Synopsis: What’s Wrong with the Malthusian Argument?

I am currently working on a book about Thomas Malthus’ “An Essay on the Principle of Population,” first published in 1798, and I have started to blog about some central arguments here. Since this will become a longer series, it may not be easy to keep track. That’s why I have decided to create this page with an overview and with links to the posts. I will also point you to other articles that are, sometimes only tangentially, related, but may elucidate my thinking further.

Here is the series of posts relating to the Malthusian argument directly:

• What’s Wrong with the Malthusian argument? — A very short and incomplete summary of what is to come.
• Malthus and His Geometrical and Arithmetical Ratios — Central to the Malthusian argument are the claims that population grows exponentially (or “geometrically” in Malthus’ terminology), and subsistence, ie. the food supply, linearly (or “arithmetically”). I begin with the discussion here, and will explore the two claims and the “proofs” that Malthus gives in further dedicated posts.
• The Malthusian “Red Whale” — Malthus puts a lot of stress on the assertion that an exponential function has greater “power” than a linear function. The only sensible interpretation is that he means that the former grows faster asymptotically, ie. as time goes to infinity, than the latter. That is incontrovertibly true, and many readers seem to think that the Malthusian argument stands or falls with this claim. They hence conclude that it is just as unassailable and find it self-evident. — However, I show that the assertion about the relative “powers” is completely irrelevant for the Malthusian argument, which depends on the infinitesimal situation, ie. loosely speaking: extremely short time spans, when an exponential functions crosses a linear function. — Apart from this, Malthus’ proof for the relative “powers” of the two functions is inadequate and falls short even by the mathematical standards of his time. — To make it worse, Malthus confuses the question about asymptotic growth with the unrelated question of estimating the rate of growth of a specific exponential function and the slope of a specific linear function. — All this is nothing but a red herring of gigantic proportions, or as I call it: “a red whale.”
• The Malthusian Worldview: The Malthusian argument is internally so weak and also contradicts easily obtainable empirical evidence that was already known in Malthus’ time that it is hard to understand how it could ever gain traction. But it did. — My explanation is that the force of Malthus’ account does not stem from the stringency of his arguments, but from a worldview that he inculcates in his readers. It is very intuitive and has a strong hold over our imagination. Even many critics of Malthus are in thrall to it. — In this post, I begin to explore the Malthusian worldview, separate from the Malthusian argument, which has become a main part of our culture and is ubiquitous even today. — The main focus here is the claim that it is “natural” for humans to have very many children, or as Malthus thinks there should be even maximum fertility when a population is “unchecked.” I will show in further posts that this has always been false.
• More on the Malthusian Worldview: I follow up on the previous post with an analysis of another part of the Malthusian worldview, namely the idea that “naturally” humans are engaged in a “struggle for existence,” a term that was coined by Thomas Malthus. One person can only be there because another is kicked out of existence. Some people just have to suffer, they have drawn blanks “in the great lottery of life” (Malthus’ own words!). This aspect of the Malthusian worldview has had particularly pernicious consequences as I will explore in further posts.
• A Very Simple, But Common Mistake: If the Malthusian mechanism of population growth until it hits a binding constraint can explain starvation and famine, then it does not follow that examples of starvation and famine are proof that the Malthusian mechanism is at work. That would only be the case if nothing else could result in starvation and famine, which is clearly false.
• Sorry, Cornucopianism is Silly: A popular attempt to counter the Malthusian argument goes by the name of “Cornucopianism.” It tries to supplant the deep pessimism with high optimism about human ingenuity. The solution to the Malthusian puzzle is supposed to be that growing populations somehow automatically invent the necessary technologies to win the race against ”population pressure.” In this post, I show why this type of argument fails. It takes what is wrong in Malthusianism and only adds further specious arguments. Cornucopians are basically Malthusians at heart. The solution lies elsewhere: There is no inevitable exponential population growth that has to be outstripped by technological progress. It is the other way around: Populations can and often do stabilize at a level well below a maximum size. They grow in response to technological progress or new resources that become available.
