[darynthe]

This is just for fun math people:
Tell me an approximate of the years (and number of generations) before human being became extint if everybody had just one child.

Use an average of reproductive age of 30 years and planet population of 6,000,000,000

If you use extra variables make sure they are reasonably supported by studies (ex. % of mortality before reproductive age or infertility, unequal male/female distribution, or % of those who doesn't want to reproduce. Also if someone adds also the variable of the minimum ammount of humans to make reproduction viable before endogamy takes over and destroys the ammount of humans left, please be my guest.)

[rufsketch1]

We will initially assume (and correct later) that each generation dies immediately after reproducing. We will also assume there are no other variables regarding child mortality rate and accidents. In other words, a strict one child limit. No more, no less. We will also assume that you meant 1 child per couple instead of 1 child per person (or the alternate translation of, 1 child for all of humanity. The answer to both of those interpretations is trivial).

[HIDE="detailed"]
If we model the population at any given time (ignoring the previous still living generation) as a sequence of 6billion, 3billion, 1.5billion. . . Xi, X(i+1)/2.

We note that Xi / 2=X(i+1)

This can be restated as Xi=(X(i+1))*2. It follows that X(i+1) = (X(i+2))*2 and X(i+2)=(X(i+3))*2. and so on.

Because Xi=X(i+1)*2, Xi can be rewritten as (X(i+1)*2). It follows that X(i+1) can be written as (X(i+2)*2). Which would make the whole form (X(i+2)*2)*2. Likewise, X(i+2) can be rewritten X(i+3)*2. So we can have (((X(i+3)*2)*2)*2).

Which means we multiply by 2 for whichever i in the sequence we happen to be on. This can be written as 2^i (multiply 2 by its self i times).

so we need to find where 2^i = 6billion.

This can be rewritten as log2(6,000,000), which equals ~32.482.

This comes to 32 generations. Assuming each generation is 30 years, that comes to 960 years. Will give our citizens a nice 70 year total lifespan, and that will add 40 to our 960 (due to the first generation) and another 70 to wait for that last guy to die out. Bringing us to 1070 years.



[/HIDE]

[Syntax]

[HIDE="My answer:"]I'm getting somewhere around a thousand years, depending on how long the last one lives. Should be about 30 generations in the simple case(where none of the extra variables you've mentioned are taken into account).[/HIDE]



If anyone wants to include mortality rate before the age of 30, here's a useful link:
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[darynthe]

Originally Posted by rufsketch1 To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

We will initially assume (and correct later) that each generation dies immediately after reproducing. We will also assume there are no other variables regarding child mortality rate and accidents. In other words, a strict one child limit. No more, no less. We will also assume that you meant 1 child per couple instead of 1 child per person (or the alternate translation of, 1 child for all of humanity. The answer to both of those interpretations is trivial).

Well, one child per person is exactly the same as one child per couple. I mean, nobody can have children by themselves and that is why there is an exponential decrease of human beings by this calculation.

I invite all the people who are posting answers to post also the math process so we can see it clearly.

Wow, 30 generations is not much.

It is amazing, I think that we human beigns are not so used to think exponentially and that makes things completely different when we start to.

[Monte314]

Would be about 30+30*log(6000000000)/log(2) = 1004.47 YEARS

The idea here is that every 30 years, the population is cut in half, so you must determine how many powers of 2 go into 6 billion. That's what the "log" stuff is... gives 32.48 generations. The multiplier of 30 is the longevity of a generation, and the 30 in the front is because the very last person lives 30 years after everyone is dead... give or take.

[Syntax]

	Originally Posted by darynthe To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Well, one child per person is exactly the same as one child per couple. I mean, nobody can have children by themselves and that is why there is an exponential decrease of human beings by this calculation.

We knew what you meant
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	Originally Posted by darynthe To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	I invite all the people who are posting answers to post also the math process so we can see it clearly. Wow, 30 generations is not much. It is amazing, I think that we human beigns are not so used to think exponentially and that makes things completely different when we start to.

I was actually surprised; I thought 30 generations seemed a bit high. My initial "guesstimate" was about 7or 8 generations(you know...just assume the human race is a piece of paper and then see how many times you can fold it in half! lol...)



The lack of "exponential thought" is ubiquitous in humans. I always laugh when someone tells me that they found out they're related to Charlemagne("I found out online!"). EVERYONE is related to Charlemagne. Not only that, if there was someone who lived during the time of Charlemagne who had children, you can bet you're one of their direct descendants also. Which means we're all incestuous. Fun fact.

[rufsketch1]

	Originally Posted by darynthe To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Well, one child per person is exactly the same as one child per couple. I mean, nobody can have children by themselves and that is why there is an exponential decrease of human beings by this calculation.

There is more than one way to have 1 child per person. For example, each couple can have two children
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.


The math process is in my spoiler, but I'll post here as well. I went beyond the generic "this is the formula for exponential decay" thing, and actually did something resembling a recurrence relation.

If we model the population change by generation (ignoring the previous still living generation) as a sequence of: 6billion, 3billion, 1.5billion. . . Xi, X(i+1)/2.

We note that Xi / 2=X(i+1)

This can be restated as Xi=(X(i+1))*2. It follows that X(i+1) = (X(i+2))*2 and X(i+2)=(X(i+3))*2. and so on.

Because Xi=X(i+1)*2, Xi can be rewritten as (X(i+1)*2). It follows that X(i+1) can be written as (X(i+2)*2). Which would make the whole form (X(i+2)*2)*2. Likewise, X(i+2) can be rewritten X(i+3)*2. So we can have (((X(i+3)*2)*2)*2).

Which means we multiple by 2 for whichever i in the sequence we happen to be concentrating on. This can be written as 2^i (2 multiplied by its self i times. Remember, i is incrementing for each element, so we can't have a constant here).

so we need to find where 2^i = 6billion.

This can be rewritten as log2(6,000,000), which equals ~32.482.

This comes to 32 generations. Assuming each generation is 30 years, that comes to 960 years. Will give our citizens a nice 70 year total lifespan, and that will add 40 to our 960 (due to the first generation) and another 70 to wait for that last guy to die out. Bringing us to 1070 years.


Most of our answers vary by a few years because of what we're defining as extinction.