Fermi's Paradox

Aliens. Extraterrestrial Lifeforms. One of the big drivers behind human space exploration efforts and the observation of stars and galaxies is the search for new civilisations like ours. Probably it bears the hope for the human community to focus on a common higher goal and therefore getting distracted from killing ourselves, probably it's the hope to find wisdom outside our planet that can pull humanity out of the hole of self destruction.

But where to search? Where could these aliens be? Are they probably already here on earth? Are the y probably already in contact with the powerful people, who keep this as their biggest of all secrets? Or don't they exist at all? Can they even exist, statistically speaking?

The Paradox

If they exist, then why are they not here?

This the gist of the so called Fermi Paradox. Enrico Fermi (1901 - 1954), an italian physicist, who formulated the paradox also delivered an answer. They're not here, because they don't exist.

The Drake Equation

The American scientist Frank Drake (*1930) came up with an equation in the 1960s, that could calculate the amount of intelligent extraterrestrial worlds in the milky way based on some external factors.

$N = R^* \times f_p \times n_e \times f_l \times f_i \times f_c \times L$N=R∗×fp​×ne​×fl​×fi​×fc​×L

The result is the number we're searching for. N is the possible amount of intelligent civilisations in our galaxy. We know one thing about this: The number must be greater or equal one, because apparently we exist fulfilling the criteria. The result depends on seven factors, each of them pretty much unknown. You could only guess. So let's start a guesssing game.

$R^*$R∗: The average rate of star creation in our galaxy. Drake estimated a number of $1/y$1/y. Conservative estimations nowadays come up with a number of $8/y$8/y.

$f_p$fp​: The planet factor. The fraction of stars that have planets. Or better: the likelihood of a star to have planets. In the meantime, we have experience from good and precise observations of our nearest neighbour starsystems. Many of these observations delivered positive results and we could correct the number upwards. However, certain star constellations like three body systems are known to be more unstable. Also it is known that the likelihood gets smaller the nearer we go towards the center of our milky way, because the star systems there have less distance between each other. Science doesn't have a clear opinion on that part of the equation. So let's take the more pessimistic approach of 0.2 - meaning every fifth star also has planets.

$n_e$ne​: The amount of planets that might support life. That is the average amount of planets within the habitable zone of a star system. Looking at the solar system, there are three planets that qualify: Venus, Earth and Mars. Additionally, many scientists think that life might also be possible on one of the moond more outside. While the optimists say three to five, we again take a more pessimistic approach and choose 2.

$f_l$fl​: The life factor. The fraction of these habitable planets, that actually spawns life. Also here we know that the number is above zero - just because our Earth made it. But our technology does not yet offer the possibility to measure oxygen or methane levels on extrasolar platents precisely. But numbers are getting better and better. So up to now, proof of life could only be found on earth, predecessors of that - like complex amino acids could also be found on e.g. comets. Additionally there are experiments that simulate the conditions of young earth with proof that such long chain proteins are forming naturally. Therefore life is not impossible but tle likelihood is not 1 (as some other scientists claim). A very speculative estimation of myself: $1/100$1/100 or 0.01. Drake estimated 100% by the way.

$f_i$fi​: The intelligence factor. The fraction of planets that spawn life, that also develops intelligence and contactability, communicative life, at least communicative enough to get detected. Well that question is highly philosophical and not backed by any scientific fact. Actually, we'll have a problem to even find a proper definition on what intelligence is. Terefore, let's put this factor on the parking lot and look at it later again. This is our $x$x

$f_c$fc​: The communication factor. The likelihood that an intelligent civilisation can and wants to communicate in a way that we can detect and decypher it. Again we are in a very theoretical field - no chance to be able to measure or proof anything. Yet the probablity might be quite high. I'm optimistic here and claim 50% or 0.5.

$L$L: The lifespan of a technological civilisation. Earth has reached this evolutionary level about 100,000 years ago. Its inhabitants can be called a "civilisation" for about 3,000 years. Human kind stood on the brink of extinction during the cold war 50 years ago. And again at the moment an with the climate crisis again in about 40 years. If we manage to survive this and create the ability to spread over several planets, we step through an important pinhole and significantly increase the probablility to survive even bigger cataclysms. And hence survive for a significantly longer time span. So I need another very personal estimation here and pick 10,000 years (scintist's estimations range between 1k and 100M).

Ok then. Let's do the math by claiming - just like Fermi did - that we are the only intelligent beings in the galaxy.

$N = R^* \times f_p \times n_e \times f_l \times f_i \times f_c \times L$N=R∗×fp​×ne​×fl​×fi​×fc​×L

$1 = 8 \times 0,2 \times 2 \times 0,01 \times X \times 0,5 \times 10.000$1=8×0,2×2×0,01×X×0,5×10.000

Or: $160 \times X = 1$160×X=1

Or: $X = \frac{1}{160}$X=1601​

So every 160th Planet that comes to life is also creating intelligent life. That sounds pretty much to me.

