Well, the universe supports life here on this planet, but there's a puzzling lack of alien life for as far as we can see.
The anthropic principal suggests that, in some space of all possible universes, the universe we are in lies in some small life-supporting region. If we were to describe the physical laws of the universe, we would be able to randomize some number of bits and still lie in that region -- change some physical constants by small amounts, say. The number of remaining bits tells us how much information is required to say "a universe that can contain life".
There is also some number of bits required to pick a point within an area and period of time in this universe containing intelligent life.
It occurs to me that these two quantities should be of approximately of the same order of magnitude. Thus, if the physical laws are very complex, we would expect intelligent life to be very rare, whereas if the laws are simple, we would expect intelligent life to fill the universe.
This idea could probably be refined to give a rough estimate of, say, the distance to the nearest alien life from earth.