I'm late to posting this, but it's important enough to be worth sharing anyway: Sandberg, Drexler, and Ord on Dissolving the Fermi Paradox.

(You may recognize these names: Toby Ord founded the effective altruism movement; Eric Drexler kindled interest in nanotechnology; Anders Sandberg helped pioneer the academic study of x-risk, and wrote what might be my favorite Unsong fanfic)

The Fermi Paradox asks: given the immense number of stars in our galaxy, for even a very tiny chance of aliens per star shouldn't there should be thousands of nearby alien civilizations? But any alien civilization that arose millions of years ago would have had ample time to colonize the galaxy or do something equally dramatic that would leave no doubt as to its existence. So where are they?

This is sometimes formalized as the Drake Equation: think up all the parameters you would need for an alien civilization to contact us, multiply our best estimates for all of them together, and see how many alien civilizations we predict. So for example if we think there's a 10% chance of each star having planets, a 10% chance of each planet being habitable to life, and a 10% chance of a life-habitable planet spawning an alien civilization by now, one in a thousand stars should have civilization. The actual Drake Equation is much more complicated, but most people agree that our best-guess values for most parameters suggest a vanishingly small chance of the empty galaxy we observe.

SDO's contribution is to point out this is the wrong way to think about it. Sniffnoy's comment on the subreddithelped me understand exactly what was going on, which I think is something like this: