When Arthur C. Clarke tells me that something is terrifying, he’s got my attention. After all, since boyhood I’ve not only had my imagination greatly expanded by Clarke’s work but have learned a great deal about scientific methodology and detachment. So where does terror fit in? Clarke is said to have used the term in a famous quote: “Two possibilities exist: either we are alone in the Universe or we are not. Both are equally terrifying.” But let’s ponder this: Would we prefer to live in a universe with other intelligent beings, or one in which we are alone?

Are they really equally terrifying? Curiosity favors the former, as does innate human sociability. But the actual situation may be far more stark, which is why David Kipping deploys the Clarke quote in a new paper probing the probabilities.

Working with the University of Sydney’s Geraint Lewis, Kipping (Columbia University) has applied a thought experiment first conceived by Edwin Jaynes to dig into the matter. Jaynes (1922-1998) was a physicist at Washington University in St. Louis, MO. Through his analysis of probabilities (statistical inference was a key aspect of his work), Jaynes laid a framework that he analyzed with rigor, one that was later tweaked by J. B. S. Haldane, a man who had his own set of famous quotes, including the familiar “Now, my own suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose.” This seems to be a day for good quotes.

Imagine a lab bench on which are a large number of beakers filled with water, roughly the same amount in each. The goal is to find out whether an unknown chemical will dissolve within these flasks. Remember, each flask contains nothing but water, all of it from the same source. You are to pour some of the chemical into each.

The logical expectation is that the unknown compound will either dissolve in each flask or not. That result should hold across the board: What happens in one flask should happen in all. What we would not expect is for the compound to dissolve in some flasks but not others. You can see what this would imply, that the tiniest variations in temperature and pressure could swing the outcome either way. In other words, as Kipping and Lewis note, it would imply that the conditions in the room and properties of the compound were “balanced on a knife edge; fine-tuned to yield such an outcome.”

Fine-tuning is telling us something: Are the conditions in the room so perfectly set that there is some kind of hair-trigger threshold that some but not all of the flasks can reveal when the chemical is added? How could that happen? Jaynes went about exploring this gedankenexperiment (and many others – he would become known as one of the founders of so-called Objective Bayesianism). The beauty of the Kipping and Lewis paper is that the authors have applied the Jaynes experiment, for the first time, I think, to the cosmos. Thus instead of beakers of water think of exoplanets, and liken the dissolving of the chemical to abiogenesis. From the paper:

Consider an ensemble of Earth-like planets across the cosmos – worlds with similar gravity, composition, chemical inventories and climatic conditions. Although small differences will surely exist across space (like the beakers across the laboratory), one should reasonably expect that life either emerges nearly all of the time in such conditions, or hardly ever. As before, it would seem contrived for life to emerge in approximately half of the cases – again motivated from the fine-tuning perspective.

Image: This is Figure 1 from the paper. Caption: In the gedankenexperiment of attempting to dissolve an unknown compound X into a series of water vessels, Jaynes and Haldane argued that, a-priori, X will either dissolve almost all of the time or very rarely, but it would be contrived for nearly half of the cases to dissolve and half not. The function plotted here represents the Haldane prior (F−1(1 − F)−1) that captures this behaviour. Credit: Kipping and Lewis.

The authors argue that the idea can be extended beyond abiogenesis to include the fraction of worlds on which multicellular life develops, and indeed the fraction of worlds where technological civilizations develop. Now we’re pondering a universe that is either crammed with life or devoid of it, with little room to maneuver in between. Which of these is most likely to be true? Can we connect this with the Drake Equation, that highly influential statement that so defined SETI’s early years in terms of the factors that influence the number of communicating technological civilizations in the galaxy?

Rather than extending the variables of the Drake Equation, a process that could go on indefinitely, the authors choose to distill it using what they call a ‘birth-death formalism.’ The result is a ‘steady state’ version of the Drake Equation (SSD).

The balance between birth and death is crucial. A civilization emerges. Another one dies. Think of the first six terms of the Drake Equation as representing the birth rate, while the final term, L, represents the death rate. The authors suggest that problems with the original equation can be resolved by paring it into this form, producing a new term F, which stands for the ‘occupation fraction’; i.e., planets with technological civilizations, a term arrived at through the ratio of births to deaths per year. Thus in the case of a galaxy filled with technological societies, F would come out close to 1. The paper fully develops how the new equation is reached but the end result is this:

Where λBD is the birth to death ratio. The particulars of how this is derived are fascinating, and can also be explored in Kipping’s Cool Worlds video.

