Within the context of the animal kingdom, our species' position is clear. Aside from a disproportionately large brain, we're fairly ordinary mammals. However we should also consider ourselves to be a member of a very different group - those species, scattered throughout the universe, which ponder the existence of life beyond their own planet. Given the vast scale of the universe, this group is likely to be even more numerous and diverse than our own animal kingdom. Which begs the question: how should we expect to stack up against these other intelligent species?
To seek an answer with only the help of a single data point (us) may seem futile. But when it comes to predicting natural occurrences, we're often playing a game with loaded dice. And these weighted dice can prove to be extremely profitable, because they are much easier to master than fair dice. Observe the outcome of just a single roll, and that's all you need in order to make a series of successful predictions. So, what can these unfair games teach us about extra-terrestrial life? The equations are left behind - those can be found in the Monthly Notices of the Royal Astronomical Society [PDF]. The objective here is to build an intuitive understanding of why both the Earth and Homo Sapiens are biased examples of their kind. They were drawn from a stacked deck, one which carries more than its fair share of aces. What does this mean? It means we can learn what the other players are holding, even before they show their hands.
The video below provides an excellent overview of the topics discussed on this site.
Video created by MinutePhysics.
The four steps below describe why we should expect our species to differ from most other intelligent species.
STEP 1: Consider the following statement:
"I am more likely to have a common blood type than a rare one"
Does this seem reasonable? If you disagree with this statement: Gather some of your personal data and compare it with the global population. These can include country of birth; blood type; hair colour; and so on. Do you find yourself falling into the higher population categories? This data should lead you to conclude that you are an ordinary human - your properties reflect the global distribution.
STEP 2: Imagine you have woken up with amnesia and have forgotten where you are from.
"I am more likely to have been born in a high population country than a low population country"
This follows from the blood test statement in Step 1. Imagine a new sensitive blood test which identifies your country of birth. The countries will small populations ike Andorra are the rare blood types, while the larger countries - any which have a population over 10 million - are the common blood types.
STEP 3: Now imagine humans have already colonised other planets such as Mars. These colonies are just like new countries, except a little further away. So in line with step 2, we must conclude that:
"I am more likely to have been born in a high population planet then a low population planet"
STEP 4: What if those colonies on other planets had not travelled from the Earth, but had evolved there?
If we reach the same end result via a different route, why should our beliefs differ? These steps bring us to the conclusion that, if other sentient species exist, we should expect ours to have an unusually high population. Take a look at the bar charts below to get an idea of just how different we may be.
How can we make meaningful predictions about the nature of alien life? Let's begin with an apparently unrelated question:
What is an ordinary football club like?
Pick the name of a football club out of a hat (a big hat - there are over 5,000 clubs in English football), and most of the time you'll end up with a team you probably haven't heard of, such as Didcot Town or Tilbury. It's extremely unlikely you'll pick one of the twenty Premiership sides. But instead of picking team names, what would happen if you picked fan names? What if you stopped people in the street and asked them who they support? The list of answers would be dominated by a handful of famous teams such as Chelsea, Manchester United, and Liverpool. The crucial point here is that there is an enormous gulf between an ordinary club, and the club of an ordinary fan. An ordinary club relies upon 1,000 supporters, own a stadium with a few hundred seats, and pays its players around £30,000 per year. Meanwhile the club of an ordinary fan boasts millions of followers, a 50,000 capacity stadium, and player salaries are around £80,000 per week .
A similar situation arises when asking "What is an ordinary country?". There is a huge difference between pulling the name of a country out of a hat, and picking a person's name out of a hat before then asking what country they are from. An ordinary country in terms of population size would be one like Slovakia (which is half way down the population rankings). But the country where an ordinary person lives is Pakistan. In other words, if you line up the world's population in order of their country's population size, then the person stood in the middle lives in Pakistan. The enormous difference between Slovakia (5 million) and Pakistan (180 million) highlights the importance of this selection effect. As with the football teams, it’s not just the population size that differs. Everything linked to population size - ranging from land area, financial power, the number of schools, the number of hospitals - all of these figures are also distorted. The properties of your country, and your football club, are unlikely to be a fair reflection of most other countries and most other clubs.
