The late-18th century philosopher Thomas Malthus wrote these ominous words in an essay on what he saw as the dire future of humanity. Humans' unquenchable urge to reproduce, Malthus argued, would ultimately lead us to overpopulate the planet, eat up all its resources and die in a mass famine.

But what is the maximum "power of the Earth to produce subsistence," and when will our numbers push the planet to its limit? More importantly, was Malthus' vision of the future correct?

Earth's capacity

Many scientists think Earth has a maximum carrying capacity of 9 billion to 10 billion people. [How Do You Count 7 Billion People?]

One such scientist, the eminent Harvard University sociobiologist Edward O. Wilson, bases his estimate on calculations of the Earth's available resources. As Wilson pointed out in his book "The Future of Life" (Knopf, 2002), "The constraints of the biosphere are fixed."

Aside from the limited availability of freshwater, there are indeed constraints on the amount of food that Earth can produce, just as Malthus argued more than 200 years ago. Even in the case of maximum efficiency, in which all the grains grown are dedicated to feeding humans (instead of livestock, which is an inefficient way to convert plant energy into food energy), there's still a limit to how far the available quantities can stretch. "If everyone agreed to become vegetarian, leaving little or nothing for livestock, the present 1.4 billion hectares of arable land (3.5 billion acres) would support about 10 billion people," Wilson wrote.

The 3.5 billion acres would produce approximately 2 billion tons of grains annually, he explained. That's enough to feed 10 billion vegetarians, but would only feed 2.5 billion U.S. omnivores, because so much vegetation is dedicated to livestock and poultry in the United States.

So 10 billion people is the uppermost population limit where food is concerned. Because it's extremely unlikely that everyone will agree to stop eating meat, Wilson thinks the maximum carrying capacity of the Earth based on food resources will most likely fall short of 10 billion. [When Will Earth Run Out of Food?]

According to population biologist Joel Cohen of Columbia University, other environmental factors that limit the Earth's carrying capacity are the nitrogen cycle, available quantities of phosphorus, and atmospheric carbon concentrations, but there is a great amount of uncertainty in the impact of all of these factors. "In truth, no one knows when or at what level peak population will be reached," Cohen told Life's Little Mysteries.

Slowing growth

Fortunately, we may be spared from entering the end-times phase of overpopulation and starvation envisioned by Malthus. According to the United Nations Population Division, the human population will hit 7 billion on or around Oct. 31, and, if its projections are correct, we're en route to a population of 9 billion by 2050, and 10 billion by 2100. However, somewhere on the road between those milestones, scientists think we'll make a U-turn.

UN estimates of global population trends show that families are getting smaller. "Empirical data from 230 countries since 1950 shows that the great majority have fertility declines," said Gerhard Heilig, chief of population estimates and projections section at the UN.

Globally, the fertility rate is falling to the "replacement level" — 2.1 children per woman, the rate at which children replace their parents (and make up for those who die young). If the global fertility rate does indeed reach replacement level by the end of the century, then the human population will stabilize between 9 billion and 10 billion. As far as Earth's capacity is concerned, we'll have gone about as far as we can go, but no farther.

This story was provided by Life's Little Mysteries, a sister site to LiveScience. Follow Natalie Wolchover on Twitter @nattyover. Follow Life's Little Mysteries on Twitter @llmysteries, then join us on Facebook.