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hippyjoe1955 Yeah, I see the arc. I also see that the shape of the arc depends on a number of factors.
For example, if at age 20 each woman reduces her fertility from 2 children to one daughter, but her life expectancy and that of her child simultaneously doubles from 40 to 90 years, then in 20 years, when her daughter has a child, there will still be 3 people, instead of 2.
Run it forward another 20 years, when the granddaughter has a child, there will be 4, etc. That is, even though the birthrate dropped 60 years ago.
Bottom line though, your fabulous research skills failed to turn up that the global fertility rate is 2.5, and life expectancy continues to increase.
There are still above replacement level being born, and people living for longer mean a larger, not shrinking, population at any point in time.