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May 29th, 2020 (Permalink)

A New Four-Letter Word

What do you call a "protest" that "turned violent" with "demonstrators" "clashing" with police and "trashing" a building that the group of "unruly protesters" threw rocks at? Consider the following headline from the recent The New York Post story from which those words and phrases were taken:

Minneapolis protesters trash police precinct during clash over George Floyd's death

The story tells us:

A protest in Minneapolis over the death of a black man in police custody turned violent Tuesday night, with demonstrators clashing with police and trashing a precinct building…. Several hundred demonstrators at about 6 p.m. splintered off from a mainly peaceful afternoon rally and marched to the Minneapolis police department's 3rd Precinct to protest the death of George Floyd…. The group targeted the precinct because it's believed the four Minneapolis cops involved in Floyd's arrest―who have all since been fired―worked there…. Unruly protesters…tossed rocks at the building's windows and vandalized at least one patrol car…. Police in riot gear arrived and fired tear gas at the protesters, who took aim at the officers with rocks, water bottles and other objects…1.

The only occurrence of the word "riot" in this short article is in the penultimate sentence where we learn that the police donned "riot gear", but why did they do that? Where was the riot in all this "clashing" and "trashing"?

Another strange thing about this report is that it contains an actual four-letter barnyard epithet that a few decades ago would not have been included in a newspaper story. Apparently, "riot" is the new four-letter word.

I don't mean to pick on The Post: this was literally the first article that popped up in my search engine. It's an egregious example, but apparently the word "riot" is now officially oldspeak, and the news media are not supposed to refer to what's happening as "riots" or those looting and burning down buildings as "rioters". Rather, the events are "protests" or "demonstrations", and the looters and arsonists are "protesters" or "demonstrators". For example, a much longer article from ABC News refers to what's happening as "chaos", but never once uses the four-letter word2.

It's amazing how fast and far such newspeak spreads in the news media. There are still a few small news outlets that are willing to call a "civil disorder" a "riot"3, but they seem to be mostly local television stations4. This is a rare case when we know when and from where the memo went out:

NBC News came under scrutiny Thursday for allegedly telling its reporters to refer to the events in Minneapolis this week as "protests" and not "riots," according to one of its anchors. Craig Melvin, an MSNBC host and co-anchor of "Today," shed some light as to how his network is framing its reporting. "This will guide our reporting in MN. 'While the situation on the ground in Minneapolis is fluid, and there has been violence, it is most accurate at this time to describe what is happening there as 'protests'―not riots,'" Melvin tweeted Thursday morning.5

Presumably, it's not Melvin himself who issued this directive, but someone higher up at the network―Melvin just spilled the beans. Another MSNBC reporter, who obviously got the memo too, stood in front of a burning building while saying the following:

I want to be clear on how I characterize this. This is mostly a protest. It is not generally speaking unruly. But fires have been started.6

Who are you going to believe: MSNBC or your lying eyes? Notice the careful language: he tells us that he wants to be clear on how he characterizes it. Why does he need to be so careful about what he says? Because he's been told not to call it a "riot", so it's "mostly" a protest. What's the rest of it? It's "not generally speaking unruly"? Only the arson and looting are unruly. Also, notice the use of the passive voice: "fires have been started". Who started them?

You could say most of the above things about the Charlottesville riots of a few years ago: They were mostly a protest. They were not generally speaking unruly: only the fistfights and the guy plowing his car into a crowd and killing a woman were unruly. However, no fires were started. If the Minneapolis protests are not riots then neither was Charlottesville.

Given that the order came down from on high, it's no wonder that MSNBC reporters would make fools of themselves following it, but why have so many other reporters from other news outlets been so quick to adopt the latest doublespeak? This is not a rhetorical question: I really wonder.


  1. Kenneth Garger, "Minneapolis protesters trash police precinct during clash over George Floyd's death", The New York Post, 5/29/2020.
  2. Ella Torres & William Mansell, "Minnesota protest live updates: Trump warns military could 'assume control' of protest response", ABC News, 5/29/2020.
  3. According to William Lutz, the previous doublespeak phrase for "riot" was "civil disorder", see: Doublespeak Defined: Cut Through the Bull**** and Get the Point (1999), p. 62. Notice the four-letter word that is censored in the subtitle, which is the same word that is uncensored in the Post story. This is progress of a sort, I guess: we can't call a "civil disorder" a "riot", but we can call this what it is.
  4. For instance:
  5. Joseph A. Wulfsohn, "NBC allegedly tells reporters not to use word 'riots' in George Floyd coverage", Fox News, 5/29/2020.
  6. Tim Hains, "MSNBC's Ali Velshi Downplays Riot In Front Of Burning Building: 'Mostly A Protest,' 'Not Generally Speaking Unruly'", Real Clear Politics, 5/28/2020. Note that the reporter is being interviewed by Brian Williams, and this interview is apparently from Williams' show The 11th Hour, which was the source of the claim that the Bloomberg campaign could have given every American a million dollars; see: Beyond Innumeracy, 3/7/2020.

