Tuesday, September 18, 2007

Total feasible human population over all time

On Usenet I recently, for fun, made a back-of-the envelope calculation for how many human beings could be born in one scenario:
  1. For simplicity of calculation, the only lifeforms are humans (no trans-humans on microchips).
  2. The limiting factor will be energy, rather than how much carbon etc. you have lying around to build things with. After all, you can fuse the useless hydrogen you come across into more useful elements, or delay peoples' births until room opens up for them.
  3. I put the energy efficiency at only .001 of total matter (dark and baryonic), partly because there will be inefficiencies with collecting/storing/transporting/transforming the energy, and partly because I'm not sure how well we can shove the dark matter into black holes. I used (3*10^-27 kg / (meter^3)) for the matter density.
  4. Having no source on how much matter we can grab or colonize before the accelerating expansion of the universe puts it out of reach, I arbitrarily guess that we can colonize all matter currently within 10 billion light-years of us.
  5. The miserly energy ration will be 300,000 nutritional Calories per day, for use for synthesizing/recycling food, and for all other pro-rated energy uses.

Google tells me:

(.01 * ((4 * pi) / 3) * ((10 billion light years)^3) * ((3 * ((10^(-27)) kg)) / (meter^3)) * (c^2) * .001) / ((300 000 (kilocalories / day)) = 10^52 person-years.


1 comment:

Roko said...

I have done similar back-of-the-envelope calculations for the purpose of working out how many lives per second,are being wasted by me not working optimally to reduce x-risk. I got similar answers, i.e. to within 10 orders of magnitude (!).

Questions like whether you count uploads or just biologicals explain the discrepancy.