Some scientists, one of them for example was Carl Sagan, have even calculated higher numbers. Some of the optimists in the science community have come to a result of 100 civilisations in the galaxy, some even claimed numbers of up to 4 million.

Playing with the parameters, you will see that the lifespan of a civilisation has a major influence on the result, just because of the span of several orders of magnitude. That's where I had guessed 10,000 years. In case a civilisation survives its dangerous mono-planetary phase (allowing catastrophes, war and technical failures to wipe out a whole planet), the lifespan can be much loonger indeed.

Explorer

This little experiment brough me to a reverse scenario. What if we conquer the galaxy? How long would it take? And another thought experiment was born. If you think in galactic or universal timespans, our exponential development in the last 200 years was tremendous. Even 1000 years are nothing compared to the 13.8 billion years the universe exists. So these are the very generous parameters of my thoughts:

• In 1,000 years latest, that is in the year 3,000, humanity will be able to create a generation ship for pioneers. Considering and not exceeding all current physical laws, that is without any science fiction magic, such a ship could reach our next star Alpha Centauri. Considering a maximum speed of 10 % of lightspeed, this can happen within 40 years. The inhabitants of the ship - thousands of people - can build a new civilisation after the arrival over there. The could use the resources of that other system even when they don't find a habitable planet.
• Another 1,000 years later, two interstellar expeditions could continue. One starting from Earth again and one starting from the surviving and thriving colony in the Alpha Centauri system. And conquer the next star system.
• The equation is based on exponential growth, but it's not base 2, because worlds in the center of the bubble that spreads are already surroundet by civilisation seeds and might not find reasonable destinations anymore. They would simply take too long with their journey to the next unoccupied star system. Assuming that the spread is mainly taking place in a spherical way, only a mantle of around 15 Ly is able to expand to new worlds.
• Doing some geometric calculations, I've ended up with a spread base of 1.0018. Or 0,18% growth.
• The result is 15.000 iterations. So within 15.000 iterations or 15 million years, the humans could occupy the whole galaxy.

Huge number, right? No. Not at all compared to galactic scales. 15 million years ago, dinosaurs were already extinct for 50 million years. If you compress the lifespan of the universe in one day, we'd talk about less than a minute.

We should also consider the defensive assumptions. Every iteration takes 1,000 years to achieve their goal although technology is evolving. And we, the first iteration, might even have the needed technology by the year 2,200 rather than 3,000.

Now let's go back to the start and bring the two Experiments together again. Let's consider the many coincidences that lead to our existence. Meteorites bringing organic material, volcanos and their warm wells creating organic mud, random mutations, humans inventing the wheel, electricity and computers. All of these events accelerated the process and brought everything to a new level. But each consecutive jump happened in smaller and spaler time spans. So one could assume that other civilisations could be here if they existed.

Yet, no one is here.

Why are there no aliens on earth?

As proven, it is actually possible that we're alone in the milky way. Or in other words that there is only one single civilisation living in our galaxy.

It is also possible, the equations show that as well, that there are other civilisations. So what could be the reasons that we haven't seen them yet?

• They don't exist. Likelyhood detected. So this must be on the list.
• There are other civilisations, but they are too far away. If there are other civilisations out there, 100 lightyears might be enough to be out of sight. We have developed radio about 100 years ago therefore thesw waves, the only objectively detectable signals from earth have just traveled that far. Our blindspot therefore covers 99.9999 % of the milky way.
• There is a far superior civilisation that leaves us alone by conscious decision. They just don't want to interfere with our development. Probably they observe us and our potential and say hallo at some turning point in history.
• They are here already. They don't only watch us. They study us. They are directing us. Thet don't reveal themselves but they take care that we don't run into one of the extinction traps. They are our guardian angels or our zoo keepers - depending on the perspective.

Conclusion

What would we , us, humainty, do in such a situation? For example when we detect intelligent life on Alpha Centauri in an earlier development stage? Probably we would also leave them alone. Very likely, we would make some experiments just like we do with gorillas or orang utans.

If I had to place a bet, I'd choose the first option. We're alone in the milky way. But wait. There are 12 billion galaxies out there. Well this changes the equation a lot, doesn't it?

But if the milky way is ours, why shouldn't we dare to start conquering it? Why don't we decouple ourselves from our home planet? Why don't we start a big experiment that will finish 500,000 hman generations later?

Probably on some lonely planet inn some lonely star system, we finally might even find another civilisation tha improves our understanding of everything.