How can this help us understand the nature of extra-terrestrial life? Consider the collection of planets in the Universe which have produced intelligent life - other organisms that have contemplated the existence life on other planets, as we have. The key implication here is that you (as an individual sentient being) should expect to be a member of the equivalent of Pakistan (or Chelsea F.C.). The Earth represents the planet of an ordinary being, and Homo Sapiens represents the species of an ordinary being. However if we want to know what our cosmic neighbours are like, that is equivalent to pulling the names of planets out of a hat, not individuals. So when scouring nearby star systems for signs of life, we should expect to find that our nearest neighbour is the equivalent of Slovakia in comparison to our Pakistan. They will be the Didcot Town F.C. compared to our Liverpool. What does this mean in real terms? Compared to our seven billion strong civilisation, their population will be much smaller. Perhaps only in the tens of millions. Not only that, but everything associated with population size is also distorted. Two of these distorted features - our planet size and our body size - are illustrated in the graphic below.
To begin, we'll dissect the following myth:
"We cannot learn anything about aliens until we find them"
The above statement might sound reasonable, and intuitive, but it lacks justification. Standing on its own, it’s just a piece of dogma. Dogma doesn’t leave room for progress or improvement. It might be a useful rule of thumb, it might fare well on many occasions, but for a few exceptional cases it will inevitably fail. And these critical points of failure often reveal the most crucial pieces of insight. For example, take the following belief
"We can’t fly to the Moon"
This might sound absurd, but it was undoubtedly a respectable viewpoint for many years after the Wright brothers’ first flight in 1903. It is another example of a dogmatic statement, where there is no application of logic, merely a blunt objection. A more meaningful statement includes some degree of reasoning, such as
"We can’t fly to the Moon with propellers because propellers work by pushing against air, and there is no air en route to the Moon"
By adding in these logical steps, a sudden chink in the armour appears. If a flying machine can be devised which does not require air as the source of thrust, then perhaps we could reach the Moon after all. So let’s revisit the statement about alien life. What is the justification for the first statement, that we are completely ignorant about the nature of life in the Universe when we only have a single reference point? The origins of this sentiment may be expressed as follows:
“We cannot learn anything about aliens until we find them because there is likely to be a very broad spectrum of life in the Universe and we are equally likely to be anywhere on that spectrum"
Now we are getting somewhere. If these additional remarks are in fact true, then our uncertainty on the nature of alien life would be hopelessly enormous. For each property that we might want to learn about other alien species (their population; what they look like; their lifespan; their technologies) there could be an extremely diverse range of values out there, and for all we know we could be towards the top or bottom end of the cosmic rankings in each of those properties. This would indeed leave us unable to learn anything, if “we are equally likely to be anywhere on that spectrum”.
But we aren’t.
There's a very large number of arbitrary ways we could divide a whole population into smaller groups. Hair colour, eye colour, blood type. If like myself you don't know your own blood type, what would you guess? Let's imagine William Hill invited you to place a bet on your blood type, and they were foolish enough to offer the same odds for each one. If you had no prior knowledge, what would your bet be?
Given the prevalence of the four different blood groups in the cartoon above, the most profitable strategy here would be to bet on "A", as that gives you the greatest chance of winning. Another way of looking at it, is that if everyone adopted that strategy, the bookmaker would lose the most money.
We can play a similar game with many different features of your life, not just your blood type. The hospital you were born in. The school you went to. The street you live on. Your employer. The bus you take to work. The country you live in. All of these examples, and many more, are collections of groups with differing sizes. You are not equally likely to belong to each group. You are more likely to have attended a school with more pupils than most other schools, and you are more likely to live on a street with more people than most other streets. This is always the case - there are no hidden assumptions about how streets were constructed. This effect becomes stronger when there is greater diversity between the different group sizes. The bottom line here is that:
We should expect to be in a large group, not an ordinary one.
Of the billions of planets in our galaxy, which are most likely to hold life? The standard approach to tackling this question is to assume that alien life requires water. Liquids such as water are very delicate - relatively small changes in temperature or pressure will cause it to freeze or boil - so the majority of planets are unsuitable for the long term storage of water, at least on the surface. This fragility helps narrow the range of planetary conditions where we should focus our search efforts. Here we’ll look at a new way to tackle this question, without assuming that life requires water.
We don't yet know the breadth of planet sizes on which intelligent life exists. Some will be larger than others. The larger planets have a greater area, and receive more energy from their star. Therefore they are capable of sustaining larger populations, on average. Combined with our earlier conclusion - that we should expect to be a member of a large population - this also means we should expect to be living on a large planet.
