Exponential Population Growth and Sustainability – Part 1

19 Oct

We all inhabit Planet Earth – a space defined by boundaries. According to the studies conducted by NEF (New Economic Foundation) it currently takes the biosphere about 18 months to produce what humanity consumes in only 12 months. This tipping point happened sometimes in 1960s.


If every nation in the planet consumed the same amount of natural resource as the US does, we would need between 5 -6 planet earths, to satisfy everybody’s needs.

The above data is from 2007. I was comparing this data to other sources, which vary for – / + 0.5. Looking at 2012 data, India increased from 0.4 to 0.8, China is up to 1.2 and Brazil to 1.9. The largest consumers of natural resources, not on this chart are the United Arab Emirates.


Source: http://esa.un.org/wpp/

Using 2012 data, China and India represent 2.6 billion people – rougly 38% of the world population – and growing.

One of the key factors related to global demand of natural resources is increasing number of population. However, we cannot neglect country’s purchasing power – their market position, access to natural resources and their level of development. For example – global oil consumption is  89 million barrels a day. United States consume 20 million barrels a day (22% of the global use) while they represent a fraction – only 4.5% of the total world population.  China currently uses 7m/b/day and has 1.35 billion people, with increasing needs and demands.

Global population growth represents exponential growth (a chart pattern that is often called a “hockey stick”).


For the last few months I’ve been working and living in Mexico and would like to demonstrate exponential growth of Mexico City. The city has between 20 and 22 million people ( 2012). In 1900, only 113 years back, the number was 0.5 million.

How does steady growth turn into exponential growth?

Let’s apply arithmetic, which I learned from Dr. Albert A. Bartlett. I have great respect for his wisdom, especially for the message he was trying to convey: “The greatest shortcoming of the Human Race is our Inability to Understand the Exponential Function.”

What is exponential function?

Exponential function is a mathematical function, used to describe the size of anything that is growing steadily, for example – 5% per year.

I came to realize how this problem affects numerous critical areas we’re facing at the moment, one of them being population growth. The case I have chosen demonstrates the importance of understanding unsustainable exponential growth and can be applied in others area; for example GDP – promotion of 5% steady growth of GDP, which is constantly brought forward by politicians as a solution to our current economic crisis.

Why it cannot work?

We are talking about a situation where the time that is required for the growing quantity to increase by a fixed fraction is constant. (e.g. 5% per year – 5% is a fixed fraction, 1 year is a fixed length of time). If it takes a fixed length of time to grow 5%, than it follows, that it takes a longer fixed length of time to grow by 100%. This longer time is called the doubling time.

a)      To calculate doubling time we need to apply a simple formula (using example of 5% annual growth)

Formula for Exponential GrowthCan we really achieve 10% growth in 14 years, 20% in 28 years and 40% and 42 years time?  Having limited amount of resources, lagging technology,  continuous investment in dwindling fossil fuel extraction and increasing CO2 emission? I think it’s about time to redefine growth!

b)      Let’s apply the calculation for population growth in Mexico City.

Based on National Statistical Data, the number of population in 1900 was approximately 0.5 million, 4.5 million in 1960 and 9 million in 1980, following the average growth of 3.5% yearly until 2000 when it dropped to 2%.


No. of population according to our calculation

Doubling time

Numbers according to Nat. Statistics



Recorded average 3.5% growth between 1900 and 2000

70/3.5 à 20

Every 20 years the number of people doubles











The growth rate fell to 2% in 2000s, it takes now 35y for the population to double






20 -22.000.000




The results of calculation match with the actual data. There is minor deviation due to the average of 3.5%  between 1900 and 2000, which is acceptable and accurate enough to confirm the validity of results. Using other important indicators, which affect life on earth we notice similar patterns.

Hockey Stick

Graphs above follow the same “hockey stick” pattern, typical for unsustainable exponential growth (Melting of Arctic Sea Ice, Global Land and Ocean Temperature, Number of Weather related Disasters, Global Ocean Acidification, Human Population Growth,  CO2, N2O and CH4 Emission, Oil Extraction).


We started off with a steady growth, lasting for 80 years, which tipped over into unsustainable exponential growth after 1980s. Mexico City has begun sprawling out and up the surrounding hills, once a home of rich biodiversity, covered with trees, to protect from landslides, today covered by concrete houses.

The natural conditions and the infrastructural foundations of Mexico City was not built to accommodate 32 million people.  What I’m currently able to see around me is poor infrastructure, inefficient transport system, pollution, poor quality of water, high level of food dependency, dependency on fossil fuels and increased social inequality. In addition to that, the city was built on plate tectonics, on soft unconsolidated sediments that fill a former Lake Texcoco, surrounded by volcanos. It has a history of earthquakes, the latest and most damaging one was in 1984 with the magnitude of 8.1 on Richter Scale. In 1980s, there were only 9 million people.