Now we have something to work with. A galaxy in which there are few births compared to deaths is one that is all but empty. Start adjusting the ratio to factor in more civilization births and the galaxy begins to fill. Continue the adjustment and the entire galaxy fills. The S-curve is a familiar one, and one that puts the pressure on SETI optimists because it seems evident that not all stars are occupied by civilizations.

Assuming that F does not equal 1 or come close to it, we can explore the steep S-curve as it rises. Here NT refers to the total number of stars. From the paper:

This is what we consider to be the SETI optimist’s scenario (given that F ≈ 1 is not allowed). Here, F takes on modest but respectable values, sufficiently large that one might expect success with a SETI survey. For example, modern SETI surveys scan NT ∼ 103-104 targets… so for such a survey to be successful one requires F to exceed the reciprocal of this (i.e. F ≥ 10−4), but realistically greatly so (i.e. F ≫ 10−4 ) since not every occupied seat will produce the exact technosignature we are searching for, in the precise moments we look, and at the power level we are sensitive to. This arguably places the SETI optimist is a rather narrow corridor of requiring N−1T ≪ λBD ≲ 1.

That narrow corridor is the SETI fine-tuning problem. The tiny birth-death ratio range available in this ‘uncanny valley of possibility’ is all the room to maneuver we have for a successful detection.

And the authors point out that the value for λBD may be ‘outrageously small’. Just how common is abiogenesis? A telling case in point: One recent calculation shows that the probability of spontaneously forming proteins from amino acids is on the order of 10-77. And having arrived at these amino acids, it would still be necessary to go through all the further steps to arrive at an actual living creature. Not to mention the issue of producing living creatures and having them develop technologies.

Image: This is Figure 3 from the paper. Caption: Figure 3. Left: Occupation fraction of potential “seats” as a function of the birth-to-death rate ratio (λBD), accounting for finite carrying capacity. In the context of communicative ETIs, an occupation fraction of F ∼ 1 is apparently incompatible with both Earth’s history and our (limited) observations to date. Values of λBD ≪ 1 imply a lonely cosmos, and thus SETI optimists must reside somewhere along the middle of the S-shaped curve. Right: As we expand the bounds on λBD, the case for SETI optimism appears increasingly contrived and becomes a case of fine-tuning. Credit: Kipping and Lewis.

Thus the birth to death ratio cannot be too low but neither can it be too high if it is to fit our history of observations. The window for successful SETI detection is small, a fine-tuned ‘valley’ in which we are unlikely to be. To this point SETI has produced no telling evidence for technological civilizations other than our own (we do pick our own signals up quite often, of course, in the form of RFI, a well-known problem!) You have to get into the realm of conspiracy theories like the ‘zoo hypothesis’ to explain this result and still maintain that the galaxy is filled with technological civilizations.

We can also weigh the result in the context of our own planetary past:

Moreover, F ≈ 1 is simply incompatible with Earth’s history. Most of Earth’s history lacks even multicellular life, let alone a technological civilization. We thus argue that F ≈ 1 can be reasonably dismissed as a viable hypothesis…We highlight that excluding F ≈ 1 is compatible with placing a “Great Filter” at any position, such as the “Rare Earth” hypothesis (Ward & Brownlee 2000) or some evolutionary “Hard Step” (Carter 2008).

So what’s actually going on in those flasks on Jaynes’ lab table? Because if some flasks are doing one thing when the chemical is added and some are doing another, we may be precisely fine-tuned to where a SETI detection will be consistent with our previous observations. But that’s a pretty thin knife-edge to place all our hopes on.

I should add that the authors introduce mitigating factors into the discussion at the end. In particular, violating the SSD might involve the so-called ‘grabby aliens’ hypothesis, in which alien civilizations do emerge, though rarely, and when they do, they often colonize their own part of the galaxy. Thus most regions fill up, but not all, and we humans have perhaps emerged in an area where this colonization wave has not yet reached. That’s sort of intriguing, as it implies that the best SETI targets might be very far away, and extragalactic SETI may offer the best hope for a reception.

But let me end by questioning that note of hope, and for that matter, the issue of ‘terror’ that the Clarke quote invokes. Because I don’t find the idea of a universe devoid of other civilizations particularly terrifying, and I certainly don’t see it as one that is beyond hope. A Milky Way stuffed with civilizations would be fascinating, but a cosmos empty of other sentient beings is also a remarkable scientific result. So of course we keep looking, but the real goal is to understand our place in the universe. If we are a spectacular contradiction to an otherwise empty galaxy, let’s get on with exploring it.

The paper is Kipping & Lewis, “Do SETI Optimists Have a Fine-Tuning Problem?” submitted to International Journal of Astrobiology (preprint). See Kipping’s Cool Worlds video on the matter for more.