Imagine a spherical alien…


I’m reading a strange paper with an interesting title: The Nature of Inhabited Planets and their Inhabitants. I’m disappointed to say it doesn’t say anything believable about inhabited planets or aliens, but is more of an essay on statistical distributions that uses planets and aliens as a sample exercise. Here’s the abstract:

Earth-like planets are expected to provide the greatest opportunity for the detection of life beyond the Solar System. This notion stems from an assumption that the Earth constitutes a simple random sample amongst inhabited planets. However, in the event that other intelligent species exist, our planet should not be considered a fair sample. Just as a person’s country of origin is a biased sample among countries, so too their planet of origin is a biased sample among planets. The strength of this effect can be substantial: over 98% of the world’s population live in a country larger than the median. Any variable which influences either the population size or birth rate is susceptible to selection bias. In the context of a simple model where the mean population density is invariant to planet size, we infer that an inhabited planet selected at random (such as our nearest neighbour) has a radius r<1.2 r_Earth (95% confidence bound). If the range of habitable radii is sufficiently broad, most inhabited planets are likely to be closer in size to Mars than the Earth. Furthermore, since population density is widely observed to decline with increasing body mass, we conclude that most intelligent species are expected to exceed 300kg. Primitive life-forms are a pre-requisite for advanced life, and so the planets which host them must trace at least the same volume of parameter space. Our conclusions are therefore not restricted to the search for intelligent life, but may be of significance when surveying exoplanets for atmospheric biomarkers.

The interesting point it makes is an attempt to infer the statistical distribution of planetary properties from our limited sample. For instance, that a typical rocky planet is going to be smaller than Earth; therefore, our experience may bias us to think that Earth-sized planets will be the cosmic average, but in reality, we’re more likely to be at the upper end of a distribution. This requires thinking purely statistically, of course, and ignoring other possible constraints, like that smaller planets are less able to hold onto an atmosphere, which might mean that Earth is on the low end of the requirement of rocky planets with an atmosphere.

The author knows this and openly acknowledges that he’s throwing away a lot of parameters. That’s fine in an exercise in statistical analysis, but not so good if you’re actually trying to predict the nature of inhabited planets.

So one conclusion is that the typical planet will be smaller than Earth. Fine, with significant caveats. His second conclusion is that the average intelligent life form will weigh 300kg, and that’s where he loses me. Once again, his calculation hinges on a limited model, reduced to just a few parameters, so he can assess where on the expected distribution our one known data point, the size of humans, falls within the distribution.

Throughout the animal kingdom, species which are physically larger invariably possess a lower population density, possibly due to their enhanced energy demands. As a result, we should expect humans to be physically smaller than most other advanced species. By marginalising over a feasible range of standard deviations, we conclude that most species are expected to exceed 300 kg in body mass. The median body mass is similar to that of a polar bear.

The logic is really unclear here, and the rest of the paper doesn’t help much. Once again, the question is where do humans fall on the expected distribution — are we smaller than we ought to be for an average species, or are we larger? The author comes down on the side of estimating that we’re individually on the small size. Why? I don’t know. He keeps harping on how species at higher trophic levels (think plankton vs whale) are both physically larger and more sparsely distributed, so population density ought to be a correlate of size.

But that makes no sense to me. If density is the proxy we’re using to estimate body size, and density and body size are inversely related, it seems to me that we have a relatively high density for our body size among comparable animals, and therefore we’re on the large end of the highly populated close-packed social animal scale. So by the same reasoning as his estimate of planet size, shouldn’t the average alien be smaller than we are?

And why is he using this simplistic relationship of body size and population size to estimate the properties of intelligent aliens? I’m certain he’s making a lot of simplifying assumptions that are unclear to me, and I’m also burdened with a lot of complicating assumptions as a biologist, so I’m just not seeing this argument at all.

Anyway, that is more a reflection of my difficulties with thinking like a statistician — maybe some of my more math-minded readers can puzzle it out. I’m willing to learn more about this kind of statistical thinking.

But I still have to say that the fact that he’s got to throw away contingency and biological constraints in order to simplify his assumptions enough to make this calculation means that it has no practical utility at all. There is no evidence or biological rationale for arguing that the typical member of an intelligent species is going to weigh 300kg.


  1. remyporter says

    It’s not that we consider the Earth a random sample, it’s that the Earth provides the only data-point we have for where life can evolve. We know it worked here. Presumably, it can work in similar environments.

  2. moarscienceplz says

    Other than humans, most of the species that seem to be remarkably intelligent are much smaller than us: Corvids, rats, parrots, octopuses. I don’t see why large size is mandatory for evolving intelligence.

  3. twas brillig (stevem) says

    [examples of intelligent, non-primates] Corvids, rats, parrots, octopuses.

