The historical importance of the notion of a black swan lies in British philosophy. Like most Britons, David Hume (writing in the eighteenth century) and John Stuart Mill (writing in the nineteenth century) had never seen one. Reasoning by induction, they might easily have concluded that all swans are white. But, as British ornithologists were aware, Dutch explorers had discovered black swans in Australia in 1697. So, the best way to use the black swan metaphor is to point out that competent experts can and do factor in data from other decades, centuries, and countries, and that competent policymakers should listen to their warnings.
Contrary to the widespread belief in US financial markets before 2007, housing prices can go down as well as up. Similarly, health experts and well-informed policymakers had been well aware before 2020 that a pandemic like COVID-19 was not only possible, but likely to strike sooner or later. In too many countries, however, political leaders failed to heed the warnings and recommendations. The world has paid dearly for their mistake.
So, this year’s COVID-19 pandemic was indeed a black swan. But the phrase is perhaps best defined not just as a sudden major development that catches the general public by surprise, but as a “tail event” – known by scientific experts and responsible officials to be a dangerous possibility (albeit one with relatively low probability in any given year).
Finally, the word “exponential” was used frequently in common speech even before the pandemic – and almost always incorrectly, to mean “rapid.” Of course, anyone wishing to play language police must confront the argument made by Humpty Dumpty in Lewis Carroll’s Through the Looking-Glass, who insisted that, “When I use a word, it means just what I choose it to mean.”
But linguistic precision is often important for achieving intellectual precision. Exponential is a mathematical term. It does not mean rapid. Hard as this may be to believe, there is not even a correlation or association between exponential and high growth rates. The money that one has in the bank changes exponentially, due to compound interest, but the rate can be low or even negative, as European interest rates demonstrate.
With the arrival of COVID-19, people finally began to use the word “exponential” correctly, to describe the number of infections. The reason why the number of cases rises exponentially is that each infected person infects a number of other people. Epidemiologists call this average ratio the rate of reproduction, represented by R. It is designated R0 in a population with no immunity and no counter-measures.
The use of R has drawbacks, particularly the difficulty of estimating it. But the concept makes an important point. If R is greater than one, as it was in the early stages of the pandemic and presumably has become again in many places, it means that things are getting worse.
R can be brought down via wearing face masks, social distancing, frequent hand washing, testing, isolation, and now inoculation with the new COVID-19 vaccines. When R falls below one, it means that the pandemic is dying out, and that the rate of exponential growth is negative.
So, here’s wishing everyone no witches to hunt, the swans they expect, and an R well below one in 2021.
Jeffrey Frankel, professor of capital formation and growth at Harvard University, previously served as a member of President Bill Clinton’s Council of Economic Advisers. He is a research associate at the U.S. National Bureau of Economic Research.