We define an advanced technical civilization as one capable of radio astronomy. This is, of course, a parochial definition because there may be countless worlds on which the inhabitants are accomplished telepaths or superb botanists but indifferent radio astronomers. We will not hear from them.
But it is possible to explore the great issue and make a crude estimate of the number of advanced technical civilizations in the Milky Way Galaxy. We should take many factors into consideration if we try to determine how many of them are there in deep space: the number of stars in the Milky Way Galaxy; the fraction of stars that have planetary systems; the number of planets in a given system that are ecologically suitable for life; the fraction of otherwise suitable planets on which life actually arises; the fraction of inhabited planets on which an intelligent form of life evolves; the fraction of planets inhabited by intelligent beings on which a communicative technical civilization develops; the fraction of a planetary lifetime graced by a technical civilization. We must not forget about evolutionary biology, organic chemistry, abnormal psychology, politics, history and many other factors.
Written out, an equation exists which defines a value and to derive it we must estimate each of these quantities. We know a fair amount about the early factors in the equation, the numbers of stars and planetary systems. We know very little about the later factors, concerning the evolution of intelligence or the lifetime of technical societies. In these cases our estimates will be little better than guesses.
Anyone can make his or her own choices and see what implications their alternative suggestions have for the number of advanced civilizations in our Galaxy (the very first equation is due to Frank Drake of Cornell).
By now, we know the number of stars in the Milky Way Galaxy, fairly well, by careful counts of stars in small but representative regions of the sky. It is a few hundred billion. Very few of these stars are of the massive short-lived variety that squander their reserves of thermonuclear fuel. The great majority have lifetimes of billions or more years in which they are shining stably, providing a suitable energy source for the origin and evolution of life on nearby planets.
There may be a billion planets on which technical civilizations now exist only in our Galaxy. Image © Megan Jorgensen