A Mathematical Twist on the Fermi Paradox

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Interesting questions arise when physicists start chatting. Back in 1950, at Los Alamos National Laboratory, physicists Enrico Fermi, Emil Konopinski, Edward Teller, and Herbert York were walking to lunch when the conversation turned to a recent spate of reports of UFO sightings.

They quickly honed in on the challenge of faster-than-light travel, with Teller opining that there was a one in a million chance that science might achieve this on the scale of small material objects within the next ten years (i.e., by 1960). Fermi begged to differ; he placed the odds at closer to one in ten, making him the optimist of the merry band physicists.

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The lunchtime conversation moved on, but Fermi continued to puzzle over the conundrum in his head, finally exclaiming, “Where is everybody?” If his rough calculations were correct, then the Earth should have received alien visitors many times over.

Thus was born the Fermi Paradox, defined as “the apparent contradiction between high estimates of the probability of the existence of extraterrestrial civilizations and the lack of evidence for, or contact with, such civilizations.”

It’s been an ongoing puzzle for scientists, and a source of inspiration for science fiction authors, ever since.

There’s still no truly convincing explanation, but that doesn’t keep physicists from trying to resolve the paradox. The latest effort is a new paper that appeared on the arXiv last week by Igor Bezsudonov and Andrey Snarskii at the National Technical University of Ukraine.

The scientists suggest that there is a limit to how big a given civilization may become, based on their models, which show civilizations growing at a given rate, reaching a threshold, then collapsing and dying. And this limited life space, in turn, reduces the likelihood of different civilizations from other solar systems or galaxies coming into contact with one another. (It’s conceptually similar to the population dynamics model first proposed in the 19th century by Robert Malthus, among others.)

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A scene from ET: The Extraterrestrial (Universal Studios)

But there’s a twist. If the two civilizations are close enough (in both time and space), the likelihood of coming into contact increases dramatically. Should this happen, say the scientists, the resulting mix of cultures and ideas will enable both civilizations to flourish for much longer than either would without that contact.

They used a cellular automaton model to demonstrate this process, using three basic parameters: the probability of civilization forming, its likely life span, and the extended life span it would enjoy should it come into contact with another civilization.

And if the values for those parameters are just right — “finely tuned” in physics speak — then a kind of phase change occurs. But instead of going from a solid to a liquid (or a gas), the universe goes from one in which civilizations scattered across the cosmos are unlikely to meet, to one in which they can. Who knows, perhaps even a federation of various civilizations could evolve — assuming there isn’t an interstellar war, with one civilization wiping out another and taking over their planet (the stuff of good science fiction for decades).

This might explain Fermi’s Paradox: we don’t have alien visitors (or communications) because our universe hasn’t undergone that critical phase change — i.e., we don’t live in that finely tuned universe where the parameters are just right to give rise to mixing civilizations. Or we haven’t been around long enough yet for the mixing to occur.

The paper ends with the only conclusion it can draw: we’ll just have to wait and see.

The arXiv blog at Technology Review points out another intriguing aspect of this new paper:

“Bezsudnov and Snarskii even derive an Inequality that a universe must satisfy to become civilized. This, they say, is analogous to the famous Drake Equation which attempts to quantify the number of other contactable civilizations in the universe right now.”

Ten years after Fermi proposed his paradox, physicist Frank Drake attempted to come with an equation to evaluate the probabilities of alien life arising elsewhere in our universe. It incorporated such terms as the rate at which stars form in a galaxy; how many stars have planets, and of those planets, how many would be habitable; of those that are habitable, how many would develop the kind of life that would evolve into an intelligent civilization capable of interstellar communication; and finally, how long such civilizations would last.

Those values are pretty much unknown, so while we have the equation, we don’t have the means of solving it. Yet. We’re not even sure exactly how life came about here on Earth, as royal astronomer Martin Rees recently pointed out while arguing against investing in manned spaceflight missions, as opposed to using robotic probes.

But the assumption made by the Drake Equation is that civilizations rise and fall within their own solar systems, with no interstellar colonization. Factor in that, and you’ve got a scenario more akin to population dynamics — or one where Bezsudonov and Snarskii’s approach might apply.

Drake himself never claimed his equation was less of a solution to Fermi’s paradox, and more a means of “organizing our ignorance” on the subject. And he recently revisited the topic in anticipation of SETI-Con — a weekend event being held later this month to celebrate the 50th anniversary of the Drake Equation:

Image (top): The SETI Allen Telescope Array (SETI Institute)