Musings on Malthus

“The power of population is so superior to the power of the earth to produce subsistence for man, that premature death must in some shape or other visit the human race.” Thomas Robert Malthus, An Essay on the Principle of Population Chapter II. Originally published 1798.

The Malthusian prediction: apocalypse, soon

The two-century-old prediction that the growth in population would outstrip production of food, so that the only solutions would be widespread hunger and death or necessary curbs on population, is one of the most famous and most studied of forecasts, particularly because it was so soundly based in logic and knowledge and ended up so wrong. It’s interesting to look back and learn the lessons of how the Malthusian apocalypse never showed up, and why, and how our present predicament — and some of the language describing it — is familiar, and some proposed solutions seem little changed from two centuries ago. And, the failure of Malthus’ predictions also frames the successful paths forward.

Background — the gathering storm

Two hundred and fifty years ago, England was evolving rapidly from a sluggish, agricultural past, with isolated towns, dominated by castles and churches, surrounded by fields worked by humans as beasts of burden. Most people would never leave a small domain of a cluster of villages and a nearby market town. Even as steam engines became commonplace during the 1700s, most households lacked anything we’d recognize as essentials: running water, toilets, decent locks, glass windows, adequate floors or roofs.

By the start of the 19th century, however, massive change was afoot. The industrial revolution was underway. Coal-driven factories (and mines) overtook central England. Then railroads spread like vines. The population grew wildly. Cities were dirty, noisy, and overcrowded. London had about 600,000 people around 1700 and almost a million residents in 1800. Squalor, crime and hunger in decrepit neighborhoods and a polite, genteel aristocracy in beautiful estates.

Against this backdrop, we have teachers and preachers informed by the teachings of Christian philosophers, such as Calvin and Hobbes. The Reverend Thomas Malthus was, principally, a Hobbesian thinker. Hobbes, over 150 years earlier had written that a social contract overseen by an all-powerful monarch was needed to prevent the decay of mankind into horrors:

“(Absent a social contract with an absolute sovereign), there is no place for industry; because the fruit thereof is uncertain: and consequently no culture of the earth; no navigation, nor use of the commodities that may be imported by sea; no commodious building; no instruments of moving, and removing, such things as require much force; no knowledge of the face of the earth; no account of time; no arts; no letters; no society; and which is worst of all, continual fear, and danger of violent death; and the life of man, solitary, poor, nasty, brutish, and short.” Cheerful sort.

In the more refined circles of rectories and colleges, intellectuals pondered the gathering storm of human misery. The Reverend Thomas Robert Malthus, armed with both a dour version of Christianity and a full grasp of algebra, put pen to paper, and predicted that demand for food would outgrow its supply, and the inevitable outcome would be famine and misery, alleviated only by curbs on population.

Forgetting invention and innovation

Malthus’ analyses fell short, and his predictions were faulty, because the spirit of human innovation and invention solved the problems he had identified.

In the societies that emerged, entities, people or companies or churches and so on, with solutions COULD execute them, without explicit permissions from a centralized, authoritarian government — a monarchy, for example. They were free to discuss them, to build the underlying science, to trade ideas in public, to find funding, and to succeed or to fail. Innovations made Malthus wrong, and these innovations occurred in all fields: popular behaviors, technology, banking, government and policy.

The Malthusian dilemma

The Reverend Thomas Robert Malthus got his mathematics right, but — clearly — got the overall conclusions wrong. His projections were that only restraints on the size of the human population could prevent widespread starvation and misery. Hunger and poverty still plague the world, but a smaller fraction of the earth’s population starves and lives in misery than was the case in Malthus’ day.

His essays contain what can be expressed as mathematical formulae, as befits Malthus’ Cambridge education, where he excelled at mathematics. However, as was the convention of time, his writings, over decades, weren’t populated with equations. (Sadly, even with a better-educated populace, that remains true today, but that’s another story. We’ll use simple formulae here, but no more than that.) His argument, in simple summary:

Agricultural output rises arithmetically with time. This, in more modern terms is: agricultural output — food — increases linearly with time.

• Equation: Food (proportional to) time

Human consumption rises geometrically with time. This, modernized is: the population of the earth increases exponentially with time.

