Re: [math-fun] Chinese family planning
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
I don't understand Henry's question. Can Henry or someone else elaborate? 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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Everything will be hunky-dory. The percentage of boys and girls should go back to normal. -- Gene From: Henry Baker <hbaker1@pipeline.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Friday, November 6, 2015 11:46 AM Subject: Re: [math-fun] Chinese family planning 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
The intuitive argument was, of course, that the expected number of sons under such circumstances is 1, and since the expected number of daughters equals the expected number of sons, the expected family size must be 2, correct? How can adding a bunch of fractions be preferred to this? On Fri, Nov 6, 2015 at 11:46 AM, 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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People of a certain kind like proofs to be math-y looking. If a proof doesn't look like math, they're suspicious of it. Go figure. Anyway, I'm thinking of blogging about this, but I'd prefer someone else did and sent me the link (so I can send it to my friend). But maybe one of you guys --- you know, the ones who write for the Guardian and the Times and places like that --- has already put an explanation of this out on the web in a prominent place, where it'll be read by thousands of people (as opposed to the mere hundreds who read my blog). Jim On Fri, Nov 6, 2015 at 3:00 PM, Tom Rokicki <rokicki@gmail.com> wrote:
The intuitive argument was, of course, that the expected number of sons under such circumstances is 1, and since the expected number of daughters equals the expected number of sons, the expected family size must be 2, correct?
How can adding a bunch of fractions be preferred to this?
On Fri, Nov 6, 2015 at 11:46 AM, 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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See problem 5 at want-to-work-at-google <http://www.wired.co.uk/magazine/archive/2012/05/start/want-to-work-at-google> On Fri, Nov 6, 2015 at 3:17 PM, James Propp <jamespropp@gmail.com> wrote:
People of a certain kind like proofs to be math-y looking. If a proof doesn't look like math, they're suspicious of it. Go figure.
Anyway, I'm thinking of blogging about this, but I'd prefer someone else did and sent me the link (so I can send it to my friend). But maybe one of you guys --- you know, the ones who write for the Guardian and the Times and places like that --- has already put an explanation of this out on the web in a prominent place, where it'll be read by thousands of people (as opposed to the mere hundreds who read my blog).
Jim
On Fri, Nov 6, 2015 at 3:00 PM, Tom Rokicki <rokicki@gmail.com> wrote:
The intuitive argument was, of course, that the expected number of sons under such circumstances is 1, and since the expected number of daughters equals the expected number of sons, the expected family size must be 2, correct?
How can adding a bunch of fractions be preferred to this?
On Fri, Nov 6, 2015 at 11:46 AM, 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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I've found https://www.quora.com/In-a-country-in-which-people-only-want-boys-every-fami... , which isn't exactly what the average person-like-my-friend is going to want to read, but I'll send it to him and see what he thinks. Jim On Fri, Nov 6, 2015 at 3:17 PM, James Propp <jamespropp@gmail.com> wrote:
People of a certain kind like proofs to be math-y looking. If a proof doesn't look like math, they're suspicious of it. Go figure.
Anyway, I'm thinking of blogging about this, but I'd prefer someone else did and sent me the link (so I can send it to my friend). But maybe one of you guys --- you know, the ones who write for the Guardian and the Times and places like that --- has already put an explanation of this out on the web in a prominent place, where it'll be read by thousands of people (as opposed to the mere hundreds who read my blog).
Jim
On Fri, Nov 6, 2015 at 3:00 PM, Tom Rokicki <rokicki@gmail.com> wrote:
The intuitive argument was, of course, that the expected number of sons under such circumstances is 1, and since the expected number of daughters equals the expected number of sons, the expected family size must be 2, correct?
How can adding a bunch of fractions be preferred to this?
On Fri, Nov 6, 2015 at 11:46 AM, 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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"in 2010 [China's birth sex ratio] was 118.08 males to 100 females" "It's estimated that by 2020, China will have 24 million more men than women of marriageable age on the mainland" http://english.cri.cn/7146/2013/02/26/2702s750680.htm Musical chairs, anyone? Of course, artificially high sex ratios like this in human history are always resolved the same way: war. The young men kill one other until the problem has resolved itself. At 11:46 AM 11/6/2015, Henry Baker 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
The excess male Chinese are called "Chinese Remainders", and the fact that this leads to war is called the "Chinese Remainder Theorem". ;-) At 12:56 PM 11/6/2015, Henry Baker wrote:
"It's estimated that by 2020, China will have 24 million more men than women of marriageable age on the mainland"
http://english.cri.cn/7146/2013/02/26/2702s750680.htm
Of course, artificially high sex ratios like this in human history are always resolved the same way: war. The young men kill one other until the problem has resolved itself.
