N = The number of civilizations in The Milky Way Galaxy whose radio emissions are detectable.
R* = The rate of formation of stars suitable for the development of intelligent life.
fp = The fraction of those stars with planetary systems.
ne = The number of planets, per solar system, with an environment suitable for life.
fl = The fraction of suitable planets on which life actually appears.
fi = The fraction of life bearing planets on which intelligent life emerges.
fc = The fraction of civilizations that develop a technology that releases detectable signs of their existence into space.
L = The length of time such civilizations release detectable signals into space.
From SETI's Carl Sagan Center for the Study of Life in the Universe - try out their Drake Equation Calculator.
There are a lot of moments in Cosmos that widened my perspective when I first watched the series. Episode 12, Encyclopedia Galactica, is filled with such moments. In the clip below, just before he launches into his vision of the Encyclopedia Galactica, Sagan addresses the probability of intelligent life in the galaxy using the Drake Equation.
Even for a person with a rudimentary understanding of mathematics like myself, the Drake Equation is a simple way to explore the potential for life in the vast Milky Way, which is always a good time. In the clip, Sagan walks us through the equation, demonstrating just how hard it is to know whether we are alone and unique in the universe, or just pedestrian intelligent life. It ends with a humbling thought:
So if civilizations do not always destroy themselves shortly after discovering radio astronomy, then the sky may be softly humming with messages from the stars, with signals from civilizations enormously older and wiser than we.
He goes on from there to succinctly summarize the central plot of Contact, and leaves us reflecting on the great value of radioastronomy and it's potential to aspire us to take to the stars:
If that doesn't open up your mind, well, you must have it closed pretty tightly.
If there are millions of technical civilizations in the milky way, each capable of radio astronomy, how far away is the nearest one? If they're distributed more or less randomly through space, then the nearest one will be some two-hundred light-years away, but within two-hundred light years, there are hundreds of thousands of stars. To find the needle in this haystack requires a dedicated and systematic search.
There are many cosmic radio sources having nothing to do with intelligent life, so how would we know that we were receiving a message? The transmitting civilization could make it very easy for us if they wished. Imagine we're in the course of a systematic search, or in the midst of some more conventional radio observations, and suppose one day we find a strong signal slowly emerging. Not just some background hiss, but a methodical series of pulses. The numbers: 1, 2, 3, 5, 7, 11, 13. A signal made of prime numbers; numbers divisible only by one and themselves. There is no natural astrophysical process that generates prime numbers. We would have to conclude that someone fond of elementary mathematics was saying, "Hello." This would be no more than a beacon to attract our attention. The main message would be subtler, more hidden, far richer. We may have to work hard to find it.
But the beacon's signal alone would be profoundly significant. It would mean that someone had learned to survive technological adolescence, that self-destruction is not inevitable, that we also may have a future. Such knowledge, it seems to me, might be worth a great price."