Getting it Wronger

The Wrong Part was Way Back There

When I was nine or ten, I spent a summer at a small town newspaper, ostensibly learning how to set type, which I was really pathetic at. But the editor mainly wanted a captive audience for his lectures, which were mostly rants about how Roosevelt (he called him Rue-sa-velt) who had been in league with the Jews, had tried to destroy the country. My only knowledge of Jews came from the Bible and Ivanhoe, which even at that age seemed to me to contradict his notions. But mostly I was just befuddled.

My introduction to delusional thinking, although way later, when I learned that a good many economists argued that President Roosevelt’s “New Deal,” had actually prolonged the Depression (and since I’d actually studied economics, I both grasped their arguments and agreed with them), it occurred to me there was a grain of truth buried in those rantings. A valuable lesson.

Madness

I’ve probably referred to this book before: Charles MacKay’s Extraordinary Popular Delusions and Madness of Crowds, published in the 1840s. The opening of his book is a clear statement of his point.

In reading the history of nations, we find that, like individuals, they have their whims and their peculiarities; their seasons of excitement and recklessness, when they care not what they do. We find that whole communities suddenly fix their minds upon one object, and go mad in its pursuit; that millions of people become simultaneously impressed with one delusion, and run after it, till their attention is caught by some new folly more captivating than the first.

In a surprisingly succinct hundred thousand words (of the first volume), MacKay gave detailed explanations of historical situations in which large groups of people (crowds) became so obsessed with bizarre notions (extraordinary delusions) that they all charged off en masse like a herd of cattle, the result being financial ruin or even death.

What was fascinating was that he wasn’t restricting himself to examples involving the poor and the uneducated, but behaviors that were extraordinary precisely because they involved prosperous and educated western societies, as in the South Sea Bubble in England (1700s) and the Tulip Craze in the Netherlands (1600s). His obvious conclusion was that human beings quite frequently made highly irrational and ruinous decisions, contrary to the assumptions in the West that education precluded this sort of behavior.

MacKay didn’t attempt to explain some deep underlying cause, just cited numerous examples. Aside from some handfuls of economists, who saw the book as a useful reminder that consumers didn’t necessarily make purely rational or logical decisions, no one paid much attention to MacKay’s book, although it seemed to me that it called attention to an important aspect of human behavior, and an enduring one. (Enduring: as I write this the Dutch are rationing electricity.)

Specifically, I would cite the sections on “Modern Prophecies,” “The Love of the Marvelous and the Disbelief in the True,” and “Popular Follies of Great Cities” both as examples of the wide spread and far ranging nature of MacKay’s examples. But hey, don’t take my word for it. You can download the 1841 text for free, courtesy of Gutenberg. It’s number 636.

Moreover I would cite modern examples of events such as Y2K, Nuclear Winter, the Climate Hysteria that began in the 1970s, and the Covid Apocalypse as exactly the types of extraordinary popular delusions and madness that MacKay described.

Now as I observed, implicit in MacKay’s discussion was that these follies weren’t the product of the poor and uneducated, but occurred in advanced western societies. So in what follows, I’ll engage in a somewhat different task: the explanation of how some major delusions began, and why they’re totally wrong, beginning with one that’s still around.

Washington Irving, Columbus, and the Flat Earth

As you may have heard, the earth is spherical. Since I’d studied spherical trigonometry during my high school years, I’m not sure I ever thought about the idea that it wasn’t, and if I did, I assumed that that any educated person realized it was round, since that branch of math (which involved logarithms, a 17^th century concept), was how navigators plotted courses on the sea and in the air.

Moreover just as one of basic axioms in plane geometry was that the shortest distance between two points was a straight like, in spherical trig, its counterpart was that the shortest distance on a sphere was a great circle, which involved a complex formula (look it up).

So decades later, when I ran across Washington Irving’s work on Columbus, and read that until his first voyage, it was believed that the world was flat, but he proved it was round, I was startled. And even more so when I discovered how many of my students believed that.

