The Drake Equation (simple form, there are a lot of variations and adjustments):But, he did something more clever than simply writing an calculable equation. It gave us a framework to think about the variables that are important in the search for extraterrestrial, intelligent life. Why do we need such a framework?
N=number of detectable civilizations in the galaxy
R*=rate of star formation
fp=fraction of those stars with planets (including their moons as part of the planet)
ne=average number of planets per star with planets
fl=fraction of planets with life
fi=fraction of planets with life with intelligent life
fc=fraction intelligent life with technology that generates a detectable signal
L=length of time of signal release
Well, the Milky Way (not to mention the Universe) is a big place. A really big place (a volume of about 1000 billion cubic light years [ly3]* containing 100-400 billion stars). It is not practical to search the entire galaxy. The Drake Equation gives us a framework for making intelligent decisions about how to constrain that search space (which is why SETI loves the Drake Equation) or even bother searching. For example, Carl Sagan's interest in environmental issues was partially driven by his belief that L (essentially the life span of civilizations) was the most important variable in the Drake Equation was very small relative to the age of the galaxy.
Which brings us to the Fermi Paradox. Assuming that the Earth is not a singular planet, given the age of the universe, why isn't intelligent life everywhere?
Which brings us to science-fiction writer Charlie Stross, who suggests that part of the paradox is that the Earth is not as habitable as we like to think. Read his post for the full argument and discussion of meat puppets, but the take home message is that only about 15% of the current Earth's surface is habitable without special equipment or knowledge. And it gets worse. Over the history of the Earth, due to lack of oxygen and nasty ice ages, those habitable conditions have only existed for about 8% of the Earth's history. The bad news is that those habitable conditions may only exist for another 0.3-1 billion years.
Stross' ruminations are, essentially, providing a framework for thinking about the parameters for fi, fc, and L. Even on an "ideal" planet like Earth, they may not be very large.
*Which is, incidently, my new favorite unit.