    Don’t forget CROWS!! I recently read, that crows are surprisingly much more intelligent than ever imagined (as in in real, scientific measurements, not just metaphorical amazement at a single incidental behavior). </minor quibble>


    I don’t see why large size is mandatory for evolving intelligence.

  4. unclefrogy says

    I can’t follow the argument at all. The starting point is arbitrary and the conclusion predetermined all the reasoning is based on selective data.
    uncle frogy

  5. brucegee1962 says

    What I’ve heard from the exoplanet search is that, so far, they’ve found lots of gas giants (which was predictable) but that they’re mostly much closer to the sun than ours are (which was more of a surprise).

    If the giants are hogging the “Goldilocks zone” that would be a problem — except that all the gas giants we know of have plenty of moons. So perhaps our biosphere is unusual for being located on an actual planet, and moon life is the norm.

  6. says

    You’re all forgetting: the paper excludes discussion of prerequisites for intelligence, just as it excludes, for instance, the relevance of planet size to atmosphere.

    It’s not about geology or biology at all. It’s about extracting statistical expectations from very tiny data sets.

  7. monad says

    @7 brucegee1962:
    More of a surprise there are many in the first place, sure. But that they are the majority is still likely an artifact of how we detect things, which is biased both toward large planets and toward ones closer to the star.

  8. John Harshman says

    Perhaps the proper lesson to draw here is that you can’t really draw much of a statistical expectation from a tiny data set, especially when the whole set is one data point.

    But the 300kg thing seems entirely reasonable, assuming that any alien species is likely to invent couches, video games, and Doritos.

  9. Phillip IV says

    But that makes no sense to me. If density is the proxy we’re using to estimate body size, and density and body size are inversely related, it seems to me that we have a relatively high density for our body size among comparable animals, and therefore we’re on the large end of the highly populated close-packed social animal scale.

    If I understood it correctly (which is possible, if unlikely), he’s using two different parameters to arrive at his graph – one is population density, and the other is the distribution of body mass among species on Earth, or more specifically distribution of body mass among the great apes.

  10. Amphiox says

    Ironically, spherical aliens, in the form of cocciform bacteria-like entities, might actually be one of the most common alien body shapes….

  11. Amphiox says

    I don’t see why large size is mandatory for evolving intelligence.

    Well, there is a physical limitation on how small and how tightly packed something that functions as a neuron can get and still function, so, if we make the assumption that alien life is cellular, and intelligence requires a certain number of neuron-like entities, there would exist a minimum size below which high intelligence becomes increasingly unlikely.

    Of course that size limit could be much much smaller than humans. The Portia spider here on earth is puny but it has remarkable behaviors.

    And aggregate intelligences could have individual members as small as single cells.

    On the other hand, if we assume that human level intelligence requires social living, then there may be a minimum population density below which group living is not sustainable and thus human like intelligence unlikely to evolve, which would mean that it would become increasingly unlikely that very large animals with low population densities would evolve intelligence.

    Furthermore, even if intelligent, culture and technology advances faster if there are higher population densities supporting more individual minds to collaborate on problems. One should expect that culture and technology would advance faster in a population of 1 million smart cuttlefish than on a population of 500 smart Sperm Whales, all else being equal….

    Speculation about alien life is fun because you can twist your reasoning in any direction to support any preconceived notion, or even all of them at the same time, and still sound statically valid.

  12. psweet says

    At this point, any attempt at modeling statistical properties of planets runs into a serious issue of bias. Basically, our methods for finding planets are heavily biased in favor of large (bigger signal) planets close to their star. (Either because of a stronger gravitational attraction for the Doppler-shift “wobble” method or because of orbital periods with the transit method — Kepler was running for five years, I believe, and assuming that we need three passes, and that the first pass occurs as soon as you start looking, then we might be able to detect Mars. Anything farther out is impossible to detect this way, since there hasn’t been enough time to see three passes. Something as far out as Jupiter might not make a single pass before we stopped looking. By the time you reach Saturn, that’s the most likely outcome.)

  13. says

    I spent a bit of time entertaining the notion of a soft sci-fi setting where humanity is the odd species out. First contact over long range communications, aliens invite humans aboard their ship/station after confirming that they can breath each other’s atmosphere and not get Rigelian plague or whatever. But when the Earthers get within visual range and try to dock. “Um… We can’t fit through your airlock.” “…I think we made a mistake converting your units of length. How tall did you say you were, again, Captain Gulliver?”

  14. machintelligence says

    Imagine a spherical chicken … wait, that is actually a pretty good approximation.

