F.A.Q.

What if aliens applied the same reasoning? Woulnd't they then think that other aliens lived on even smaller planets?

They certainly should apply the same reasoning. If everyone on Earth declared "My country has a higher population than most others", then over 98% of us would be correct.

Why should I think I am an ordinary individual, rather than an ordinary planet or an ordinary species?

The clue is really in the question - you are the one doing the thinking. But perhaps the most compelling way to verify this is to actually run some experiments with your own personal data. Write down various groups you fall into - blood type; country of birth; religious group; favourite sports team, and so on. Now, do you notice a trend? Do you tend to fall into the big groups or the ordinary groups?

Now consider what would happen if humans had set up colonies on other planets. Aside from their slightly distant location, these planets have simply formed new countries. So, if you are happy with the reasoning that you are not in an ordinary country, you must also be happy with the reasoning that, in this example, you should not expect to be on an ordinary planet.

To complete the connection with the discussion about alien life, ask yourself: what if these colonies had not travelled from the Earth, but had evolved there independently? Why would their origins have changed my conclusions?

"Aren't there much bigger factors that influence population size?"

Brief answer: There certainly are, but they don't change the results of the calculation.

Longer answer: If there were only a handful of other planets with life, then other random factors which control population size could dilute the effects of body size and planet size. However if there is any hope of finding life on other planets, there must be a large number of planets with life in the Universe. Therefore, for the case we're interested in, the other factors do not influence the results.

"How can you draw any inferences from one data point?"

It's a complete myth that a single data point is inadequate for making predictions. For example, let's take Usain Bolt's 100m World Record of 9.58 seconds. Imagine that was the only data point we had regarding human running speed. Wth that one data point we could confidently make a powerful prediction, that anyone we pick from the world population will take more than 9.58 seconds to run 100 metres. So where does the myth come from? It's based on the fact that if one draws a fair sample from a population, we can't estimate the variance of the population. But neither our planet nor our species can be considered fair samples from their respective parent populations.

"Do you assume that bigger aliens are more intelligent?"

No, there is no assumed link between intelligence and body size. In order to conclude that alien species are probably larger than ours, only a single assumption is required: the average population of larger species is lower than the average populations of smaller species.

"Why should I consider myself to be a 'random' individual?"

It might sound alarming to describe yourself as ‘random’, but it shouldn’t be. Treating yourself as a random individual does not mean you were actively selected by some roll of the cosmic dice. It’s just a marker of our own ignorance. It only indicates that we lacked information about which group we're in.

Here on Earth, at this moment in time, there are approximately seven billion remarkable lumps of mushy goo, each weighing little more than a bag of sugar. Every lump is capable of generating a weird and wonderful phenomenon we call consciousness. They are, of course, our brains. Perhaps not just human brains - it’s probable that other animals with large brains, such as dolphins and elephants, experience a similar sensation of consciousness. But as there are only a few million of them, they don’t have much impact on the total number we've counted. So to reiterate, there are about seven billion lumps, and you are the result of one of them. Everything you remember, everything you think, and everything you ever feel is directly related to that lump of goo which sits safely embedded within your skull.

Precisely how consciousness arises is very poorly understood. It's possible that significant progress will be made in the not-too-distant future, as organisations like Google DeepMind forge increasingly complex forms of artificial intelligence. But the question I’m going to ask isn’t related to the nature of consciousness itself. My question is simply this: Why did you end up in your particular lump of goo?

Now, I’ve no idea. I think it’s fair to say that nobody does (except perhaps those that believe they are a prophet). But it is fair to say that everyone’s brain is physically near-identical. So if I hadn’t yet figured out where I was on the planet, and was shown an atlas which pinpoints all of the seven billion conscious brains and asked “where are you?”, I would assign an equal chance to each lump of goo. That means that I have a higher chance of finding myself living on continents with more lumps. I notice that there’s only a few on Antarctica, for example, so I doubt I’m down there. I could be, but it's extremely unlikely.

But why stop there. What if I was shown a map of the entire galaxy, which included other planets that are also home to conscious-giving brains. If the Earth wasn’t labelled on this map, how should I rate my chance of being on any given planet? As before, I would argue that you are more likely to find yourself on a planet with more brains. After all, if it applies to continents, why would it not apply to planets?