A similar connection between area and population is seen among countries on Earth. Those with a larger population also tend to have a larger area. This effect is not quite as strong as you might think, due to the way countries are formed. A tiny region of land is less likely to declare its independence if only a handful of people were living in that region to begin with. The smallest countries therefore tend to have slightly higher population densities. Overall though the trend is clear, larger countries do hold significantly larger populations. Most countries are smaller than sixty thousand square kilometres, yet most individuals live in a country of over one million square kilometres.
If we are to estimate the size of an ordinary alien planet - one that hosts intelligent organisms - we first need to make two decisions. The first is the connection between population size and planet size. The simplest approach is to suppose that, on average, the population density will not change with planet size. For small changes in planetary radius this ought to be a good approximation. For planets much larger than Earth one could imagine that a larger proportion of the planet’s surface - for example near the poles and the equator - tend to become uninhabitable. A more detailed study of planetary atmospheres, and the prevalence of water, is needed to give a better answer here. For now we shall stick with the simple model where the average population of a civilisation increases with the planet’s surface area.
The second decision is what breadth of planet sizes are inhabited. As mentioned earlier, the greater the diversity in group sizes, the stronger the selection effect becomes. For example, if all alien life forms inhabit planets of the same size, then by construction all alien planets are all going to match our one sample of the Earth. On the other hand, if life emerges on a wide range of planet sizes, then a strong selection effect comes into play. The bigger planets can hold considerably larger populations than the smaller ones, so in that case we should expect to be on a larger one. In other words, most alien planets will be smaller than the Earth.
At first glance our answer appears to have reached two different outcomes depending on the range of inhabited planet sizes. However there is a consistent aspect to these two scenarios. No matter what degree of variability is chosen, alien planets are very unlikely to be much larger than the Earth. To be specific, we can say with 95% confidence that another planet with intelligent life, such as our nearest neighbour, will have a circumference no more than 20% greater than that of the Earth.
The table above shows the odds a bookmaker ought to offer for the size of an intelligent alien species. Some examples of animals with adult body masses lying within each range are listed for reference. Where did these numbers come from? Let's begin with the following principle:
Physically larger species will on average have lower population densities.
This trend has been observed across the full breadth of the animal kingdom. From birds to fish to mammals and all the way down to insects and even bacteria. Is it reasonable to expect this trend to hold on other planets too? One might be tempted to argue that alien planets could provide radically different environments to what we're used to seeing on Earth, and as such we shouldn't dare assume anything about how biological systems function there. But we can be sure of one thing: all life in the Universe obeys the laws of thermodynamics. Every species in the Universe must be consuming less energy than is available in its surrounding environment. Ultimately that source of energy is the host star, in our case the Sun. The largest populations will be using up a good fraction of that available energy, but they can never exceed it.
Larger bodies cost more energy to maintain and to move around than smaller bodies. That's not only simple physics, but it is another trend which has been measured across the animal kingdom. So the maximum population a species can reach will tend to be less for larger animals than the smaller ones. To give an extreme example, if humans tried to match the worldwide population of ants, then our combined metabolic rate would require more energy than is provided by the Sun across the entire planet.
You might be tempted to think that most of our energy is spent moving around or by fighting against gravity. But actually the energy we use just from staying alive - called the basal metabolic rate - accounts for the bulk of our energy needs. Most of this is the power needed to operate our major organs such as liver, brain, and kidneys. Only around 10% is actually due to physical activity such as pumping the heart and breathing. But even if the setup was different on other planets, with different physiologies, and their energy demand was limited by movement, this kind of energy usage ought to increase for more massive creatures. We know this because we can be sure they obey the laws of physics.
"What if there's a type of large alien that is very energy efficient?"
Indeed, there may well be, but all that actually matters for our calculation is the average abundance of aliens of a given size. So even if there are planets which violate this trend, it doesn't matter provided these are either rare, or are counterbalanced by others which show a stronger trend in the opposite direction. It's extremely difficult to imagine a counter-balance to the Earth in which the largest creatures so vastly outnumber the smaller ones.
From a more social perspective, bigger animals simply need more space. How we decide our living arrangements, and those for other animals, usually boils down to our body size (budget airlines take note). We would feel very uncomfortable in rooms which are not at least a few times larger than us.