His claim was absurd for all sorts of reasons, the first one being that even if you accepted Irving’s claim, sailing from Spain to the Caribbean islands hardly proved the world was round—at most all it established was that it was pretty big, since the only way he could have “proved” it was round was if he circumnavigated it, which he obviously didn’t.

As I’m sure you know, educated men had decided the earth was round for a very long time (like 1500 years), just as the Genese seafarer knew that there was land to the west: he referred to that in his letters. Supposedly his “error” was that he assumed that this terra incognita was the Indies. But in fact, Queen Isabella funded his expedition because he wrote a lengthy Latin text arguing that the Garden of Eden was there.

Now Irving’s delusion is actually fascinating, and for three reasons. The claim was ludicrous in and of itself (simple logic). More importantly, by the time he came along mariners had been plotting great circles for quite a while, and third, as a supposedly educated man, he should have known that the knowledge of the earth’s actual shape was not exactly a deep dark secret: the only real uncertainty was its circumference.

So the only mystery was deciding whether Irving was a fraud, an idiot, or delusional. But I’ll be charitable, assume the last, so his case is the classical example of delusion: a belief easily contradicted by both logical reasoning and concrete knowledge (why I began with spherical trigonometry).

And the reason for the delusions is equally fatuous: Irving’s belief that “science” was opposed to “religion.” But as anyone familiar with the life and works of Sir Isaac Newton is aware, this is nonsense. The man who discovered all sorts of basic laws governing the behavior of physical objects, developed differential calculus, was clearly a great scientist. He was also a devout Christian. Surprised? I refer you to chapter sixteen of David Brewster’s authoritative biography (available on Gutenberg as ebook 53311). Irving’s opposition was bunk, especially when coupled with his obvious ignorance. But like a great many failed ideas, it’s had remarkable persistence, especially amongst people whose knowledge of basic mathematics is like his.

The Delusions of Thomas Malthus

in 1798 Malthus, who was born in 1756, published An Essay on the Principle of Population, in which he argued that that the “abundance of the earth” was insufficient to support the growth of the population. Malthusianism is still around with us today, so the basic errors are interesting, even though they’re hardly ever discussed.

The dates are important, and here’s why. The “law” he believed he was formulating had two ideas: the fixed capacity of agriculture and the inevitable growth of humanity. Two convenient assumptions, indeed, but by the 1790s Great Britain’s progress completely contradicted the former and there was no actual information on the latter.

The latter is easily explained. Although there had been sporadic attempts to estimate the size of the population of the UK, the first real census didn’t occur until 1841, so not only was there nothing much to compare it to (which is kind of important!), but in the 1790s, the general belief in the UK was that the population was declining (see, for example, the discussions of this in M. Dorothy George, London Life in the Eighteenth Century).

Now the error in the first part is trickier, as it rests on a flawed assumption: that agricultural output per hectare (or whatever) is fixed. But given the parson’s life, he had to have seen the fallacy, because the evidence was all around him. We don’t have the kind of systematic data about the past that we’d like to have (the great problem economic historians have), but what we do have for the UK is pretty convincing. Through selective breeding, British ranchers had increased the size of sheep and cattle twofold over the course of the 18^th century.

But the growth in size isn’t accompanied by a proportional growth in consumption. They may weigh twice as much but they don’t consume anything near twice as much food. Moreover, bigger animals are less vulnerable, produce a good deal more meat, wool, and leather. (again: see Kenneth Maclean, the Agrarian Age: A Background to Wortdsworth, published in 1950 by Yale).

As best we can tell, there were similar advances in other areas of agriculture, although not as dramatic—those increases occurred later in the 19^th century.

So in both cases we have the spectacle of supposedly educated men arguing for bizarre ideas that are formulated either in deliberate ignorance or delusion.

But I suppose you could say that the good parson has the last laugh, since by the time he passed away (1834), his intellectual descendants were busy gearing up to crank out similar fantasies, e.g., Karl Marx’s labor theory of value.

What’s interesting about Malthus is that is demographic claims continue to this day.

