Uncertainty of the Coronavirus Pandemic: Humility Before Nature

William Goldman, the talented Hollywood screenwriter (1931-2018), summed up the impossibility of predicting which movie will be a hit and which not, with this pithy perspective: “Nobody knows anything.” (He qualified his statement with “Not one person in the entire motion picture field knows for a certainty what's going to work. Every time out it's a guess and, if you're lucky, an educated one.” But no one quotes the long qualifier when three words do a far better job than thirty.)

William Goldman - "Nobody knows anything"

Goldman’s 3-word phrase springs to mind when we hear all the punditry and stupidity (the latter emanating mostly from the clueless, ignorant liar-in-chief narcissist in the White House) surrounding the coronavirus pandemic. Nobody knows anything. Well, some experts in the field, mostly researchers who have studied pandemics all their lives in the field or in the lab, probably know something but what they do not know - and they will be the first one to tell you - is so much more than what they do that, even for them, the ratio of the known to the unknown is practically zero.

What is worth reflecting on is the rate at which the killer virus is leaving death in its wake. One word that sums it up is “exponential,” a mathematical concept many of us are familiar with from such media phrases as “CEO compensations are increasing exponentially” or “Many species of the world are decaying exponentially.”

If the coronavirus infects 1 person today, who in turn infects 2 tomorrow, each of whom infects 2 the following day to make it 4, and so on, it is an exponentially increasing (doubling) function. It is base 2 raised to d, the number of days since the 1^st infection, that is, 2^d. What if the 1^st person infects 3 rather than 2, and those 3 each infect 3 the following day, and so on. In that case, it is 3^d, the base being 3 (tripling) rather than 2.

You can see what we need to do to make the infection rate decay: Make the base less than 1, until the number of infections “asymptotically” (that is, very close to but not exactly equal to) approach 0.

But that decay rate is nowhere in sight.

For example, on Tuesday, March 17, it was reported that there were just more than 5,700 confirmed coronavirus cases in the United States. That number climbed above 11,500 on Thursday, March 19, and officials indicated the number will continue to rise sharply as more test results become available.

The number doubled in 2 days. The exponentially increasing function is now (5700)2^d/2, where 5,700 is the initial count and d is the number of days since the initial count.

If somehow we could replace that base 2 (doubling) with say, 0.7, then (5700)(0.7)^d/2 will rapidly “approach” 0.

One way to understand the numbers is to take this paragraph from a recent opinion piece by the NY Times columnist Tom Friedman:

“One of the hardest things for the human mind to grasp is the power of an exponential, something that just keeps relentlessly doubling and doubling, like a pandemic. The brain just can’t appreciate how quickly 5,000 cases of confirmed coronavirus infection in America can explode into one million if we don’t lock down now. Here’s a simple way to explain the exponential threat we face, in a way an oft-bankrupt real estate developer like Donald Trump might understand. It was also offered by Bill Joy: ‘The virus is like a loan shark who charges 25 percent a day interest. We borrowed $1 (the first coronavirus to appear here). We then fiddled for 40 days. Now we owe $7,500. If we wait three more weeks to pay, we’ll owe almost $1 million.’”

Let’s do the math.

A loan shark charges me $0.25 per day compounded on a $1 I borrowed from him (I am not aware that there has ever been a woman loan shark. It's always men!) So, at the end of the first day, I, the borrower, owe the shark $1.25. At the end of the 2nd day, I owe the shark interest on interest, which amounts to (1.25)² (1.25 raised to the power of 2.) So, at the end of 40 days, I will owe him (1.25)⁴⁰ = $7,523.16, which rounds off to $7,500. After 3 more weeks, that is, 61 days later, I owe the shark (1.25)⁶¹ = 815,663.05, which is close to 1 Million Dollars!

The way to win this battle, and also the war, is to make that 1.25 LESS than 1, say, 0.8, so we experience exponential decay. In that case, after 40 days of decay, the number reduces to (0.8)⁴⁰ = 0.0001329, which is one-hundredth of 1%! It's in the math. We need to make that number in the parenthesis less than 1 before we can resume normal life.

So how do we make the base of the exponential function less than 1? That’s the trillion-dollar question facing us today. Social distancing, better-equipped health workers and hospitals, proper hygiene, and a combination of many more yet unknown factors can perhaps force the killer virus to be on the decaying curve. But again, we just don’t know! No matter how much fancy statistics and solutions we weave and spin, we just don’t know!

While the mathematics of increasing and decaying exponential models are known with certainty, the nature and the destructive power of the coronoavirus pathogen is unknown. We only know that unchecked, it grows exponentially, but if somehow checked, will decay and eventually, for all practical purposes, disappear.

Consider Hemingway’s insight in this dialogue from his 1926 novel “The Sun Also Rises”: “How did you go bankrupt?" Bill asked. “Two ways,” Mike said. “Gradually and then suddenly.”

The initial increase from 1 to 2 to 4 seems gradual when suddenly, before we know it, the virus has infected over 65,000 and then more, and yet more, with its limitless, voracious appetite.

People who spout certainty when life is fundamentally uncertain are the real ignoramuses, no matter how powerful or wealthy or apparently smart they may appear be. In contrast, those with real knowledge are humble when confronted with the unknown. They know that nature’s imagination is superior to human imagination. To glimpse into the inner workings of nature, whether of physical laws or of pathogens, they know that first they must acknowledge, “I don’t know.” This is also true from a theodicy perspective. Priests, Rabbis and Imams afflicted with religious chauvinism who think they know how God’s mind works with certainty are as guilty as arrogant scientists and political leaders in misleading us.

“Doubt is an uncomfortable condition,” said Voltaire, “but certainty is a ridiculous one.”

In the next year or two, brilliant but humble researchers will undoubtedly have made slow but significant progress in deciphering the working of the killer coronavirus and ways of neutralizing it. The rate of their progress will be anything but exponential. Yet they offer us hope that one day this virus will have met its match in their ingenuity. If you were to ask one of them what the catalyst was for her breakthrough, she will unhesitatingly tell you, “I began by acknowledging that I didn’t know.”