This is a rough estimate of the number of alien civilisations in our galaxy, obtained from the Drake equation. Last week I went to a Institute of Physics local branch general talk, by Alok Jha. He quoted this equation. The Drake equation is clearly a bit of a guess, but it is an interesting way to think about the question of whether we are alone in the galaxy, and if we are not alone, is it likely that aliens will signal us, or even invade us.
The Drake equation assumes that the number of alien civilisations on planets in our galaxy is the product of a number of factors. It can be broken down into two bits. First, we can ask what is the rate at which planets that can support life are formed. Call that RPL. In the Drake equation this is expressed as
RPL = R * fP *ne
where R is the rate at which stars form in our galaxy, fP is the fraction of these stars which have planets, and ne is the average number of planets in solar systems with planets.
Then, N, the number of civilisations that could drop us a line is
N = RPL * fL * fI * fC * L
where fL is the fraction of planets where life can evolve, fI is the fraction of cases where when life evolves, that it evolves intelligence, and fC is the fraction of cases where when intelligent life evolves, that it develops the ability to emit signals (e.g., radio waves) into space. L is the length of time a communicating civillisation exists.
So we have 7 numbers, most of which we can just guess. But guessing can be fun, and I guess the point is that R is estimated as around 7 per year. This may not sound much, but over billions of years, this adds up. Also, we now know that planets are common, over 800 exoplanets are currently in the exoplanet encyclopedia.
So our best guess at the product of all these factors is of order 100 million civilisations that could potentially drop us a line. Of course our galaxy is very large, so even if it is accurate, the nearest one would probably be a long way away. Or this estimate could be way off, but it is fun to think about these things.