Alien Civilizations - How Do the Odds Stack up?

A journal published by the International journal of Astrobiology puts the number of advanced and stable alien civilizations to be atleast 361 in our very own Milkyway. The simulation run by the publishing body relies on our current working knowledge of the stars and planetary systems as well as the accepted viability and ability of primitive life to evolve into an advanced and intelligent form. If it is also assumed that life can seed out from one planet to another through organic molecules etched into asteroids, the number jumps to around 40000 intelligent civilizations!

The drake equation is one of the key components in computing the number of alien civilizations cohabiting the galaxy:

where:

N = the number of civilizations in our galaxy with which communication might be possible;

and

        R^* = the average rate of star formation per year in our galaxy

f_p = the fraction of those stars that have planets

n_e = the average number of planets that can potentially support life per star that has planets

f_ℓ = the fraction of the above that actually go on to develop life at some point

f_i = the fraction of the above that actually go on to develop intelligent life

f_c = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space

L = the length of time such civilizations release detectable signals into space.

Given the vast expanse of the universe, an entire civilization could come and pass before we can detect anything using the conventional radio frequencies. The propagation of electromagnetic waves is governed by the inverse square law, meaning when the radio waves reach the nearest star system, the Alpha Centauri, the intelligent life forms there won't hear more than fickle ripples against the background radiation. This means that we'll need an extremely powerful, intelligible transmission directed at us from the alien world  for us to know with certainty that we're not alone. 

Alright, lets take the distances involved into perspective and see how plentiful life really is out there. take the number of 361 civilizations at face value and assume simultaneous existence of all these life forms, including us. Look up wikipedia and you see that the volume of the Milkyway is roughly 23000 billion light years (23 trillion). Lets remove the inhospitable region of the galaxy core and the very cool spiral edges and we're left with a 'lukewarm' region of livable space, around 250 million light years. This yields a civilization density of 690,000 lightyears / civilization. Now if you know anything about volumes, this gives a radial separation of around 630 light years between each neighbor. This means the our neighboring brethren should have started signalling us in the early 13th century for us to hear anything now!   You might also be interested in: Eavesdropping on Aliens: Could changing channels tune into Alien Civilizations?