Despite the apparently mathematical nature of this page, it actually isn’t so; we are just using the “Drake Equation” to organize our thoughts. It predicts the number of ETs by taking the rate at which they appear, and multiplying by how long they last. This is necessary because we are not trying to figure out how many ET civilizations there have ever been – we want to know how many there are now (because we want to hear from them now). We have to consider how often they are born, and how long they live. For example, if fireworks typically glow for 10 seconds, you’d better shoot them off about once every 10 sec if you want it to be true that whenever you look you’ll probably see one in action. If you do that, but it turns out they actually glow for 100 sec, then you’ll probably see about 10 at any given time, while if they glow for 10 sec but you only shoot them off once every 100 sec, odds are you typically won’t see one when you look… We can write this as:

NIC = RIC x LIC

NIC is the number of current “intelligent civilizations”, meaning only that they produce radio signals we can detect and recognize as artificial. We use radio here because we already know that is a practical means of communication, even at our level of technology, and it works at the speed of light. If you think some other way would be used, just substitute it wherever you see “radio” below. Transmission (or travel) times are not important here; they’ll always be short compared with evolutionary timescales. We will confine ourselves to calculating this for the Milky Way Galaxy, since other galaxies are too far away to be very interesting in this context (we think).

RIC is the rate at which “intelligent civilizations” appear, and LIC is their typical “lifetime”, or time during which they produce recognizably artificial signals (which is our working definition of “intelligent” here). We will try to figure out what RIC is, and leave the final answer in terms of LIC , which we can all agree we have no real clue about.

To calculate RIC, we have to know some Astronomy, some Biology, and some Sociology. The astronomical part is in the best shape, the biology is coming along (but we need to know a lot more), and the sociology is pure guesswork at this time. That means that any final answer we give is going to be at best an educated guess (and not all that educated). But it is instructive to see what would have to be true in order that lots of messages are out there to be heard.

We can break RIC down into the rate at which stars appear, times a bunch of probabilities that the other conditions necessary to the transmission of radio messages will occur, if you start with a star. I supply my own optimistic estimates for each factor. They are all arguable, but I don’t think one can make it much more favorable than I do here, with strong justification. We can do it something like this:

RIC = Rstar x Pplanets x Phabitability (Astronomy)

x Psimple life x Pcomplex life (Biology)

x Pradio transmissions (Sociology)

Astronomy

Rstar is the rate at which stars appear in our Galaxy, which is measured by observing newly born nearby stars. After adjusting for the entire Galaxy we get a rate of roughly 1/year at the moment. But that rate does not account for the ~300 billion stars which are now in the Galaxy, since the Galaxy is about 10 billion years old. Thus, a better average rate is 30/year. The initial formation of the Galaxy had a higher rate than now, and for our purposes that is fine, since those “extra” stars have had more time to allow life to evolve around them. On the other hand, we might want to exclude low metallicity stars, binary systems with “planetary” separations, and stars which are too low in mass (although we don’t really know what “too low” really is). Let’s compromise on 20/year.

Pplanets is the probability that a star will have planets. We observe a rate of about 0.05 right now, but we see protoplanetary disks in great abundance, and know that our search techniques are currently missing most planets. On the other hand, a lot of stars are binary and some system configurations are unfavorable for planets, and some stars don’t show disks early on. This number is not likely to be higher than about 0.5.

Phabitability is the likelihood that a planet in the system will be habitable. We used to think that this meant it had to be a lot like the Earth, but now that seems overly restrictive. It is not obvious that it has to have a particular surface temperature, for example. The ice moon of Jupiter, Europa, is now being seriously considered as a possibly habitable place, because it has a liquid ocean beneath its thick layer of ice. Larger-than-earth terrestrial planets might be analogs of this: they will be able to retain internal heat very well, are likely to have a higher water content near the surface, and more likely to be geologically active. Given these conditions, it is at least vaguely plausible that life could arise (at the equivalent of deep-sea volcanic vents). Such a planet is fairly impervious to most hazards from the sky, and actually can survive being ejected entirely away from its star without affecting its habitability much. Let’s be optimistic and set this probability to 0.1. Here is a place where perhaps one might go as high as 0.5, but could easily go much smaller too.

Biology

Psimple life is the probability that given a habitable planet, simple (one-celled) life will arise on it. The only real argument we can make here is that the Earth shows evidence for such life almost as soon as it became possible. Once the surface of the Earth had cooled enough, and the rate of giant impacts became less than totally devastating, life seems to have arisen. There is a good argument that therefore the probability is high; we’ll set it 1.0 (as optimistic as possible).

