I posted a theory sometime back.
The assumptions are:
-There is only one intelligent lifeform in our universe, ie us.
-Life around any star is infinitely difficult to form.
-There is an infinite number of star systems in the universe.
The results are:
-Probability of life happening in our universe is 0.64.
-Probability we are in a universe where there are 2 or more lifeforms is 0.264.
-These numbers are all lower bounds.
If we consider only the stars around our solar system out to a distance of 20 light years, there are 108 stars, some of them in multiple systems, ie binarys, trinaries, etc. Of these, 5 are G-type stars, the most similar to our sun. Alpha Centauri A, one of the G-types, is in a trinary system. Because such systems are complex, we discount them. Effectively, there are 4 G-type stars within 20 light years of us.
Based on the mathematics at the bottom of this post, if we want a 0.1 chance of finding life within the 108 stars closest to us, there must be 1 lifeform per 1025 star systems. If we loosely assume that all G-type stars have life, we see that the odds are indeed very good within our 20 light year radius (0.037 vs 0.000976 indicated by mathematics).
For an ealier proof of the mathematics, please see:
http://www.singastro.org/viewtopic.php?t=288
A slightly revised version can be found at:
http://www.sciforums.com/showthread.php ... genumber=2
Some later developments not included in the text linked above:
p(another intelligent lifeform in the universe) = [(x-1)/x]^(x-1)
where x represents the number of star systems.
As we let x tend to infinity, the probability tends to a value of 0.64.
It's all better than formulating tons of equations and later on finding some new information that denies all that was done...
"The universe is composed mainly of hydrogen and ignorance."