  15. brett says

    PSweet beat me to it, but our exoplanet finding is still biased towards bigger planets in closer orbits around smaller stars. We’ve found a couple of planets around stars bigger than red dwarfs* in what we think are habitable orbits, but only a handful – and most of those are still stars smaller than our sun, like K-class stars. It’s a massive improvement to find “super-Earths”** versus the gas giants we used to only find, but still a big limitation.

    If or when we can reliably find planets in the Mars to Earth range in Earth-like orbits around Sun-like stars, then we’ll know for sure as to whether Earth is common in certain properties. Even better would be if we got oxygen, methane, nitrogen, and other such signals after doing spectrographic analysis on the light coming off their atmosphers.

    * Red dwarfs seem rather dubious to me in terms of habitability. They can flare up heavily, or have major sunspot outbreaks that drastically dim the luminosity of the star for years at a time. They have a long “hot” phase early in their life-spans for a billion or so years where they are much more luminous than they will be later on for most of their lives (meaning planets in what would otherwise be habitable orbits will likely have runaway greenhouse effects). And if the planets are really close in some of their habitable zones, they’ll have issues with tidal heating.

    ** Some of the modeling and analysis of extra-solar planet samples seems to indicate that there’s a threshold around 1.5 Earth radius for planets (which translates to about 5-6 times Earth’s mass). Planets below that are much more likely to be rocky terrestrial planets with Earth-like densities (or more dense), while planets above it tend to turn into “gas dwarfs” with hydrogen atmospheres that grow increasingly thick.

  16. birgerjohansson says

    To avoid hot jupiters (who will disrupt orbits of terrestrial planets) just discount stars with a high content of metals.
    Our sun has 1,7% matter that is not hydrogen or helium. The cut-off point for systems with hot jupiters is higher, I don’t recall exactly where.

  17. Daniel Dunér says

    Other than humans, most of the species that seem to be remarkably intelligent are much smaller than us: Corvids, rats, parrots, octopuses. I don’t see why large size is mandatory for evolving intelligence.

    Hm, no. You’re not wrong in that they’re remarkably intelligent. But I can simply counter with pigs, primates, cetaceans and elephants that are just as often cited for their perceived intelligence.

    I think we generally tend to underestimate other animals, due to the massive speciecism inherent in our culture and thinking. If you look at the research you find lots of intelligence in most complex animals. Including cows getting kicks from figuring stuff out, fish using tools or sea lions learning cross-modal transitive logic.

  18. ijkcomputer says

    Lemme give it a shot.

    This is a cousin of the “Doomsday Argument”, and in a sense of the anthropic principle. It’s a purely statistical argument, but it’s potentially useful (though certainly not conclusive.) Let me try and put it in another context.

    The basic idea here is, “the odds – literally – are that I’m a typical random observer.” So, say, suppose I wake up with amnesia. I know nothing about anything. (Except, apparently, Bayesian statistics, I guess?) Wondering about my species, I measure my height, which happens to be 5’9″. I figure human height probably follows a normal distribution, and the odds are I’m more or less in the middle; lots of people are around my height.

    I happen, in this case, to be right. Had I woken up and found I was 6’10”, I would have been wrong to guess most people are about my height. But in a sort of hypothetical sense, I will rarely wake up and find I’m 6’10”; I’ll probably be around the average height. Right? So I’ve made a statistically pretty good prediction.

    Now it gets a little weirder. Suppose I instead say, like the paper suggests, “is my country bigger than average, or smaller?” The answer is, probably bigger; most countries are smaller than mine. I know this without knowing anything about the size of my country, or even its name, because I am more likely to wake up in a country with a larger-than-average population. Right? The distribution of the-number-of-people-in-countries-of-a-particular-size is certainly not normal! Our person with amnesia is far more likely to wake up in China or India than in Luxembourg or Bermuda.

    The size thing is a continuation of that story. If we assume – and obviously one could argue with this assumption – that, as in the wild, bigger-bodied species tend on average to have lower total populations (there are far more ants than sperm whales), and we’ve previously sorted out that we are more likely to be part of a large-populationed-species, then we must conclude that we are also more likely to be part of a smaller-bodied species.

    To put it a slightly different way, suppose the Universe had two intelligent species, “Space Sperm Whales” and “Space Ants”. We awaken and, due to some kind of crazy sensory deprivation device, can’t tell anything about which we are. But we know that space ants are tiny and there are trillions of them, while space whales are huge and there are only dozens of them. Well, knowing nothing about ourselves, chances are we’re an ant. Yes?

    There are both philosophical and practical questions that can be raised about this argument. And it’s only a probability from ignorance; it doesn’t mean that we can’t turn out to have been the guy who was just actually really tall. And PZ’s point that we could / should incorporate what we know about life and intelligence is both logically reasonable, and entirely possible to do in Bayesian stats, and many further interesting points might come out of attempting to do so. But at any rate I hope I’ve explained a bit of what the idea is.