New Book: Expert Failure
May 22nd, 2020 (Permalink)

When Experts Fail

Title: Expert Failure

Author: Roger Koppl

Date: 2018

Quote: "Experts have knowledge not possessed by others. Those others, the laity, must decide when to trust experts and how much power to give them. We hope for a 'healer' but fear the 'quack,' and it is hard to know which is which. Experts may play a strictly advisory role or they may choose for others. … There is, then, a 'problem with experts,'…. When do we trust them? How much power do we give them? What can be done to ensure good outcomes from experts? What invites bad outcomes? And so on. … We rely…on the opinions of experts. We rely on experts even though we are conscious of the risk that experts may give bad advice, whether from 'honest error,' inattention, conflict of interest, or other reasons. The 'problem of experts' is the problem that we must rely on experts even though experts may not be completely reliable and trustworthy sources of the advice we require from them."1

Comment: This book couldn't be more timely even though it was published two years ago. This is not the first book on expertise and its discontents that we've seen here, and it almost certainly won't be the last. While it's too soon to do a post-mortem on the failures of experts in the current epidemic, it's not too soon to realize that there have been failures―major ones. No doubt there should and will be books in the years to come examining the role of experts in dealing with the epidemic, and I look forward to reading them. However, it may be instructive to read one that was written just prior to the epidemic and, therefore, not influenced by the illusions of hindsight.

As I discussed a decade ago2, the "problem of experts" goes back at least to Socrates. It's not really a single problem, though, but a group of related ones including:

Hopefully, this book is not like the former "book club" entry Wrong: Why Experts Keep Failing Us―And How to Know When Not to Trust Them3. A limitation of that book is that the "experts" that were "wrong" were largely pseudo-experts, especially those that appear on television or in other major media―for example, the quacks promoted by Oprah Winfrey. There is certainly a place for debunking such charlatans, but they're only a small aspect of the problem.

A more recent book that discussed another related problem was The Death of Expertise4, though it turned out that it wasn't expertise that had supposedly died, but people's trust in it. This is similar to the claim that we live in a "post-truth" era, in that the complaint is not that somehow there's no longer any truth, but that people allegedly don't respect it anymore. One thing that the current situation has shown is that, if anything, people trust experts too much, or perhaps they put their trust in the wrong experts.

Putting aside the snake oil salesmen, experts are human beings and, therefore, fallible. We can't reasonably expect them to always get it right, and when they are wrong bad things happen, such as bridges falling down5. For example, one of the expert failures of the current epidemic was the excessive concern that there would not be enough ventilators in the nation to handle the number of patients who would need them6. As it turned out, we were never even close to a nationwide ventilator shortage7, though there may have been some localized ones.

The failure in this case seems to have come from a single, early estimate made largely in ignorance by one expert, together with a failure to refine the estimate as more information became available. This particular failure had serious consequences in that it was used by politicians to justify "flattening the curve", which was itself used to justify shutting down the country's economy, and we won't know for months if not years the full extent of damage done by it.

Roger Koppl is a professor of finance, which isn't the most obvious basis for writing about the failures of experts, but there is no field of "expertology"―or whatever it would be called―that studies the problems of expertise. Even if there were such a field, we would still be faced with the same problem: How do we tell who is a real expert about expertise? At some point, we are all forced to rely on our own inexpert judgments.


  1. "Introduction".
  2. New Book, Too, 5/12/2010.
  3. See:
  4. See:
  5. That's a picture of the Tacoma Narrows bridge collapse on the front cover of the New Book, see: The Editors of Encyclopaedia Britannica, "Tacoma Narrows Bridge", Encyclopaedia Britannica, accessed: 5/12/2020.
  6. For details, see: How many ventilators do we need?, 4/17/2020.
  7. Bill McCarthy, "Can anyone who needs a ventilator get one? So far, it looks like it", Politifact, 4/24/2020. This report was written about the time the epidemic and the demand for ventilators peaked in the United States.

Weird Science Fantasy
May 10th, 2020 (Updated: 5/15/2020) (Permalink)

Invasion of the Murder Hornets

Some recent real-life headlines:

'Murder Hornets,' With Sting That Can Kill, Land In US1

Monstrous 'murder hornets' have reached the US2

Like something out of a 1950s monster movie, the giant hornets are coming to get you. You can tell that the hysteria surrounding the novel coronavirus and the disease it causes is dying down because the news media are jumping on a new scare. The latest coming attraction is the invasion of the United States by Asian giant hornets, alias "murder hornets" or "hornets from Hell"3.

