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Since any alien radio message we might receive would have been lumbering through space at the finite speed of light — and since space is big — many folks assume that the signal must have been sent “millions of years ago.” The obvious corollary is that the alien broadcasters may have long since cashed in their chips.

My response to this melancholy logic is to note that most of the star systems examined by SETI scientists are less than a few hundred light-years away. So a signal from one of these wouldn’t be a million years old. And since a few centuries isn’t really much time, I usually offer an analogy: It takes the postal service three days to deliver a letter from my aunt. But it’s unlikely that she died in the interim because three days is brief in comparison to the average lifetime of aunts.

The new paper offers a similar argument, mathematically elaborated. The authors assume a simple scenario in which extraterrestrial societies spring up at random places in the galaxy at random times, and that they broadcast their talk shows (or whatever) into space. You can imagine these transmissions spreading like ripples across the plane of the Milky Way, reaching more and more star systems as time goes on.

A further assumption is that at some point — due to unspecified events (including, one presumes, self-destruction) — the aliens’ transmitters go silent. So each alien society’s radio signature is like an expanding doughnut, with an outer boundary representing the moment their transmissions start and an inner boundary defined by the moment they stop.