Guest Contribution: “The Year 2020 in Three Phrases”

Today, we present a guest post written by Jeffrey Frankel, Harpel Professor at Harvard’s Kennedy  School of Government, and formerly a member of the White House Council of Economic Advisers. A shorter version appeared at Project Syndicate and The Guardian.

 December 31, 2020 — Let us consider the past year through the lenses of three particular phrases: “witch hunt,” “black swan,” and “exponential.”  Each is widely applied, but not necessarily in the most useful way.

1.  Witch hunt  

Donald Trump has used the words “witch hunt” approximately once every three days on average during his presidency, just counting tweets alone.  It wasn’t just his impeachment trial, which ended with the Senate voting to acquit on February 5 of 2020. He continued during the year to use “witch hunt” to describe accusations that he mis-managed the Covid-19 response (April), inquiries into his tax returns (July), investigation into alleged criminal conduct at the Trump Organization (August), and other challenges.

Most people long ago developed their own well-formed opinions about whether President Trump was innocent or guilty of the various violations with which he has been charged.  But neither his supporters nor his critics have given full thought to the linguistic implications of “witch hunt.”  Perhaps it doesn’t mean what they think it does.

The original witch hunts, of course, were religious persecution of (usually) women accused of witchcraft, that began in early-modern Europe.  An estimated 40,000 were executed between 1450 and 1750.  Americans think of the Salem witch trials of 1692-93.

(Incidentally, if we are changing the names of buildings named after people now known to have been associated with egregious evil, does it not follow that Harvard should change the name of Mather House, due to the Mathers’ associations with the witch trials?)

The witch-hunt phrase only came into widespread use in the mid-20th-century, as a metaphor for the frenzied search for communists “under every bed.”  Arthur Miller wrote The Crucible, his 1952 play about the Salem witch trials, as an allegory for the McCarthy hearings into suspected communists.

The 17th century witch trials and the McCarthy hearings have important differences.  For one thing, communists really existed, whereas witches did not (with apologies to any latter-day Wiccans).  But the two historical episodes had one thing in common, which the accusations against Mr. Trump (whether true or false) do not have.  In a genuine witch hunt, the hunters start from the firm belief that a particular type of evil-doers — witches or communists — walk amongst the innocent public, and it is the witch-hunter’s job to figure out who they are.  This does not describe the nature of the attacks on the 45th president.  The claim by Trump and his many supporters that his detractors are out to get him one way or another, is not a claim of a witch hunt.  It is a claim that his detractors start from the firm belief that he is no good, and that they view their job as finding crimes to pin on him.  Words like “persecution” would more accurately convey what they are trying to say.

Once again, this linguistic point has little to do with Democrats versus Republicans or guilt versus innocence.  Put it this way: special prosecutor Ken Starr’s Javert-like investigation of President Bill Clinton was not a witch hunt; rather it was a fishing expedition.  (It was a fishing expedition that – after various dead ends — eventually caught a genuine fish, though the Lewinsky affair took place well after the Starr investigation had started in 1994.)

When federal authorities charged gangster Al Capone with tax evasion in 1931, it was not a witch hunt.  The murderous target of the investigation was determined first; then the charges that could put him away were identified (constrained by corrupt law enforcement at the state level).

Fishing expeditions that find genuine fish everywhere they look merit yet another characterization.  They may be simply an application of the rule of law

2.  Black swans

The second phrase to characterize the year 2020 is “black swan.”  When the coronavirus spread beyond China and suddenly impacted the health and jobs of people around the world, many described it as a quintessential black swan.

A 2007 book by Nassim Taleb made black swan almost into a household expression, because it was seen to fit the 2007-09 housing finance crisis so well.  He defined the term to mean a major event which nobody realized was even a possibility, because they had never seen one before.  But the metaphor is more insightful than that.

The historical importance of the renowned bird lies in British philosophy.  David Hume (1740) and John Stuart Mill (1853), like most Britons, had never seen a black swan.  Reasoning by induction, then, they might easily have concluded that all swans are white. But Dutch explorers had discovered black swans in Australia in 1697 and British experts in ornithology were aware of this.  The best way to use the metaphor is to point out that competent experts can and do factor in data from other centuries and other countries, and that competent policy-makers should listen to their warnings.

Contrary to what had been widely believed in US financial markets before 2007, housing prices can go down as well as up, as had been illustrated by other countries (Japan in the 1990s) or in other centuries (the US itself in the 1930s).  Similarly, health experts and well-informed policy-makers had been well aware before 2020 that some pandemic like the new coronavirus, not only was possible — the pandemic of 1917-18 comes to mind — but was likely to strike sooner or later.  In too many countries, political leaders failed to heed the warnings and recommendations. The world has paid dearly for the consequences.