In fact, these hornets primarily murder honeybees, not human beings. Hopefully, these invasive pests can be prevented from establishing a permanent presence in North America but, even if they do, their main threat is to bees rather than humans. Nonetheless, the giant hornets could be a problem to people since honeybees are important agricultural pollinators, and they already have enough problems without marauding hornets attacking their hives.

If, like me, you're experiencing deja vu right now, it's probably because you're old enough to remember the killer bees. These bees were a hybrid of regular honeybees and African bees that was developed in a lab in Brazil, apparently by a mad scientist. Some of the bees escaped from the lab, rather as the coronavirus may have done, and then began to spread northward. Eventually, they did indeed make it across the Rio Grande into the U.S., but that was about it. It seems that they didn't like the colder weather up north so stayed mainly in the far south4.

As a result of all the media hype about the slow spread of the "killer" bees northward, there was a swarm of B monster movies about them that came out in the '70s, including "The Bees", "Killer Bees", "The Savage Bees", and―my favorite―"The Invasion of the Bee Girls". There was even a big budget one, "The Swarm", from "master of disaster" Irwin Allen, which was a disaster movie in more than one way: it flopped. Obviously, these horror movies capitalized on the morbid interest generated by the news media coverage, but they probably also contributed to it.

"Killer" bees didn't live up to their reputation, though people have occasionally been killed by them5. Africanized bees tend to be more aggressive than regular honeybees, and people may die if stung a large number of times. Also, some people are allergic to bee venom, and even a small number of stings might be deadly to them.

The hype about the "killer" bees and "murder" hornets comes not so much from misinformation, but from the way the news is spun. Take as an example the following article:

Potentially fatal 'murder hornet' spreads across the globe

Scientists in the US are preparing to try to eradicate a new, potentially fatal, invader from the east: a huge insect with a lethal sting. The Asian giant, or 'murder' hornet can grow up to two inches long with a sting that delivers a potent neurotoxin. … The hornet can sting through most standard beekeeper suits and delivers nearly seven times the amount of venom as a honey bee. Swarms have been known to kill people in Japan, even those with no allergic reaction, and it is there that the insect earned the grim sobriquet, the 'murder hornet'.6

Notice that the hornet is called in both the headline and the first sentence "potentially fatal", and the first sentence says that it has a "lethal sting". This suggests, if not outright claims, that you could die from a single sting from a single hornet, which may be true if you are allergic to its venom, but most people stung by these hornets do not die.

What's missing from this account is a sense of perspective: some people who are allergic can die from honeybee stings, though it might take more than one sting to be fatal. So, are honeybees "potentially fatal"? Do they have "lethal stings"? Yes, they are and they have, but can you imagine a news headline referring to "potentially fatal" honeybees with "lethal stings"?

The article itself indicates that it is hornet swarms that have killed people in Japan, including those who are not allergic. Similarly, it's multiple stings from swarms of native bees and hornets that are usually fatal to people here.

Despite its lurid headline, as the article goes on to point out, the main threat from the hornets is to honeybee populations and not to human beings, but you have to read past the scary headline and first paragraph to get to the good news. This is typical tabloid newspaper writing that now appears to be invading the mainstream news media just as the hornets are trying to invade North America.

One thing I'll say in favor of the news media is that there was an almost immediate debunking of the hornet hype by one mainstream outfit. Remarkably, it was the Associated Press, which five days ago published the first of the headlines shown above, then a few days later debunked its own hype:

Insect experts say people should calm down about the big bug with the nickname "murder hornet"―unless you are a beekeeper or a honeybee. The Asian giant hornets found in Washington state that grabbed headlines this week aren't big killers of humans, although it does happen on rare occasions. … Numerous bug experts told The Associated Press that what they call hornet "hype" reminds them of the 1970s public scare when Africanized honeybees, nicknamed "killer bees," started moving north from South America. While these more aggressive bees did make it up to Texas and the Southwest, they didn't live up to the horror-movie moniker. However, they also do kill people in rare situations. This time it's hornets with the homicidal nickname, which bug experts want to ditch. "They are not 'murder hornets.' They are just hornets," said Washington Agriculture Department entomologist Chris Looney, who is working on the state's search for these large hornets. … Looney has a message for Americans: These hornets are not coming to get you. "The number of people who are stung and have to seek medical attention is incredibly small," he said in an interview. … Asian giant hornets at most kill a few dozen people a year and some experts said it's probably far less. Hornet, wasp and bee stings kill on average 62 people a year in the United States, according to the Centers for Disease Control and Prevention. … "This is 99% media hype and frankly Iím getting tired of it," said University of Delaware entomologist Doug Tallamy. "Murder hornet? Please." Retired University of Montana bee expert Jerry Bromenshenk said in an email, … "Do we want this hornet―surely not. But the media hype is turbo charged." … For people, the hornets are scary because the world is already frightened by coronavirus and our innate fight-or-flight mechanisms are activated, putting people on edge, said risk expert David Ropeik….7

Many of these news media scare stories follow the same template, whether they're about hornets, bees, or the coronavirus: an animal or disease that can be deadly to a small fraction of people is invading the country. The news media play up the scariness of the animal or disease as much as possible, then track its spread through the country and report every case. A running count of cases is frequently updated and seldom put in perspective by being compared to similar cases from more familiar animals or diseases, or cases from previous years. Occasional skeptical stories will be published, but for every such story several ones that follow the template will appear. Finally, a year or two later, the post-mortems will appear: scholarly symposia will be held, and issues of academic journals will discuss what went wrong with the reporting. Recommendations will be issued for how similar journalistic failures can be avoided in the future, but nothing will change and the next scare will be reported following the same template. Rinse and repeat.

