[natejenkins]

I think the Drake equation is worth mentioning here. It estimates the number of civilizations in the Milky Way Galaxy whose electromagnetic emissions are detectable (https://www.authorea.com/11048). Knowing some of the numbers involved, it can be reduced to approximately:

N ~= 2flfefcL

where fl is the fraction of habitable planets hosting life, fe is the fraction of life-bearing planets that develop an intelligent life-form, fc is the fraction of intelligent life-forms that decide to communicate, and L is the length of time a given civilization is transmitting "visible" communications. Taking ourselves as an example, L is already on the order of 100 years. The original estimates for these values were fl = 1, fe = 1, fc = 0.1-0.2, and L = 1000-100,000,000 (http://en.wikipedia.org/wiki/Drake_equation).