## South African Skeptics

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# Best guess

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Rigil Kent
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Three men make a tiger.

 « on: July 13, 2010, 06:50:02 AM »

For those who enjoy estimating stuff just for the hell of it -

Say there are 6,000,000,000 people in the world, and global legislation is passed forcing couples to have a maximum of one child only. How long will it take before no more humans are left, assuming that   all other population dynamics remain constant?

Mintaka
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Hermes
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 « Reply #1 on: July 13, 2010, 15:28:01 PM »

I'll make the following crude assumptions:

1.   You require 2,3 births per couple to keep the population constant, compensating for various reasons why not all babies become parents and males and females are not equally numbered.

2.   The average parental age at birth is 25.

3.   The shrinking population remains in contact.

The number of births will therefore drop by a factor (1 / 2,3) each generation.   How many generations before we have only one birth?   Call it n.

6 000 000 000 X (1 / 2,3)n = 1

n log (1 / 2,3) = log (1 / 6 000 000 000)

n = 27.

Check the answer: 1 X 2,327 = 5 840 000 000, which is about the 6 000 000 000 we started off with.

27 generations X 25 years = 675 years.

Add to that antiAdam's life of 75 years, so we are at 750 years.

Do I pass?

Was this in the Fun section to provoke humour rather than a calculation?

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Teleological
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Ex Nihilo Nihil Fit

 « Reply #2 on: July 13, 2010, 15:58:04 PM »

I do not know all the constants of population dynamics but....
Assuming half the people are female.
Assuming that each female is only allowed to have 1 child and actually has a child.
Assuming that females are born 50% of the time.

How about the... 32nd or 33rd generation?

Generation   Females
1      3,000,000,000
2      1,500,000,000
3      750,000,000
4      375,000,000
5      187,500,000
6      93,750,000
7      46,875,000
8      23,437,500
9      11,718,750
10      5,859,375
11      2,929,688
12      1,464,844
13      732,422
14      366,211
15      183,105
16      91,553
17      45,776
18      22,888
19      11,444
20      5,722
21      2,861
22      1,431
23      715
24      358
25      179
26      89
27      45
28      22
29      11
30      6
31      3
32      1

Assuming an average generation of 30 years, Kosie or Sannie should be able celebrate the coming of the third millennium maybe with even ouma and oupa on the stoep. .
 « Last Edit: July 13, 2010, 16:42:10 PM by Teleological » Logged
Brian
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 « Reply #3 on: July 13, 2010, 16:19:52 PM »

depends on the assumptions you make: and you asked 'how long' not how many generations. of 6 billion at least half would be younger than say 36yrs. At least 20% are not yet of child bearing age... Assume another 20% are beyond child bearing age Above 45 yrs: that leaves:
1st gen: 6 000 000 000 less 20% ballies = 1.5 billion who should die off within 27 years (72 life expectancy) without further issue: another 3.6 billion are couple = 1.8 billion couples who can have 1 child only; plus the lities who come of age in say the same 27 years would add another 1.5 billion/2 = 750 000 000 couples hence children: so in the first generation of 27 years= the popultaion would have ended up being 6 000 000 000-1 500 000 000+180 000 000 + 750 000 000 = 7.05 billion/.
seems like a never ending story
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Hermes
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 « Reply #4 on: July 13, 2010, 16:44:07 PM »

I don't agree with Brian's conclusion, but he has a point that the current demographics should be considered.   Only the part of the current population that has not already got any children should be considered - the others may not reproduce.   This would probably cut my estimate by one generation from 750 years to 725 years.
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Brian
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 « Reply #5 on: July 14, 2010, 07:51:23 AM »

the thought of pushing the calculations to the n-th degree tired me...but I agree it would eventually peter out to 1
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GCG
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 « Reply #6 on: July 14, 2010, 17:18:03 PM »

i still say neuter them all at birth
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