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The Fermi paradox is the contrast between the likelihood of life existing elsewhere in the universe and the lack if evidence for it.

This is a significant conundrum. On the one hand, there is a strong sense that the conditions on Earth that led to the emergence of life cannot be unique. This makes it seem likely that life must be common.

But on the other, astronomers have scoured the cosmic haystack for the needle that would represent signs of intelligent life elsewhere in the universe and come up with nothing. As a result, many observers have concluded that there are no obvious signs.

Others disagree. Back in 2010, the astronomer Jill Tarter and colleagues argued that alien radio beacons could be obvious and common in our galaxy but that astronomers would not know because their searches have been incomplete.

These searches, said Tarter and co, are like searching a drinking glass of seawater for evidence of fish in all Earth’s oceans.

That’s a colorful metaphor, but given the considerable effort put into the Search for Extra-Terrestrial Intelligence (SETI), how accurate is it?

Today, we get an answer thanks to the work of Jason Wright and colleagues at Pennsylvania State University. These guys have characterized the parameter space that astronomers need to search for signs of alien life. They say this space is so vast that SETI searches so far have done little more than scratch the surface.

Wright and co’s method is straightforward. They begin by creating a mathematical model of the search space astronomers need to explore and then calculate what fraction has been investigated so far.

“We develop the metaphor of the multidimensional ‘Cosmic Haystack’ … into a quantitative, eight-dimensional model and perform an analytic integral to compute the fraction of this haystack that several large radio SETI programs have collectively examined,” they say.

This parameter space is vast. The relevant dimensions include the three dimensions of space, the frequency range of potential signals, their repetition rate, polarization, and modulation, the transmission bandwidth, and the sensitivity of searches to this transmitted power.

The volume of three-dimensional space that can be searched is the volume of the universe centered on our solar system out to a specific distance. Wright and co define this as 10 kiloparsecs—about 30,000 light-years, or roughly the distance to the globular clusters that orbit the Milky Way galaxy.

Most radio telescopes are able to observe signals in both polarizations at the same time, but this has not always been true in the past. So this is a dimension that limits the exploration of the parameter space.

Other dimensions are complex to characterize. The signal repetition rate, for example, is tricky to handle in the model. Continuous signals are easy to deal with, but signals that repeat rarely are difficult. One relevant example is the famous Wow! signal recorded in 1977 at Ohio State University’s Big Ear radio telescope. It is so called because researchers annotated the data by writing “Wow!” in the margins.

But despite various attempts, this signal has never been observed again. That may be because it is entirely spurious, but it may be because the repetition rate is so low.

Defining the size of this cosmic haystack is then the task of adding all these spaces together. As Wright and co put it: “The volume of the haystack is then a definite volume integral in this 8D space, and the fraction searched can be calculated given the sensitivity function for a given survey.”

The result is a space of truly gargantuan proportions. “This leads to a total 8D haystack volume of 6.4 × 10^{116} m^{5}Hz^{2} s/W,” say Wright and co.

But how much of this have astronomers explored? Wright and co say that the searches to date have covered just 5.8 x 10^{-18} of this volume.

That’s a tiny fraction. To put this in the context of Tarter et al.’s original comparison, the total volume of Earth’s oceans is 1.335 x 10^{21} liters. So the total search to date is equivalent to searching 7,700 liters of seawater. Since a cubic meter is 1,000 liters, that’s about the size of a large hot tub.

That’s significantly larger than Tarter et al.’s estimate of a drinking glass, but it is still tiny in the greater scheme of things. “Even our larger estimate underscores how little searching has actually occurred,” say Wright and co.

That’s interesting work because it puts the searches for extraterrestrial intelligence in context. The picture from Wright and co suggests not that SETI has failed, but that it has barely started.

Clearly, there is plenty more searching to be done, even though the task seems more daunting than ever. As Wright and co put it: “One hopes that the Cosmic Haystack is rich with needles.”

Ref: arxiv.org/abs/1809.07252 : How Much SETI Has Been Done? Finding Needles in the n-Dimensional Cosmic Haystack

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