You may say it’s an extreme example, and yes, I agree – it is. It just happens to be that I’m currently working and living in this city, hence it’s real to my eyes and I have a direct overview and experience of how it functions on daily basis.

Such extreme examples indicate our extreme inability to connect the dots and think & live sustainably. This example shows we don’t think carefully enough about the future, we don’t protect the environment and the generations yet to come and we are not ensuring them access to clean water, healthy food and breathable air.

Such is the case with Mexico City. Despite all, Mexicans remain one of the happiest, most optimistic and good hearted people I have ever met and I’m fully grateful for the experience. I only wish they would be encouraged to think about the bigger picture, not only about the American dream, that exists only in dreams. Most of the people living in this city struggle to earn their daily bread, to make it through the day, week or month. Current system doesn’t do much to support and/ or encourage a more sustainable way of thinking and living. My comments are made based on general observation and conversation I had with variety of people including students and faculty from privately owned and state Universities.

MexicoCity,22mpeople1,485squarekmMexico City

We can apply exponential growth to other areas. Graphs above show a similar pattern in many critical areas we’re presented with at the moment. They are affecting the whole globe. Knowing how exponential growth works, we can realize that current understanding of steady GDP growth is not only impossible; promoting such growth by policy makers and certain experts is deceiving and destructive in a long term. It can simply not be sustained.  We all inhabit Planet Earth – a space defined by boundaries.

Next: Part 2: Deforestation


8 Responses to “Exponential Population Growth and Sustainability – Part 1”

  1. sumant October 20, 2013 at 10:38 AM #

    any idea what percentage of the Earth’s surface humans inhabit? that will also give us an idea whether the present population is sustainable

    • Lillie October 20, 2013 at 7:18 PM #

      I’m not sure it’s the question we should be asking. That’s why I was very careful about not only focusing on numbers – I gave an example – the US has 4.5% of world population, yet they consume 22% of global oil. Their ecological footprint is one of the highest and their ways of living most unsustainable.
      It can also be misleading to generalize – each country is specific and people have a right to satisfy their basic needs.
      Hence, the question is “how do we reach people, how do we make educational system more transparent and just and how do we educate them, so they can choose to live and act more sustainably”?

      • flyingbirdman October 21, 2013 at 6:38 AM #

        In early 2012 once-in-a-century floods submerged swaths of Great Britain and Ireland, causing some $1.52 billion in damages. Then in June record-high temperatures in Russia sparked wildfires that consumed 74 million acres of pristine Siberian taiga. Months after that, Hurricane Sandy pummeled seven countries, killing hundreds and running up an estimated $75 billion in damages. Just this week, a tornado of virtually unheard of size and ferocity tore through a small city in Oklahoma, leaving 24 people dead. ..This should change peoples minds,but most seem to almost get offended by climate change talk.I have been doing a little experiment on Facebook(the most narcissistic place to be) talking to people about climate change..they all seem to ignore everything i have to say..some even unfriended me.

      • Lillie October 21, 2013 at 4:01 PM #

        Hi Flyingbirdman… thanks for your sharing! I can relate to what you’re saying… perhaps we should completely ignore the word itself “Climate Change”… it seems it attracts too many adverse reactions. I was thinking about this issue. What kind of communication is required to get the message across without instant reaction and rejection. Dunno… stories that related to community, stories that are directly linked to what we eat and need on day by day basis – showing dependency between all this areas. Often enough it seems that we lost the ability of system’s thinker – as if we forgot to link the dots. Had one inspiration this morning about it. Already made a draft, so bear with me, I’ll share it soon. There’s so much more to learn as we thread this journey – for everybody. If we persist, I’m sure we’ll find a way 🙂
        Best of luck to you too!

      • sumant October 21, 2013 at 7:23 AM #

        I guess you are right and it can definitely be misleading to generalize about countries. but I wonder how much educating people will help. People on Easter island destroyed their last tree and never understood the implications. modern humans are neither wiser nor do they understand the consequences. but I guess we have no other choice other than educating people

      • Lillie October 21, 2013 at 4:01 PM #

        🙂 … best of luck to us!

  2. Miguel A. Vera August 28, 2014 at 7:20 PM #

    Good illustration of Professor Bartlett’s conference…

    • Lillie August 28, 2014 at 11:35 PM #

      He was a nice one. I’m very grateful for the wisdom he shared. He helped me realise few things, expecially seeing them in a much clearer way.

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