After a 6+ month hiatus driven by grad school and personal projects, I am finally able to continue my sequence on astrobiology. I was flabbergasted by the positive response my last post got, and despite my status as a biologist with a hobby rather than an astronomer I decided to take a more rigorously mathematical approach to figuring out our biosphere's position in space and time rather than talking in generalizations and impressions.
Post is here: http://thegreatatuin.blogspot.com/2016/03/space-and-time-revisited.html. Seeing as this post is an elaboration on the last one, I am posting a link rather than reproducing the text.
To summarize, I found some actual rigorous observational fits to the star formation rate in the universe over time and projected them into the future. These fits show the Sun as forming after 79% of all stars that will ever exist, and that 90% of all stars that will ever exist already exist. This makes sense in the light of recent work on 'galaxy quenching' - a process by which galaxies more or less completely shut off star formation through a number of processes - indicating that the majority of gas in the universe probably won't form stars if trends that have held for most of the history of the universe continue to hold. It relies heavily on analysis I began in comments on this site a few months ago.
I then lift two distinct metallicity normalizations from a paper that was making the rounds here a while back ("On The History and Future of Cosmic Planet Formation"), in an attempt to deal with the fact that that is a measurement of STAR formation, not terrestrial-planet-with-a-biosphere formation. Depending on which metallicity normalization you use (and how willing you are to take a couple naive assumptions I make in order to slot the math that is too complicated for me to comment on on top of my star formation numbers) the Earth shows up as forming after either 72% or 51% of all terrestrial planets.
These numbers are remarkable in how boring they are. We find ourselves in an utterly typical position in planet-order, even if I am wrong by quite a bit. We are not early. Of interest to many here, explanations of the so called Fermi paradox must go elsewhere, into the genesis of intelligent systems being exceedingly rare or the genesis of intelligent systems not implying interstellar spread.
Now that I seem to have a life again, I will be getting back to my original plan next, talking about our own solar system.