Whether this new scare gets any traction in the coming months will depend both upon how quickly the current COVID-19 frenzy fades away, leaving a fear vacuum, and whether efforts to eradicate those hornets that have made it to North America succeed. If the hornets gain a foothold on the continent and begin to spread, you can bet your last buck there will be a slow but steady series of news stories tracking it. The first American to die from hornet stings will make the front pages of every newspaper in the country. There will be runs on hornet-killing bug sprays, and store shelves will be emptied8. This could turn out to be the "Summer of the Hornet" instead of the "Summer of the Shark"9.


  1. Nicholas K. Geranios, "'Murder Hornets,' With Sting That Can Kill, Land In US", Associated Press, 5/4/2020.
  2. Mindy Weisberger, "Monstrous 'murder hornets' have reached the US", Live Science, 5/5/2020.
  3. Brian Handwerk, "'Hornets From Hell' Offer Real-Life Fright", National Geographic News, 10/25/2002.
  4. "Africanized Bees", Smithsonian Institution, accessed: 5/10/2020.
  5. For a comparatively recent example, see: Danielle Elliot, "What makes 'killer' bees so deadly?", CBS News, 7/29/2013.
  6. "Potentially fatal 'murder hornet' spreads across the globe", Sky News, 5/5/2020.
  7. Seth Borenstein, "Bug experts dismiss worry about US 'murder hornets' as hype", Associated Press, 5/7/2020.
  8. So stock up now!
  9. If you're too young to remember the "Summer of the Shark", see: Jeordan Legon, "Survey: 'Shark summer' bred fear, not facts", CNN, 3/14/2003. The "Summer of the Shark" reporting did not follow the above template exactly, but exemplified most of it.

Update (5/15/2020): Here's more headline evidence that the news media are searching for a new monster to frighten us with:

Georgia warns of 4-foot-long lizards that 'eat just about anything they want'1

Giant, 4-foot-long lizards posing a major threat to Georgia wildlife2

Large invasive lizard that can grow up to 4 feet long gaining foothold in Georgia, officials warn3

Let's check it against the template: Invasive? Check; just like the monster hornets, this lizard is a non-native species that originally came from South America4. Scary? Check; they're "giant", "large", and eat whatever they want. Spreading? Check; they're getting a foothold in Georgia, though two out of the three news stories don't mention that they're coming up from Florida, where they've been for nearly two decades.

That's just the start of the template, though. Like the hornets, the lizards are not primarily a threat to people but to native non-human animals. As far as I've been able to ascertain, unlike the hornets, they don't kill people, so it's likely that this scare won't be sustainable.

Just wait'll the news media find out that there are already up to a quarter of a million lizard-like reptiles in Georgia that can grow up to sixteen-feet long and weigh over 800 pounds. They also "will eat almost anything they can catch5", including pets and small children6. They're called "alligators".


  1. Leanda Gore, "Georgia warns of 4-foot-long lizards that 'eat just about anything they want'", AL, 5/15/2020.
  2. Christina Maxouris, "Giant, 4-foot-long lizards posing a major threat to Georgia wildlife", CNN, 5/14/2020.
  3. Caitlin O'Kane, "Large invasive lizard that can grow up to 4 feet long gaining foothold in Georgia, officials warn", CBS News, 5/143/2020.
  4. Laurie Vitt, "Tegu", Encyclopaedia Britannica, accessed: 5/15/2020.
  5. "Alligator Fact Sheet", The Georgia Department of Natural Resources, revised: 9/16.
  6. Eliott C. McLaughlin, Joshua Berlinger, Ashley Fantz & Steve Almasy, "Disney gator attack: 2-year-old boy found dead", CNN, 6/16/2016.

May 2nd, 2020 (Permalink)

Hard Pills to Swallow

Paul Patient has a severe case of puzzler's syndrome. He has been prescribed two pills to treat it, and is to take one of each type of pill once a day at the same time. Both pills are tablets, but one type is red and the other green. Unfortunately, Paul is color-blind and not able to tell the pills apart by sight. However, the two types of pill come in two different bottles.

