Life Beyond the Stars: A Mathematical Analysis of the Chances of Alien Life

Humans have been obsessed with the idea of aliens for centuries: portraying them in our movies, searching for their traces across the galaxies, even coming up with bizarre conspiracy theories involving extraterrestrial shapeshifting kitten-eating lizards posing as politicians. Our curiosity has also allowed us to create an equation which gives a rough estimate of how many aliens we would make contact with within our lifespan as a species, but this comes with a caveat: it depends on several quantities we have no reasonable estimate for. It’s known as the Drake equation, after Dr. Frank Drake, who came up with it in 1961.

The Drake Equation.

Here’s what each symbol means:

N: The number of civilizations in our galaxy with whom contact is possible. This is what we are looking for.

R∗: The rate of star formation in the Milky Way. R∗ is one of the few quantities in this equation we know with reasonable certainty. Brushing aside the complex math, the final answer is between 1.5 and 3 new stars per year, with an average mass equal to half of that of the sun.

Photo by Yong Chuan Tan on Unsplash

fp: The fraction of stars which have planets around them. Studies have found that fp approaches 1; that is, stars almost always have planets around them.

ne: The average number of planets which can support life around the stars which have them at all. This is the subject of much debate: after all, we have no clue whether life can develop in non-earthlike conditions or not. Some argue that life is just inherently tough and will develop anywhere it is able to, giving a figure between 3 and 5. Some go with the Rare Earth hypothesis which requires several extra conditions for life to evolve. My personal estimate would be around 0.3.

fl: The terms fl and beyond are where we devolve into pure guesswork. This factor is the fraction of all the above planets which actually develop life. There are several arguments about what it could possibly be, but the bottom line is that we simply do not have enough information. I myself consider fl to be around 1.

fi: This is the fraction of all of the above planets which go on to develop life intelligent enough to communicate with us. At this point we have barely any real data to work on, and what we do have is wildly complex and indecipherable: does it matter that Earth had a moon to stabilize its orbit? What about the fact that we orbit at such a distance from the center of the galaxy so as to remain out of the arms for tens of millions of years, thereby being shielded from the radiation emitted by novae? I believe this to be around 1 too, simply because evolution would mean that at some point or the other intelligence would appear on its own.

fc: The fraction of intelligent civilizations which send out interstellar signals which we can detect. Most just assume this to be 1, even though we ourselves barely do anything to broadcast our presence to the galaxy.

L: The Longevity Factor. This is by far the most hotly-contested figure in the entire equation, since it signifies the amount of time a civilization broadcasts its presence to the Universe. Estimates range from a mere 300 years from a pessimistic viewpoint to over a billion from a wildly optimistic one.

Using different values of these gives N ranging from 10 to the power of negative 13 to over 15 million. From this, it is pretty clear that the Drake equation is not meant for finding N so much as to give people something to think about. During the original conference, it was determined that N L, with the majority consensus being that all the fractional f terms would be close enough to 1 to be irrelevant. There have been arguments against this too, with some claiming it is ne or fi which is responsible for the small value of N, considering that we haven’t yet encountered any signs of extraterrestrial life. However, let us for a moment step back and assume that the N L equation is true. What would this mean for us as a species?

The gap in the staircase represents the Filter.

The answer ties together beautifully with the Fermi Paradox: if life is as hardy as it appears to be on Earth, where are all the aliens? It proposes a ‘Great Filter’, a certain step in the development of life which is nigh-impossible to cross successfully. What the issue is that we have no way of knowing exactly where the filter is on the evolutionary pathway: what is the hardest stage to overcome to flourish as a species? It could be something we have already overcome, like abiogenesis or the evolution of photosynthetic processes, or it could be something that is yet to be encountered, like large-scale nuclear warfare or climate-induced civilization collapse.

Imagine a long staircase which the human race is standing on. We started out as unicellular organisms at the bottom, and have climbed up to reach where we are today, each step an evolutionary leap. In this analogy, the Great Filter would be a gap between two stairs leading down to extinction below. Now it will be all well and good if we have already passed this trap, but if we haven’t, then we could expect to die out sometime in the future, which is not a pleasant thought. If we find another technologically-advanced civilization within our galactic neighborhood, then the situation changes. Two societies developing so close to one another would mean that life is common, and that no Filter exists at all. It would imply that we have a long life as a species ahead of us, because if N is large, then L is large too.

Another corollary of this is that it would be actively bad if we discover alien life which isn’t as advanced as humanity, since that would make it more likely that the Filter is in front of us, rather than behind. With the state of the human race as it is today, I would not be optimistic about our chances of crossing any conceptual Filter of Death with any certainty.

This whole discussion ends up leading back to where it started: are aliens real? Should we contact them? Or are we wasting our time? And here we get stuck once again. With our sample size of 1 planet, it is simply impossible for us to predict anything meaningful about extraterrestrial abiogenesis and life in general. Even if we do get a signal sometime in the future, there is no consensus on how to respond to one, let alone how to negotiate for the whole of the Earth. As said by Calvin in Calvin and Hobbes, ‘The surest sign that intelligent life exists elsewhere in the universe is that it has never tried to contact us.’

Proofreaders: Mokshit N., Durga C., Anusree

Student at IIT Bombay by day, reader by heart. My linktree: