"Where the Hell is Everyone?"

Given the age of the galaxy, it seems that spacefaring alien life should be all around us

I recently read a post on Reddit titled “the Fermi paradox is stupid”. From this we can conclude a few things. Firstly, the author has taken onboard the lesson that one must never bury the lede. Somewhat more importantly, it is a reminder that humans struggle to conceptualise large numbers. But this got me to thinking: is the universe larger than it is old? Or vice versa.

What am I on about?

Consider. The argument from the above Redditor was basically: ‘since space is very large, it’s not surprising that we can’t see any evidence for aliens’. The intuition appears to be that life may be abundant, but space is simply SO BIG that the gaps between advanced civilisations might make detection impossible, even for modern science with all its other wonders. I think this intuition is correct! The frankly incomprehensible size of space makes it possible that you could scatter a million Earths across the galaxy and we would be quite ignorant of each other.

This line of thinking is incomplete, however, because whilst space is indeed vast, it is also exceedingly old. And it turns out this is a countervailing pressure on the other side of this equation. Time gives life plenty of opportunity to emerge and preponderate. More time should mean more life. Revisiting the analogy above, if we did have a million Earths scattered throughout the galaxy, how long would we expect them to stay ignorant of each other?

To decide whether the Fermi Paradox is indeed stupid, we need to decide which of these factors overpowers the other? In other words, is space bigger than it is old?

Let’s start with a simple comparison. The galaxy is 100k light years across and 13bn years old. These numbers are incomprehensible on first flush, but in comparison we can see that you ‘only’ need to travel at 2km per second to cover the width of the galaxy in the time the galaxy has existed. Voyager 1, a long distance space probe, is currently blasting out of the solar system at 17km per second. This is a first hint that age might overwhelm size - after all, this simple maths suggests that the galaxy is traversable in the time we have available with the sort of technology that existed in the 1970s.

But we can do better.

Let’s consider a simple simulation. Let's say that: 1) every 1000 years Earth sends out a colony ship to a random star; 2) it has a 25% chance of arriving, and a 25% chance of setting up a colony (6.25% total); 3) if the star is already colonised, it has a 0% chance; and 4) every successful colony follows the same pattern every 1000 years.

I view this as an extremely pessimistic model. Firstly, it assumes that an occupied planet can send out colonisation ships no faster than once a millennium. Secondly, it assumes that only a small fraction of those ships successfully achieve a colony even once sent out, even assuming they reach an uncolonised star. Thirdly, it assumes they head out at random not knowing if the star they arrive at will be empty. Fourthly, it assumes no improvement in success or pace of colonisation, even by the time that tens of thousands of years have passed and a meaningful fraction of the galaxy is colonised.

Yet, even under this very pessimistic model, this suggests that it ‘only’ takes 850,000 - 1,000,000 years to colonise the 200bn stars in the galaxy. Tweaking it slightly so that it’s a 50% chance of arriving and a 75% of setting up a colony, the time drops to less than 150,000 years. If you drop the rate at which planets send out colony ships to one per every century (hardly wildly aggressive even then), it drops to less than 100,000 years. The point is, tweak your inputs however you like, you get to an answer in the hundreds of thousands of years to colonise everywhere.

These times are trivially short in the span of the galaxy and even the Earth. Dinosaurs lived hundreds of millions of years ago. A human-like civilisation could have colonised the galaxy literally several thousands of times over since then. Anatomically modern humans have existed for 300,000 years. If human-like life had emerged anywhere in the galaxy at all since humans started looking like humans, we wouldn’t just be looking for aliens with radio telescopes, we’d be living next door to them.

Let’s try another way to conceptualise this: if we compare the 13bn years of our galaxy to a single day, then the few hundred thousand years that colonising the galaxy takes would be a single second in that day. Cosmically speaking, the difference between ‘no advanced life’ and ‘advanced life on every single rock and pebble’ is a blink of the eye. Or in other words, the galaxy is older than it is big.

And I find this all very strange. The Fermi Paradox is named for Fermi who, allegedly, on discussing space with some of his colleagues blurted out ‘where is everybody?’. Honestly before I read the aforementioned Reddit post, I was probably guilty of not taking this question very seriously. I just assumed aliens were out there somewhere, and we’d find them one day. But having spent the time actually doing some playing with the maths on this, I find myself actually quite bothered by it. It seems like a single successful civilisation at any point over billions of years should be living on Earth, not to mention blasting their presence across the entire night sky.

So where the hell actually is everybody?

Appendix - Simulation Approach

import numpy as np

# ---------------------------------
# Parameters
# ---------------------------------

total_systems = 200_000_000_000        # Total number of star systems in the galaxy
ship_survival_prob = 0.25          # Probability a ship survives the journey
colony_found_prob = 0.25           # Probability a surviving ship successfully establishes a colony
years_per_round = 100             # Each simulation round = 1000 years
max_rounds = 10000                 # Maximum number of rounds (10 million years)
n_simulations = 1000  # Number of runs

# ---------------------------------
# Simulation Function
# ---------------------------------

def simulate_colonisation():
    colonised = 1                          # Start with Earth
    uncolonised = total_systems - 1       # All others initially uncolonised
    rounds = 0

    while colonised < total_systems and rounds < max_rounds:
        ships_sent = colonised

        # Probability that a ship results in a successful new colony
        p_success = ship_survival_prob * (uncolonised / total_systems) * colony_found_prob

        # Simulate how many new colonies are founded this round
        new_colonies = np.random.binomial(ships_sent, p_success)

        # Ensure we don't exceed the number of available systems
        new_colonies = min(new_colonies, uncolonised)

        # Update state
        colonised += new_colonies
        uncolonised -= new_colonies
        rounds += 1

    return rounds * years_per_round if colonised >= total_systems else None

# ---------------------------------
# Run Simulations and Compute Stats
# ---------------------------------

results = [simulate_colonisation() for _ in range(n_simulations)]
results = [r for r in results if r is not None]  # Remove any failed runs (should be none)

average_time = np.mean(results)
min_time = np.min(results)
max_time = np.max(results)

# Output results
print(f"Simulations completed: {len(results)}")
print(f"Average colonisation time: {average_time:.0f} years")
print(f"Minimum colonisation time: {min_time} years")
print(f"Maximum colonisation time: {max_time} years")