|The woo is out there|
|Aliens did it and ran away|
- N represents the number of civilizations with which we might be able to communicate;
- R* is the average rate of star formation in our galaxy
- fp is the fraction of those stars that have planets
- ne is the average number of planets that can potentially support life per star that has planets
- fℓ is the fraction of the above that actually go on to develop life at some point
- fi is the fraction of the above that actually go on to develop intelligent life
- fc is the fraction of civilizations that develop a technology that releases detectable signs of their existence into space
- L is the length of time such civilizations release detectable signals into space.
 Origins of the equation
Frank Drake formulated the equation at the famous Green Bank SETI meeting, reportedly just before giving his talk and as little more than something to write up on the board; Carl Sagan later popularised and refined it, adding variables for other vital components of a healthy life and technology supporting system.
 Applying the equation
The Drake Equation is essentially a model for the number of civilisations we can detect, taking in variables that would affect this number and representing it as an equation. The application of the equation is relatively straightforward. Starting with the number of stars (which is around 100 billion or so), each subsequent term is a fraction that whittles this number down to the final value of N. For example, if one thinks that 50% of stars will have planets, then this leads to 50 billion. If you think that only 10% of these will be capable of supporting life, the number drops to 5 billion. If only a small fraction, 1%, actuall do develop life you get 50 million planets with life. The remaining factors are regarding how this life develops and evolves. So if only 10% of life bearing planets develop intelligent life and only 10% of those develop communications technology, then we see 500,000 civilisations. The final factor about a civilisation's longevity is difficult to think about, but is essentially "how many of these civilisations will survive long enough for us to see them now?" 10%? 1%? Even these small figures lead to several hundred, if not several thousand observable civilisations in just our galaxy. Given that there are more galaxies in the universe than there are stars in the galaxy, applying the Drake equation to the whole universe makes life appear very common indeed, even more the most conservative estimates for each indiviudal term.
 Main assumptions
Where the Drake Equation is limited, it is due to it making several assumptions about life and the universe in general. It probably goes without saying that from the outset the Drake Equation outright rejects theological or supernatural origins for life in favour of naturalistic processes. Each term in the equation is purely natural in origin, and including a term to factor in magic would make the equation even less useful and more subjective than it already is - we can make intelligent guesses for all factors in the Drake equation, but "the fraction of planets God seeds life onto" can take any value between 0 and 1, with no room for refinement.
Secondly, the equation is restricted to life "as we know it", as the factors involved imply that planets for life to evolve on must be Earth-like. This ignores the possibility of far more exotic forms of life, such as life evolving in the atmosphere of gas giants or by thermal vents in otherwise frozen moons, as we have a term for detecting Earth-like planets in habitable zones. This can be made more general by asking "what is the fraction of planets with environments that can form life", but this is more difficult to refine given our present ability to detect exoplanets. The next assumption is that life must evolve on a planet, ignoring the conjecture that life could form out of the super-fast quark reactions inside a neutron star, or sentient gas clouds having emergent thoughts over periods of millions of years.
Therefore, these assumptions are mostly valid for practical purposes, particularly when it comes to actually detecting this life. The exotic forms of life are of interest to science fiction authors, but from a practical point of view there are limitations regarding observation of these civilisations and what relevance they would have to us. Underwater or gaseous life would probably not be able to develop communications technology, and the aforementioned exotic life inside neutron stars would - hypothetically - evolve and die out in a blink of an eye, making detection completely impossible.
 Variability and the Drake Equation guessing game
Many scientists believe in the existence of (intelligent) life for statistical reasons, since our Milky Way galaxy is only one of the billions of galaxies in the universe. With this as a given, those interested in the subject enjoy tweaking the values of the Drake Equation to come up with their own pessimistic or optimistic result. This is considered an acceptable scientific pastime as many of the issues are relevant to real science - planet formation is of great importance to astrophysics and conditions that conducive to forming life are relevant to biology and geology.
Each term in the equation is open for lively debate due to the numerous unknowns and the speed at which research is generating data to give more informed values for these terms. As technology and knowledge of the universe increases, the guesses may become more informed and the values applied may be more representative of reality. The first two terms, for example - the rate of star formation and the number of planets - are two that are becoming more clear with additional research; the discovery of numerous exoplanets in recent years indicates that this could be a very favorable number. Currently, however, the variables are all of a nature that cannot be accurately determined. The number of planets capable of hosting life (at least "as we know it") is unknown, as technology is biased to discovering exoplanets that aren't suitable for life - namely large planets, like gas giants, that orbit very close to their stars. The other terms, involving the formation of life and the development of intelligent life are still questions that are wide open. On the one hand, we haven't observed any signals from intelligent life, indicating that it is rare - but on the other hand (although this is rather cheeky reasoning) the one planet that we're aware of that has produced life has also produced intelligent life, a success rate of 100% for fi and fc.
Despite the wild unknowns, even the most conservative estimate produces a high likelihood of another technological society inside our galaxy, given the number of stars. Low estimates put the number of detectable civilisations in our own galaxy as many thousands, but these would be spread so thinly that active communication and interaction would be difficult, if not impossible.
With the terms regarding the development of life being almost entirely conjectural, possibly the most interesting factor is "L", the time a civilization might spend indicating its presence. This can be inferred by looking not at the stars, but ourselves; the longer that mankind succeeds in not annihilating itself and continuing to broadcast detectable signals, the longer we can guess other civilizations will do the same. Current developments in communications technology have lead to this component of the Drake equation being the most hotly contested.
 Reliance on radio communication
Highly advanced civilisations are likely to just "disappear" as the observable waste they generate is reduced to zero. This is taken into account in the final part of the Drake equation which is the "longevity" of a civilisation. Originally this factor was thought to represent the amount of time it took for a civilisation to destroy itself - rending itself unobservable due to extinction - but recent developments in Earth's communication technology has lead to the the disappearance of broadcast signals.
As well as trying to find intentional signals that are broadcast to outer space, such as the Arecibo message, observation of alien life also relies on "accidental" broadcasting, i.e., broadcasts that are not intended to send messages other planets but radiate out from an alien homeworld anyway. This ranges from simple communications to TV broadcasts, which on Earth have enough power to travel to other stars and potentially be received with some clarity. However, these means of communication may cease in favour of more efficient methods of communications. This can be seen in the development of human technology; as cable television and the internet are replacing high power broadcast stations for both TV and radio. Satellite communications (such as the GPS signals), while still radiating into space, are highly directional and are much lower powered than the TV broadcast signals that dominated the 20th century. Radio itself is an inefficient means of communication - as a species grows, it's efficiency increases (or at least has to increase) meaning that radio is one method that would have to be dropped in order to support a large and advanced civilisation. Increases in energy efficiency could also lead to civilisations becoming effectively invisible at all wavelengths.
 See also
- A BBC article featuring Drake and some pretty good comments