Population is mostly a function of how many babies you can keep alive to breeding age.
The main things that limit this are disease and famine. Since most people farm their own food historically, more kids meant more production/food/money. It also meant that when one fell to disease, you had backup children.
In the west, people started to move away from farming significantly, around the 1900s was when technology and culture reached a point where having more children was not advantageous, as medicine kept kids alive and people were buying food not making food. However, culture and technology grew together in the west.
Around the same time in China, all this technology was brought to a culture that had not seen any of these changes in ideas. China had big families, with a population of 500mil even in 1900, so all of a sudden you had a whole generation of kids in large families, that didn’t die, and then they each had just as many kids.
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