Thomas Robert Malthus, economist and philosopher in the late 1700s, posited that "population increases in a geometric ratio, while the means of subsistence increases in an arithmetic ratio;" in other words, that humans were a drain on the world's resources.
Malthus was proved completely wrong with the advent of modern farming techniques. You'd never know it, however, if you listened to the religious fanatics of the environmentalist movement.
I don't doubt that there will, eventually, be a tipping point; however, I do not believe that it has anything to do with the idea that the earth is pure, and human beings are nothing more than a self-perpetuating pollutant (I've personally heard us compared to a virus). Nor do I believe that we'll run out of the ability to feed all of the people--modern farming techniques, from biological engineering done since the dawn of time (you didn't really think that wild grains have as high a yield, did you? or that food animals are exactly the same in the wild as they are on farms?) to careful and scientific application of plowing and fertilizing techniques to pest control, will see to that. Nor do I believe that we'll turn the earth into a polluted, barren chunk of rock orbiting our sun.
No, I believe the tipping point will come when we simply crowd ourselves off the planet. I also believe that, by that point, we'll have viable space travel, multiple colonies where the best and brightest, stifled by Earth's transnational progressivist, Marxist communist, self-chosen elite, will choose to relocate to, and all that'll be left on this particular planet will be the Darwinian rejects.
You know, the ones like we currently have sitting in congress and the White House.
Read Heinlein. And Kratman.
1 hour ago