Paul habitually takes his medications before going to bed at night. One night, he opened the bottle of red pills, tipping one pill out onto the palm of his hand, and then opened the bottle of green pills. Momentarily distracted, he accidentally let two green pills fall from the bottle into his palm.

Now, Paul was faced with a puzzle. There were three pills in his hand: one red and two green. However, he could not tell one pill from another; all three pills looked the same to him. He was only supposed to take one pill of each color, and it might harm him to take two green ones.

Paul looked at the bottles and saw that the bottle of green pills was now empty, and there was only one remaining red pill. However, this would not solve the puzzle. He could show the three pills to some person without color-blindness who could tell him which pill was red and which ones green, but it was late at night. Paul didn't want to have to bother someone so late.

Being a patient with puzzler's syndrome, and now being past the time he usually took his medication, Paul was obsessed with the puzzle of the three pills. Is there some way I can take the proper dosage now without needing to ask for anyone's help later in identifying pills, he wondered.

Thankfully, Paul was able to solve the puzzle and take his medication without needing any help. How did he do it?

Recommended Reading
May 1st, 2020 (Permalink)

Mayday! Mayday!

As is usual with these recommendations, I don't necessarily endorse everything expressed in them, but I do think they are all worthwhile. Also, as is usual with these sources on the coronavirus epidemic, I am not including any exercises in fear-mongering. If you're a fan of horror stories and love to have the stuffing scared out of you, just access any mainstream media source. This round-up is intended as a counterweight to the on-going news media hysteria.

*Specifically, nine children below the age of fifteen have died in the United States; see: "Provisional Death Counts for Coronavirus Disease (COVID-19)", Centers for Disease Control and Prevention, accessed: 4/30/2020.

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April 21st, 2020 (Permalink)

New Fallacy: Over-Extrapolation

I've added a new fallacy to the files, which is the first one in quite a while. It's an old one in the sense that I've been aware of it for many years, and have alluded to it a few times in this weblog1. I failed to create an entry for it because it's a statistical fallacy and seemed perhaps too esoteric and technical. However, I've come across more than one recent example that involves the current coronavirus epidemic, so the fallacy has become a timely one. Check it out.

Fallacy: Over-Extrapolation

Update (4/25/2020): Here's an example that I probably would have used in the entry for the above fallacy, but I just came across it:

Dr. Ezekiel Emanuel, chair of the department of medical ethics at the University of Pennsylvania, warned Friday [March 27th, 2020] on MSNBC's "Morning Joe," that based on the current rate of spread, there will likely be 100 million Americans infected by the COVID-19 virus in four weeks. … "Right now, if you look at the numbers, we probably have a million COVID-19 cases in the country. And if this is doubling every three to four days, that means that we'll have 100 million people who have COVID-19 in about four weeks, and that's a frightening thought."2

That is a frightening thought, and I bet many people who heard it were indeed frightened. Emanuel made this claim just four weeks ago yesterday, and there were still less than a million confirmed cases yesterday3. So, Emanuel was off by two orders of magnitude.

This is another example of exponential extrapolation, which is even more dangerous than the linear kind. In the case of epidemics, there is a period of growth near the beginning when the number of cases may indeed be growing exponentially, but such growth cannot continue for long. As the epidemic continues, the doubling time increases. The doubling time for COVID-19 deaths in the United States was around three days on the first of this month, but today it is over two weeks4.

If you do the math on this claim, assuming that there were one million cases on the 27th of last month, doubling every three or four days, then there should have been 128-512 million cases yesterday. I assume that Emanuel must have taken the slower doubling rate of every four days, and then rounded down to the nearest hundred million. Why he included the faster doubling rate of every three days, when such a rate would have hit 100 million in the middle of this month rather than near its end, may be because that was the doubling rate at the time. However, at that rate the number of cases would have exceeded the entire population of the country a few days ago, which should have warned him against extrapolating so far into the future. Perhaps he realized that the rate would slow and tried to be conservative by using the four-day rate.

Note that Emanuel is a medical ethicist: how ethical is it to go on national television and unnecessarily frighten many people? As ethical as shouting "Fire!" in a crowded theater?


  1. See, for instance: New Book: Proofiness, 8/26/2010.
  2. Tim Hains, "Ezekiel Emanuel: U.S. Will Have 100 Million Cases Of COVID-19 In Four Weeks, Doubling Every Four Days", Real Clear Politics, 3/27/2020.
  3. "Cases of Coronavirus Disease (COVID-19) in the U.S.", Centers for Disease Control and Prevention, accessed: 4/25/2020.
  4. "Doubling Time of Coronavirus Deaths and Pandemic Control", Princeton Election Consortium, accessed: 4/25/2020.

April 17th, 2020 (Updated: 4/18/2020) (Corrected: 4/19/2020)(Permalink)

How many ventilators do we need?

