Counting Calculi

The Linearity Fallacy of Thomas Malthus

Why Malthus' pessimistic prophecy was wrong

by Kevin McLaughlin

“The reason for his failure as a prophet lies entirely in simple fact that even if we observe today what appears to be a historical tendency or trend, we cannot know whether it will have the same appearance
tomorrow.”
-Karl Popper, The Open Society and Its Enemies r1

Two weeks ago I described how humans commit the linearity fallacy when they simplify complex nonlinear systems, including almost all that involve humans, into simple linear ones. I closed by suggesting that when we commit the linearity fallacy, we often underestimate how much potential we humans have to solve even our most intractable problems, giving the linearity fallacy a pessimistic bias. Perhaps the best example of the pessimistic bias of the linearity fallacy is the prediction from the 18th-century scholar Thomas Malthus, that the world is forever doomed to famine and starvation because of population growth. Here we will take a look at why he was wrong and why it matters.

In his book An Essay on the Principles of Population, Malthus states:

“Population, when unchecked, increases in a geometrical ratio. Subsistence increases only in an arithmetical ratio. A slight acquaintance with numbers will shew the immensity of the first power in comparison of the second.” r2

For those who’ve lost their “slight acquaintance” with algebra, a geometrical ratio is another word for an exponential function, while an arithmetical ratio is another word for a linear function. So Malthus is saying that population can grow exponentially, while sustenance (ie food) can only grow linearly. Because “food [is] necessary to the life of man,” r3 and food production can never keep up with population growth, Malthus, therefore, determined that the next century (the 19th) would be one of constant famine and starvation. Here is a graph showing a simplified version of Malthus’s prediction:

Instead, this is what actually happened r4:

And this and this and this.

So what did Malthus get wrong? He correctly predicted the exponential growth of population. But, he assumed food production must grow linearly, thus committing the linearity fallacy. What he failed to account for is that food production does not just depend on the amount of land available for farming but on the growth of human knowledge which, as David Deutsch points out in the Beginning of Infinity, is unlimited. r5 Since the time of Malthus, humans have developed crop rotations, tractors, genetically modified dwarf wheat, and the ability to fix nitrogen, just to name a few. 1 This growth of agricultural knowledge is not linear but compounding and thus exponential.

This leads me to a larger point. Strictly speaking, the linearity fallacy can lead us to be either overly optimistic or pessimistic. But it tends towards overly pessimistic prophecies like Malthus’ because it fails to predict the growth of knowledge. As Deutsch says “we do not yet know what we have not yet discovered”. r6

By all accounts, Thomas Malthus was not a dour man. And he was genuinely concerned with the welfare of his fellow humans. Furthermore, he accurately described a problem. Before the growth of our agricultural knowledge, human beings really did starve. His tragic error was treating the starvation as an inevitable prophecy, instead of a problem to be solved. Anti-humanist policies resulting from the same error, like the harsh population control measures of 20th century China and India, demonstrate that we must not make the same mistake. r7


1. See Enlightenment Now by Steven Pinker ^


r1. Karl R. Popper and Alan Ryan and and E. H. Gombrich, The Open Society and Its Enemies, Kindle Location: 8997 ^

r2. Thomas Malthus, An Essay on the Principles of Population, Kindle Location: 111 ^

r3. Thomas Malthus, An Essay on the Principles of Population, Kindle Location: 112 ^

r4. Max Roser, Our World in Data, Daily per capita supply of calories ^

r5. David Deutsch, The Beginning of Infinity: Explanations That Transform the World, Page: 193, Kindle Location: 3325 ^

r6. David Deutsch, The Beginning of Infinity: Explanations That Transform the World, Page: 206, Kindle Location: 3550 ^

r7. Steven Pinker, Enlightenment Now, Kindle Location: 1519 ^