• Equation: Population (and food consumption) (proportional to) e^t

This is really, really bad news. It imagines food output as increasing by a steady amount per year. Let’s say a county currently produces ten thousand tons of food per year. In Malthus’ depiction, output might rise by a further 500 tons per year. So, this year: 10,000; next — 10,500; the following year — 11,000, etc. It imagines appetite as rising by a steady percentage per year. A person today consumes 1,500 to 2,000 pounds of food per year — nearly a ton. So, a community of 10 thousand individuals will consume (not accounting for wastes) will consume, say, 10,000 tons of food per year.

BUT, if the population grows at 5% per year, the food needed to sustain it will rise to 10,500 one year out; then 11,025; then 11,576 … and soon, agricultural output falls way short of what is needed to sustain the population.

Malthus’ depiction of the inevitability of human hunger was based on the difference between linear and exponential growth, and the idea that food output would only grow linearly, while human population and food needs would grow faster. Why are these valid ideas? And what happened such that Malthus’ analyis went so badly wrong?

Why should food output grow linearly?

Malthus lived from 1766 to 1834. So, as of the time he graduated from Cambridge University, in 1791, he was 25 years old. This was a time before much mathematical, technical, engineering contribution to agriculture.

Farming mostly centered on the fertile soils near rivers, at the bottoms of valleys. (An odd quirk, surely irrational for modern times, is that many great cities of the world are built on the most fertile soil, near great rivers.) Even then, the best fields, with the richest, most fertile soil, was taken. To increase agricultural output, farming had to expand away from river bottoms. Upwards. To hilltops not covered with organic-rich alluvial soil (Malthus described the new soil as ‘barren’). A simple, but perhaps erroneous, way to think of this would be to consider a river as a straight line, with fields close to it. Moving away from the river gets you more area — but not enormously more, if the field area doesn’t greatly increase as you leave the riverbank. But the soils do get worse. So: more fields, but it’s harder work to get them to yield. So: food output increases, but only linearly.

Why should population — and food demand — grow exponentially?

Meanwhile, however, the mathematics of population growth is easier, at first encounter. Human population, he believed, has increases in any period that are proportional to the amount already present. And that amount increases, so the rate of increase itself becomes more rapid in proportion to the increasing total size. In present-day USA, the average American woman in 1800 bore seven or eight children. Many, of course, would not survive to adulthood, and the parents (particularly the women) died earlier than they do now.

An example. Assume a couple has five children survive to adulthood. So: a couple that marries in year one, would be in a family of six or seven people 25 years later. That’s a simple example, that would yield a growth rate of 4.5% per year. This is a highly simplified example — it excludes that older relatives might die during the time. Nonetheless, the estimate is helpful. It’s also indicative of how fast populations were growing 200 years or so ago. In 2020, the world’s highest rates of natural population growth — excluding considerations of immigration and emigration are in a few sub-Saharan countries, where growth is slightly over 3% per year (in Angola, Mali, Malawi, and Burundi). The average growth rate of the world’s population from 10,000 BCE to 1700 was about 0.04% per year. Tiny. The fastest growth occurred in between 1950 and 1987, when the population doubled in 37 years — a rate of about 2% per year.

The population of the world was about 1 billion in 1800, as Malthus wrote. It took 128 years — until 1928 — to reach 2 billion. The next billion came in 1960, 32 years later. And the next took 15 years (1975). 12 years to add the next billion. Actually: each subsequent billion took about 12 years, as population growth has ebbed — the world’s population has been growing approximately linearly — by a constant amount per decade, rather than a constant percentage per decade — since the early 1960s, until recently, when it accelerated again. In general, it’s well established that population growth is ebbing: populations are growing at less than exponential rates. But still, they have normally been growing MUCH faster than linearly, and they’ve been doing so for the two centuries since Malthus’ predictions.

Pulling large numbers of people out of ‘food insecurity’ to a level where they routinely ate enough to be fit and hale would further increase the per-capita food demand, and push upwards the total amount of food needed even beyond that demanded by just the population growth.

The data available to Malthus in the early 1800s did, indeed, suggest that food production would fall short of food needs for the expanding population.

So, what went so right so that Malthus was so wrong?