Last month, we saw a rather silly example of innumeracy in the news media1. As far as I know, that incident didn't do any harm, except to the dignity of those involved. However, during the current epidemic we are seeing innumeracy that is doing real harm.

For instance, one reason given for some of the most draconian restrictions on public life adopted by the government has been the fear that, unless the spread of the coronavirus is slowed, we will run out of ventilators. Ventilators are machines that are used to breathe for patients who can't breathe on their own, and for those who need them can be life-savers.

A few weeks ago, some in the news media claimed that a projection showed that the United States would need one million ventilators to deal with coronavirus patients, whereas only 160-200 thousand were currently available. The claim seems to have originated with the august New York Times, and spread from there2. However, the projection estimated that a million patients would need ventilators over the course of the epidemic, not that a million machines would be needed. Since a single ventilator may be used by multiple patients over the course of the epidemic, it's possible that the available machines would be sufficient for a million patients. This sort of innumerate misreporting does real harm by unnecessarily frightening people, and may lead to excessively harsh public measures and counter-productive diversions of resources.

According to the Institute for Health Metrics and Evaluation (IHME) projection, we've already passed the peak demand for ventilators on the fourteenth of this month, and on that day less than 17,000 ventilators were needed3. This, of course, is about a tenth of the low-end number of available ventilators given above. So, what went wrong with the original estimate?

A good candidate is the initial estimate that one million patients would need ventilators over the course of the epidemic. As I write this, less than a million total cases of COVID-19 in the United States have been confirmed4, and only a fraction of that million will need ventilator support. The estimate in question came from the following passage in a report by the Society of Critical Care Medicine:

Estimates of hospitalized patients requiring critical care and mechanical ventilation: … A recent AHA webinar on COVID-19 projected that 30% (96 million) of the U.S. population will test positive, with 5% (4.8 million) being hospitalized. Of the hospitalized patients, 40% (1.9 million) would be admitted to the ICU, and 50% of the ICU admissions (960,000) would require ventilatory support. Such projections, however, are gross estimates. Some assumptions underlying these projections are uncertain, and the pacing of a large outbreak would influence whether ICU resources in isolated locations or nationally are severely taxed over many months or quickly overwhelmed over a shorter period. Additionally, COVID-19 patients may remain mechanically ventilated for indeterminate periods of time, with some developing prolonged or chronic critical illness requiring the extended use of ICU beds, ventilators, supplies, and trained clinicians.5

As you can see, the report itself makes it clear that the estimates are uncertain because the underlying assumptions that they are based on are uncertain. The estimate that nearly a million patients would need ventilators was based on the initial estimate that 30% of the American population would become infected, 5% of those infected would be hospitalized, 40% of the hospitalized patients would need intensive care, and half of those needing such care would require a ventilator*. Each of these percentages is uncertain, so with each step of the calculation, uncertainty is piled upon uncertainty. Let's examine the percentages individually:

  1. What percentage of the population will be infected with the virus? We don't know. The estimate of 30% appears to have come from one public health expert in a web seminar for the American Hospital Association conducted on February 26th of this year6. How was the estimate arrived at? I haven't been able to find out. I'm sure the expert gave his best guess, but this was near the beginning of the epidemic, and it's clear now that his ventilator estimate was way off. What I don't understand is why there haven't been attempts to refine those estimates in the month and a half since.
  2. What percentage of those infected will need hospitalization? We should have a good handle on the number of people hospitalized, but since we don't know the answer to the previous question, we don't know what percent it is of those infected. This number has the same problem as the death rate: we can count how many people die or are hospitalized with the virus, but both rates are fractions and we have the numerators but lack the denominator. Where did the estimate that 5% of those infected would be hospitalized come from? I haven't been able to find out.
  3. What percentage of those hospitalized will need intensive care? Finally, we have a statistic that we can do more than guess at: a recent source claims that 16-20% of hospitalized patients are admitted to intensive care7, which is half the original estimate.
  4. What percentage of those in intensive care will need ventilators? Unfortunately, I haven't been able to find any more recent estimate of this number.

Any estimate based on guesses is going to be itself guesswork. Despite this, some news media are still using the original, six-week old estimate, though it's now obviously outdated. For instance, the article that provided the answer for the third question, above, uncritically repeats the original February estimates, even though it was published just today7.

Update (4/18/2020): I've been trying to figure out where in the following graphic the estimate discussed above fits:

Garbage Math

It's not in the graphic, but in the same spirit I think it's:

Garbage × Precise Number/Garbage × Precise Number × Possible Garbage =
Misleadingly Precise Garbage

Source: Randall Munroe, "Garbage Math", XKCD, accessed: 4/18/2020.

*Correction (4/19/2020): This sentence originally began: "The estimate that nearly a million ventilators would be needed…", which is incorrect since the estimate itself was how many patients would need ventilators.