• World Economic History in One Picture: It might seem like my critique of the Malthusian argument is irrelevant because it is so old. However, Malthusianism is alive and kicking. In a side-series of posts I discuss what I think is wrong with Gregory Clark’s book “A Farewell to Alms,” which was published in 2007. And I think there is a lot wrong with it. This post is introductory: I take a close look at the very first chart in the book that is supposed to show “world economic history in one picture,” how income per capita in the world has developed since 1,000 BC. Looks like there are no data behind this graph and Gregory Clark has just made it up.
• You Can’t Prove an Empirical Claim Apriori: This is a very basic point. Empirical claims are those that can be true or false and not just one of the two. I explain why it is not possible to obtain them only from assertions that can only be true or false. Although that is not difficult to see there are many cases where someone gets this wrong and thinks they can do it. Thomas Malthus is one such example as I show in this post.
• Not Much Happened Until Very Recently?: My contention is that the Malthusian worldview is part of our culture. It informs even those who would not think of themselves as Malthusians in a narrow sense. Here I look at a tweet from the renowned development economist William Easterly. I would say that the mistake he makes here is easy to explain with the Malthusian worldview in the background. It is basically the claim that not much happened before 1800 and then something weird occurred. As I show: A LOT happened before 1800.
• Subsistence Increases in an Arithmetical Ratio?: One of the central claims of Malthus’ theory is that the food supply increases linearly over time. As I show here, Malthus has no argument for this and just begs the question. ie. assumes what he wants to prove. At the same time, Malthus also claims that linear growth is not possible, which contradicts his supposed natural law. All in all, one of the central tenets of the theory is simply unfounded.
• Human Populations Do NOT Grow Exponentially: The central idée fixe of the Malthusian worldview is that populations just can’t stop growing at a fixed rate, ie. exponentially, as long as they are not stopped by some brutal mechanism. Malthus even thinks that growth would be at the maximum rate possible. As I show in this post, actual human populations do not do this by far. Population growth in the past was at most modest, in many cases not there, and in some there was even shrinkage. Mortality cannot be the explanation, and the plausible conclusion is that populations targeted a stable size and only occassionally grew into opportunities. If stabilization was the norm, then there was no inevitable “population pressure,” and the Malthusian end-game is called off. As I show humankind has never even come close to carrying capacity.
• Population Increases in a Geometrical Ratio?: I dissect Thomas Malthus’ argument that “population, when unchecked, increases in a geometrical ratio,” ie. grows exponentially. He never makes his case explicitly, but distracts his readers with inessential side questions. With some work, it is possible to piece an argument together. — Malthus implicitly defines a state of society “when unchecked” as one where a population can and does have minimum mortality, where it can have maximum fertility, and where it refrains from all practices that might lower fertility. Then he uses another unfounded assumption that “the passion between the sexes will remain nearly in its present state” in a non-obvious interpretation to establish that the population indeed has maximum fertility. — All this is just a reformulation of the assumptions. Maximum fertility and minimum mortality are constants because of human nature, and so the assumption is equivalent to population growth at the maximum rate, which again is just another word for exponential growth at the maximum rate. But then the supposed conclusion is nothing but the assumptions that Malthus plugs in, ie. “begging the question.”
• The Amish Have Quadratic Population Growth: Exponential growth is not even in principle possible for a species when it can only expand in two dimensions. Assuming it is just an idée fixe that Malthus created and that has a hold on our imagination. Even Malthusians would have to concede this point. The plausible model with geographical expansion is quadratic growth. As I demonstrate for the Amish, this fits the data better than exponential growth. The consequence is that extrapolations based on the assumption of exponential growth may be way off.
• More on Quadratic Population Growth: Expanding on my previous post, I look into population growth in Europe and different countries. Here again quadratic growth yields a better fit than exponential growth.
• An Explanation of the Malthusian Argument and Its Main Problems: There are many criticisms of the Malthusian argument, but this one is central in my view. I explain with graphs how the Malthusian argument works in its ideal form for a population “when unchecked” and with a constraint for the food supply, and then what it means to first introduce the “positive checks,” which raise mortality, and then the “preventive check,” which lowers fertility. Already in the first step, crucial conclusions do not carry over from the ideal case. There is also a confusion of effects that have to do with a constraint for the food supply and that don’t. After the second step, the theory is so flexible that it can accomodate anything. None of the central conclusions from the ideal case have to remain intact. A population can simply stabilize long before it reaches a constraint for the food supply. Modern industrial societies are an obvious example for this, but probably also all other societies over the past 100,000 years.