All of the above factors - both empirical and theoretical - suggest we should associate a larger body size with a lower population density. This won't be true for all cases, but again, we are only interested in the average. What are the consequences of this relationship? If larger species form smaller populations on average, then an ordinary individual should expect to be a member of a physically smaller species. So if a project such as Breakthrough Listen succeeds in hearing from another civilisation, it should be of no surprise to find that they are physically much larger than us.
Just how big should we expect aliens to be? In order to forge a tangible answer we must first be a little more specific in how population density is influenced by body size. A simple rule of thumb would be
A species with twice the body mass of another, will on average have half the population density.
In detail the trend is not always the same, some types of animal show a slightly stronger trend and others weaker, but the above statement is a good description of the general behaviour. And for our purposes, the average is all we care about.
To begin the calculation, we start with a blank slate. We will consider it equally likely that the Universe is dominated by intelligent life which is 1kg or 1,000 kg. If we had a solid understanding of how intelligence emerges from a menagerie of evolving creatures, then perhaps we could start from something more sophisticated than a blank slate. It might seem reasonable, for example, to assume that very small life forms, under 0.1 kg, won't be able to develop sufficient intellectual capacity, because their brains are so small. But the safest starting point is one of complete ignorance, so we don't apply any external limitations here.
Our best guess for an individual alien's mass is the same as our own, which is around 70kg. Then, what is our best guess for the size of an ordinary intelligent species? Tantalisingly, to answer this question we need to estimate only one quantity: how much variation in size exists between intelligent species. As was the case with alien planets, if all intelligent species are exactly the same size, the variability is zero, and we would conclude that all alien species must be the same size as us. But we can be sure that the variability is not zero. The mix of different circumstances, environments, and even changes in the strength of gravity will ensure that intelligent life comes in a fascinating assortment of different shapes and sizes. But just how much variability should we expect? Rather than having to pick a single value, we can actually select a whole range of values which we consider reasonable. That's an important feature of what's known as Bayesian statistics, that we can average over many different realities that we think are possible. So what we need to decide is not a single value of the variability, but a range. We need to pick the lowest and highest values that we think are feasible.
What's the narrowest spread of body sizes which could be considered reasonable? It would be extremely surprising if aliens showed more similarity in size than a small group of closely related species on Earth. There are seven species of great ape, ranging from the chimp's modest 50 kg up to the imposing frame of the gorilla which weighs in at around 160 kg. The specific numbers aren't important, only how much of a relative change in body mass there is between the seven different species.
What's the largest variation in body size we would consider to be reasonable? This is a little more tricky to pin down. It would be unwise to completely exclude the possibility of life being radically different from what we see here on Earth. But equally, one might expect some natural boundaries to be set at very large body sizes (due to the need to act against gravity). So this helps set our upper bound, for the greatest diversity we would expect between alien body sizes.
Now we have all we need - our data point of the human species, and the lower and upper bounds on the degree of variation. Running these through the calculation brings us to an answer: an ordinary intelligent species is about 310 kg. To put this into context, this is similar to the average mass of an adult polar bear (adult male polar bears can exceed 400kg, while the females are closer to 200 kg). What does this value of 310 kg really mean? Think of it like a spread bet in a sporting event. If a strong team plays a weak team, bookmakers offer a handicap of several points to the weaker team in order to ensure the odds of each team winning are even, at 50%. It's a similar situation here - it's not that we should expect an alien species to be exactly 310 kg, but there is an equal chance of an alien species being heavier or lighter than 310 kg. The full probability distribution is shown in the graphic above, along with some terrestrial species for reference.
If you'd like to learn more about the details of the calculation itself, here are a few relevant resources:
What are Bayesian statistics?
If you are keen to learn more about Bayesian Statistics, and already have a reasonably solid grounding in mathematics, I can highly recommend Professor David MacKay’s free textbook and lectures on Information Theory. I was very fortunate to be taught by David as a lecturer and supervisor.
Why should I believe I am a member of a large group?
The median individual is always in a group at least as large as the median group. A proof of this, which briefly appears in the MinutePhysics video, is available to download here.
Why should my group be different to most other groups?
If a variable (like planet size) is positively correlated with population size, then the observed mean will always exceed the group mean. A brief proof of this lemma is available here.
Where can I find the full calculation?
The scientific article is available at MNRAS Letters.
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.