After all, no matter even if life, and subsequently intelligent life, is statistically unlikely, its existence elsewhere is statistically certain. Further, since it is extremely unlikely that humans are the first intelligent life to emerge in our galaxy, then the seeming absence of intelligent life is a puzzle that needs explaining.
A decade later, Frank Drake formulated an equation supplying the terms that must be considered in contemplating how many extra terrestrial intelligences (ETI's) there might be.
In successive decomposition, it goes something like this: the number of stars, the fraction that have planets, the fraction of those that have habitable planets, the fraction of them that go on to develop life, the fraction of life bearing planets that yield intelligent life, the fraction that release detectable signals into space, and the duration those signals are emitted.
Of all those parameters, only the number of stars is approximately known, is large enough so that even the multiplicative combination of very low probabilities means the existence of ETI's is certain.
There are two potential resolutions to the Fermi paradox.
The first wasn't even remotely predictable in the 1950s and 1960s. At the time, radio and TV signals were often broadcast from 100,000 watt transmitters. What no one could predict then is a near certainty within a couple decades: our planet going dark. The combination of low power satellite transmitters, cellular networks and near-pervasive landline networks have rendered high power transmitters all but obsolete.
Now that alone doesn't eliminate the Fermi paradox, because even if other ETI's don't radiate enough energy to be detectable is of no real help. The likelihood that even one ETI has developed long before we did is a near certainty; therefore, such a civilization should long ago have pervaded the galaxy.
That, in turn, requires a more or less heroic assumption — that moving even anything more than trivial masses to other stars is possible.
Taken in combination, it is possible that the galaxy is littered with ETIs that will be forever confined to their stars, and undetectable from every other ETI.
But what if the certainty the Drake Equation predicts is? What if there has been widespread optimistic presumptions about some of its elements greatly overstating their likelihood?
The problem with the Drake equation is that it provides discrete estimates to each of the factors.
To quickly see the problems point estimates can cause, consider the following toy example. There are nine parameters (f1, f2, . . .) multiplied together to give the probability of ETI arising at each star.
Suppose that our true state of knowledge is that each parameter could lie anywhere in the interval [0, 0.2], with our uncertainty being uniform across this interval, and being uncorrelated between parameters.
In this example, the point estimate for each parameter is 0.1, so the product of point estimates is a probability of 1 in a billion. Given a galaxy of 100 billion stars, the expected number of life-bearing stars would be 100, and the probability of all 100 billion events failing to produce intelligent civilizations can be shown to be vanishingly small: 3.7 × 10−44. Thus in this toy model, the point estimate approach would produce a Fermi paradox: a conflict between the prior extremely low probability of a galaxy devoid of ETI and our failure to detect any signs of it.
Instead, the authors account for our uncertainty by applying a Monte Carlo simulation — randomly assigning a probability in the range [0, 0.2] for each factor, then combining the values for each of the factors.
More than 22% of the simulations produce a galaxy devoid of even one ETI.
But wait, there's more.
If, instead of assigning point probabilities to each factor, model each factor as itself a combination of factors. Take the existence of life as an example. Abiogenesis is a transition from non-life to life that "… occurs at some rate per unit time per unit volume of a suitable prebiotic substrate." Using informed guesses about rate, volume, protein folding, etc, yields a range of estimates for the existence of life on suitable planets spanning 20 orders of magnitude. (There is much more to this than I am presenting, btw.)
Applying uncertainty distributions reflecting current knowledge to each of the factors in the Drake Equation, what do you suppose the likelihood is that we are alone, not just in the galaxy, but in the entire observable universe?
I sure didn't see that coming.