Recently it has been proposed that human civilization is the only advanced civilization in the universe. This seems to be agreed upon by nobel prize winners, elite professors and academia in general (see Gribbin in particular (Are we Alone?)). According to Gribbin this is something we have to get used to.
Well there is something that these nerds have to get used to:
Human civilization is NOT an advanced civilization. It might be a dead-end, destructive and demented civilization but it is not at a general level of description an advanced civilization.
Therefore the very assumption that scientists base there arguments on is patently false. Gribbin refers to the "Fermi paradox" if there should be many advanced civilizations then where is the evidence (where are they?). I replace this with the "smelly pair of sox" wherein truly advanced civilizations would: 1. Do everything they can to avoid human civilization, 2. Do everything they can to avoid being detected by civilization, 3. Do everything they can to make sure human civilization tends to its destruction.
The ONLY civilization that human civilization might make contact with is a civilization just as dead-end, destructive and demented as itself. And it couldn't happen to nicer people.
But this leaves open the question of how many advanced civilizations there could be in the universe.
Most scientists base their estimates on empirical data. Counting the number of sun-like suns, galaxies, exo-plantets and so on. These numbers can then be input to the famous Drake equation which takes these estimates and outputs the estimated number of earth-like planets. But there is no general agreement on what numbers to put in.
Of course the SETI project is based on the assumption that there may be signal-producing and signal-detecting outside of our solar system. But so far none have been detected.
I now put forward another approach to estimating the number of advanced civilizations in the universe. Take this proposal with a grain of salt because it is only at a prototype level and is (the method) not at all used in science.
The proposal is based on two theorems: 1. The "level of description" theorem of E.Rosch, the brilliant American psychologist, and 2. The "secretary theorem" of probability.
The secretary theorem imagines a secretary who has N letters and N envelopes and puts the letters in the envelops randomly. Incredibly no matter how large N is the probabilities of 1,2,3,4,... letters reaching the correct address is the same. More importantly this theorem is related to the natural constant e (and e is related to pi, see Anarchism and a new math identity, Portland Indymedia)).
The work of Rosch shows that the level of description of a category is important in understanding the cognitive processes of reasoning and of perception. This relates to the Drake equation because stars, planets, galaxies, moons, atmospheres and so on can only be understood at a particular level of description. Change the level and the numbers input to the equation also change.
I propose that given the "correct" level of description, the number of "advanced civilizations" can be estimated using the secretary theorem. This means that (leaving aside the "now" problem with regard to the size of the universe) there should be, in all probability, between 2 and 5 advanced civilizations in the universe.
The dynamics of this proposal remains to be calculated. It means that as the universe evolves levels-of-description are somehow matched to their physical counterparts (that is, letters are assigned to envelopes). Much work would be needed (and creativity) to make this hypothesis credible.