A Galaxy On Earth

Our galaxy has about three hundred billion stars, and Earth today has about seven billion people. Assuming only half as many useable planets as stars, we could combine these two numbers into an initial crude guess for the size of a galactic civilization, and define a “galaxy of people” to be a thousand billion billion (or 1021) people. Now consider some famous galactic civilizations in science fiction.

One of the most popular science fiction stories ever was Issac Azimov’s Foundation series. It tells of the fall and rise of a galaxy-wide civilization, whose capital, Trantor, was a planet-wide city a kilometer deep into the ground. Trantor’s population was said to be forty billion, in a galaxy with millions of populated planets and a total population of a million billion (or one millionth of a “galaxy” as defined above).

Star War‘s Coruscant is also a planet-wide city and capital of a galaxy wide civilization, with planetary population of a thousand billion, in a galaxy also of millions of planets and a total population of a million billion. Some say Coruscant’s buildings averaged two kilometers tall. In Star Trek‘s Federation of 150 planets a few centuries hence, which controlled a few percent of the galaxy, each planet had no more than about our Earth’s seven billion, though some say the Federation held ten thousand billion people.

These all seem like dramatic underestimates to me. If Earth were paved over with a city the density of Manhattan today (1.6 million in 59 square kilometers), Earth would have a population of 14 thousand billion. Since Manhattan now has an average building height of 25 meters, a two kilometer deep version could hold a million billion people, and a two thousand kilometer deep version (Earth’s radius is 6400km) could hold a billion billion people.

There is roughly another thousand times as much useable material nearby, in other planets, comets, and the sun itself, allowing a solar-system population perhaps a thousand times larger. This brings us to a thousand billion billion, or a “galaxy” of people, the same as my initial crude population estimate for an entire galaxy above, and vastly larger than most science fiction galaxy estimates.

Furthermore, android ems (whole brain emulations in simulated bodies) could take up a lot less space than humans. I once somewhat conservatively estimated that an em might stand at 1% of human height (and run one hundred times faster). Since such an em would take up only one millionth of a human’s volume, a two kilometer deep Earth city could hold a “galaxy” (or thousand billion billion) of ems. And a solar system civilization might fit a billion billion billion ems, or a million “galaxies.”

Of course we have a long long way to go, not only to generate such huge populations, but also to develop the energy, manufacturing, heat-dumping, etc techs to allow us to support them. And yes, eventually we would run out of energy and material near our Sun, and need to go elsewhere to grow.

But we have strong economic reasons to stay close to one another as long as there is enough energy and material nearby, and especially as long as we continue to innovate. So most of our descendants’ economy should stay close to our sun until congestion here gets severe. We may well have a solar system population of a billion billion billion before the time comes when most of our descendants are closer to other stars.

Most science fiction seems to vastly underestimate the population that a single planet or star can hold, and the strength of the economic pressures to keep an economy close together, rather than spread across vast distances. Someday we will learn to tell stories that treat planets and stars as the vast spaces of possibilities that they really are.

Added 11a: Even an unmodified sun radiates enough energy to cover the calorie consumption of over a hundred “galaxies” of humans, and far more ems.

The timescale to grow from today’s population to a “galaxy” of descendants would be 600 years at an industry-style 15 year doubling time, 40 millennia at a farming-style thousand year doubling time, and four years at at next-singularity-style monthly doubling time.

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  • dWj

    Unless there is a lot of relativistic travel, a civilization spread over even hundreds of light years will experience enough allopatric isolation to drift apart; cultural memes can, in principle, travel at the speed of light, but I think, given the way humans “do” culture, most light-speed cultural transmission would be weak; I don’t think you would have a single civilization spread over more than a few hundred star systems before different parts would become effectively different civilizations. At least not if the agents are recognizably human.

    • Konkvistador

      Parallel evolution might mitigate this to a certain extent.

  • http://abstractengineer.blogspot.com/ Alex Waller

    If Earth were a city-planet like Coruscant, how do we provide food for our population? Most science fiction involving city-planets is hazy on how the natural resources are provided to a city like that. Even turning Mars into a farm world would only get us so far.
    It seem like you shouldn’t base a theoretical population limit on square footage of Earth, but rather on the limits of resources required to sustain the population there.

