PART V · Room Two · Observational Astronomy & Life

The Drake Equation — How Many Civilizations in the Galaxy,
and Why Is It So Quiet?

Our galaxy alone holds hundreds of billions of stars. Of those, just how many host a civilization we could communicate with? In 1961 Frank Drake tamed this daunting question with a single multiplication. Yet when you run the numbers, civilizations seem as though they ought to be fairly common — and still the sky has never answered. So where is everybody?

§1An Equation That Organizes What We Don't Know

In 1961, the radio astronomer Frank Drake, preparing for a small meeting in Green Bank, West Virginia, broke the question "how many communicating civilizations are there in the galaxy" into a product of seven factors. Starting from the rate at which stars are born, then the probability that such a star has planets, the number of planets where life could survive, the probability that life actually arises there, the probability it evolves into intelligence, the probability it emits a signal we could detect, and finally how long such a civilization endures — you multiply them one by one.

In plain words Rather than trying to answer the enormous question all at once, it slices it into "step 1 × step 2 × step 3 …". The value of each step is still mostly unknown. So the Drake equation is less a calculator that hands you the answer and more a map that lays out, item by item, "exactly what it is we don't know."

§2Plugging In Values — Between Optimism and Pessimism

The trouble is that the later you go, the more viciously uncertain the values become. The astronomical terms up front (the star formation rate, the probability of planets) have been narrowed considerably by recent exoplanet observations, but when it comes to life, intelligence, technology, and lifetime, we hold a sample of exactly one — Earth. So feed the same equation optimistic values and it says the galaxy holds millions of civilizations; feed it pessimistic ones and out comes a value far below 1 — that is, "we may be the only ones in this galaxy right now." In the experiment on the right, move all seven sliders yourself and watch how N swings.

§3The Fermi Paradox — But Where Is Everybody?

One lunchtime in 1950, the story goes, the physicist Enrico Fermi was chatting with colleagues about alien civilizations when he blurted out — "But where is everybody?" The galaxy is billions of years old and stars and planets abound, so if civilizations were common, someone should have reached us long ago — yet the sky is silent. This mismatch is called the Fermi paradox. The proposed answers run in several directions. Perhaps civilizations are exceedingly rare; perhaps on the road to civilization almost everyone trips over an enormous barrier, a Great Filter; perhaps a civilization destroys itself as soon as it gains technology; or perhaps the scale of distance and time is simply too vast, and the moments to meet keep missing one another; or perhaps someone is deliberately staying silent. The second experiment below shows the "timescale" explanation with your own eyes.

From here on, this is speculation

The latter part of this chapter is different in character from the physics chapters before it. The tail terms of the Drake equation and the answers to the Fermi paradox are open questions for which there is still almost no data to test against, with no settled answer. Here we treat them as a thought experiment that savors the uncertainty itself — guard against overblown conclusions, but do feel why the question "are we alone?" is so bewitching.

Key points

  • The Drake equation N = R⋆·f_p·n_e·f_l·f_i·f_c·L — a framework for estimating the number of communicating civilizations
  • Not an equation that hands you the answer, but a tool for organizing "what we don't know" into items
  • The tail terms (life, intelligence, technology, lifetime) rest on a sample of one — Earth → their values are highly uncertain
  • Fermi paradox: civilizations ought to be plentiful, so why not a single trace — "where is everybody?"
  • If the lifetime L is short, civilizations miss one another along the time axis and rarely meet
EXP.16 — The Drake EquationN ≈ —
1.5 /yr
0.90
0.40
0.50
0.10
0.20
10,000 yrs
Observe — N is the product of the seven values. The astronomical terms up front are relatively stable, but nudge the trailing f_l·f_i·f_c·L even slightly and N heaves by factors of a million. Toggle between 「Optimistic」 and 「Pessimistic」 — from the very same equation you get both "the galaxy teems with civilizations" and "we are alone."
EXP.16b — The Fermi Paradox: Why So Quiet
The horizontal axis is cosmic time (about 13.8 billion years). Many civilizations flare up briefly at their own moments and then vanish. The civilizations that overlap the instant the yellow 「Now」 line passes through are the ones we could meet. Raise the lifetime L so the bars grow longer, and watch the overlaps increase.
COSMIC SILENCEContemporary civilizations —
L = 10,000 yrs
L (the civilization lifetime) is the key variable behind the silence. If a civilization glimmers only briefly and disappears (short L), then across the galaxy's billions of years of time the probability that two civilizations overlap in the same era is vanishingly small — which is why the sky is quiet. Stretch L to the scale of hundreds of millions of years and the bars begin to overlap, and only then does a "meeting" become possible.
DEEP DIVE — Equations & History
The Drake EquationDrake, 1961
$N = R_\star \cdot f_p \cdot n_e \cdot f_l \cdot f_i \cdot f_c \cdot L$
R⋆ the galaxy's annual star formation rate · f_p the fraction of stars with planets · n_e the number of life-friendly planets per such star · f_l the probability that life arises on that planet · f_i the probability that life evolves into intelligence · f_c the probability it emits a detectable signal · L the length of time (years) such a civilization endures while sending signals. The first three terms are narrowed by observation, but the last four are essentially estimates, so the equation is closer to a list of questions than an answer.
The Great Filter · Why the Sky Is SilentGreat Filter
$P_{\text{contact}} = \prod_{k} p_k \;\ll\; 1 \qquad\Rightarrow\qquad N \approx R_\star \cdot L \cdot \prod_{k} p_k$
The road to civilization has countless gates p_k, and if the probability of any single one nears zero, the whole product collapses — this is the idea of the Great Filter. The frightening question is this: is that filter behind us (the birth of life and intelligence being a miracle we have already passed), or is it ahead of us (technological civilizations don't last long) and yet to come — no one knows.
HISTORY — Questions Toward the Silence
1950
Fermi, over a lunch conversation, asks "But where is everybody?" — the future Fermi paradox
1959
Cocconi & Morrison propose searching for alien signals via radio (the 21 cm hydrogen line)
1960
Drake, Project Ozma — the first serious SETI radio search begins
1961
The Drake equation is presented at the Green Bank meeting
1977
An Ohio radio telescope catches a powerful unidentified signal, the 'Wow!' signal (never re-observed)
Behind us, or ahead?

If the Great Filter lies behind us, that is good news — it means we have already cleared the hardest gate. But if simple life turns out to be easily found on Mars or an icy moon, that would mean the emergence of life was common, and then the filter must lie somewhere ahead of us — in the future of technological civilization — an ominous hint. This is why the Fermi paradox is more than idle curiosity: it makes us look back at ourselves.

← PREV
Exoplanet Hunting