• Long Story Short: The Malthusian Argument and Its Main Problems: A short version of the former post that presents the argument in a condensed form.
• The Regularity of Demographic Transitions: Demographic transitions puzzle Malthusians because they should not happen. Actually, they happen everywhere and all the time, not only over the past few hundred years, but they have occurred all through human history. As for modern demographic transitions, there is the curious fact that they regularly lead almost to the same result within a narrow range. There is a lot of variation for timing and how fast demographic transitions work out, but the move from preindustrial conditions to those in modern industrial societies leads to a boost by a factor of roughly 12. That shows that the driver can not be the particular development, but only the general move to modernity. I demonstrate this for continents and countries: Apart from a new location via migration, the share of populations on the continents will be almost the same for populations in 2100 as it was in 1600.
• Quadratic Versus Exponential Population Growth Again: I look into another example where quadratic population growth turns out to be a better explanation than exponential population growth: England from 1815 to 1869. As I demonstrate, extrapolations based on quadratic and exponential population growth to 2015 lead to vastly different predictions. The one with exponential growth is off by 150%. A forecast with quadratic population growth, though, yields 69 million predicted population versus 58.4 million actual population. Since my claim is not that quadratic population growth goes on forever, and instead that there should be a slowdown after some time, the forecast is actually quite decent although it goes over almost one and a half centuries and is based on no more than about half a century of data.
• Quadratic Population Growth and Cowen’s Second Law: The argument for quadratic population growth is actually quite simple: If a population grows by expansion on a two-dimensional surface, then its size should increase quadratically. According to Tyler Cowen’s Second Law, “there is a literature on everything.” However, I have not been able to locate it. Help appreciated.
• A Discussion of Other Models for Population Growth: I look into the logistic and the hyperbolic models here. More to come in further posts. My conclusion: These models add value, but have problems of their own. The fundamental misunderstanding is to search for one simple function that can describe everything, as also with the exponential model. Perhaps population dynamics are simply more complicated than that.
• Actual Populations Are Not Malthusian: I show why a Malthusian explanation for population dynamics in England looks implausible, both for what happened in the Middle Ages, and also over the past few centuries. Fertility developed in long waves as should be expected if a population target a population size. Mortality did not play a role in driving dynamics.
• Will South Korea Die Out? (Spoiler Alert: Probably Not.): I analyze data for the demographic transition in South Korea that came very fast from the 1970s to the 1990s. Some commentators have drawn the conclusion that the population will just fade away. But my conclusion is quite different: It looks plausible that South Korea will shrink from the peak after a fast ramp-up, but only to a size that is still much larger than where it started out. I also look into data for West and East Germany, and draw some tentative conclusions for low fertility in medieval cities and cities in general.
• Computation by a Population: This is a “bleg,” a post where I have a question. To have control over population dynamics, a population effectively has to do computations. I am thinking here not only a human population, it could also be some other species because I think this is a ubiquitous phenomenon. Such a population has to estimate inputs, apply certain rules to them to obtain a result, and then it has implement it and control and adjust the outcomes. Populations can do all this in other regards. There are many ways how they can do estimations, calculations and steer processes. However, the basic operations should be different from computers. There are also constraints. Now my question is: Has anyone already thought about what can be computed with a limited set of operations that may not be perfect? Note also my remarks in the comments: A population might also be one within a body, especially the population of brain cells. I also refer to various topics that may be relevant here.
• Sorry for the Current Demographics Overload: Apologies to my readers who are interested also in other topics that I cover. I explain why I am interested in this topic although in a deeper sense I am not. I think it is important to get these things right and I am afraid that is often not the case.
