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‘How Many Humans Can the Earth Support?’ Mathematics Professor Addresses Ahead of World Population Day

‘How Many Humans Can the Earth Support?’ Mathematics Professor Addresses Ahead of World Population Day thumbnail

Humans are the most populous large mammal on Earth today, and probably in all of geological history. This World Population Day, humans number in the vicinity of 7.5 to 7.6 billion individuals.

Can the Earth support this many people indefinitely? What will happen if we do nothing to manage future population growth and total resource use? These complex questions are ecological, political, ethical – and urgent. Simple mathematics shows why, shedding light on our species’ ecological footprint.

The mathematics of population growth

In an environment with unlimited natural resources, population size grows exponentially. One characteristic feature of exponential growth is the time a population takes to double in size.

Exponential growth tends to start slowly, sneaking up before ballooning in just a few doublings.

To illustrate, suppose Jeff Bezos agreed to give you one penny on Jan. 1, 2019, two pennies on Feb. 1, four on March 1, and so forth, with the payment doubling each month. How long would his $100 billion fortune uphold the contract? Take a moment to ponder and guess.

After one year, or 12 payments, your total contract receipts come to US$40.95, equivalent to a night at the movies. After two years, $167,772.15 – substantial, but paltry to a billionaire. After three years, $687,194,767.35, or about one week of Bezos’ 2017 income.

The 43rd payment, on July 1, 2022, just short of $88 billion and equal to all the preceding payments together (plus one penny), breaks the bank.

Real population growth

For real populations, doubling time is not constant. Humans reached 1 billion around 1800, a doubling time of about 300 years; 2 billion in 1927, a doubling time of 127 years; and 4 billion in 1974, a doubling time of 47 years.

On the other hand, world numbers are projected to reach 8 billion around 2023, a doubling time of 49 years, and barring the unforeseen, expected to level off around 10 to 12 billion by 2100.

This anticipated leveling off signals a harsh biological reality: Human population is being curtailed by the Earth’s carrying capacity, the population at which premature death by starvation and disease balances the birth rate.

Ecological implications

Humans are consuming and polluting resources – aquifers and ice caps, fertile soil, forests, fisheries and oceans – accumulated over geological time, tens of thousands of years or longer.

Wealthy countries consume out of proportion to their populations. As a fiscal analogy, we live as if our savings account balance were steady income.

According to the Worldwatch Institute, an environmental think tank, the Earth has 1.9 hectares of land per person for growing food and textiles for clothing, supplying wood and absorbing waste. The average American uses about 9.7 hectares.

These data alone suggest the Earth can support at most one-fifth of the present population, 1.5 billion people, at an American standard of living.

A man works recycling plastic bottles outside Hanoi, Vietnam. REUTERS/Kham

Water is vital. Biologically, an adult human needs less than 1 gallon of water daily. In 2010, the U.S. used 355 billion gallons of freshwater, over 1,000 gallons (4,000 liters) per person per day. Half was used to generate electricity, one-third for irrigation, and roughly one-tenth for household use: flushing toilets, washing clothes and dishes, and watering lawns.

If 7.5 billion people consumed water at American levels, world usage would top 10,000 cubic kilometers per year. Total world supply – freshwater lakes and rivers – is about 91,000 cubic kilometers.

World Health Organization figures show 2.1 billion people lack ready access to safe drinking water, and 4.5 billion lack managed sanitation. Even in industrialized countries, water sources can be contaminated with pathogens, fertilizer and insecticide runoff, heavy metals and fracking effluent.

Freedom to choose

Though the detailed future of the human species is impossible to predict, basic facts are certain. Water and food are immediate human necessities. Doubling food production would defer the problems of present-day birth rates by at most a few decades. The Earth supports industrialized standards of living only because we are drawing down the “savings account” of non-renewable resources, including fertile topsoil, drinkable water, forests, fisheries and petroleum.

The drive to reproduce is among the strongest desires, both for couples and for societies. How will humans reshape one of our most cherished expectations – “Be fruitful and multiply” – in the span of one generation? What will happen if present-day birth rates continue?

Population stays constant when couples have about two children who survive to reproductive age. In some parts of the developing world today, couples average three to six children.