  1. Beyond Innumeracy, 3/7/2020.
  2. Jeryl Bier, "How Misinformation About the U.S. Needing '1 Million Ventilators' Spread", The Dispatch, 4/6/2020.
  3. "COVID-19 Projections", Institute for Health Metrics and Evaluation, 4/17/2020.
  4. "COVID-19 Tracker", Bing, accessed: 4/17/2020.
  5. "United States Resource Availability for COVID-19", The Society of Critical Care Medicine, 3/19/2020.
  6. Lydia Ramsey, "One slide in a leaked presentation for US hospitals reveals that they're preparing for millions of hospitalizations as the outbreak unfolds", Business Insider, 3/6/2020.
  7. Erin Schumaker, "What we know about coronavirus' long-term effects", ABC News, 4/17/2020.

Maths on the Back of an Envelope
April 14th, 2020 (Permalink)

BOTEC1, the Book

Title: Maths on the Back of an Envelope

Subtitle: Clever ways to (roughly) calculate anything

Author: Rob Eastaway

Date: 2019

Quote: Once a statistic…is out there, published in a newspaper, quoted on a website, it becomes "fact", and it can be re-quoted so often that the source may go unquestioned and very quickly be forgotten altogether. It's an important reminder that the majority of statistics published anywhere are estimates, many of them worked out on the equivalent of the back of an envelope. When back-of-envelope calculations produce a very different answer from the one that's been put forward, it doesn't necessarily mean that the estimate is wrong. It means rather that the published figure deserves more scrutiny.2

Comment: I've been cheerleading for many years for the value of "back of the envelope calculations", so I'm excited to see a new book that teaches how to do them. In recent years, I usually speak of "sanity checks" or "plausibility checks" instead of BOTECs, since the purpose of the calculation is to check the plausibility of a number. The phrase "back-of-the-envelope" calculation really refers to estimates that can be used to check if a number is reasonable. When you use a BOTEC to check a number that you meet "published in a newspaper" or "quoted on a website", it doesn't prove that the number is right or wrong. However, if the estimate and the published number diverge by a lot, then "the published figure deserves more scrutiny", as Eastaway puts it, above.

Knowing how to do a BOTEC is a very useful critical thinking skill that is, unfortunately, seldom taught in critical thinking classes or books, though I've seen some signs in recent years that it's catching on. If you're at all wary about learning it because it involves math, and you're scared of math, don't worry! BOTECs seldom require more than the most basic mathematics: adding, subtracting, multiplying, and dividing. If you know how to do these operations, whether in your head, on paper, or with a calculator, you can do a BOTEC. Not only that, but BOTECs are fun! They're rather like puzzles and, unlike most mathematical tasks, there are no right or wrong answers!

Here's how Eastaway describes the book's structure:

I've divided the book into four sections. In the first section, I explore how precise numbers can be misleading, and why it's good not to be entirely dependent on a calculator. The second section includes the arithmetical techniques and the other knowledge that is an essential foundation if you want to embark on back-of-envelope calculations. This includes a refresher on how to do arithmetic that you may not have needed to practise since you left primary school, as well as short cuts that you probably never encountered there. The rest of the book shows how to use these techniques to tackle problems, from everyday conversions, to more serious issues like helping the environment. And at the end, there is a collection of so-called Fermi questions: quirky and esoteric challenges to come up with a reasonable answer based on very little hard data.3

Rob Eastaway is the author of some other books on math, some on puzzles, and one on cricket, though I'm sorry to say I haven't read any4. This book appears to have been published in the United Kingdom5, and I don't know whether or when it will appear in an American edition, but I think you can still get copies here in the states, though they may take longer to arrive. What better way to spend your quarantine time than learning how to do back-of-the-envelope calculations? While you wait for the book to arrive, you can try your hand at several such problems from earlier entries in this weblog, see:


  1. Back Of The Envelope Calculation.
  2. "Prologue", emphasis in the original.
  3. "Prologue".
  4. Except for the one on cricket: I'm glad I haven't read that.
  5. Why else use the plural "maths" in its title? For one thing, "maths" is hard to say, and it sounds like you're lisping. In American English, "math" is short for "mathematics", and "cricket" is a type of insect, not a sport.

April 12th, 2020 (Permalink)

Don't Put All Your Easter Eggs in One Basket

The Easter Bunny was hopping down the bunny trail on Easter morning with a basket full of colorful eggs. E.B. met a boy and gave him half of the eggs in the basket plus half an egg. Then, E.B. met a girl and gave her half of the remaining eggs in the basket plus half an egg. Then, E.B. came across another boy and gave him half of what remained in the basket together with half an egg. Finally, E.B. met another girl and gave her half of what was left in the basket plus half an egg. E.B.'s basket was now empty and not a single egg had been broken!

How many Easter eggs were in the Easter Bunny's basket at the start of Easter morning?