• Is Quadratic Growth a General Phenomenon?: I developed the argument in the context of demographics that if you have something that shifts from a lower to a higher level at a location and that expands slowly on a surface, then you should expect to see quadratic and not exponential growth in the aggregate that later even falls off and converges to a higher plateau. — In the growth phase, this can deceptively look like exponential growth. However, conclusions on this basis are then completely wrong. What is going on here is only one shift, not something that drives itself forward at a fixed rate. The regular growth does not come from a flow of events at the local level, but only from geographic expansion. — Now, the dynamics do not depend on the quantity being population density, it could also be something else. So, it seems plausible that you have the same thing also for economic growth: There is perhaps only one big shift from a lower to a higher level at a location behind it plus geographic expansion. A search for a flow of innovations would then be futile and lead to the same confusions as in the demographic case.
• Estimating Population Densities: As a constructive argument against Malthusianism, I try to develop a non-Malthusian explanation for population dynamics. What I presuppose is what I also discussed in my post “Computation by a Population.” I conjecture that two major inputs are involved: population density and a measure for general distress, centered around nutrition. Before a population could use this to control its dynamics, it needs to estimate the inputs. In this post, I focus on esimation population density. While it may seem as if this were extremely hard, I show that many species including humans should be able to do this easily, and probably really do. I discuss examples for bacteria, locusts, birds, whales, various territorial species, and also humans. My conclusion is that density estimation is eminently feasible.
• An Illustration of Quadratic Growth: The argument for quadratic growth so far was rather abstract. It may seem that a lot of assumptions are needed, and if they are violated, you get something completely differerent. I run a small simulation here with a toy model that deviates quite a bit from ideal assumptions of an expansion from a center on an infinite plane. However, you still get almost quadratic growth, which simply has to be there with an expansion in two dimensions.
• A Flashier Illustration of Quadratic Growth: As the title insinuates, I have some nicer graphs here. Basically, I first create a random geography with oceans and mountain ridges. Then I run the same process as before, only it has to stop at the coasts and it is harder to settle the mountains. And I found a better graphics routine in Scilab. All this is not meant as proof, only as an illustration to flesh the basic intuition out and show that even major deviations leave the result intact.
• Two Great Famines and Their Aftermath: Malthusians see the bright side of death. Those who survive have it better with higher real incomes. However, that should also mean that they immediately start to grow the population again and waste the windfall. — Yet, as I show for the Great Famine in Europe in the early 14th century and the Black Death that did not happen. For example the population of England shrank to about half its size over one and a half century. Only then did it start growing again, but slowly. Population shrinkage went along with rising and high real incomes, population growth with falling real incomes. This is a complete refutation of the Malthusian claim. — The second Great Famine I look at is the one in Ireland in the 19th century. Curiously, you have the same pattern and even almost the same outcome, a halving of population over the next century, even long after the catastrophe. — My explanation is that populations pursue a population target that depends on the level of distress. There is a slow-moving estimation in the background that leads to persistence even over generations. Catastrophic events lead to a much higher estimate for the level of distress that casts a shadow for a long time. As a reaction the population yanks the target size down and pursues it from then on, mostly via fertility, in the Irish case also via emigration. However, what that means — if I am right, of course — is that there is a long-running aftermath where a population is still afraid of another catastrophe. That puts higher real incomes into perspective, those might be more like larger buffers against unfortunate events that are expected.
• A Short Explanation of Population Momentum: Demographics attracts charlatans because it is basically quite simple and anyone can immediately do some calculations in Excel. I don’t mean the academic discipline here, but the topic. In this post, I explain one important concept that such people regularly don’t know about. Population momentum means that current events have repercussions over decades, and that runs out only after more than half a century. For example, high fertility now can lead to population growth much later on. If you don’t understand this, you can get many things completely wrong. What you observe might not be the result of what happens at the moment, but of what happened decades ago. In my experience, ignorance of population momentum is a safe way to spot the charlatans.