Pcomplex life is the chance that given simple life, it will evolve into complex life (complex enough to become technological). Here the evidence from the Earth is less comforting: our planet sat with only simple life on it for 3 billion years before anything else happened. It is only in the last 0.5 billion years that the Earth has had life of any real complexity on it. We don’t know what induced that to happen, or how long the typical period is. An optimistic estimate here is definitely lower; we’ll go with 0.1.

Sociology

Pradiotransmissions is the likelihood that complex life will construct and use radio transmitters of sufficient power that we could hear them, and send signals we could recognize as artificial. It is by no means obvious why organisms should do this, or how likely they are to do it. All we know is that we have been doing it for a very short interval so far. It could be that life on water-worlds will never do this, or that other beings are far too clever to waste their time on radio when there is something much superior, or that they will communicate by telepathy, or whatever. We must recognize that we have no way of scientifically estimating this number, nor the other piece of sociology: how long transmissions would continue assuming they actually began.

I am inclined to put in a number smaller than the numbers above, since the circumstances for this are much more specific than for the other considerations. Since we are being optimistic I won’t take it down too far, say 0.01. Clearly there is room for almost any number here, and your guess is as likely to be right as mine. Most would agree that this is on the optimistic side, I think.

Evaluating the Drake Equation: Putting in the Numbers

That’s it, we are done! Let’s see what we get.

To recap, we have:

NIC = RIC x LIC = LIC x

Rstar x Pplanets x Phabitability x Psimple life x Pcomplex life x Pradio transmissions

= LIC (years)x20/year x 0.5 x 0.1 x 1 x 0.1 x 0.01 = LIC (years) / 1000

What does this mean??? You have to supply your own guess about the total time any given planet harbors complex creatures which are transmitting radio signals ( LIC ). What is clear is that if that lifetime is 1000 years or less, then we are likely to be the only civilization currently doing so in the Galaxy. Note that this is true even if thousands of such civilizations have arisen over time, because the Galaxy is 10 billion years old. It is easy for them to be spread out in time enough that they tend to miss each other, unless they last for timescales that are interesting by Galactic standards.

The problem is even worse if we would like our nearest current neighbor to be within, say, a thousand light years of us. In order to have a reasonable chance of that, there would have to be roughly 10,000 such civilizations currently broadcasting, because the Galaxy has a diameter of 100,000 light years! Using our solution above, you can easily show that the average lifetime of radio broadcasts has to be around 10 million years!!

We don’t have to decide how likely that is – we can just say that it’s what is required in order that there is someone “nearby” to talk to. The same thing applies if you are talking about spacecraft visitations instead of radio messages. If you are even more wildly optimistic than I have been, it is very hard to reduce it to fewer than a million years. A clear implication of this is that if we do hear from someone, they are likely to be far more advanced than us (we have been technological for a tiny fraction of millions of years).

On the other hand, it is quite easy to be less optimistic than I have been, and easily reach the conclusion that we are the only civilization currently broadcasting artificial radio signals in the Milky Way Galaxy. There is great room for pessimism on the sociological front, and the biology is really unclear in the absence of examples of life other than on the Earth.

Life in the Galaxy

If you want instead to ask only about how many planets have life on them, the situation changes drastically. Now we have

NSL = RSL x LSL = LSL xRstar x Pplanets x Phabitability x Psimple life

We can use the numbers from before, except that LSL should be a much longer number if life tends to hang onto planets once it starts (which seems to be the case with Earth). Then a reasonable number is LSL= 5 billion years (half the lifetime of the Galaxy), and we find that NSL = LSL = 5 billion! There should be billions of planets in our Galaxy with simple life on them now. If complex life typically lasts 1 billion years (and only appears on 0.1 planets with simple life), the number of planets now populated with interesting complex alien organisms is of the order 100 million. This makes it clear why most astronomers believe the Galaxy is teeming with life (our estimate could be 1000 times too high and that would still be true).

Conclusion

It is important to end by saying that I don’t think a valid conclusion of all this is that we should abandon SETI: the search for extraterrestrial intelligence. Firstly, there was a lot of guesswork above – maybe we are missing something. For example, it is probably possible for civilizations to set up automated, self-repairing broadcast stations that could last essentially forever (if they chose to do so). Secondly, it doesn’t cost much for us to listen, and the payoff is extraordinarily important if we hear something. Nonetheless, it makes sense to be realistic about the chances of hearing something, so that we don’t misinterpret silence (if that is the eventual result of our efforts). One conclusion seems to be that we should consider ourselves to be currently Galactically important; that makes it well worth taking good care of ourselves!