## Wednesday, February 10, 2016

### Mathematical Argument for the Likelihood of Extraterrestrial Life

Great news from the Kepler Space Telescope data: astronomers are finding lots of planets in the habitable zones of our neighbor stars. So many in fact, that if you extrapolate to the entire universe, there may be, depending on who you ask, 5x10^19 habitable planets (i.e. rocky, with temperatures that would allow for liquid water). Intuitively, one would think it fairly certain that there are other planets with life given this massive number. To support this intuition, one can make the following mathematical argument:
Suppose for simiplicity there are 10^19 habitable planets in the universe.
And let L represent the chances that life of any sort forms on a habitable planet.
If L is 1/10^18 or better, then there is almost certainly life on other planets (for instance, if L = 1/10^18, the chances of exactly one planet (and no more) are 0.05%) (based on the Poisson formula).
If L were by sheer coincidence exactly 1/10^19 then you might actually have exactly one planet with life (i.e. earth), but even then the chances of exactly one planet are 1/e, or appx 36% (again based on the Poisson formula) (for the mathematically inclined reader, this could also be represented as lim (as x-->infinity) of (x-1/x)^(x-1) which, beautifully, equals 1/e).
If L is 1/10^20 or worse, then the chances of any planets with life becomes increasingly tiny. (even if L = 1/10^20, chances of life having formed anywhere at all would be 10%, and if L = 1/10^21, then chances are 1%).

The fact that life formed soon after Earth's temperatures became habitable means that L is likely WAY better than 1/10^19 (to give you an idea, there are appx 10^19 grains of sand on Earth).
A couple interesting articles:

1) It's actually possible that we could identify life on other planets within the next ten years by searching for "biosignatures" in planets' atmospheres (looking for combinations only likely to occur w/ life)

2) Possible alien megastructure could explain some unusual data from a particular star, discovered by the Kepler Space Telescope: