I read the bit about Rosling but didn't catch the TED shout-out. My bad. I wonder what role the diminishing influence of religion has on the population curb? "Go forth and maketh babies and baptise them in the blood of our savior that they might too bring forth the seed of god". Catholics are famous for large families. Grow the flock! I made up that bit of verse. My guess is that something analogous is in the bible somewhere... :)
I'm not really sure what direct influence religion has on these trends. But I can say that ridiculing the pope for preventing the distribution of condoms in Africa is justified. We must make sure that all methods of contraception are easily attainable and widely used throughout the world. They help people plan how many offspring they want. And most educated people in urban settings opt for smaller families. The faster we can stabilize the world population the better.
I grew up going to catholic school with some affluent families that were on average, pretty large. -Not a very scientific data set, just my personal experience. Your point isn't lost on me though.