So, this year’s COVID-19 pandemic was indeed a black swan event.  But the phrase is perhaps best defined not simply as a sudden development that catches the general public by complete surprise, but, beyond that, as a “tail event” which was known by scientific experts and responsible officials to be a dangerous possibility, but one that has a relatively low probability in any given year.


3.  Exponential

The word “exponential” was used frequently in common speech even before the past year’s coronavirus experience, and almost always wrongly.  It was used to mean “rapid.”  Of course, anyone wishing to play language police must confront the argument by Humpty Dumpty, the ill-fated character in Lewis Carroll’s Through the Looking Glass, who insisted, “When I use a word, it means just what I choose it to mean.”  (2020 was the year when I gave up insisting that my students treat the word “data” as plural.)  But precision in language is often important for achieving precision in thought.

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 growth rates that are exponential and growth rates that are high.  The correct usage is that a quantity, such as the number of bacteria in a colony, increases exponentially if its rate of increase is proportionate to the quantity itself.  At any point in time, the rate of increase can be either high or low.  It can even be negative, as with the radioactive decay of a block of uranium.

The amount money that one has in the bank increases exponentially, due to compound interest.  That is true even though the rate of increase is now very low.  These days, the interest rate is even negative in Europe or Japan, implying exponential decay of one’s wealth (like that block of uranium).  The process is still exponential.

Conversely, a car may be traveling at a high rate of speed, but it is not moving exponentially if it is not accelerating as it goes.  What matters for exponentiality is only that the rate of change be proportionate to the level.

With the arrival of the pandemic in the year 2020, people finally began to use the word “exponential” correctly: to describe the number of cases of the disease.   The reason that 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 countermeasures.  (Very early estimates of R0 — before any measures had been taken in response to the virus — were in the range of 1.5 to 4.0.)

The use of R has drawbacks, particularly in that it is difficult to estimate.  But the concept can help make an important point.  If R is greater than 1.0, as it was in the early stages of the pandemic and presumably has become again in many countries recently, it means that things are getting worse.

That may seem obvious.  But consider the mostly widely used statistic: the number of reported cases of Covid-19. If it is rising over time, or is higher in one country than another, this does not necessarily mean that things are worse.  It may mean that the number of tests is high or rising, which is a good thing, being an important component of the strategy to fight the virus.

R can be brought down, via masking, social distancing, handwashing, testing, isolation, and now inoculation with the new vaccines.  When R is brought below 1.0, it means that the pandemic is dying out, that the rate of exponential growth is negative.

May everyone have a 2021 with no witches to hunt, the swans they expect, and an R well below 1.0.


This post written by Jeffrey Frankel.

3 thoughts on “Guest Contribution: “The Year 2020 in Three Phrases”

  1. Barkley Rosser


    As someone mentioned by Taleb in the pb edtion of his Black Sawn book, I must strongly disagree with your analysis of black swans. Taleb himself argued that several events people called that were not, includin 9/11 and the 2008 market crash and following Great Recession. I am sure he would not agree this year’s pandemic was one either.

    This is the old quantifiable risk versus unquantifiable Keynes-Knight uncertainty, with black swan events being the latter. Taleb identifies the Oct. 1987 stock market crash as one, still the largest single day decline ever, and completely unexpected. Fat tail distributions do not provide black swans, but in his own terminology, grey swans. Indeed, various people had warned of the danger of a 9/11 event; as you noted housing markets do go down and lots of people saw housing was a bubble, certainly by 2005, with some of us warning its decline would trigger a bad recssion, and the pandemic was so widely expected it was used by government officials in the US as recently as last year to test emergency procedures, a pandemic of a highly contagious lung ailment. Not remotely a black swan event.

    White swans arise from Gaussian normal distributions.

    Regarding exponential and the pandemic, what we really saw were logistic functions, which are essentially exponentials that run into a limit.

    Happy new year, you all.

  2. Moses Herzog

    I thought this was an outstanding editorial by Professor Frankel. We’ve seen certain people here in the comments section before, try to suggest they are the sole arbiter of the English language. Readers see it for what it is for—and you gave them the proper reply. Readers see it for what it is.

  3. Barkley Rosser


    I have to agree with Moses that “you gave them the proper reply.” You said nothing. Congratulations.

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