Random 14 Dec 2013 01:26:51

Thought Experiment: Population

Imagine a community of N people following these three rules:

  1. Every day, at most 1 person is born
  2. Every day, at least 1 person dies
  3. Over time, the population does not decrease (tomorrow, N must be ≥ the N of today)

What is the minimum value possible for N to start as?

What other social or biological constraints you choose to enforce is up to you, but it is probably most fun if your initial simulation follows modern norms. Then you can skew the variables to see how bizarre a community you can create.

My first step is to start out with simplified rules based on biological averages and see where that gets us:

  • Women are fertile from age 13 to 50
  • Men are fertile from age 13 until death
  • Pregnancy lasts for 40 weeks
  • People die at age 80
  • Every day 1 person dies and 1 is born
  • The male/female birth ratio is 50/50

Since people die at age 80, there must be N=29200 people (80×365), meaning we have 14600 women and 14600 men. Is that enough? Let’s do the math…

We’ll only need 280 pregnant women at all times (40×7), which it sounds like we have. But, given it takes a while for girls to reach fertile age, we at any given time have 2372.5 girls who are too young (13×365/2; the /2 because 50% boys). We also have 5475 women who are too old ((80−50)×365/2), leaving us with 6752.5 women in the fertile age range (14600 − 2372.5 − 5475). So yeah, there’s enough women.

How about if we impose some social rules?

  • Women refrain from getting pregnant until age 18

That changes the number of available women capable and willing to get pregnant to 5840.

Add another social rule…

  • Women refrain from getting pregnant for 2 years after having a kid

That removes a mere 730 potential women from the pool (365×2), leaving 5110 – still well above the 280 minimum.

Ok then, how about…

  • Women refrain from getting pregnant after the age of 35

This removes another 2737.5 women from the pool, leaving 2372.5 which is still over 8 times the required minimum.

In conclusion, that was far less interesting than I thought it was going to be. Unless I messed up the math somewhere, which I am sure someone will point out if that is the case, then you have to veer far from current biological and social norms to get interestingly crazy results.

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