It depends on the sign of the exponent. Negative exponential growth, as we see in wild animal populations, is not guaranteed to turn into an S-curve. As the passenger pigeon would attest, were any of them left.
Meanwhile, to consider a positive exponent case, there's a real question of what will actually cause the bend in the curve of human population. Will it be getting our collective shit together and slowing down? Or will it be a massive die-off after we've destroyed the ecosystems we depend on for things like air to breathe and water to grow our crops?
Sigmoid functions are defined over real input values (not integers). If you were to model the decline in (integer) numbers of passenger pigeons with reals, you would get a sigmoid function were the number at the end approximates, but never reaches zero.
b) Using real numbers to reason about integer base values is not wrong per se. You just need to know how to interpret the result.
No. We got rich and having kids was less economically valuable (in fact it becomes a cost in rich societies). The Elon Musks of the world are now more concerned about lack of growth than the opposite.
Who knows if Elon is right or you, but it's not as trivial as it seems to predict whether we will ever hit the carrying capacity of the planet.
https://consciousnessofsheep.co.uk/2022/07/01/bigger-than-yo...
The whole world is on the way to doing this (Africa will, too, as they will develop… and, in a note of good news, probably become as economically powerful in the 22nd century as Asia is in the 21st). It’ll lead to a cratering of the working population unless we basically start to eliminate retirement (not desirable!) and enact a ton of pro-natalist policies now (in addition to as much immigration as possible).
A thing people don’t understand is that the biggest resource limit is people. Population decline won’t mean abundance but the exact opposite as the dependency ratio shoots through the roof and will be incredibly stubborn to come down (as to try to reverse it with pro-natalist policies will actually make it significantly worse for a couple decades), especially as willing migrants dry up (yes, I realize how counter-narrative that is, but it’ll happen… in the latter part of this century, Africa will become sick of being the cheap labor source of aging Europe and Asia).
The bigger questions are whether global warming or WW3 will fuck us all before we get there, not to mention the question of whether fully general AI will be its own mega disaster.
tang ping
Having a rich data set doesn't help. https://twitter.com/SonerCagaptay/status/1389387850551005192
It's also the initial part to a bell curve.