Now, I have not read this book, and therefore I am not fully versed in their arguments. I plan to read the book and make a more detailed argument, but I wanted to lay down my base hypothesis first. Also, Wikipedia does an ok job at summarizing their argument.
So, before we get to their equation, let's look over some data:
- It is estimated that there are 200-400 billion stars in the Milky Way Galaxy.
- It is estimated that there are about 100 billion (1011) galaxies in the universe.
- Galaxies tend to contain between ten million (107) and one trillion (1012) stars.
Now let's make some guesses. In the famous Drake Equation, it is estimated that half of all stars will have planets. So that gives us a more manageable number of 1010 stars with planets. For the sake of argument, let's say that our solar system is fairly typical, and maybe the average number of planets in a solar system is around 6. I think I am being generous to the Rare Earth-ists here, as a solar system could easily have tens of planets, not to mention life-supporting moons. That gives us 6 * 1010 planets in the universe. Disregarding the Drake estimate of 2 planets per star supporting life, let's say that, I don't know, 1/8 of planets support complex life.
So, we have finally arrived: 60,000,000,000 planets could support life. Sixty billion seems to be far from the estimate of 1. If my estimates have an error of 99.9%, there would still be 7,492,500,000 planets supporting complex life. Of course, some of that may have died off already, and most (statistically) we would never be able to find. (If you read the numbers above, and you're good with visualization, you should already have realized the size of the haystack in which we are searching for a proverbial, uh, 60 billion needles.)
As I have said, I will in fact be making a more detailed argument later. However, I assert that the vast immensity of the universe makes the Rare Earth theory extremely unlikely, statistically. And I haven't even broached the subject of carbon-based vs. non-carbon-based life or the general assumptions of what a 'life-supporting planet' requires.
QED.