Nearly 50 years ago, a young researcher called Frank Drake led a discussion at a meeting at the Green Bank Radio Observatory. It was an early discussion group on the possibilities of life in the universe. He went to the board and sought in real time some way of organizing this difficult subject, which involves many disciplines. The equation he wrote on the board has become a basis for astrobiology, an organizing principle that most people recognize. It's the way of calculating N, the number of intelligent communicable civilizations in our galaxy at any time. Notice those modifiers. We're looking for intelligence, we're looking for technology, and the ability to communicate, and we're looking for some contemporaneous existence, where they exist with us such that we can communicate. Notice also, we're only talking about the Milky Way. Logically, whatever the number N is, we must multiply it by 100 billion for the number of intelligent communicable civilizations in the universe. But we assume that those are mostly at distances far too far to even imagine communication. What are the factors of the Drake equation? The first factor is the rate at which new stellar systems that could host planets are being formed in the Milky Way, the star formation rate of Sun-like stars. This number is a few, three to five, and it's well-determined by astrophysics. The next number is the fraction of those stars that have planets of any kind. Exoplanet searches are pinning this number down. This fraction is going to be close to one. Already it's known to be more than about 20 or 30 percent. The third number is the number of earth-like systems within each exoplanet system. This is the subject of intense investigation in astrobiology. We don't know the answer, but it's looking like N is one or two. There are typically a couple of earth-like planets in each solar system out there. These numbers are all either determined or about to be determined by astronomical observation. The next factors we'll recognize as completely indeterminate or uncertain. The next one is the fraction of those earth-like planets that have life. We don't know what that fraction is. We might imagine if a planet is habitable, it's almost inevitable that it has life, and so that fraction is close to one. But some biologists argue that that's not the case. That life's formation on the earth involved some unlikely steps and so that fraction is small, maybe only one percent or less. We don't have the data to decide until we find life elsewhere and get some statistical basis. The next fraction is the fraction of those planets where life form, where an intelligent species eventually develops. Again, we have no idea of that fraction. Some argue that it's inevitable because it happened here, others argue that it took a long time or it involves a lot of contingency in evolution, and so it's a low number. There's no way to decide. The next to last fraction is the fraction of those intelligent species that develop the ability to communicate or travel in space. On the earth, we have a handful at least of intelligent species, only one of which, us have the ability to do that. But again, we have no idea what that fraction is in the general case. The final number is critical because it involves time. It's the lifetime of that hypothetical civilization in their communicative state. Since N is proportional to L, the entire product is driven by L. If L is a small number, then N may be a small number. If N is large, N may be large, what is L? For us, it's hard to tell. We've only had the communication ability in space or to travel for 50 years, say, 100 as a round number, but people looking at human history will realize we nearly extinguished ourselves in that time when there were 40,000 nuclear weapons in the world and the Cold War was in its darkest days. So if human civilization with intelligence and technology is unstable, we don't know what the cosmic average of this number is. Perhaps, civilizations always are unstable, or perhaps where there are exceptions, the immature ones who almost self-destructed. When you get through your teething adolescence, you live forever or for millions of years. You can see the huge uncertainty in the Drake equation. It's a simple trope of mathematics, that the product of a series of numbers is as uncertain as the largest uncertainty. So the fact that we know the first three factors through astronomy increasingly well doesn't mean that the uncertainty goes away for the factors where we know nothing. Even Frank Drake recognized the limitations of this equation, and he called it a container for ignorance. It is also worth pointing out logically that it's thick number of intelligent communicable civilizations in the Milky Way. If some civilizations live a very long time, they could have the possibility to travel between galaxies. At one tenth light speed, the trip to Andromeda is perhaps 20 million years. For newly eternal civilization, this is not a long time, and it's a small fraction of the age of any galaxy. We're heading into extremes of speculation here talking about the longevity of civilizations. But it's also important to point out that the Drake Equation involves an average, and that the possibilities of intergalactic civilization and communication may depend on the longest lived members of that club rather than a short-lived members. You can see that the Drake equation conceptually is a series of subsets. There's the subset of all the stars that have earth-like planets, the subset of those that host life as opposed to the ones that are sterile or stillborn, and then the subset of those where life develops sentience, and then intelligence, and eventually technology. As we winnow down the very large number of sites for life, the initial real estate from the habitable planets searches, we could end up with a very small number. Logically, it's possible that N is one, where it we're unique in the galaxy as an intelligent technological civilization. Also logically, and some have argued like Carl Sagan, that N is more likely to be 100,000 or a million, in which case, there's a large set of potential Pen Pals out there. Sociologists, and psychologists, and evolutionary biologists have also weighed in on this subject even though it's mostly governed by an astronomy arguments. Because when we're talking about the biological and cultural aspects of the equation, we have to do that kind of analysis of our situation. But the uncertainty of the Drake equation doesn't go away. In the end, we simply have to do the experiment and look. It's striking and probably a coincidence that Thomas Wright, a physicist living in England in the middle of the 18th century speculated about the size of the Milky Way Galaxy during a time when Herschel was mapping it out with his telescopes. He came up with an estimate of 170 million habitable worlds in the universe, which at that time was the galaxy. This is actually close within a factor of two, and certainly an order of magnitude of the true modern astronomical estimate. So people have been thinking in these terms for centuries. There are more sophisticated ways of thinking about the Drake equation, and there's a theoretical construct which stops using the binary on off life exists or it doesn't, it's intelligent or it's not, and takes into account the contingencies of evolution and the fact that all of these attributes will exist on a spectrum, and that some of the relationships between the factors are not independent. They are coupled. This is called a Bayesian framework for estimation. It's important that we use as few prior assumptions as possible in studying the Drake equation. Either way, there's an enormous possibility for intelligent civilizations in the universe. The Drake equation seeks to organize our knowledge and our ignorance of astrobiology in one formalism, a simple equation to calculate N, the number of intelligent communicable civilizations at any time in one galaxy, ours. The first few factors of the equation are astronomical and they're being determined by current and future observations. The latter factors are completely uncertain because until we find life elsewhere, we won't know how likely it is for life to develop on a habitable planet or subsequently evolve to intelligence and technology. Finally, the Drake equation is proportional to the longevity of a civilization in the communicable state, and that number is also completely uncertain. If N is a large number, and there are many durable civilizations out there, then we will have many potential Pen Pals.
