Aliens are Big

Imagine you are a fish. You know every one of the 300 fishies that share your pond by name, but everything beyond the water is a mystery. There is no way to leave the pond. Being a fish, you wonder if there are other schools of trout and bass out there in their own ponds. What are they like? Are they bigger or smaller than you? This is a problem not unlike one proposed by Astrophysicist Fergus Simpson: How can we make predictions about what other Alien Civilizations are like based on only one data point - us? Believe it or not, both us and the fish can answer this question using the power of statistics!

Introduction

Recently, I re-watched a very old MinutePhysics video. The entire video is based on a paper by Fergus Simpson. In it, Simpson attempts to estimate various characteristics of Alien civilizations. Without any of the extra-terrestrials around, you might consider the question purely fanciful. After all, with only one data point (us) how can we extrapolate anything about Alien civilizations? However, as the video points out, we have one powerful tool to tackle the problem: Bayesian Statistics!

Using clever math, and a lot of assumptions, we can determine the median population for a civilization and how much they weigh on average. Turns out, according to Simpson, the average civilization has only 15 million members and they weigh about as much as a polar bear. They also live on planets about half the size of Earth. This differs from popular beliefs of Alien civilizations in media. Typically, they are galaxy spanning empires with billions, if not trillions of individuals. Can we really expect that the average civilization would be so much smaller than our own?

Problem

If you scroll down below MinutePhysics’ video, you’ll find a lot of negative comments:

perhaps it’s time to do a video on how people misuse statistics and fail to grasp the limitations of statistical analysis.

…What if we have a small population compared to the majority of other worlds?… We only know what we’ve experienced. You need to [have] two points to make a line.

If everyone assumes [they’re] in the big group simply because it’s statistically more likely than for them to be in a large group than small group, are Aliens looking for planets that are smaller than theirs with life forms physically larger than they are but with a smaller total population than they have?

Skeptics argue that using one data point, Earth, is not enough to extrapolate about anything related to Alien civilizations. What if we are like the fish, a small population in a small pond, unable to even imagine the ocean. While these concerns are valid, statistics, especially Bayesian statistics, offers us a way to refine our predictions. We can do this even with limited data.

Population Bias

If you picked a random person, from any where in the world, where are they likely to come from? What is the chance that this person is from China? India? Finland? Naively, you might say there are 193 member states of the UN, so there is a $\frac{1}{193}$ chance of that individual being a citizen from any given country. This is a misguided approach. There are many countries with significantly more citizens than others.

Source: Wikipedia

Using the above table, we can calculate that the top 10 highest populated countries have about 56% of Earth’s population. Going further, about 98% people live in country with a population above the median. As Fergus Simpson writes, if your country and you both said “‘I live in a big country’, half of the countries will be incorrect, but over 98% of us, as individuals, will be correct”. Even though the average person lives in a big country, the average country is much smaller. This is what is known as population bias.

It may seem like a paradox, but it is an observable fact. Even though the average person lives in a large country, most countries are small. When we apply this same logic to civilizations, it suggests that, while most civilizations must be small, most intelligent beings likely live in the less common large civilizations. Therefore, you and I, as random individuals, are highly likely to be living in a large civilization.

Just like with our countries on Earth, this same pattern pattern is likely to apply to civilizations. But how can we actually utilize this insight to predict the average population size of Aliens? This is where Bayesian statistics comes in. It is a proven mathematical tool for making predictions by updating our prior assumptions based on available data, even when that data is limited.

The Power of Bayesian Statistics

Bayes formula is a powerful tool for determining the probability of something that is difficult to measure. It’s been used by the Allies to accurately estimate german tank production in WW2, build email spam filters, and even classify images into categories.

Even though the math can be scary, the basis for it is probably something you do every day. Imagine that you want to know if it is going to rain today. You believe that in your city, it usually rains 25% of days in the month of April. However, you also noticed that when it is very cloudy outside, there is now a 75% chance of rain. By gathering more data, we update our beliefs and can make more accurate prediction. This is essentially what Bayes theorem does. The math looks something like this:

We start with our prior beliefs (what we assume about Alien civilizations), and we adjust it based on new data (what we know about our civilization on Earth). Above, we have the probability Aliens have some characteristic (A) given what we know about Earth (E). Like in the paper, we can also make an approximation by ignoring the denominator (the probability that Earth exists the way it does). This simplification lets us focus directly on how Aliens are likely to have certain characteristics based on what we know about Earth.

On the right side of the equation, the second term $P(A)$ is our prior belief about Aliens. Thus, the first term $P(E|A)$ is simply the probability of the Earth existing given what we assume to be true about civilizations at large. Using our prior belief we are a large civilization in a galaxy full of smaller ones, and combining that with astronomical observations of exoplanet sizes and conditions for life, Simpson estimates that most civilizations must be much smaller than ours; only 15 million members. He uses similar logic to estimate what aliens must weight and other characteristics.

Back to The Fish

Given your knowledge of Bayesian statistics and population bias, you may assume that your pond of 300 fish is average, or even might be larger than average. But, as a human observer, you know that the ocean exists. The ocean has way more than 300 fish. The fish in that small civilization would have predicted wrong. This is what many of those commenters argued that we as humans of Earth have done. Does this prove Simpson wrong? No, because I did not choose a random fish pond. I picked it specifically because it was small. If you picked a fish truly at random, it would probably live in the ocean. The chance that we live in an average civilization is very small. Rather, we’re more likely to be part of something much larger.

If we are one of the largest civilizations out there, we have a unique responsibility to reach out, explore, and share our knowledge. The universe might be teeming with small, disconnected planets that yearn for the stars, but are unable to utilize the resources of a large population. Or maybe we really are a small planet, unable to imagine the creatures swimming in oceans over the horizon. Either way, the possibilities are endless, and it’s our duty to explore them.

Please read more about Fergus Simpson’s work on his website:
https://www.thebigalientheory.com