The Children Keep Coming: How Many Can Live on Earth?

I’m Calli, a child of the valley
Born in muck, bred in misery
—R. L. Goings, The Children of Children Keep Coming (2009)

Much has been said and written about the woeful state of the US economy: loss of jobs, loss of homes, cost of health care, gyrations of the stock market, and the like. Serious as they are, these issues pale in comparison to a more fundamental problem that, without remediation, will in time sink the global economy altogether.

There is an irreconcilable clash of views between traditional free-market economists, who see growth as the engine of a successful capitalist economy, and scientists who, like me, study the nature, acquisition, and utilisation of the planet’s energy resources. Whereas the principles of economics are academic propositions over which economists debate interminably, the laws of physics are experimentally verifiable proscriptive constraints on the workings of the physical world that affect all persons whether they choose to accept these laws or not. Foremost among them from an economic standpoint is the fairly obvious assertion that continual growth on a finite planet is not sustainable. This applies especially to the human population, whose rate of growth (currently at about 1.1%) lies at the root of virtually all major economic ills.

Of the forces that could eventually cause collapse to all economic systems, the most serious—in terms of its immediacy and reach—is starvation. Traditional economists may think that a growing human population is good; that it means more consumption, hence more demand, more production, and ultimately more wealth. They discount the possibility of global famine, trusting instead that the scientists and engineers amongst us will always figure out a way to enhance food production to keep up with growth. That belief, however, is delusional. The physics of the Sun, together with some basic chemistry and the geometry of the Earth, allows one to estimate with reasonable accuracy an upper limit to the number of human beings who can obtain a sustainable food supply. No amount of human ingenuity short of relocating to another habitable planet (none has yet been found) can circumvent the consequences of a critical number—the Solar constant—which quantifies the rate at which the Earth receives energy from the Sun.

Nuclear fusion within the Sun gives rise to about 0.325 Calories of energy per square meter every second at the top of the Earth’s atmosphere. The Earth intercepts this energy flow like a great circular disk of radius 6400 kilometers (about 4000 miles). It is a matter of simple arithmetic, then, to show that the mean energy received in a 12-hour day by the side of the Earth facing the Sun is about 1.8 billion billion Calories. In order to function normally, a human requires at least 2000 Calories per day. If all this solar energy could somehow be used directly to feed people, it would supply 2000 Calories a day to 90 thousand billion people. In reality, that number is wildly impossible because many constraints remain to be taken into account.

We live on a planet whose surface is predominantly water, but crops must be grown on soil; the ratio of land area to total area is 0.29. Not all the land is good for growing food; the fraction of arable land is 0.33. Not all the sunlight illuminating the Earth’s atmosphere reaches ground; the fraction not scattered away by clouds, ice, snow, and water is about 0.23. Of the sunlight reaching the ground, only a fraction 0.25 falls within a narrow spectral band suitable for photosynthesis. The efficiency of photosynthesis to make plant sugars out of carbon dioxide and water is very low, about 0.02. Only about 0.10 of the plant material consumed by humans is converted into chemicals from which humans derive energy. Finally, humans are but one of at least 9 million species of living organisms on the planet; for our own survival we cannot keep all the solar energy to ourselves. Suppose we share 50%. The quantity of solar energy, then, that goes into nourishing the human population is reduced by a factor 0.29 x 0.33 x 0.23 x 0.25 x 0.02 x 0.10 x 0.50 = 5.5 millionths.

Thus the number of humans sustainable by Sun-based agriculture alone would be the product: 90 thousand billion people x 5.5 millionths reduction factor = 4.97 billion people—i.e. a number very close to 5 billion people. The current human population (as of December 2011) is 6.84 billion. Physics and chemistry give us reason to believe that the number of people may already be beyond the carrying capacity of the planet.

It may be argued that the above estimate (simplified for purposes of a general essay for nonspecialists) made no mention of non-agricultural food sources such as fish in the sea or non-solar energy sources such as nuclear fission. These considerations would hardly change the equation. A growing population will deplete the oceans; already the world’s fisheries are in serious decline. Moreover, fissile materials like uranium-235 are themselves nonrenewable resources whose mining will require increasingly intensive energy outlays to recover increasingly poorer grades of ore. Economically, this process will terminate once a unit of energy expended equals a unit of energy recovered.

The overpopulation of the Earth is a catastrophe not fated for the far distant future. Simple math, of the kind (geometric growth) that determines the compounding of an interest-bearing account, shows that it can happen well within the lifetime of a present-day high school student. At an annual growth rate of 1.1% the number of years for the human population to double to about 14 billion is log(2) divided by log(1.011), which yields close to 63 years. This estimate is actually slightly longer than what a more exact calculation based on exponential (rather than geometric) growth would yield, but close enough to reveal the imminence of a disaster in the making.

To the argument that economic doomsday prophecies have been made numerous times in the past, yet the human population has continued to grow and—at least in industrialised nations—to prosper, it must be stressed that the situation is really different this time round. Never before has the human population reached a level where human activity is depleting the natural capital of the planet. Technological advances that rescued humanity in the past, such as mechanised and industrialised agriculture, required unconstrained expenditures of fossil fuel energy for machinery and chemicals, as well as extensive encroachments on natural ecosystems which turned forests, grasslands, and wetlands into cropland. However, the exploitation of fossil fuels and the denudation of natural ecosystems cannot be continued indefinitely.

If nothing is done to prevent it, the human population will most likely collapse well before two doubling times (to 28 billion) take place. The dearth of energy, food, water, and living space, together with mounting pollution and accelerated climate change, will, as Malthus projected, lead to famine, disease, extensive migration, violence, and war. In the end, by one way or another, the human population will be reduced to what the then remaining resource base can sustain. Economists and politicians impervious to scientific reasoning can argue the fine points of their ideologies from now to Armageddon—but in the end nothing and no one are exempt from the laws of physics.

Op-ed piece submitted to the Wall Street Journal (2011).

Note: The Calorie (with upper case C) is 1000 calories (with lower case c). The "calories" printed on food labels should actually be "Calories".

About the author

Mark P. Silverman is Jarvis Professor of Physics at Trinity College. He wrote of his investigations of light, electrons, nuclei, and atoms in his books Waves and Grains: Reflections on Light and Learning (Princeton, 1998), Probing the Atom (Princeton, 2000), and A Universe of Atoms, An Atom in the Universe (Springer, 2002). His latest book Quantum Superposition (Springer, 2008) elucidates principles underlying the strange, counterintuitive behaviour of quantum systems.