• Why Are There So Few Lions?: My theory is that human populations target a reasonable size that depends on conditions. One reason many will reject this is the belief that all other species do not do this and are “Malthusian.” However, that is not true. Here I discuss an interesting empirical finding. If you look at the biomass of prey and the biomass of predators (biomass=their combined weight) in a biome, a community of species, you might expect that the latter increases superlinearly or at least linearly in the first. If there is more prey, there can be proportionally more predators, or even more than proportionally because hunting becomes easier. Yet, the regular finding is that the relationship is sublinear: there are more predators with more prey, but less than proportionally so. With abundant food, the ratio between predators and prey goes down, and does not remain the same or even increases. That is baffling from a Malthusian or Darwinian vantage point. In the article I analyze, the authors think they find a power law here with an exponent of 0.75. But as I show there is a simple explanation that leads to the same result and that in what we can also find for human populations. If that is correct, the relationship is not a power law, which is only an artifact of the analysis.
• Malthus Before Malthus: A common misconception seems to be that Thomas Malthus was some kind of trailblazer who had some deep insights. Sometimes it is even claimed that he invented demographics. Nothing could be further from the truths. Malthus was actually a late-mover in a debate that had been going on for centuries. Practically all his central ideas were not new. What he added, like the claim about linear growth for the food supply was transparently false and unimportant for his argument. This is not to say that Thomas Malthus was not innovative. But his contribution lay elsewhere: He created a worldview and hammered it in. And he connected his assertions with pressing problems at the time. While others had made similar arguments before that had an impact on contemporary and later writers. In this post, I present two examples where others argued as Malthusians before Malthus. One is the Church Father Tertullian in the third century, the other Giovanni Botero in the 16th century. This is a first installment in a series where I will look more closely at the intellectual forebears of the Malthusian argument.
• Implicit Population Targets: I pursue the line of argument further that I started in my post on South Korea. Under the assumption that the relationship that I found there is univeral, I back out implicit population targets also for other countries. That works very well for Japan. Russia is a more complicated case with a much less stable developments and apparently shifting population targets. In another posts, I will look into the interplay between population dynamics and immigration, which is relevant for many other countries.
• My Forecast for Japan — Population and Fertility: I run a simulation with a model based on my analysis for South Korea, but geared towards the situation for Japan. This yields a very good explanation for what has happened there. Then I use this setup to forecast what will happen in the future. Contrary to conventional wisdom, my take is that the population will shrink, but not by much. Fertility should rise considerably, and even go above the replacement level. It looks like Japan will have a “baby boom” later in the century. Since noone has to believe my forecast, I offer to bet on population size and fertility for Japan.
• More About Why Japan Will Do Fine: Following up on my last post, I use my simulation to derive also structural data for the population of Japan: share of working age, share of seniors, share of minors, labor force participation, mean age, and dependency ratios. Many of the conclusions that are frequently drawn appear unfounded at best or rather simply as wrong.
• The Best Way To Spot Demographic Nonsense: In a little sub-series, I explain some telltale signs that an expert on demographics might be a charlatan who has not understand the basics. Here I explore the pitfalls of birth and death rates as indicators for fertility and mortality. Consistent confusion about the concepts is a great way to spot those who only pose as experts. Another one is when someone has not grasped population momentum, see my post here.
• Micro-Foundations for Stabilizing a Population: This is the beginning of a longer sub-series of posts where I explore the ramifications of a simulation model for population dynamics I have set up. Note that this is a work in progress where I report on my newest findings and speculate about what is going on. I am not always right, and sometimes I have to retract or refine a first hunch in later posts. Once certain parts will have become stable, I will write the results up also in dedicated posts. — It is one thing to assume on a macro-level that a population knows a population target and then pursues it in the aggegate, and another to have an explanation how they could do it on the micro-level as individuals. It is not obvious how this could work. People can only use data as inputs that are readily available, and also only simple compuations are feasible. On top of that, there has to be continuity over generations where target sizes are handed down, but not in an explicit way. What I am aiming for is something so simple that even species could do it that lack human capabilities. — I start from my observations about the behavior of the population of South Korea and derive a model that satisfies all these requirements. As I demonstrate it works, not only broadly, but astonishingly well. There is stabilization for millennia, which raises the question: Why does it work so well?

