# Limits

In addition to being constrained by the available energy, humans are also constrained by other limits. The one obvious restriction is the limit set by our finite Earth. Let’s consider limits due to these restrictions.

## 1. No Limits

First, for reference, let’s consider no limits. We know human population is expanding exponentially. This uses the common exponential growth equation. For this study, we will use the year 2000 for the initial conditions. Then, the population was 6,127,700,428 and the population growth rate was 1.323.

Assuming a constant growth rate then in 1000 years, the population would be 3,400,000,000,000,000. This is a million times greater than the initial.

## 2. Limited by Land

Let’s assume that humans are constrained to living on land. As well, let’s assume that a human needs at least one square metre of land on which to live. Given this, then the Earth’s land area will constrain the number of people.

The Earth’s land area is 1.4894×1014 square metres.

On using the same equation and conditions as with the first example above, we determine that people will cover the land surface in only 771 years from the year 2000.

While the land surface does limit us, it is obviously not realistic as living requires more than one square metre. Let’s assume it anyway and then refine our conditions next.

## 3. Limited by Acceptable Land

Humans can’t live on all types of land cover on Earth. For instance, we don’t naturally live on Antarctica. To account for this, we reduce the available land area by removing land not conducive to human life.

We use land cover designation as set by the U.N. and remove all surfaces described as Barren (15.2%), Inland Water (2.6%) and Snow and Glacier (9.7%).

With these removed and using the same initial conditions as above, humans will cover all the viable land area in 746 years from the year 2000.

## 4. Limited by the Need to Eat

Humans need to eat for both nutrients and energy. We can eat almost any living thing from phytoplankton to bears. And we have specialists, e.g. farmers, who get food to our table.

Traditionally, we eat only a few types of animals and plants that we grow upon select land. Knowing the area of agricultural land allows us to determine a population limit based upon our need to eat.

We will use the same U.N. source to define the agricultural land area. The source lists cropland (12.6%) and grassland (13%) as the agricultural areas. We assume that people use all grassland for grazing by domesticated animals. Also, we ensure that the additional population gets their required agricultural land.

Let’s assume the amount of agricultural land per person remains constant. With this condition then 11.6 billion people will be standing shoulder to shoulder in 51 years.

## 5. Limited by Infrastructure

Our dependence on human technology also constrains us. For example, we rely upon roads and railways to deliver food. And we rely upon houses to mitigate inclement weather. Using the same UN source, the Artificial Surfaces amount to about 0.6% of the Earth’s land surface. Let’s add it.

Perhaps surprisingly, these do not greatly influence limits. At maximum, 11.5 billion people will stand shoulder to shoulder in 50 years.

## 6. Limited by Energy

We consume a lot of energy. It amounted to over 108,000TWh in 2000. Solar power provided just 1.1TWh of the total. If all energy supplies came from solar power then in 2000, we’d have needed over 9.4 million square kilometres of collectors installed.

If we account the same for barrens, agricultural and artificial surfaces land covers and include land area for total solar power generation then 10.1 billion of us will be standing shoulder to shoulder in our one square metre box in 40 years.

## Summary

With a few assumptions, we’ve determined that the Earth could have filled with people in a number of decades. This exemplifies the current, dramatic, real alarm many people express and the need for finding immediate solutions. We are nearing the limit imposed by our finite Earth; we need positive action and soon.

We made many assumptions in the above calculations. There are three main clarifications that give us some time;

• i. the human population growth rate is decreasing,
• ii. humans get a lot of food from oceans, lakes and rivers, and
• iii. domesticated animals don’t use all the grassland.

All these contribute to increase the upper population limit and to increase the time to reach the limit.

Other factors reduce the time to the limit, including;

• i. ecosystem degradation (i.e. pollution, soil failure, die-off),
• ii. debt (borrowing from the future), and
• iii. climate change.

All these decrease the upper limit and decrease the time to reach the limit. And they impoverish future generations.

Further, remember our definition of the limit, it was when each person had one square metre on which to live and land to grow their food. This is impracticably small. And, we allowed no viable land area for other, non-domesticated animals or plants. Is this the future we want? Contact us and let’s plan for a defined, reasonable future.

Here’s a code samplet if you want to repeat the analysis;

``````
EarthInfraLandArea(1)=EarthLandArea*(1-0.152-0.026-0.097-0.126-0.13-0.006);
InfraLandPerPerson=(EarthLandArea - EarthInfraLandArea(1))/Pop1(1);
Pop5(1) = 6127700428; # https://en.wikipedia.org/wiki/Estimates_of_historical_world_population
flag5 = false; # set flag for printing year of limit
# assume a constant rate
for ii = 2:1:nYears
if Pop5(ii-1) < EarthInfraLandArea(ii-1)
#exponential growth
Pop5(ii) = Pop5(ii-1)*(1+PopRate(ii-1));
EarthInfraLandArea(ii) = EarthInfraLandArea(ii-1)-InfraLandPerPerson*(Pop5(ii)-Pop5(ii-1));
else
#plateau
if flag5 == false
fprintf('Limit 5 at %i with population of %e \n', ii, Pop5(ii-1));
flag5 = true;
endif
Pop5(ii) = Pop5(ii-1);
EarthInfraLandArea(ii) = EarthInfraLandArea(ii-1);
endif
endfor
``````
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