    • Khoth

      Star Wars isn’t really about that sort of thing, but it is described in Foundation – Trantor imports the vast majority of the natural resources it needs from other planets. The fragility of that system contributes to the fall of the empire.

      • billswift

        As far as I can tell, Star Wars has the purpose of seeing how stupid they can make a “science fiction” movie and still get people to pay to watch it.

      • Star wars fan

        Actually, in star wars there are whole planets dedicated the agriculture where jedi unable to become jedi knights are assigned to use the force to speak with plants and accelerate their growth. Further a majority of the worlds in the mid to outer rim section are mainly agricultural or used for natural resources to support the larger population worlds.

      • tony

        I’ve read some interesting talk about urban hydroponic factory farms that could make sense in a city planet context.

    • Solutionist

      Perhaps hydroponics would be a viable solution for food supply? Though requiring more energy intensive methods, it would dramatically reduce the square meters of space needed. This would be especially effective if the hydroponic systems were multi-storied structures, either set below the other builds, or perhaps between them. Of course, more efficient recycling of water resources would be necessary to allow the increased human population to be sustained. 

  • spindritf

    What about sprawl? Even on Earth Manhattan or Hong-Kong are more of an exception than the rule.

    • Solutionist

      Urban sprawl is a product of our present economics system more then anything else. As it becomes economically viable for taller buildings to be constructed, with a sufficient apartment size catering to human needs, there will be considerably less sprawl. A city with an average height of a thousand meters should be possible with our current materials, but simply isn’t possible due to economics..

  • http://www.uweb.ucsb.edu/~criedel/ Jess Riedel

    Exponential notation throughout would make this a lot easier to read.

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  • Roy

    Food could be produced in huge orbiting farms, some possibly orbiting the sun. The Ag technology of half a milenium in the future should not be underestimated

  • http://ourdinnertable.wordpress.com Seth

    Nice post. As a side note, since I was young I’ve had an issue with single climate planets portrayed in science fiction. The tiny island of Maui has several climates. I just didn’t find single climate planets that convincing.

    Looking forward to the day I can drop my consciousness into a box and go where ever I want, refueling with some solar cells or by breaking some atoms apart.

  • lurking_physicist

    Scattering around the universe reduces existential risks. You want your eggs in baskets that are as far as possible from one another, and different kinds of baskets too. In a post-singularity setting, even a meme may have catastrophic consequences.

    This is an important theme in the Dune universe.

  • Darren

    How well does this model explain the population density of Europe before the colonization of America?

  • Proper Dave

    Heh, I just red Zendegi by Egan and his satire seems almost spot on…

    Anyway c is likely above 100, for your upload EM scenario, more in the 1000’s range if you want any fidelity in your biological and physics model (remember that Electromagnetic coupling between neurons discovery of earlier this year?) , remember we are simulating the brain without understanding it’s “macro” functions.

    EM’s needing many kilowatts isn’t going to take over the world, not to mention the first one is going to need a megawatt powered supercomputer (and run many times slower).

    Now if you have a couple of Jupiter masses of computronium all bet’s are off, you’ll definitely save the world!
    :)

  • Neal

    Of course we have a long long way to go, not only to generate such huge populations, but also to develop the energy, manufacturing, heat-dumping, etc techs to allow us to support them.

    If such technologies are possible.

    So most of our descendants’ economy should stay close to our sun until congestion here gets severe. We may well have a solar system population of a billion billion billion before the time comes when most of our descendants are closer to other stars.

    Has this been considered as a possible answer to the Fermi paradox?

    40 millennia at a farming-style thousand year doubling time,

    In the grim darkness of the 41st millennium, there is only war.

    • Scott

      I’ve seen it mentioned in Charles Stross’s Accelerando – the solution to the Fermi paradox is given by the speed of light.

      Not his argument, but: all things being otherwise equal, miniaturization is preferred over expansion – you want to be as close as possible to anything you’re interested in, to minimise lightspeed delay. This is a concern for humans even now; ask any gamer whether they like playing first-person shooters on an overseas server.

