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I want to create a world set on our Earth but with humans converted entirely to machines, so the population can be larger than would be possible with biological humans.

In contrast to biologically shrinking humans, as the population increases they transfer their minds into machines that can sustain an entire human mind without the need for a brain. Some of these have robot bodies, others exist only as computers. Over time as the population increases all other life is wiped out, and human machines exist as a maximised population on a planet devoid of biological humans or any other biological creatures (no need to explicitly wipe out microbes, but no effort is made to support them - all energy gathered is used for the human machines).

If they make use of the entire surface of the Earth, collecting as much solar power as possible without overheating the Earth beyond what the machines can withstand (no need to preserve biological life) what is the maximum population that could be sustained long term?

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  • $\begingroup$ You're basically talking about putting ourselves in The Matrix right? $\endgroup$ – Liath Oct 8 '14 at 13:46
  • $\begingroup$ @Liath yes if the population is larger than can fit on the surface of the Earth as tiny robots then most people would have no experience of the outside, but could still interact with each other virtually. $\endgroup$ – trichoplax Oct 8 '14 at 13:52
  • $\begingroup$ Any particular reason to limit to solar power and the earth? $\endgroup$ – NPSF3000 Oct 9 '14 at 1:56
  • $\begingroup$ @NPSF3000 No need to limit to solar power if you can demonstrate that they could use more than that and still keep the Earth cool enough for the machines to operate. Any additional power sources should be similarly sustainable - I want to know the population that can be sustained not just an achievable peak value. $\endgroup$ – trichoplax Oct 9 '14 at 6:28
  • $\begingroup$ @NPSF3000 The Earth just happens to be the setting that I'm asking about. The maximum population in a different setting would be a different question. There may be colonisation of other places but it's the sustainable Earth population that is required here. $\endgroup$ – trichoplax Oct 9 '14 at 6:36
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For a back-of-the-envelope energy balance, I think we can make some basic assumptions:

  • The human brain is reasonably energy-efficient, and it is a difficult but feasible target for a machine to run at the same efficiency. We are a long way from that goal currently.

  • Similarly for human-body level activity for sensors and manipulating objects. This may be an over-estimate, but may compensate for a likely underestimate for running the brain. The two values are of the same magnitude, so it doesn't make a substantive difference for the kind of estimate we will make. In addition, we may want to have communications networks and other energy-expensive systems to create an environment for these brains to exist within, and we can use our body-equivalent budget for that.

  • Therefore we can guesstimate that we can run one machine for the same energy cost as one human at a personal level, but we have broken away from much of the need to have an ecological footprint (water, air, space for growing foodstuff).

  • Put aside an arbitrary percentage (say 50%) of energy for maintenance of the machinery, at all scales from minor repairs to the presumed chip-fabrication plants etc.

A typical human uses an average of around 100 Watts of power. Roughly 20 Watts of that is used directly by the brain.

A 20% efficiency solar cell could collect around 200 Watts of power per square metre. Halve that to 100 Watts for maintenance etc.

So very roughly we can run one of our robots for every square metre dedicated to collecting solar energy.

There is roughly 50 million square kilometres (each of which is a million square metres) of the Earth's surface currently dedicated to pasture or growing crops. This part of the surface is going to be suitable for our solar cells. We could maybe get more if we added deserts etc, but we know that the arable land can be settled by humans, therefore we don't have high costs for difficult repairs or damage from hostile environments - none of which we can really estimate.

So, in short I think roughly 50,000,000,000,000, or the equivalent of 7,000 times the current Earth population.

Of course this is a very rough estimate with many many assumptions. You could easily multiply or divide by 100 by adding some argument or counter-argument.

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  • $\begingroup$ Interesting estimate, but if OP wants maximum possible, we can add few improvements: (1) humans sleep 30% of the time (2) brains is extremely inefficient, most of the energy is spent to pump Na+ ions across cell wall to build electric potential, (3) most of brain is used to run biological functions of the body which would not exist (4) to get more energy we can build solar panels over desert, wind turbines and even nuclear power plants, to power several orders of magnitude more brains. Energy would unlikely be a limit. $\endgroup$ – Peter M. Dec 9 '14 at 12:31
  • $\begingroup$ @Peter: I agree. However, I think the additional thinking is covered in a general hand-waving way by my last paragraph. Ultimately, this is a very difficult estimate to make, with many assumptions that could be argued to alter the estimate by an order of magnitude. I think the answer needs to stop after just a few assumptions, otherwise it will be a gigantic pile of conjectures. It might be simple though to assume total solar energy incidence on the Earth (instead of arable land), if we remove all air, water, organic material etc. $\endgroup$ – Neil Slater Dec 9 '14 at 13:58
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Right, time for some maths! If they were capable of harvesting unlimited solar energy, they would need Aluminium, primarily for building disk platters to store all their information on.

The Earths crust contains roughly 1,528,000,000,000,000,000,000 grams of Aluminium and a standard HDD uses about 104 grams of platters. Assuming they can store the approximate size of human memory (2.5 Petabytes) on a HDD that weights about twice as much, with all of the Aluminium in the Earths crust they could support 7,346,153,846,153,846,153 human brains.

But this does not take into account getting to it all, let alone processing it all. This also doesn't take into account advancements in storage technology or whether all of this will degrade.

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  • $\begingroup$ I'm not looking to just store their memories. I'm looking to have human minds living and interacting, just without being biological. While availability of essential materials may be an important limiting factor, I need to know about factors that will restrict computation, in addition to storage. $\endgroup$ – trichoplax Oct 8 '14 at 14:50
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    $\begingroup$ Also, aluminium is one of the more abundant elements in the Earth's crust. I would expect the limiting factor to be something other than aluminium. $\endgroup$ – trichoplax Oct 8 '14 at 14:51
  • $\begingroup$ Well, without biological needs the sun can be completely used for energy, so energy isn't a concern. The only limitations would then be size and materials. Size can't be predicted as advancements in technology come into play. Materials, technology is made using silicon (of which there is a hell of a lot more than Aluminium) and glass (Fibre) or copper as for connecting (which can also be mass produced). I chose the least abundant material. $\endgroup$ – James Hunt Oct 8 '14 at 14:58
  • $\begingroup$ I stated in the question that the amount of solar power that can be used may be limited by the overheating of the Earth, and even using all of it doesn't allow for an arbitrary amount of processing power. I'd need something to back up the claim that "energy isn't a concern". $\endgroup$ – trichoplax Oct 8 '14 at 15:05
  • $\begingroup$ Aluminium is not an essential part of a computer and as such not a limiting factor. Most computing devices at present do not require any aluminium, so there is no reason to think that its shortage would limit future computers. $\endgroup$ – trichoplax Oct 8 '14 at 15:14

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