Malthus’ time and philosophy hindered his analysis, despite his more-than-adequate mathematical background. Instead of arguing:

• Rate of growth of population (and food consumption) > rate of growth of agricultural food production, therefore dire outcomes

Malthus could have argued:

• Unless Rate of growth of agricultural food production now + improvements > rate of growth of population, then dire outcomes

And then the entire argument would have hinged on what would have to be true such that improvements were sufficient. And what were the improvements that showed up such that the inequality in the Malthus equation disappeared? So many, but it’s important to list a few:

Agricultural output improved for some technology-driven reasons, including these:

1. Machines took over from beasts of burden (including men and women): steam-driven ploughs emerged in the 1850s — but static, steam-driven threshers were more important
2. Mass-production of chemicals enabled fertilizers; before the early 1800s, the only fertilizers most farmers could use were manure, ground bones, wood ashes, etc. And there was little scientific basis for their application. Slowly, in successive decades, calcium superphosphate and potassium-based fertilizers were manufactured or mined, and their appropriate application studied.
3. Scientific oversight of cross-breeding generated higher-yielding crops — particularly by the 1890s, John Garton in England, and then his American disciple, Luther Burbank — made large-scale scientific study of crop variation and creation of high-yield crops feasible, and the modern seed industry emerged.
4. Faster transportation — and then refrigeration, and particularly the invention of mechanical chillers — meant fewer crops and meat spoiled between farm (or abattoir) and table: this not only meant more food, it meant better food and more nourished citizenry. The British and Prussian armies that defeated Napoleon in 1815 used horse-drawn trains on steel rails to move their materiel. Subsequent wars in Europe occurred well after steam engines criss-crossed Europe on sturdy railways; the train track beside Walden Pond in Massachusetts was there by the time of Henry David Thoreau’s 1850s book extolling his time there pondering the necessities of life in bucolic isolation. His cabin lay about a third of a mile from the tracks — and the railway line had more frequent and more noisy train service then than it does now. Refrigeration originally used natural ice which had to be carved from northern lakes and shipped — a business that started in the USA as early as 1806, and at its peak, in the late 1800s, employed 90,000 people. By the 1850s, factories were making ice and Willis Carrier’s inventions starting in 1902 made refrigeration increasingly affordable.

Agricultural output also improved for non-technical reasons, including:

1. The creation of crop futures as a financial product — meaning investors could loan money today for crops to be delivered next season. This only makes much sense at a large scale — loaning money to ten farmers in a single area is very high risk as the same adverse factors will affect all. One bad storm and all is lost. However, a large loan, syndicated over a large region, with many farms in different soils and weathers, meant better outcomes for all, including farmers.
2. The spread of literacy and of low-cost publications — newspapers and pamphlets meant that farmers could learn more about technical advances — and markets, and that the populace could learn about, and frequently object to, widespread hunger, empowering movements to oppose hunger and privation.
3. Government policies that moved toward stabilizing agricultural science and finance, including (in the USA) the creation of universities (particularly the land grant, agricultural and mechanical colleges) and departments specifically focused on agricultural support. These had the important effect of giving farmers true technical or financial data for their business decisions. Government policies also enabled companies to independently pursue business opportunities that could increasingly separate business failure due to poor execution or bad luck from flat-out fraud.

Many of these changes further had the effect of moving farms away from tiny, subsistence-level plots, barely providing enough sustenance for a poor family to eke out a living. Instead, the era began of large farms — still not the industrial-scale agriculture of today, but still real businesses, equipped with a growing set of tools to enable their success. And, these in turn, meant that farmers no longer needed more children to populate the farm with involuntary labor. Mules and machines took over.

The role of innovation

Malthus’ predicted apocalypse did not occur because:

• An increasingly literate society knew about the problems, and the opportunities; mass-produced newspapers alerted readers to abominations (such as nearby famines) and to discussion of government policies that affected them.
• An increasingly technical set of agricultural scientists emerged to help farmers (and those trying also to help agriculture)
• An increasingly powerful set of technologies emerged
• Bankers and policymakers (sometimes) stepped forward to enable scaled-up solutions

Nobody planned the response. It emerged across the then-developed or developing world.

In the societies that emerged, entities, people or companies or churches and so on, with solutions COULD execute them, without explicit permissions from a centralized, authoritarian government — a monarchy, for example. They were free to discuss them, to build the underlying science, to trade ideas in public, to find funding, and to succeed or to fail. Innovations made Malthus wrong, and these innovations occurred in all fields: popular behaviors, technology, banking, government and policy.