      Our effort goes into getting smaller rather than securing new planets. As I currently understand it, we might be able to spot a planet developed like ours. Drop our size by one order of magnitude and it’s harder. Drop it by two or more and I’m pretty confident we wouldn’t be able to tell Earth from any other planet.

      To paraphrase Hugo deGaris from last year’s Australian Singularity Summit, we take this to the extreme – civilisations keep shrinking, first through nanotech, then femtotech, and so on – and the Fermi paradox might have a surprising answer: we DO see intelligent civilisations, whole galaxies of them! We just call them quarks and haven’t been able to look inside yet.

  • Brandon Reinhart

    Robin, you may have interest in reading the paper “Applied Cosmology and the Long-Term Fate of Intelligent Beings” by Cirkovic.

    On page 12 he gives an equation for a rough estimate of quantity of information lost per 100 years of delay in started the colonization of the local supercluster. This equation is defined in terms of solar luminosity, time-averaged fraction of free-energy that hypercivilization converts into work, temperature of the calculations, etc.

    He estimates that the number of potentially viable human lifetimes lost per 100 years of postponing the onset of colonization is ~5 x 10^46.

    As an aside, was the size of the Culture ever estimated?

  • bbsmith

    Steve Sailer’s observations on affordable household formation and demographics mitigate against this scenario. The population growth in rural areas in the developed world is still positive, while population in dense areas like Manhattan, Tokyo, and Hong Kong are extremely negative, a drop of about 50% per generation. Essentially, this “urban planet” would just genocide itself down to the point where civilization is once more mostly suburbia, or even mostly rural (the suburban population growth rate continues to decline too and will probably be negative soon).

    • http://entitledtoanopinion.wordpress.com TGGP

      Evolution would eventually adapt folks to the new dense urban environment.

      • Solutionist

        Perhaps, though I think it more likely that humanity will advance it’s technology to the point where our cities meet the requirements of our present psychology.

    • Solutionist

      Isn’t the present birth rate in developed countries, and especially urban environments simply a product of the economics of this system? 

  • http://daedalus2u.blogspot.com/ daedalus2u

    10e18 people (a billion billion) will dissipate ~100 watts each from their metabolic processes. That is 10e20 Watts, or about 574 times the heat the Earth receives from the Sun (174 petawatts).

    To dissipate this much heat by radiation into space, the surface of the Earth would have to get hotter, given an average temperature of 287.2 K now, the temperature would have to go to ~1400 K to radiate that much heat into space.

    • Scott

      It’s possible to turn heat back into work – thermocouples spring to mind – and it’s then possible to remove that energy from the Earth without boiling the crust (safety concerns aside, petawatt lasers aimed at the asteroid belt, anyone?)

      • http://daedalus2u.blogspot.com/ daedalus2u

        No, that doesn’t work. You end up with second law of thermodynamics problems. The only way to get rid of heat is to dissipate it to a sink at a lower temperature.

        Thermocouples only generate electricity from a temperature difference, and there is heat flow from the hot source to the cold sink and only a fraction can be converted to electricity.

        Lasers are not emitting heat, they are emitting work.

        In principle you could pump the heat to a higher temperature to emit it with a lower area surface, but that takes work and that work also has to be dissipated at heat at the higher temperature. If you double the temperature (to 2800 K), you only need 1/16 the area. But pumping that heat from 1400 K to 2800 K would take work equivalent to the heat you are pumping, so you would have to dissipate twice as much so you would need 1/8 the area.

        You would have to pump the metabolic heat from 300 K to 1400 K in the first place. I neglected that but it would be more than the metabolic heat (~5x more) to do so.

  • http://www.nancybuttons.com Nancy Lebovitz

    But we have strong economic reasons to stay close to one another as long as there is enough energy and material nearby, and especially as long as we continue to innovate.

    This depends on how much you want to innovate. If you want to do something significantly different socially, you want some distance.

  • Michael Wengler

    In terms of both meat-based humans and sims it seems the energy available would speak more to the limits of population than the volume.

