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OPINION | MASTERSON ONLINE: An exponential virus

by Mike Masterson | November 28, 2020 at 9:28 a.m.

I recently expressed ignorance over the mode of incredibly rapid transmission of covid-19 as thousands of new cases and hospitalizations are reported each day.

One reader in a recent letter to the editor managed to confuse my confusion (and perhaps that of other readers) by implying I was somehow against wearing masks for protection when I was openly wondering how could it possibly be spreading so fast when many infected are wearing masks and washing their hands.

Surely there can't be that many maskless people constantly coughing or singing or inadvertently spitting on each other each day to warrant numbers that are soaring by the thousands daily?

In short, I had limited understanding of how diseases spread "exponentially," and remained somewhat bamfoozled over the mechanism by which the virus covers such a wide swath daily.

Reader Larry Coleman of Little Rock, a professor emeritus from the physics department at the University of Arkansas Little Rock, kindly graced me with an explanation worth sharing.

I also should say I do understand, since covid can be asymptomatic, that increased testing for the virus is bound to naturally reveal additional positive cases, usually many. Even at that, it's still difficult for me to fathom how fast and wide it's spreading.

"I was struck by your comments Sunday about the rapid spread of covid," said Coleman. "Others must have wondered the same but you stated the question more eloquently than anything I've seen.

"A physicist named Al Bartlett at the University of Colorado made almost a career of giving a lecture worldwide on exponential growth 1,741 times. He famously said, 'The greatest shortcoming of the human race is our inability to understand the exponential function.'"

In expressing surprise at the rapidity of exponential growth, he said I'm in a "world of company."

Coleman told me about Louis Slotin, an expert on the exponential function and a physicist at Los Alamos during World War II, who became a victim of exponential growth on May 21, 1946, dying nine days later.

"Slotin was working with a sphere of plutonium intended for a third bomb against Japan. Though plutonium nuclei within the globe were continually fissioning and releasing energy and two neutrons with each fission, it was at such a low rate the sphere was safe enough to use as a coffee table ornament.

"You see, each of the two emitted neutrons can strike other nuclei and cause fissions of those nuclei. This progression can build rapidly into an explosion, except that in Slotin's small sphere most neutrons leave without striking other nuclei."

However, Slotin manipulated the neutrons, thus reflecting them back into the sphere and a second chance to produce progressive fissions. "Others said he was 'tickling the tail of a sleeping dragon,'" said Coleman.

An exponentially growing pandemic creates an analogous situation. Say a single infected person infects two others. And each of those in turn infects two others. "The number of people infected at each stage goes as: 1, 2, 4, 8, 16."

Coleman cited the example of a parlor game in which people vie to double a sheet of ordinary printer paper as many times as possible. First, folding it in half, then again, making the paper twice as thick as before.

"Then double it again, making it four times as thick," he said. "Keep going for as many folds as you can, which will be seven. The folded paper will be 128 times (2, 4, 8, 16, 32, 64, 128) thicker than the original sheet, or about half an inch."

That's what's so deceptive and dangerous about the covid-19 spread. "Because if you continue folding for a total of 42 folds--OK, let's agree that no one has ever done this or ever will, but if you could--after 42 folds the paper would be thicker than the distance from Earth to the moon!"

Shocking even to experts, Coleman added, is this comes from doing a simple sequence of seven folds just six times. After seven folds the thickness is a half-inch. After the next seven it's 5 inches, then 700 feet, then 17 miles, 2,200 miles, and finally 280,000 miles. "Only three more cycles of seven and the thickness exceeds the distance to the nearest stars."

"The math is the same for an out-of-control pandemic," he explained. "In the U.S., exponential growth of covid-19 started about March 1. For the next month the number of cases doubled about every 2.5 days. That's like the paper being folded every 2.5 days for a total of 11 folds before the end of exponential growth about March 28, two weeks after the March 15 order to social distance.

"March 28 is when masks and distancing began to take effect, each infected person infected fewer than one person, which meant the curve became non-exponential."

Coleman said epidemiologists recognize it is crucial to attack a pandemic while numbers remain low. Waiting until they become worryingly large is too late. "We desperately want to avoid those last doublings because that is when the cases explode, hospitals fill and deaths occur.

"The key to avoiding exponential growth is to see that each infected person infects, not two additional people but fewer than one, on average," he continued. "If so, cases do not grow, exponentially or otherwise. Of course, we can limit transmission by masks, distancing and washing."

Louis Slotin died because he lost respect for exponential growth in his plutonium experiment. "Nobel laureate Enrico Fermi told him, 'if you keep doing that, you will be dead within a year,'" said Coleman. Turned out, Fermi was generous with that prediction.

"We've been warned by another Italian American, Anthony Fauci. If we are not serious about masks and distancing," Coleman concluded, "we are tickling the dragon's tail and headed for a catastrophe this winter. From the rising caseload we already see that, like Fermi, Fauci is being ignored. The covid virus is uncaring. We are the ones who must care."

Comparing coverage

Speaking of comparisons, it will be revealing for at least 73 million people in our divided nation to closely watch how the national news media that has relentlessly picked President Donald Trump apart on every level will treat President-elect Joe Biden and Vice President (president in waiting) Kamala Harris.

Will Biden's administration also be repeatedly questioned and attacked from day one and on every level by these news organizations? Or will they perhaps be coddled and protected by those with a sacred obligation offered by the First Amendment toward fairness and impartiality in their "objective" news-gathering responsibilities, regardless of a power-hungry political party's instructions?

Gallup finds six in 10 among us have "not very much" trust (27 percent) or "none at all" (33 percent) to report the news "fully, accurately, and fairly." What a shameful disgrace for my craft and the necessary vital credibility it has damaged through its painfully partisan actions and inactions.

Anyone care to venture your own wild guess how the mainstream coverage (including social media) will go with Biden and Harris? Oh, go ahead. From what I've seen, I suspect the most difficult questions may involve his favorite flavor of ice cream, his dogs' adapting to the White House and perhaps even how well he's been sleeping.

Now go out into the world and treat everyone you meet exactly like you want them to treat you.

Mike Masterson is a longtime Arkansas journalist, was editor of three Arkansas dailies and headed the master's journalism program at Ohio State University. Email him at


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