# The Fermi Paradox and the Drake Equation – Intro

Enrico Fermi was various kinds of brilliant. His estimate of the yield of the Trinity nuclear test by measuring the displacement of confetti by the shock wave is surprisingly accurate. In science fiction circles, of course, he is best known for the Fermi Paradox. The Fermi Paradox, for those unfamiliar with it, can be stated as: if the Earth is typical, the universe should be full of intelligent life. Why do we have no evidence of it? Or, as Fermi himself more succinctly put it, “Where are they?”

Consider: it seems plausible that humankind could develop interstellar travel within a thousand years. That’s a tiny sliver of the age of the galaxy. Even if interstellar travel were very slow, say 1% of the speed of light, it would only take about 10 million years for our descendants to permeate the Milky Way galaxy. Since the Milky Way is about 13 billion years old, there has been ample time for aliens to have evolved intelligence, developed star travel, and reached Earth. And not just once–hundreds of times over. And even if interstellar travel is essentially impossible, the galaxy’s radio frequencies could be full of messages. Radio signals bearing I Love Lucy and The Honeymooners are now 60 light years away from us and still going.

To help estimate the number of alien civilizations that might be detectable by radio, Frank Drake defined the Drake Equation:

N = R * f_p * n_e * f_l * f_i * f_c * L

where:

N = the number of civilizations in our galaxy with which communication might be possible;

and

R = the average rate of star formation per year in our galaxy
f_p = the fraction of those stars that have planets
n_e = the average number of planets that can potentially support life per star that has planets
f_l = the fraction of the above that actually go on to develop life at some point
f_i = the fraction of the above that actually go on to develop intelligent life
f_c = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space
L = the length of time for which such civilizations release detectable signals into space

Although directed to interstellar signals, the general logic of the Drake Equation applies to interstellar travel. Substitute f_c with a new term, f_s, the fraction of civilizations that develop interstellar travel.

Either way, if N is close to zero as observation suggests, at least one of the factors in the Drake Equation is close to zero. In future posts, we’ll discuss which one(s), with reasons why. We discuss R, the average rate of star formation, in our next post.