking these same questions. If there are that many, then the vast majority figured out how to survive their youth. I would certainly like to know something like that.