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January 31st, 2023 (Permalink)

Rigging the Debate & Over-counting the Dead

• David Zweig, "How Twitter Rigged the Covid Debate", The Free Press, 12/26/2022

  I had always thought a primary job of the press was to be skeptical of power—especially the power of the government. But during the Covid-19 pandemic, I and so many others found that the legacy media had shown itself to largely operate as a messaging platform for our public health institutions. Those institutions operated in near total lockstep, in part by purging internal dissidents and discrediting outside experts.

  Twitter became an essential alternative. It was a place where those with public health expertise and perspectives at odds with official policy could air their views—and where curious citizens could find such information. … But it quickly became clear that Twitter also seemed to promote content that reinforced the establishment narrative, and to suppress views and even scientific evidence that ran to the contrary.

  Was I imagining things? Was the pattern I and others witnessed proof of purposeful intent? An algorithm gone rogue? Or something else? In other words: When it came to Covid, and the information shared on a service used by hundreds of millions of people, what exactly was being amplified? And what was being banned or censored? … Here’s what I found.

  The United States government pressured Twitter to elevate certain content and suppress other content about Covid-19 and the pandemic. Internal emails that I viewed at Twitter showed that both the Trump and Biden administrations directly pressed Twitter executives to moderate the platform’s content according to their wishes. … And it wasn’t just Twitter. The meetings with the Trump White House were also attended by Google, Facebook, Microsoft and others.

  When the Biden administration took over, its agenda for the American people can be summed up as: Be very afraid of Covid and do exactly what we say to stay safe. In July 2021, then-U.S. Surgeon General Vivek Murthy released a 22-page advisory concerning what the World Health Organization referred to as an “infodemic,” and called on social media platforms to do more to shut down “misformation.” “We are asking them to step up,” Murthy said. “We can’t wait longer for them to take aggressive action.”

  That’s the message the White House had already taken directly to Twitter executives in private channels. One of the Biden administration’s first meeting requests was about Covid, with a focus on “anti-vaxxer accounts,” according to a meeting summary by Lauren Culbertson, Twitter’s Head of U.S. Public Policy. … By the summer of 2021, the day after Murthy’s memo, Biden announced publicly that social media companies were “killing people” by allowing misinformation about vaccines. … The summary of meetings by Culbertson…adds new evidence of the White House’s pressure campaign, and illustrates how it tried to directly influence what content was allowed on Twitter. Culbertson wrote that the Biden team was “very angry” that Twitter had not been more aggressive in deplatforming multiple accounts. They wanted Twitter to do more. …

  At Twitter, Covid-related bias bent heavily toward establishment dogmas. Inevitably, dissident yet legitimate content was labeled as misinformation, and the accounts of doctors and others were suspended both for tweeting opinions and demonstrably true information. …

  In my review of internal files, I found numerous instances of tweets about vaccines and pandemic policies labeled as “misleading” or taken down entirely, sometimes triggering account suspensions, simply because they veered from CDC guidance or differed from establishment views. For example, a tweet by…a self-proclaimed public health fact checker with more than 18,000 followers, was flagged as “misleading,” and replies and likes disabled, for showing that Covid was not the leading cause of death in children, even though it cited the CDC’s own data. … Tellingly, the tweet…that was labeled “misleading” was a reply to a tweet that contained actual misinformation. Covid has never been the leading cause of death from disease in children. Yet that tweet not only remains on the platform, it is without any sort of “misleading” label.

  So, correct information was labelled "misinformation" and censored while genuine misinformation was not. No wonder surveys show that the American people are significantly misled about the risks of COVID for children¹.

  Whether by humans or algorithms, content that was contrarian but true, and the people who conveyed that content, were still subject to getting flagged and suppressed. Sometimes this was done covertly. … But many instances were public facing. …

  Throughout the pandemic, Twitter repeatedly propped up the official government line that prioritizing mitigation over other concerns was the best approach to the pandemic. Information that challenged that view—for example, that pointed out the low risk children faced from the virus, or that raised questions about vaccine safety or effectiveness—was subject to moderation and suppression.

  This isn’t simply the story of the power of Big Tech or of the legacy press to shape our debate—though it is most certainly that. In the end it is equally the story of children across the country who were prevented from attending school, especially kids from underprivileged backgrounds who are now miles behind their more well-off peers in math and English. … If Twitter had allowed the kind of open forum for debate that it claimed to believe in, could any of this have turned out differently?