As it happens, we actually make use our own ‘randomness’ on a regular basis, perhaps without thinking about it. For example, if a doctor hands you some medicine, and informs you that 80% of people will see their symptoms vanish within three days, what do you take away from that fact? Most people, I imagine, would conclude that their own chances of being cured within three days are 80%. It would be very odd to object by responding “That statistic is irrelevant, because I’m not a random person!”. So where is the logical step from saying that 80% of people are cured in that timeframe, to your own probability? Essentially the population has been divided into two groups - those that were cured in that timeframe and those that weren’t. And you don’t yet know which group you fall into, but the chances of you falling into the “cured” group are higher as there are more people in that group.

"Why can't aliens be small?"

They could, it's just statistically very unlikely. It does also seem reasonable that organisms less than 1kg do not have sufficient brain capacity to be wondering about their place in the universe. But that is not an assumption within the calculation.

"How could you know about evolution and gravity on other planets?"

This problem is bypassed - the calculation doesn't care about how the variation in body sizes came about. Just as, when estimating that you live in a country with a high population (over 6 million), I do not need to account for the complex history, politics and wars that went into creating the world's nations.

One caveat is that there may be a link between average body size and planet size, which could slightly amplify the expected relationship between body size and population size.

What might these 300 kg creatures look like... could they look like us?

The results of the above calculations are insensitive to the detailed physiology of other intelligent species. However the different size of extra-terrestrial species, and their environments, might divulge some clues as to their appearance. Species on earth which are over 300kg usually stand on more than two legs, making it easier to support their body weight (although at around 6,000 kg, T. Rex is a hefty counterexample.) But to make a fair comparison we need to consider the weaker gravitaitonal fields on the surfaces of smaller planets.

The surface gravity on a planet is given by g ∝ M/R2, where the planet mass rises as M ∝ R3.6 due to the higher densities associated with more massive terrestrial planets. This leaves us with g ∝ R1.6.

Pressure is given by weight divided by area, so P ∝ mg / m2/3 where m is the mass of the organism. For a constant pressure, then m ∝ R-4.8. This means, for example, that an organism living on a planet which is three quarters the radius of the Earth (0.75 R ⊕ ) would have to be four times larger than an equivalent organism on Earth in order to experience the same pressure. So a 75 kg (1.8 metre) human on earth is subject to the same physiological stresses due to gravity as a 300 kg (2.9 metre) humanoid on a planet with R=0.75 R ⊕ .

There is therefore little reason to believe that a ~300 kg intelligent species would necessarily take a fundamentally different form to our own.

"If the big aliens did the same calculation, wouldn't they get the wrong answer?"

Yes, they certainly would. But there is nothing worrying or paradoxical about this. Although a large number of groups reach the incorrect conclusion, very few individuals are in those groups. Similarly, if all humans say ‘I live in a big country’, half of the countries will be incorrect, but over 98% of us, as individuals, will be correct.﻿

Focussing on the "what ifs" - the few who reach the wrong conclusion - is the source of one of the most widespread misconceptions on the topic. Many scientists have fallen into this trap, such as Lee Smolin in his article from 2004, where he points out that an individual living ten thousand years ago would have considered it very unlikely that the future population would continue to expand as dramatically it did. It is then tempting to conclude that we can't trust this line of reasoning, because it doesn't work 100% of the time.

In science there is never absolute certainty, only varying degrees of confidence. We should never be 100% sure of anything. When stating the degree of confidence in a result, typically 95%, it should be in full knowledge that one time out of twenty, we will be wrong. 5% of the time we will be misled by statistical chance.

Now if one of the earliest humans estimates the number of future human births, based on how many there had already been, they will underestimate the truth. Because we now know there has been many more. But those first 5% of people who ever lived represent the 5% of the time we expect to be wrong. This is a basic premise of how science functions, how it uses statistics. We must be wrong some of the time. Every scientific discovery, such as the recent detections of the Higgs boson and gravitational waves, relies upon statistics. In principle they could both be wrong too, but the chances of this are tiny.