TravisTR points out some new research that aims to update and supplement the Fermi paradox — the idea that if intelligent life was as common as we expect, we should have detected it by now. The academic paper (PDF) from scientists at the National Technical University of Ukraine is based on the idea that civilizations can't expand forever on their own. The authors make the assumption that an isolated civilization will eventually die out or go dark through some other means, which leads to some interesting models of intergalactic colonization. "In certain circumstances, however, when civilizations are close enough together in time and space, they can come into contact and when this happens the cross-fertilization of ideas and cultures allows them both to flourish in a way that increases their combined lifespan. ... Bezsudnov and Snarskii say that for certain values of these parameters, the universe undergoes a phase change from one in which civilizations tend not to meet and spread into one in which the entire universe tends to become civilized as different groups meet and spread. Bezsudnov and Snarskii even derive an inequality that a universe must satisfy to become civilized. This, they say, is analogous to the famous Drake equation which attempts to quantify the number of other contactable civilizations in the universe right now."