A Probabilistic Analysis of the Fermi Paradox

Abstract

The fermi paradox uses an appeal to the mediocrity principle to make it seem counter-intuitive that humanity has not been contacted by extraterrestrial intelligence. A numerical, statistical analysis was conducted to determine whether this apparent loneliness is, in fact, unexpected. An inequality was derived to relate the frequency of life arising and developing technology on a suitable planet in the galaxy, the average length of time since the first broadcast of such a civilization, and a constant term. An analysis of the sphere reached thus far by human communication was also conducted, considering our local neighborhood and planets of particular interest. We clearly show that human communication has not reached a number of stars and planets adequate to expect an answer. These analyses both conclude that the Fermi paradox is not, in fact, unexpected. By the mediocrity principle and numerical modeling, it is actually unlikely that the Earth would have been reached by extraterrestrial communication at this point. We predict that under 1 percent of the galaxy has been reached at all thus far, and we do not anticipate to be reached until approximately half of the stars/planets have been reached. We offer a prediction that we should not expect this until at least 1,500 years in the future. Thus the Fermi paradox is not a shocking observation, and humanity may very well be contacted within our species' lifespan.