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The Malthusian argument forms the basis for Charles Darwin’s theory of “natural selection.” If it is in trouble, this also causes problems for the Darwinian argument. Not to be misunderstood: I think that “natural selection” in a strict sense is one plausible mechanism. I am an atheist and have no stake in silly claims about “creationism” or “intelligent design.” That is not my thrust.

Just like the Malthusian argument is weak, but became popular anyway because of its associated worldview, also the Darwinian argument seems so persuasive not for its inherent logic, but because Darwin created a similar worldview. The Darwinian worldview is actually nothing but the Malthusian worldview writ large. Many arguments were already foreshadowed in “An Essay on the Principle of Population.” And Darwin acknowledged his indebtedness to Malthus directly. Since the Darwinian worldview is perhaps even more a part of our culture than the narrower Malthusian worldview, it reinforces the persuasiveness of the Malthusian argument. But then this is circular because Darwin assumes the Malthusian argument as incontrovertibly true, which it is not.

Originally, I listed my posts developing a critique of the Darwinian argument here because the topics are so intertwined. However, by now this has become too unwieldy, and so I have started a separate overview of my writing turning around the Darwinian argument more specifically:

Synopsis: What’s Wrong With the Darwinian Argument?

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My take on “worldviews” is perhaps somewhat idiosyncratic. That’s why I explore it in a further series of posts. Here is a first installment:

• Worldviews, Narratives, and Ideologies: The main thrust is that a worldview is an intuitive panorama of how the world works. It has static parts for relationships between different entities, but also dynamic parts, which work as “narratives.” And a worldview is also intertwined with moral and sometimes even aesthetic judgments. — The human mind is built for worldviews. We can handle them intuitively and with ease. By constrast, rational thought is hard. Humans can do it, but often find it too laborious. — Rational arguments about the world are organized into “ideologies” (in my definition). Most people may not have an explicit one, but we all have our worldviews. There is an interplay here where ideologies shape worldviews, but also worldviews ideologies. What matters more, though, are worldviews because they are intuitive and popular, which does not necessarily imply that they are irrational. They only have a far lower standard of stringency than rational arguments. — To understand many developments it is too shallow to only focus on the ideologies and miss the worldviews through which they have an impact.
• More on Worldviews and Ideologies: As the title suggests, I explore the topic more deeply here, especially how worldviews and ideologies interact. I also demonstrate what I mean with some concrete examples.
• Everyone Has a Worldview: My analysis that there is a Malthusian worldview might seem like a blanket argument to dismiss it because I can call it a “worldview.” I flesh my understanding of the term in this post further out and why that would be silly. You have to tackle the argument. Only if it is false, can you then wonder whether the mistake stems from a worldview. Everyone has one, and so this is no slam-dunk argument against specific claims without addressing them outright.

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Somewhat related to the general line of argument, but more entertaining is this post on how the obsession with the exponential function can lead you astray:

• If You Had Brought $1 Dollar to the Bank in 0 AD …: … how much would you have now?

I will keep this page updated as the argument grows and expands in different directions. This will help you keep track, which would otherwise be difficult if you only had to follow links between articles. You can also have a birdseye overview of the whole argument, which is perhaps easier to grasp in this way than if you have to understand it from a “Froschperspektive” (frog’s perspective).