Richard Jewell
April 6th, 2020 (Permalink)

Movie Review:
Richard Jewell

In addition to reading, another thing you can do in these times of anti-social distancing is to stay home and watch a movie. The recent film Richard Jewell is out on DVD, and perhaps available from some streaming services. I mentioned it previously in connection with the media frenzy and misreporting surrounding the case that it dramatizes1.

This is only the second movie review I've ever written here2, and the first for a fiction film, though this one is "based on a true story". I suppose that most people are now familiar with at least the broad outlines of the Jewell case, so I won't bother with the usual plot synopsis that you find in movie reviews. If you're unfamiliar with the case, check out my previous entry on it1.

My interest in this movie arose out of an interest in the Jewell case, and the light it sheds on the news media. In this case, most of the damage done by media malpractice was to Jewell and his mother. Currently, millions of people are suffering due not to the new virus, but to the media's misreporting of it. However, that's a subject for a later time.

Unfortunately, Richard Jewell is really two movies in one, and they mix like oil and water. The movie is at its best in portraying the "good guys"―Jewell, his mother, and their lawyer―but the "bad guys"―FBI agents and a local reporter―are portrayed as cartoonish movie villains.

The worst treatment is reserved for the local reporter, Kathy Scruggs. I didn't believe the portrayal for a second, but I don't think this is the fault of the actress who played her, but that of the screenplay. To call it a "caricature" would be unfair to caricatures. Caricatures are exaggerated but they're still supposed to look like the person portrayed, whereas this character doesn't look like any actual person. Instead, she is a sort of cross between a film noir femme fatale and the female reporter from His Girl Friday. Of course, I never met the real Scruggs, so I suppose it's possible that she was really like this, but I find it difficult to believe.

I can forgive the unrealistic portrayal of the FBI agent characters because they were given phony names. What's unforgiveable is that Kathy Scruggs was a real person whose real name is used in the move. Since Scruggs died, she cannot defend herself against this defamation, and the movie ends up doing to her what it is seemingly exposing as having been done to Jewell. Would it have been alright if the media had waited until Jewell was dead before smearing him? Presumably, the FBI agents in the film are given fictional names, because the real-life agents are still alive and would sue for libel if they were named, whereas Scruggs can't sue. The makers of this movie sure don't deserve any awards for courage.

The only excuse that I can see for the portrayal of Scruggs would be if it were well-established that she acted in real-life the way the character does in the movie. However, based on everything I've read, there's no evidence that she seduced an FBI agent in order to get her scoop on Jewell3.

Another thing that bothered me about the movie is the frequent foul language, mostly from the FBI agents but some from the Scruggs character, but then I'm old-fashioned. As far as I can tell, this movie earned its R-rating entirely on the basis of language: there is no nudity, and only one mildly sexual scene when the Scruggs character seduces the FBI agent; the only violence is when the bomb explodes, and you see a few people covered in phony blood. It could've easily been a PG-13 or even PG, if only the language had been toned down. I doubt that FBI agents talk like the fictional ones in this movie, but then I don't know any real ones. However, if you're like me and hearing the F-word in every other sentence bugs you, then you may want to avoid it.

I've been very critical of this film, which deserves it, but despite all that I recommend it, at least if you can stomach the language. Paul Walter Hauser starts out portraying Richard Jewell as a buffoon, but by the end of the movie he has become a believable and sympathetic person. Kathy Bates' performance as Jewell's mother is both believable and moving from beginning to end. The other actors are generally fine, even when their characters are written as cartoonish, cussing baddies.

There's nothing wrong with this movie that a better script wouldn't have fixed. If only the FBI agents were portrayed as flawed human beings instead of comic book villains, and the script had not taken a cheap shot at a dead woman, this would have been a great film instead of a merely good one. If you do decide to see it, however, keep in mind that it's not history, it's Hollywood.


  1. See: Richard Jewell and "The Voice of God", 12/31/2019
  2. For the first review, see: Movie Review: Best of Enemies, 2/23/2016
  3. Julie Miller, "The Richard Jewell Controversy―And the Complicated Truth About Kathy Scruggs", Vanity Fair, 12/13/2019

Recommended Reading
April 2nd, 2020 (Permalink)


If you're trapped inside during this double pandemic of coronavirus and fear of it, you might as well do some reading. I usually do these "Recommended Reading" lists at the end of the month but, like last month, I'm moving this one up. Hopefully, by the end of this month, you won't be stuck inside your house or apartment, so you won't need this list so much. Even now, I suggest reading something completely unrelated, such as the rest of The Fallacy Files! However, if you must keep reading about the virus, then at least read some articles that will put it into perspective.

Note that I do not necessarily agree with or endorse every claim made in the following readings. Moreover, I am definitely not trying to strike a balance between pro-panic and anti-panic articles: if you want to read scare-mongering stories, just go to any mainstream media site and you can get your fill.

Here's an article on why you shouldn't obsess about the current virus, and how to stop doing so:

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