We cannot wish natural resources into existence. Couples, however, have the freedom to choose how many children to have. Improvements in women’s rights, education and self-determination generally lead to lower birth rates.

As a mathematician, I believe reducing birth rates substantially is our best prospect for raising global standards of living. As a citizen, I believe nudging human behavior, by encouraging smaller families, is our most humane hope.

The Conversation

20 Comments on "‘How Many Humans Can the Earth Support?’ Mathematics Professor Addresses Ahead of World Population Day"

  1. Harquebus on Thu, 12th Jul 2018 6:22 pm 

    I have posted this before. My apologies for the repitition. It can’t be said often enough.

  2. JuanP on Thu, 12th Jul 2018 6:30 pm 

    “I believe reducing birth rates substantially is our best prospect for raising global standards of living.”
    I’ve believed this all my life. That is the main reason why I had a Vasectomy and no children.

  3. JuanP on Thu, 12th Jul 2018 6:44 pm 

    “I believe nudging human behavior, by encouraging smaller families, is our most humane hope.”
    I disagree on this. This is where a mathematician could go wrong. I have been reading on demographics, fertility, etc. all my life; it is my biggest obsession. Research proves that we don’t need to nudge human behavior or encourage smaller families. Providing voluntary, free education (including sex ed), contraceptives, and abortions to all the population would do the trick. It could be done in a very short time if the will existed. The number of accidental unwanted pregnancies exceeds population growth. Preventing unwanted pregnancies is the key.

  4. Boat on Thu, 12th Jul 2018 6:55 pm 


    Start with the Muslims then. Then blame immigration and go back home. Be responsible and blame religion.

  5. Makati1 on Thu, 12th Jul 2018 7:17 pm 

    Juan, not to mention religions saying that large families are good and preventing conception by making it a sin.

  6. Makati1 on Thu, 12th Jul 2018 7:19 pm 

    Boat, Catholics, Mormons and Muslims all promote large families. As does lack of sexual education, even in US schools.

  7. Duncan Idaho on Thu, 12th Jul 2018 7:25 pm 

    Boat, Catholics, Mormons and Muslims all promote large families. As does lack of sexual education, even in US schools.

    If you want social equality and a smaller population, just have women have equal political and economic rights.

  8. JuanP on Thu, 12th Jul 2018 7:48 pm 

    Most religious institutions promote big families and some oppose equal rights, education, abortion, and/or contraception. Religions tend to be an obstacle in this fight.

  9. JuanP on Thu, 12th Jul 2018 7:55 pm 

    Boat “Then blame immigration and go back home.”
    I do think that international migration is counterproductive in the predicament we find ourselves in. In an ideal world free global migration for all would be best, though. I would not be solving anything by moving back home. I would be one person moving from one overpopulated country to another. And the global population wouldn’t be affected at all. The only solution is reducing fertility, immigration considerations are a distraction from the real problem.

  10. Jeorge on Thu, 12th Jul 2018 10:46 pm 

    I’ve lost count of how many articles I’ve read about overpopulation of humans and the need to do *something*. But it’s always the same unworkable suggestions: educate women, modernization, promote contraception, etc. And of course there was China’s One Child policy which I think very few think was a great solution and certainly a non-starter most everywhere else. The only solution I’ve come across is the one the late Daniel Quinn (author of Ishmael) advocated: start with the food supply and habitat range. Humans are after all animals and pretty much every life form in the history of our planet has had it’s numbers directly tied to a ebb and flow of it’s food source and/or habitat. In practice that means a couple of things. First, an end to incentivizing ever-increasing food supplies since that literally drives up the population of feeders, whether it’s hamsters or humans. This can be done by a variety of means such as compensating producers by some other criteria other than by volume/weight, and ending the commoditization of food stuffs. Second, reintroduce regionalism to create the boundaries of the human habitats from which the inhabitants will derive the bulk of their livelihood, ie. localized food production within the enclosed bio-region. Obviously these bio-regions would vary in their carrying capacity and thus the populations they can support. To be sustainable the boundaries will have to be held, meaning an end to completely unregulated migration.

