# On Extraterrestial Life

I used to think that the interest astronomers seeking life on other planets have for exoplanets in the “Goldilocks zone” that can sustain liquid water, or for signs of water in this solar system, or for signs of complex organic molecules outside Earth, that this interest is misguided. After all, they’re looking for the materials that are the building blocks of life on this planet, but it’s perfectly possible that life on other planets is made out something completely different, such as having ammonia as a substrate or having silicon as the core constituent of complex molecules (and these are relatively mild modifications, they’re building life on the same general plan and just substituting one material for another). Perhaps searching for Earth-like life is the best scientists can do given the absence of any other information on what to expect aliens to be like, but we shouldn’t think these clues are actually the right guides for finding life on other planets.

There are two reasons to think that intelligent life is rare across the universe. The first is Fermi’s paradox: Across the extremely large space we can observe, we can’t find any signs of life originating outside Earth. This is especially a strong argument if you think that a significant fraction of intelligent life will in the long run develop civilizations more advanced than ours that span stars and galaxies, and leave easy-to-detect large-scale traces. The second reason is that in the one case that we know of of the creation of intelligent life, it was a long, complex process. Even if each individual step of our evolution and historical development seems to be scientifically explicable, the combined chance that all of these steps will occur togethers seems much less likely.

Now I’ll express the second reason more mathematically. I want to emphasize that although I am using mathematical language, this calculation will not be precise at all. It cannot be, given how much we know. The purpose of the mathematics here is not to give any sort of quantitive estimate, but to more clearly express a certain qualitative point.

Imagine we divide the development of intelligent life into $n$ steps and these steps have probabilities $p_0, p_1, \dots p_{n-1}$ respectively. For example, these steps could be “first self-replicating object”, “development of eukaryotes from prokaryotes”, and “development of a nervous system”. Each of these probabilities is less than one, perhaps only slightly smaller. The combined likelihood of intelligent life is the product $p_0 p_1 \dots p_{n-1}$. Even if none of the $p_i$s is very small, multiplying them can result in an incredibly small probability. If each $p_i$ is around the same value the probably decreases exponentially in $n$, so tiny values like $10^{-200}$ are not out of the question.

Next, consider the development of different fundamental building blocks, for instance using ammonia as a substrate instead of water. Dividing this process into the same $n$ steps, there is a different set of probabilities $p'_0, p'_1, \dots, p'_{n-1}$. The ratio of water-based lifeforms and ammonia-based lifeforms is given by $\frac {p_0 p_1 \dots p_{n-1}} {p'_0 p'_1 \dots p'_{n-1}}$, which can be factored as $\left( \frac {p_0} {p'_0} \right) \left( \frac {p_1} {p'_1} \right) \dots \left( \frac {p_{n-1}} {p'_{n-1}} \right)$. At each step we expect the probability $p_i$ the step will occur with water-based life to be close to the probability $p'_i$ it will occur with ammonia-based life, and so usually $\frac {p_i} {p'_i}$ will be close to $1$. However, some of these probabilities will not be so close, and accumulating these ratios in the product $\left( \frac {p_0} {p'_0} \right) \left( \frac {p_1} {p'_1} \right) \dots \left( \frac {p_{n-1}} {p'_{n-1}} \right)$, I expect the discrepancy will diverge away from one, becoming either very large or very small. By the theory of random walks you can estimate (very loosely!) that the ratio will be roughly exponentially in the square root of $n$. For example, if you think the total probability of life forming is less than $10^{-11}$ per star, the order of magnitude needed to ensure there is no other life in this galaxy, it seems unlikely that the total ratio will come out within $100$ of one, so it will likely be either greater than a hundred or less than one in a hundred.

In other words, either there are at least hundred intelligent lifeforms with a water-based biology for every one with an ammonia-based biology, or there are at least a hundred intelligent lifeforms with an ammonia-based biology for every one with a water-based biology. Of course, determining the individual probabilities $p_i$ or $p'_i$ is far beyond the abilities of current science, so we cannot tell which kind is dominant just using a priori reasoning. However, with this picture in mind, the small fact that our life is water-based becomes more significant: If we believe that life on Earth is a representative sample of how advanced life develops anywhere in the universe, then our observation that our life is water-based is a hundred times more likely if water-based life is dominant than if ammonia-based life is dominant. This leads to the prediction that if we ever find life on other planets it will probably have a water substrate, and that the more advanced life evolves the more likely it is to be water-based.

To put it in another way, our uncertainty on the commonness of life is logarithmic: We don’t know if it’s closer to $10^{-3}$ per star system or $10^{-200}$ per star system, and it could be anywhere in between. So if there’s more than one process that could produce life, what are the chances that both processes would work with a remotely similar frequency, and that the universe is filled with both kinds of life? This phrasing makes it clear that my argument does not depend on both processes being divided into a similar series of steps, as I described it above. In fact, if another process for forming life is so utterly different that our own that it can’t even be divided into the same steps, then it is even less likely that the frequency of this process would be the same as the one we’re familiar with.

Note that this argument applies most strongly to differences that affect “filter steps”, i.e., steps in the development of complex life that are particularly unlikely and so are responsible for life’s current rareness (this term “filter step” is inspired by the established term “The Great Filter“, but I don’t want to imply that there is only one such filter). That’s why I don’t predict that aliens will look like humans with rubber foreheads and listen to the same music as we do: I don’t expect the fine details of the species’s body plan and musical tastes to substantially affect its probability of making contact with humans. If we had a better idea which developmental steps are strongly filtering then we would also have a more accurate idea which steps would be most similar across planets. For example, one hypothesis I particularly like is that most of the filtering occurs in the creation of the first self-replicating object — after all, the necessity of a highly specific genetic sequence to catalyze the replication of its own genetic code lends itself naturally to exponentially small probabilities. If this hypothesis is correct, then you can expect all life to have formed in pretty much identical conditions, with the first self-replicator being very similar in all planets. After that, evolution can go free and could be a larger diversity of different pathways all leading to intelligent life.

Finally, I want to re-emphasize that I am far from certain of this conclusion; there’s no way to compensate for the absence of any real information on extraterrestrial life, and my argument rests on many explicit and implicit assumptions. For example, there is little evidence that life on Earth is representative of life elsewhere.