How long do civilizations last? The Drake Equation, Bel‑Air mansions for everyone, & the Great Filter; or, where is everybody when $160 million a year incomes are normal? (Behind the paywall, at least initially, because I am not yet happy with this. But it is time to let it out, as the last class of the semester is today)…

The arithmetic is not comfortable. If you take the back-of-the-envelope Drake Equation seriously, plug in optimistic values for everything up through “planets that develop life,” and then assign only modest probabilities to the steps from life to technological civilization, you still wind up with an implication that ought to make you, me, and everyone else sit up straight.

Call:

• R* the rate at which the galaxy makes new stars: roughly one a year.

• fₚ the fraction of those stars that have planets: now, post–Kepler, we think that is about one.

• nₑ the number of “habitable” planets—rocky, temperate, capable of sustaining liquid water—per such star: again, order of magnitude one.

• fₗ the fraction of such planets on which life actually gets going: here biologists argue, but if we are at all optimistic about abiogenesis, we do not want to make this too small—again, I think about one, for replication, computation, variation, and then natural selection are processes in this universe, after all. (Others, notably Sandberg-Drexler-Ord, sharply disagree.)

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So then we get to the three scary terms:

• fᵢ, the fraction of life-bearing worlds that develop intelligent, tool-using, symbolic, culture-making creatures;

• f_c, the fraction of those that go on to industrialize and radiate their presence into space via radio, lasers, junk satellites, and whatever else;

• L, the length of time such a civilization is “visible” before it stops being so.

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If we are generous and say that fᵢ and f_c are each on the order of three percent—one in thirty life-bearing planets manages the jump to intelligence, and one in thirty intelligent species stumbles into an industrial revolution—then the expected number of visible civilizations N in the galaxy at any given moment is:

N = R* × fₚ × nₑ × fₗ × fᵢ × f_c × L.

If the early terms are all roughly one, and fᵢ and f_c multiply to something like 0.001, then N ≈ 0.001 × L.

Now plug in the observational fact that, as far as we can tell, there is no obvious galactic internet; no alien megastructures dimming their stars in recognizable ways; no steady, powerful beacons screaming “we are here” at us. In other words, N appears to be less than or equal to one, and the one is likely us.

If N ≤ 1 and N ≈ 0.001 × L, that implies L ≤ 1000.

That is the Fermi Paradox in one particular, very unforgiving form.

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