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• Leana S. Wen, "We are overcounting covid deaths and hospitalizations. That’s a problem.", The Washington Post, 1/13/2023

  According to the Centers for Disease Control and Prevention, the United States is experiencing around 400 covid deaths every day. At that rate, there would be nearly 150,000 deaths a year. But are these Americans dying from covid or with covid? Understanding this distinction is crucial to putting the continuing toll of the coronavirus into perspective. Determining how likely it is an infection will result in hospitalization or death helps people weigh their own risk. …

  Two infectious-disease experts I spoke with believe that the number of deaths attributed to covid is far greater than the actual number of people dying from covid. Robin Dretler, an attending physician at Emory Decatur Hospital and the former president of Georgia’s chapter of Infectious Diseases Society of America, estimates that at his hospital, 90 percent of patients diagnosed with covid are actually in the hospital for some other illness. “Since every hospitalized patient gets tested for covid, many are incidentally positive,” he said. A gunshot victim or someone who had a heart attack, for example, could test positive for the virus, but the infection has no bearing on why they sought medical care. … If these patients die, covid might get added to their death certificate along with the other diagnoses. But the coronavirus was not the primary contributor to their death and often played no role at all.

  Dretler is quick to add that the imprecise reporting is not because of bad intent. There is no truth to the conspiracy theory that hospitals are trying to exaggerate coronavirus numbers for some nefarious purpose. But, he said, “inadvertently overstating risk can make the anxious more anxious and the skeptical more skeptical.”

  The problem is not bad people conspiring to exaggerate the numbers of COVID deaths. Rather, it's the fact that there are financial incentives, created by the government, for hospitals to label every patient they can as a COVID case². In addition, there's a financial motive, again created by the government, for putting COVID as a cause on death certificates. Funerals are extremely expensive, and you can't blame families for wanting to get the $9K from the government to bury a family member. You also can't blame sympathetic physicians for yielding to family pressure to put COVID on the death certificate even if it had nothing to do with the patient's death. The problem is not bad people but bad incentives.

  Another infectious-disease physician, Shira Doron, has been researching how to more accurately attribute severe illness due to covid. After evaluating medical records of covid patients, she and her colleagues found…a good proxy measure for hospitalizations due to the coronavirus. … Doron’s work was instrumental to Massachusetts changing its hospitalization reporting a year ago to include both total hospitalizations with covid and those that received [the proxy]. In recent months, only about 30 percent of total hospitalizations with covid were primarily attributed to the virus.

  This tracks with Doron’s experience at her hospital, Tufts Medical Center, where she also serves as hospital epidemiologist. … During some days, she said, the proportion of those hospitalized because of covid were as low as 10 percent of the total number reported.

  Determining the true number of hospitalizations from covid has immediate, practical purposes. “It allows for better forecasting of hospital capacity,” Doron told me. “If our hospital beds are full and we attribute it to covid, we might think that we’ll get the beds back when the wave of infections is over. But if people are sick from other causes, the beds could stay full.” … They want the public to see what they’re seeing, because, as Doron says, “overcounting covid deaths undermines people’s sense of security and the efficacy of vaccines.”

  Some people are mocking this op-ed article as too little, too late³, but it would probably have been declared "misinformation" as recently as last year and censored. The fact that it was written and published at all is what's most important, not what it says. Wen was one of the more gung-ho supporters of masking, lockdowns, and vaccine mandates in the first two years of the pandemic⁴, so the fact that she published this in the unofficial journal of the political establishment tells us that it's now acceptable to acknowledge that deaths were probably over-counted.

  Interestingly, Wen got in trouble just a few months ago for, among other things, suggesting that we should learn to live with COVID⁵, despite the fact that the bellwether of the "public health community", Anthony Fauci, had suggested the same thing months earlier⁶. Wen was forced to back out of an appearance at an American Public Health Association (APHA) conference because of a petition campaign against her from some members of that organization⁷. Ironically, the talk that she was scheduled to give was supposed to be on the backlash from members of the general public mad about masks and vaccine mandates. In this case, the backlash was coming from inside the so-called public health community itself. Wen is now a heretic from public health orthodoxy and must be ostracized.

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Notes:

1. See: The Pandemic of Pseudoknowledge, 1/11/2022
2. See: How many people who died with COVID-19 died from COVID-19?, 11/30/2022
3. For instance: Post Editorial Board, "Chief COVID crazy finally admits we’re overcounting cases — but it’s years too late", The New York Post, 1/18/2023
4. See, for instance: "CNN Newsroom", CNN, 9/9/2021
5. Leana S. Wen, "The Gridiron Club outbreak shows what living with covid-19 looks like", The Washington Post, 4/8/2022
6. "Meet the Press - November 28, 2021", NBC News, 11/28/2021
7. Colleen Flaherty,
   • "Backlash to Dr. Leana Wen Talk on Backlash", Inside Higher Education, 8/23/2022
   • "Speaker Leana Wen Backs Out of Public Health Meeting", Inside Higher Education, 11/9/2022

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Disclaimer: I don't necessarily agree with everything in these articles, but I think they're worth reading as a whole. In abridging them, I have sometimes changed the paragraphing and deleted emphasis.