    How doable something like this is is an open question. Certainly it flies in the face of the way most westerners currently live. That said, I think a return to regionalism and living smaller has some appeal as it would likely lead back to tighter knit communities, authentic cultures, and greater respect for the natural environment which is ultimately the foundation on which we build our lives.

    Food Production and Population Growth: A Conversation with Daniel Quinn and Alan Thornhill Ph.D ; 1997 ; aprox. 3 hours – Part 1 – Part 2

  11. Anonymouse1 on Thu, 12th Jul 2018 11:04 pm 

    Boatietard is a bible-thumping moron with a blame muslim fetish. As it is already been pointed out, ‘Muslims’ have no monopoly on pro-natalist theology. Boatietards fundy churches and money-grubbing, pedophile televangelists and preachers, love babies and the extolling the virtues of unlimited population growth as much as boatretard loves his coloring books and Saturday morning cartoons.

    So yes, the world needs fewer muslims, and LOT less boatretards. So do your part, and if you happen to see boatretard sitting on a park bench in texASS drooling all over himself, be a good citizen of the world and offer to pay to have him ‘neutered’, as the exceptionalturd likes to say.

    You know, just in case he gets any ideas…

  12. Antius on Fri, 13th Jul 2018 7:42 am 

    Take a look at the stats and you will see that with only a few exceptions, all of the nations with population growth rates above replacement rate (2.2-2.5 per woman) are Islamic or Black African.

    We face the worst of both worlds. The productive parts of the world will soon face a peak in working age population and declining GDP per capita. The most useless, barbaric and backward parts of the world that cannot even feed themselves, are the parts with the highest birthrate. It doesn’t bode well.

    In the Muslim world, suggestions like ‘educating women’, don’t go down very well. Women that try things like that get stoned to death or shot by Al Qaeda. The Africans on the other hand, aren’t really forward thinking enough or smart enough for that sort of solution to be an option. These people never invented the wheel. So we are left with the likelihood of Malthusian collapse.

  13. GetAVasectomyAndLetTheHumanRaceDie on Fri, 13th Jul 2018 7:52 am 

    I like to use youtube as a window into people minds. Went youtube and search for white extinction. Was surprised to read in the comment section how many blacks were cheering and wishing white extinction.

    Do black people what a race war. Because it sure look that way.

    Western values and ideas are only possible if you have enough energy. The western world is simply building on the mastering of energy and law of physics. Once the energy goes, so does the western value.

    Maybe white people see that and don’t see the point of reproducing. Will be fund to watch low IQ Black and Arab fight together for a death earth that cannot support life anymore.

  14. GetAVasectomyAndLetTheHumanRaceDie on Fri, 13th Jul 2018 8:04 am 

    Maybe white people see that and don’t see the point of reproducing. Will be fund to watch low IQ Black and Arab fight against each other for a death earth that cannot support life anymore.

  15. Sissyfuss on Fri, 13th Jul 2018 8:21 am 

    “How many humans can the Earth support?” Rather, how much destruction of the natural world before humans lose their life giving support?

  16. GetAVasectomyAndLetTheHumanRaceDie on Fri, 13th Jul 2018 8:25 am 

    The solution to overpopulation is dead. Maybe we should go on with task and start killing each other based on race.

    It took only a year to turn Syrian into a shit by bombing water purification station, hospital, electrical generation plants.

    Maybe we could the same think with Africa. You knows it might work.

    There is no other to reduce population then death.

  17. MASTERMIND on Fri, 13th Jul 2018 5:42 pm 


    They can run but they can’t hide..

  18. MASTERMIND on Fri, 13th Jul 2018 5:52 pm 

    Doomie preppers want to live like wild savages!

  19. Bob on Fri, 13th Jul 2018 7:28 pm 

    How many Humans can the Earth support? is not quite the right question. How many Humans can the Earth support and not interfere with Nature? is closer to the question we need to answer. That would put us with a population less than during the Roman Empire; about a 90% reduction from where we are now. Probably fewer people than that, but that would be a good starting point as to how many we can really sustain.

    This Author offers only the weakest ideas as to how many people that would be and how to get there. How about: every Woman on the planet needs to swear to only raise 1 child during their lifetime until our population is reduced 90%? (Never going to happen).

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