It depends massively on birth rate. If it stays the same, never, we die out shortly. If it goes back up to a (conservative) premodern 5 children per woman, with the same negligible early death rate, log5(8,000,000,000/120)=~11 generations. Rounding up and assuming 25 years per generation, that’s 300 years. Also genetic diversity isn’t as good and there’s more genetic illnesses.
Anything in between is possible. Child and some adult mortality meant premodern populations grew very slowly, on the order of some percentage per century, so that’s an option. Then it’s basically whenever they advance to a 19th century level. If they manage to save and use the frozen sperm samples that exist, the genetic diversity issue could also be avoided.
It depends massively on birth rate. If it stays the same, never, we die out shortly. If it goes back up to a (conservative) premodern 5 children per woman, with the same negligible early death rate, log5(8,000,000,000/120)=~11 generations. Rounding up and assuming 25 years per generation, that’s 300 years. Also genetic diversity isn’t as good and there’s more genetic illnesses.
Anything in between is possible. Child and some adult mortality meant premodern populations grew very slowly, on the order of some percentage per century, so that’s an option. Then it’s basically whenever they advance to a 19th century level. If they manage to save and use the frozen sperm samples that exist, the genetic diversity issue could also be avoided.