Once we can see them, it’s too late

Abstract

We study a model of the growth of civilizations across the universe. We assume that civilizations expand at a constant speed, approaching the speed of light, and reproduce in a way that their new offspring are uniformly distributed over the surface of a sphere. We show that almost all civilizations would eventually become stuck inside spheres, and would asymptotically fill an increasingly smaller part of the sphere as time goes by. This raises the question, why don’t we see signs of past civilizations? We propose that, to avoid being stuck in spheres, civilizations must be sufficiently advanced to be able to change their direction of expansion, e.g. by using wormholes, or must be willing to slow down and to merge with other civilizations, which might be possible given the (nearly) infinite amount of time available. – AI-generated abstract.