After “Do you want to be the next Patrick Moore?” and “I’m a Capricorn”, the most common response I get when I tell people I work in astronomy is, “Do you think there is life on other planets?” Apparently, according to a talk given by Alan Boss to the American Association for the Advancement of Science in Chicago, the answer should be “Yes”:

If you have a habitable world that is sitting around for four, five or ten billion years around a star, how are you going to stop it from forming life? It’s like taking a refrigerator, unplugging it, shutting the door and then coming back a couple of months later; you’d be amazed to find what’s growing there. … That’s what life’s like. The fridge analogy may not be the same as the origins of life, but life is so tenacious, it’s hard to stop. If you had a planet sitting there at the right temperature with water for a million years, something’s going to come out of it.

The theory of spontaneous generation is alive and well, it seems.

But how many planets have actually formed life? Being extremely simplistic, we could express it as follows:

\[N_L = P(L | H) N_H\]

where \(N_L\) is the number of planets that have formed life, \(P(L\vert H)\) is the probability that a planet will form life, given that it is a habitable planet, and \(N_H\) is the number of habitable planets. So if there are 100 billion habitable planets in the Milky Way Galaxy, and \(P(L\vert H) = 0.01\), then we can expect that 1 billion planets in our Galaxy have formed life (whether they would still harbour life today is a different question).

\(N_H\) isn’t too difficult to guess, in principle. But if we want to estimate \(N_L\), we need to find \(P(L\vert H)\). This is more tricky.

One approach is to create life in the laboratory, and then estimate how long it would take for the same processes to take place outside the laboratory. Now, I freely admit that I know almost nothing about current research in this area, except that life has not yet been created in a laboratory. And until it has, we need to proceed in a different way.

The other approach is to estimate \(P(L\vert H)\) given what we know about the existence of life on Earth. Let’s assume for the moment that we know \(t_L\), the time it took for life to appear on Earth. This is generally estimated to be perhaps a few hundred million years. Then we assume that \(t_L\) for Earth is fairly typical for habitable planets, and then it’s pretty easy to find the result we’re looking for.

But there are a few serious (really serious!) problems with this approach. For example:

  1. Who says that \(t_L\) is a fairly typical length of time? Why is life arising on Earth after however many million years necessarily typical? Maybe it’s extremely unusual. We could even ask this: What part of “planet Earth formed life after \(t_L\)” is inconsistent with life being so improbable that it would not have arisen more than once in the entire Universe?
  2. How are we supposed to factor out our own existence? This is the issue of anthropic bias in the Drake equation. Why is it reasonable to assume that Earth is a typical habitable planet? Was it chosen at random? Of course not. So when we find \(t_L\) for Earth, that is not \(t_L\) for any old habitable planet, but \(t_L\) for a habitable planet that is home to intelligent life. Why should \(P(t_L)\), the probability distribution for \(t_L\) for habitable planets in general, be the same as \(P(t_L\vert I)\), the probability distribution of \(t_L\) for habitable planets that are (or will become) the home for intelligent life forms, such as our own?
  3. How are we supposed to know that the Earth has ever formed life anyway? Many people believe that life was created by a supernatural being. What scientific experiment could we conduct to distinguish between the two hypotheses, H1, “Life on earth arose from non-living substances by ordinary physical processes”, and H2, “Life on earth was specially created by a divine being”? In order to put a figure on \(P(L\vert H)\), we have to assume H1, but this not established empirically.

In summary, while there are often good reasons to be optimistic about the number of planets that support life (e.g., to gain funding and/or publicity for your pet project), I would err on the side of caution and argue that we don’t have a clue - scientifically - how many planets have formed life.