Basis of the fermi Paradox
It is obviously difficult to comment on the sociology of a possible extraterrestrial civilization. A fact which seems nevertheless to be essential is that such a civilization would inevitably end up seeking to spread itself beyond its planet of origin. One can quote three reasons for which this objective seems natural:
Exploration consists of sending a mission towards other stars once the necessary technological level are reached. There is hardly a doubt that this must happens one day, whether it is by curiosity or for prestige reasons.
Colonization as this is the underlining goal of most terrestrial civilizations since the beggining of times, for religious reasons as well as for economic or political reasons. Unless we assume that other intelligent beings would be more reasonable than us, the temptation of colonization would then be probably widespread.
Lastly, the third reason, and surely the more important one is survival. The lifespan of a star in a stable form is limited. For example, in approximately 5 billion years, the Sun will cease to be the stable star which we know. It will become a red giant that will probably absorb the Earth. Under these conditions, sooner or later, space flights and interstellar flights will prove to be essential to the humanity's survival. Any extraterrestrial civilization will be one day or the other confronted with a similar problem.
Are we the only technologically advanced age of the Universe? The Drake's equation are based on multiple factors such as the fact that there are an estimated 250 billion stars in the Milky Way and 70 sextillion (7 x 10.22) in the visible universe.
Taking the historical values given by Drake and his colleagues in 1961:
Based on current lower estimates:
The current pessimistic fi parameter is much lower than the original Drake estimate due to the rare low radiation present on Earth.
Taking into account the original estimate, the result rise to 0.08 civilizations in our galaxy.
While these calculations result in N<<1, some observers believe this is still compatible with observations due to the anthropic principle:
no matter how low the probability that any given galaxy will have intelligent life, the galaxy that we are in must have at least one intelligent species by definition.
There could be hundreds of galaxies in our galactic cluster with no intelligent life whatsoever, but of course we would not be present in those galaxies to observe this fact.
Enrico Fermi assumed the existence of only one extraterrestrial civilization capable of intersidereal travel (at a speed lower than the speed of light). He assumed that this civilization would be interested in the conquest of the Galaxy and that it progressed by jumps, colonizing a planet during a few hundred or thousands years, then sending tens of vessels towards new conquests.
The problem is that after only a few million years, the whole of the Galaxy is under the influence of this extraterrestrial civilization (the low rate of travel being largely compensated by the exponential increase of the vessels number).
Simulations of an expansion show that it is possible for one civilization to colonize the whole galaxy in about 10 million years, a short time compared to the age of the Galaxy (ten billion years).
The question then arising, and famously formulated by physicist Enrico Fermi in 1950: since only one extraterrestrial civilization could spread in a relatively short time, how is it possible that that we never saw the extraterrestrial ones and that our radio telescopes never collected signals of suspect origin?