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Comment by lacker | Hacker News Reader

I do not believe the world will hit peak child, unless there is a catastrophe.

Looking at overall birth rates might make it seem that way. But logically, in order to hit peak child, every subgroup will also have to hit peak child. Will every single country hit peak child? Will every religious group hit peak child? All it takes is one of those groups to keep expanding, and the world will not hit peak child. There are so many subgroups with drastically different birth rates and retention rates, I don't believe we will hit peak child. There will just be a transition period as the world starts to contain fewer Italians and more Mormons.

For an interesting take on a single subgroup's demographics, the Amish, check out this article: https://medium.com/migration-issues/how-long-until-were-all-...

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> In order to hit peak child, every subgroup will also have to hit peak child.

This is an interesting argument; thanks for sharing it. I didn't understand it right away and my intuition was that you must be incorrect. But after playing with some actual numbers I've come to understand. In an attempt to restate your claim in a way that's more intuitive to me:

If a group is reproducing above the replacement ratio, then they haven't hit peak child yet. So if only one subgroup remains that hasn't hit peak child, then that subgroup is also the only one that's growing (all others are shrinking). Assuming that trend continues (read: assuming subgroups have birth rates that reflect their culture, and that culture will be preserved in the next generation), this subgroup will grow without bound.

The pressure-release on a system like this (one which the article you linked points out in its conclusion) is that birthrate within a subgroup isn't fixed. The birthrate among the Amish appears to be declining slightly, perhaps influenced by economic forces in the US. In your example, while it's true that _tommorow_ there will be more Mormons and fewer Italians than today, that doesn't guarantee that eventually the world will be populated entirely by Mormons, because the birthrate in that subgroup isn't wholly 'inherited' (in the cultural sense) -- it may change in ways that we can't forecast today.

> every subgroup will also have to hit peak child

Not really, because subgroup membership is flexible: people can enter and leave a subgroup. But even ignoring that objection, calculating that the Amish will eventually outnumber everyone else is a crazy bad extrapolation, whereas predictions of world population are based on much more modest and justified extrapolations.

If you took some old population data you could perhaps extrapolate that Shakers were destined to increase exponentially, but what happened to them? I'd say that the destiny of a single religious group is typically a short-term and local phenomenon that doesn't much affect the long-term development of world population.

I don’t claim that the Amish will eventually outnumber everyone else. I merely claim that for the global population to hit peak child, every subgroup has to hit peak child. That is a very mathematically sound statement. To me it seems intuitively unlikely that every subgroup will exhibit the same trend. What I expect in practice is not that the Amish will outnumber everyone else, but that over time many different subgroups that are expanding their population will continue growing, and thus world population will continue to grow.

Your "mathematically sound" statement seems obviously false, which probably means I'm misunderstanding it. Perhaps you should state it more formally.

Claim: In order for the overall population to hit a maximum number of children, every subgroup within it must also hit a maximum number of children.

Proof: Assume the opposite, that there is a subgroup S that never hits a maximum amount of children, but the overall population has a maximum amount of children X. Since S does not hit a maximum amount of children, S at some point has more than X children. This contradicts the initial assumption. QED

Oh, that's boring. It's almost as boring as saying that the number of any countable physical thing must reach a maximum because it is bounded by the mass of the universe divided by the mass of an electron, or something equally tedious. I don't think we're gaining any insight here.

World population decreases because people are dying, and increases because people are being born. It's enough to decrease the total population to have the global reproduction become lower than global mortality.

By the same token, if a certain group keeps reproducing at a high pace, but the majority of the world keeps having fewer and fewer children, the overall number of children will decrease, so the curve will be past the peak.

No, my statement is very simple and mathematically correct. In order for the global population to hit peak child, every subgroup must also hit peak child. You cannot have a finite set contain an infinite set. You may think that every subgroup will hit peak child and thus the global population will hit peak child - that is logically consistent. But you cannot believe that some subgroups will expand indefinitely, but the global population will peak.

Your assertion seems true only if subgroups can maintain a positive growth rate indefinitely, which is theoretically possible but hardly proven, particularly as history show that subgroups that grow too much splinter, and the splinters do not all maintain the parents growth rate. Most splinters dwindle, so a simple exponential growth does not apply for long. (On a global scale.)

> But logically, in order to hit peak child, every subgroup will also have to hit peak child. All it takes is one of those groups to keep expanding, and the world will not hit peak child

No, it just has to make less children than it did eighteen years before.

Your condition of "make less children than it did eighteen years before" does not cause a permanent decline. That one subgroup keeps growing. Eventually, the population of that subgroup exceeds today's world population, and your condition is no longer met.

I must have misread you, because I thought you were writing "All it takes is one of those groups to keep having children".

Well yeah, obviously as long as the population keeps growing [1] (and for that it is sufficient that a subgroup does indeed), there can not be a peak child.

I was assuming that the article posited the existence of a population peak in the future, and was speculating about how many years would it be preceded by a child peak.

1. or rather, renew generations, since the population can grow without renewing generations.

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