The Drake equation is one of those rare mathematical beasts that has leaked into the public consciousness. It estimates the number of extraterrestrial civilisations that we might be able to detect today or in the near future.

The equation was devised by Frank Drake at the University of California, Santa Cruz in 1960. He attempted to quantify the number by asking what fraction of stars have planets, what fraction of these might be habitable, then the fraction of these on which life actually evolves and the fraction of these on which life becomes intelligent and so on.

Many of these numbers are little more than wild guesses. For example, the number of ET civilisations we can detect now is hugely sensitive to the fraction that destroy themselves with their own technology, through nuclear war for example. Obviously we have no way of knowing this figure.

Nevertheless, many scientists have attempted to come up with a figure with estimates ranging from a handful of ET civilisations to tens of thousands of them.

Of the many uncertainties in the Drake equation, one term is traditionally thought of as relatively reliable. That is the probability of life emerging on a planet in a habitable zone. On Earth, life arose about 3.8 billion years ago, just a few million years after the planet had cooled sufficiently to allow it.

Astrobiologists naturally argue that because life arose so quickly here, it must be pretty likely to emerge in other places where conditions allow.

Today, David Spiegel at Princeton University and Edwin Turner at the University of Tokyo say this thinking is wrong. They’ve used an entirely different kind of thinking, called Bayesian reasoning, to show that the emergence of life on Earth is consistent with life being arbitrarily rare in the universe.

At first sight, that seems rather counterintuitive. But if Bayesian reasoning tells us anything, it’s that we can easily fool ourselves into thinking things are far more likely than they really are.

Spiegel and Turner point out that our thinking about the origin of life is heavily biased by the fact that we’re here to observe it. They point out that it’s taken about 3.5 billion years for intelligent life to evolve on Earth.

So the only way that enough time could have elapsed for us to have evolved is if life emerged very quickly. And that’s a bias that is entirely independent of the actual probability of life emerging on a habitable planet.

“In other words, if evolution requires 3.5 Gyr for life to evolve from the simplest forms to sentient, questioning beings, then we had to find ourselves on a planet on which life arose relatively early, regardless of the value of [the probability of life developing in a unit time],” say Spiegel and Turner. #

When you strip out that bias, it turns out that the actual probability of life emerging is consistent with life being arbitrarily rare. In other words, the fact that life emerged at least once on Earth is entirely consistent with it only having happened here.

So we could be alone, after all.

That’s a sobering argument. It’s easy to be fooled by the evidence of our own existence. What Speigel and Turner have shown is the true mathematical value of this evidence.

Of course, that doesn’t mean that we are alone; only that the evidence can’t tell us otherwise.

And if the evidence changes then so to will the probabilities that we can infer from it.

There are two ways of finding new evidence. The first is to look for signs of life on other planets, perhaps using biogenic markers in their atmospheres. The capability to do begin this work on planets around other stars should be with us in the next few years.

The second is closer to home. If we find evidence that life emerged independently more than once on Earth, then this would be a good reason to change the figures.

Either way, this debate is set to become a major issue in science in the next few years. That’s something to look forward to.

Ref: arxiv.org/abs/1107.3835: Life Might Be Rare Despite Its Early Emergence On Earth: A Bayesian Analysis Of The Probability Of Abiogenesis