Although I still haven't figured out what Henry meant by "what happens in the next & succeeding generations ?", here's one possible interpretation: If a propensity to have female vs. male children were heritable (in either males or females), could the Chinese family planning algorithm change the composition of the gene pool over time? (Yes, I realize that the question is vague, since I haven't specified a mathematical model for this propensity. One reason I like asking questions on math-fun rather than MathOverflow is that you guys are a lot more tolerant of imprecise questions. And asking an imprecise question is appropriate when you haven't figured out what the right precise question is.) Jim On Fri, Nov 6, 2015 at 2:46 PM, Henry Baker <hbaker1@pipeline.com> wrote:
Yes, but what happens the next & succeeding generations ?
(Assuming 1:1 "traditional" marriages.)
At 11:42 AM 11/6/2015, James Propp wrote:
Has anyone in the pop math biz tackled the mathematical side of the news story about China's (now abandoned) one-child-per-family policy?
Specifically, many families adopted the family planning algorithm "Have kids till you have a son, then stop", which (under idealized assumptions) gives rise to families of average size exactly 2.
A non-mathematician friend of mine asked me at dinner last night why the expected size of a family that stops when the first son is born is 2. I began to give him an intuitive argument that doesn't involve calculation, but he ended up preferring the argument that shows that 1/2 + 2/4 + 3/8 + ... = 2 by way of summing the formulas 1/2 + 1/4 + 1/8 + ... = 1 1/4 + 1/8 + ... = 1/2 1/8 + ... = 1/4 ... to obtain 1/2 + 2/4 + 3/8 + ... = 1 + 1/2 + 1/4 + ... = 2
Is there a place where this is explained, and explained well?
Jim Propp
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