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Okay, so we are figuring out, that at least for how we are running things now, our Earth can fit about 10 billion people. We can probably raise if your economy distributed resources more efficiently, but their is another route, SPACE!

Earth has a lot of problems

Anyway, so we get really efficient at going into space. My question is, how many humans would our entire support, until we start getting into population issues again?

  • As for technology, we get good at terraforming, world-building, and matter to hawking radiation conversion.
  • We also are time dilation ourselves (either by moving close to strong gravitational bodies, or by moving really fast.) We move a million times slower, relative to the galaxy itself.
  • I'm not asking this in terms of "connecting to machines inserting algae into our veins." I'm talking about where everyone has about a slightly better standard of living similar to Earth today. No really weird stuff.
    • Note though, that eating pure nutrients in liquid form isn't too unrealistic, even now. enter image description here
  • Don't forget that we will probably be using more energy than we do now.
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  • $\begingroup$ Are we living strictly on planets/moons, or are we also building space stations? $\endgroup$ – Josh Jul 28 '15 at 15:17
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    $\begingroup$ This isn't answerable with reasonable accuracy. The best that can be done is write our assumptions, dust off the Drake equation, assign values to the factors (along with our reasoning), and spit out a number. The answer would be lucky to be within 3 orders of magnitude. $\endgroup$ – Jim2B Jul 28 '15 at 15:18
  • $\begingroup$ @Josh Building stations $\endgroup$ – PyRulez Jul 28 '15 at 15:39
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    $\begingroup$ Where do you expect to get the material to build entire solar systems? Do you intend to disrupt the nebulae that are already building stars? ...Come to think of it, if we can build solar systems, why is there even a question of how large the human population can grow in the human-driven expansion of the galaxy? $\endgroup$ – Frostfyre Jul 28 '15 at 15:44
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    $\begingroup$ "We move a million times slower, relative to the galaxy itself." Uh, no. $\endgroup$ – Serban Tanasa Jul 28 '15 at 17:16
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So we've got a type III civilization on the Kardashev scale, and we want to figure out how many people it can support.

Answer: a lot.

But that answer isn't good enough. We want numbers.

The logical starting place is the amount of energy that the milky way gives out, which wikipedia says is around $10^{37}W$. This is the total amount of energy that our civilization can potentially harness to fuel itself. We can't directly fuel human beings on starlight, so we'll be converting this into a nutrient rich gruel for our humans to subsist on. (Probably produce through some inorganic process, as plants are fairly inefficient, and only use a portion of the spectrum our energy is available in.)

Of course, energy conversion into food won't be 100% efficient, even with some really advanced processes for doing so. Let's assume we get 50% efficiency in this process, and further assume that we only get to use 50% of the galaxy's energy for food production. This gives us a total energy of around $2.5\times10^{37}W$.

So how many people is that? Well, each person consumes 2000 Calories in a day, which is equal to 2324 Watt-hours (approximately), or an average energy consumption of around 96.8 Watts. Dividing our total energy available for human consumption by the amount of energy a person consumes, we get a total of around $2.5\times10^{35}$ people in our galaxy.

Of course, if all of those people are time-dilated by a factor of 1,000,000, we can increase this to a total of $2.5\times10^{41}$ people in our galaxy.

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    $\begingroup$ The numbers seem a little more complicated than this, but it looks like a good start. For example, did you account for planets needing energy as well so we can survive on them? Space stations need to maintain their own environment, so more energy we can't use. $\endgroup$ – Frostfyre Jul 28 '15 at 16:17
  • $\begingroup$ It makes a couple assumptions, but good answer. How long would it take to make all those humans? $\endgroup$ – PyRulez Jul 28 '15 at 16:25
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    $\begingroup$ I don't get the time-dilated bit. Wouldn't the energy to time-dilate people and food be better used in context to feed regular people regular food? Also, don't we need shelter, electricity, robo-sex-slaves, etc? $\endgroup$ – Serban Tanasa Jul 28 '15 at 16:54
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    $\begingroup$ @Frostfyre there's definitely quite a bit of room for error in these calculations. I assumed that we'd use 25% of our energy budget for habitation needs, but it could easily be 90% or higher. I'd hedge the numbers I came up with as "within two orders of magnitude, probably." $\endgroup$ – ckersch Jul 28 '15 at 17:06
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    $\begingroup$ "I can tell you with 68% certainty that we are 81% sure that 94% of the numbers are made up." :) $\endgroup$ – Frostfyre Jul 28 '15 at 17:38
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Since PyRulez has already made a great answer covering the energy angle of this question, I'll tackle it from a different approach.

There are 100 billion planets in the Milky Way (our galaxy). If we were VERY good at terraforming and perfect energy storage and distribution we could possibly live on all of them, though many planets would be too far away from their nearest star to get enough energy to be habitable. Let's go with the idea that we could only comfortable live on planets in the habitable zone of a star and orbit Sun-like stars, as well as be Earth sized. There are an estimated 40 billion of these types of planets in our galaxy. I presume these would be acceptable for terraforming.

It's difficult to say what we'd be eating in the future, but it's doubtful everyone will go vegan anytime soon. If we go by your assumption in the question that the Earth could support a population of 10 billion on current or near future diets and technology, and there are 40 billion Earth-sized planets out there. Each of these Earth-sized planets would more or less be able to support the same number of people.

A conservative estimate of the total human population that could be supported on planets (not including space stations) in our galaxy would be 10^9 x 40^9 = 4x10^20

This could no doubt be improved upon with better energy conversion technology, living in space stations so planets can be devoted solely to food production and new types of crops.

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Population capacity very much depends on technology. The population limit in Australia increased because of the introduction of farming and the decline in hunting and gathering.

If humans require earth like planets to live, then the population limit of the galaxy would be considerably lower than if they were able to teraform their own environments.

Lets say that humans could mine out asteroids for resources, and then build little factories on those asteroids that feed space dust into vats of genetically engineered bacteria, and then synthesize food from those bacteria. Lets say that humans had cold fusion technology, and could convert hydrogen gas into raw energy, and as a bi-product, produce every other element that we have use for. Humans could systematically convert every piece of debris floating around interstellar space into automated space stations that collect dust and astroids in order to increase the capacity of its farming operations. They could then blow up every star and planet to create more dust and debris to harvest util every piece of matter in the galaxy had been converted into either a human, or the environment that sustains them. They can then genetically engineer themselves to be smaller, so that each human requires less matter to exist.

The population of the galaxy could potentially be inconceivable... or it could be relatively minuscule.

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If we're allowing time dilation, perhaps we could just send people straight into sagittarius A* towards the end of their life, so that from the point of view of the rest of the galaxy they never die (Lets ignore what happens in their own frame of reference). Then we can get on with the task of converting the galaxies mass into people. There is about $10^{41}$kg of normal matter in the galaxy (I'm assuming you can't turn dark matter into people), so I think $10^{39}$ people might be an absolute upper limit, giving us ~30kg of energy per person for our extensive breeding and transport program.

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  • $\begingroup$ Being thrown in to something towards the end of your life counts as "weird" I think. $\endgroup$ – PyRulez Jul 29 '15 at 16:40
  • $\begingroup$ Well you could make them live on a space station arbitrarily close to the event horizon for a similar effect if you want to be nicer about it. $\endgroup$ – patstew Aug 14 '15 at 8:16

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