Is the proof constructive, and tell us who they're going to fight? More generally, does it offer an effective algorithm to discourage the human race from constantly turning every scientific advance into an agent of misery? WFL On 11/6/15, Henry Baker <hbaker1@pipeline.com> wrote:
The excess male Chinese are called "Chinese Remainders", and the fact that this leads to war is called the "Chinese Remainder Theorem". ;-)
At 12:56 PM 11/6/2015, Henry Baker wrote:
"It's estimated that by 2020, China will have 24 million more men than women of marriageable age on the mainland"
http://english.cri.cn/7146/2013/02/26/2702s750680.htm
Of course, artificially high sex ratios like this in human history are always resolved the same way: war. The young men kill one other until the problem has resolved itself.
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One day, back in the late 1980s, I went out for dim sum in San Francisco with geometer Dan Freed and two other mathematicians. All the portions were for three or six people: none were for four. I groused "I guess there's some corollary of Murphy's Law that says that when a bunch of people go out for dim sum, the number of portions is never divisible by the number of diners." Dan instantly responded "Sure there is; it's called the Chinese Remainder Theorem." Jim On Fri, Nov 6, 2015 at 4:21 PM, Henry Baker <hbaker1@pipeline.com> wrote:
The excess male Chinese are called "Chinese Remainders", and the fact that this leads to war is called the "Chinese Remainder Theorem". ;-)
At 12:56 PM 11/6/2015, Henry Baker wrote:
"It's estimated that by 2020, China will have 24 million more men than women of marriageable age on the mainland"
http://english.cri.cn/7146/2013/02/26/2702s750680.htm
Of course, artificially high sex ratios like this in human history are always resolved the same way: war. The young men kill one other until the problem has resolved itself.
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At the MITSFS and the SIPB, in the late 70's, we were already using "Chinese Remainder Theorem" to refer to exactly this incommensurability between the number of Peking ravioli and the number of diners. On Fri, Nov 6, 2015 at 5:22 PM, James Propp <jamespropp@gmail.com> wrote:
One day, back in the late 1980s, I went out for dim sum in San Francisco with geometer Dan Freed and two other mathematicians. All the portions were for three or six people: none were for four.
I groused "I guess there's some corollary of Murphy's Law that says that when a bunch of people go out for dim sum, the number of portions is never divisible by the number of diners."
Dan instantly responded "Sure there is; it's called the Chinese Remainder Theorem."
Jim
On Fri, Nov 6, 2015 at 4:21 PM, Henry Baker <hbaker1@pipeline.com> wrote:
The excess male Chinese are called "Chinese Remainders", and the fact that this leads to war is called the "Chinese Remainder Theorem". ;-)
At 12:56 PM 11/6/2015, Henry Baker wrote:
"It's estimated that by 2020, China will have 24 million more men than women of marriageable age on the mainland"
http://english.cri.cn/7146/2013/02/26/2702s750680.htm
Of course, artificially high sex ratios like this in human history are always resolved the same way: war. The young men kill one other until the problem has resolved itself.
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Note that this disparate ratio was not achieved by the suggested family planning algorithm. It was done by aborting more female fetuses. Brent On 11/6/2015 12:56 PM, Henry Baker wrote:
"in 2010 [China's birth sex ratio] was 118.08 males to 100 females"
"It's estimated that by 2020, China will have 24 million more men than women of marriageable age on the mainland"
http://english.cri.cn/7146/2013/02/26/2702s750680.htm
Musical chairs, anyone?
Of course, artificially high sex ratios like this in human history are always resolved the same way: war. The young men kill one other until the problem has resolved itself.
At 11:46 AM 11/6/2015, Henry Baker 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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Detected via a medical ultrasound scanner ... WFL On 11/6/15, Brent Meeker <meekerdb@verizon.net> wrote:
Note that this disparate ratio was not achieved by the suggested family planning algorithm. It was done by aborting more female fetuses.
Brent
On 11/6/2015 12:56 PM, Henry Baker wrote:
"in 2010 [China's birth sex ratio] was 118.08 males to 100 females"
"It's estimated that by 2020, China will have 24 million more men than women of marriageable age on the mainland"
http://english.cri.cn/7146/2013/02/26/2702s750680.htm
Musical chairs, anyone?
Of course, artificially high sex ratios like this in human history are always resolved the same way: war. The young men kill one other until the problem has resolved itself.
At 11:46 AM 11/6/2015, Henry Baker 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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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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participants (8)
-
Allan Wechsler -
Brent Meeker -
Eugene Salamin -
Fred Lunnon -
Henry Baker -
James Propp -
Tom Rokicki -
W. Edwin Clark