Problems of Demography

In the case of Great Britain and the United States, it’s true that with the advent of systematic census data in the 19^th century, we began to be able to measure the growth and/or decline in national populations, and to a degree that’s true in certain other countries. But those countries by no means contain the majority of the population, even in the mid nineteenth and early twentieth century.

What complicates matters to the point of mystery is that we only have hard data for what’s basically a small piece of the globe at a brief moment in time. Brief: human beings have been around for several thousand years (at least). The minimum figure is 3,500 years, so all we have is a sample of about six percent—at most.

There are large areas where we have no real idea of how many people were there in the past, like South America and Africa. Increasingly, archaeologists are finding the evidence of the existence of cities in places that have only recently been discovered—a trend that’s been going on since the cities of the Mayans were uncovered in the 1840.

So the basic idea that Malthus had can’t even be dignified by calling it a claim, because there’s no evidence at all. It had to be true because he wanted it to be true. An observation that explains both a good deal about human beings and the enormous difficulty of countering their delusions.

The Failure to Understand Numbers

The other failure in Malthusianism in particular, and demography in general is more interesting, because it reveals a misapplication of mathematics. Malthusianism is often stated as the food supply increases arithmetically and the population increases geometrically. That is, the one increases over time by increments, and the other increase at the rate of 2,4,8,16, 32, and so forth. The math is very tidy.

But here’s the problem. In the actual sciences, aka the real world, changes, insofar as they can be measured and recorded, exhibit a much different behavior. In a good many (like just about all) cases, the resulting curve is technically Gaussian, which is, somewhat misleadingly, called the “bell” or “normal” curve.

An early and extremely significant example of that came in 1840, when William Farr, studying the spread of smallpox in the UK, noticed that its spread could be described by what he called a “normal” curve. Farr observed that the same was true for the incidence of other infectious diseases he had examined. During Covid I kept waiting for someone to mention the good doctor Farr. Must have missed it.

But the neat thing about Gaussian curves is that the rate of increase and decrease can be predicted by a formula. In fact using a standard internet search tool, you can probably find a handy explanation that shows you what the curves look like as well as the formula.

But there’s a catch. In order to understand the formula you have to (a) know calculus, (b) grasp the basics of Probability Theory and Statistics, and (c) understand that formulae can be graphed. By the way, when you look at the dates for these developments (or inventions) all three were both conceptualized and put into practice by the time Malthus and company were writing.

So Farr, looking at the data, observed the shape of the curve (Gaussian), and hence Farr’s Law about the rate of the spread, and the point at which it would reach its limit. In the phenomenon he was interested in, what that meant was that at a certain point, the limit would be reached, that is, everyone who could catch the disease had gotten it, and the incidences would decline.

But if you didn’t understand the two areas of math I named, when you looked at an even that was being measured and graphed, in the initial stages, it would look like a geometric progression, even though it was Gaussian. But it wasn’t, and since you could predict the overall shape of the curve, it was easy to tell.

But visually, although Gaussian curves come in many different versions of a “bell,” at some point in time, they all have one or more sections that looks like a straight line. I think that’s probably the basic reason for error—along with mistake of not realizing that the curve isn’t the data, it’s just a convenient visual display of the data.

Anyway, it’s kind of fascinating to see all the claims made about rates of growth and decline that just ignore the above.

And by now it’s become almost routine. When Leon Daudet called the Nineteenth Century “stupid,” and listed the twenty-two fundamental stupidities, he wasn’t ranting. On the contrary, the beliefs were widespread. Marx was a great example, but hardly unique.

I’ve quoted Daudet before, specifically his Sixteenth Stupidity.

Property is Theft; Capital is War.

But here are the first two on his list:

The 19^th Century is the Century of Progress, the Century of Science.

But science without math is like a car without an engine. No matter how shiny and perfect it looks, you can’t go anywhere in it.

And the point of this essay is this: it’s not difficult to see the errors, but lots of luck in trying get people to abandon their delusions.