    The U.S. in 2008 ran on 10 KW power per person of generated power. Another 100 W per person of food can be ignored for the purposes of this calculation.

    The total solar energy hitting the earth is 2e17 W (200 Million Billion W). At 10 KW each, earth could support 2e13 people (20,000 Billion). If Earth were populated as densely as Manhattan, Robin says 14000 Billion people. That is close to the limit if we continue to need 10 KW each.

    What if we increase our solar collecting area? Dyson sphere is the limit, a sphere at the radius of earth surrounding the sun getting the Sun’s total power output available for use. That ups the ante by a factor of 0.5 Billion.

    The total energy output of the Sun could support 500 Billion Billion people at 10 KW each, the current American usage rate.

    Now do ems require less power than current meat-people? A current laptop runs about 5-10 W when running. A smartphone ~0.2W. Neither of these is even vaguely close to running an Em at this time. Presumably, when and if ems are runnable, it won’t be too long until they are runnable on laptopt/smartphone form factors. If this is true then ems will enjoy a significant power advantage over meat-humans.

    • Proper Dave

      “Now do ems require less power than current meat-people? A current laptop runs about 5-10 W when running. A smartphone ~0.2W. Neither of these is even vaguely close to running an Em at this time. Presumably, when and if ems are runnable, it won’t be too long until they are runnable on laptopt/smartphone form factors. If this is true then ems will enjoy a significant power advantage over meat-humans.”

      Not a chance, EM’s will need thousands of petaflops, with any accurate biophysical model under the hood (which will be needed, if you are going to “upload” any human brain). You may have some intelligence at teraflop ranges (your future smartphone) but it won’t be an EM.

  • Vaniver

    Most science fiction seems to vastly underestimate the population that a single planet or star can hold, and the strength of the economic pressures to keep an economy close together, rather than spread across vast distances.

    <3
    I am long-term pessimistic on space exploration for exactly this reason, but most of my friends were raised on science fiction and don't seem to fully realise that without FTL everything collapses.

    • billswift

      >without FTL everything collapses.

      Not necessarily. What about using fusion, running on ice “comets” between the stars, as part of a gradually extending sphere. That is, many small, dense communities rather than just one super-mega “community” around the sun.

  • http://speculative-nonfiction.blogspot.com Michael Caton

    This immediately suggests another Fermi-paradox-relevant argument. If as Robin calculates here, the energy and material from our solar system can support so many more cells (be they human or otherwise), and if we think there are aliens elsewhere that got a head start, shouldn’t some of them have expanded to fill at least their own solar system much more effectively, and more efficiently use the matter and energy available? So assuming the calculation is correct the question again becomes, where are they? Shouldn’t we see the effects? Either the dust we see around so many other close stars IS them (which begs the question of why they’re not here) or I’ve just given Robin more ammo for his Great-Filter-is-Ahead argument.

    • http://hertzlinger.blogspot.com Joseph Hertzlinger

      When we look at the apparent distribution of galaxies, we see large voids where the suns don’t shine. Obviously, ETs are intercepting the light. We don’t see them around here because the nearest void is a few hundred million light years away.

      They’ll get here eventually. Just be patient.

      • http://daedalus2u.blogspot.com/ daedalus2u

        Interesting explanation for dark matter. ETs capturing and using all the energy within a volume and radiating the waste heat at the ambient temperature so they are invisible against that background.

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  • Modernjan

    Why not have planets with 40 billion people on them?

    Well how about this: nobody wants to live on such a planet (no fresh air, no peace and quiet, no privacy, no space, no natural beauty) and since few people actually want to raise 10 kids, we won’t create 40 billion people worlds unintentionally either. Oh yeah, a world of 40 billion people will burn through resources very quickly, that’s why a 40 billion people world doesn’t make economic sense either, when you also consider the long term.

  • Crichton Costello

    Maybe the population estimates are within reality who knows the Galaxy is a huge entity. But travel will be an interesting problem unless you can have instantaneous transfer but then energy becomes the limiting factor for population, food and transportation. Older civilisations if they exist are most likely wiser and more cautious and not prone to long distant commutes.