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January 29th, 2023 (Permalink)

The Troublesome Triplets

Detective David Davidson had met some strange suspects in his years on the force, but these three took the booby prize. They were the Taylor triplets: Abner, Benji, and Carlo. Despite being identical triplets, the three young men could scarcely have turned out more differently. Abner was the only one of the three who had gone to college, where he had studied Kantian philosophy. Taking Kant very seriously, Abner refused to lie even if it was to save one of his brothers from prison. Benji, in contrast, was a pathological liar who could not tell the truth even if he wanted to, which he didn't. The third brother, Carlo, was the only relatively normal one: sometimes he told the truth and sometimes he lied.

A teller had identified one of the three brothers as the culprit in a brazen bank robbery. The brother had simply walked into the bank in the middle of the afternoon, handed a threatening note to the teller, and walked out with a bag of full of cash. Of course, the teller had not been able to identify which of the three had actually done the deed. As a result, the detective had the triplets brought in for questioning and placed in separate holding cells.

Davidson wasn't even sure which brother was which, and certainly he couldn't charge all three. In fact, he couldn't charge even one until he identified who was who. So, he questioned them one-by-one.

"Which brother are you?" he asked the man in the first cell.

"I'm Carlo."

"Who stole the money?"

"I did."

Davidson moved on to the second cell. "Which of your brothers is in the first cell?" he asked.

"That's Benji."

"Who stole the money?"

"One of my brothers."

Finally, Davidson asked the man in the third cell which brother was in the first cell.

"Abner."

"Did you steal the money?"

"Nope."

Davidson sighed as he left the third cell. He now had a confession from the man in the first cell, but perhaps he was lying to protect one of his brothers. Until Davidson knew the identities of the three men he couldn't trust the confession.

Can you help Detective Davidson identify which brother is in each cell?

Extra Credit: Which brother stole the money?

Solution

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Disclaimer: The puzzle you have just read is fictitious. The names have been changed to protect the innocent.

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January 15th, 2023 (Permalink)

No Orchids, "Which Half?" & the Pyramid of Propaganda

• From the back cover of No Orchids for Miss Blandish by James Hadley Chase¹:

  "A brilliant piece of writing!" GEORGE ORWELL

  From "Raffles and Miss Blandish" by George Orwell:

  Now for a header into the cesspool. No Orchids for Miss Blandish, by James Hadley Chase…is not, as one might expect, the product of an illiterate hack, but a brilliant piece of writing, with hardly a wasted word or a jarring note anywhere. …[I]t takes for granted the most complete corruption and self-seeking as the norm of human behaviour. …[S]uch things as affection, friendship, good nature or even ordinary politeness simply do not enter. … Ultimately only one motive is at work throughout the whole story: the pursuit of power. …[T]he book is not in the ordinary sense pornography. … The thing that the ordinary reader ought to have objected to—almost certainly would have objected to, a few decades earlier—was the equivocal attitude towards crime. It is implied throughout No Orchids that being a criminal is only reprehensible in the sense that it does not pay. Being a policeman pays better, but there is no moral difference, since the police use essentially criminal methods. … In a book like No Orchids one is not, as in the old-style crime story, simply escaping from dull reality into an imaginary world of action. One’s escape is essentially into cruelty and sexual perversion. …. In No Orchids anything is ‘done’ so long as it leads on to power. All the barriers are down, all the motives are out in the open. … Several people, after reading No Orchids, have remarked to me, ‘It’s pure Fascism’. This is a correct description, although the book has not the smallest connexion with politics and very little with social or economic problems. … It is a daydream appropriate to a totalitarian age. In his imagined world of gangsters Chase is presenting, as it were, a distilled version of the modern political scene, in which such things as mass bombing of civilians, the use of hostages, torture to obtain confessions, secret prisons, execution without trial, floggings with rubber truncheons, drownings in cesspools, systematic falsification of records and statistics, treachery, bribery, and quislingism are normal and morally neutral, even admirable when they are done in a large and bold way.²

• "The following story was told by Dr. Earl Peacock when he was chairman of the Department of Surgery at the University of Arizona:"

  One day when I was a junior medical student, a very important Boston surgeon visited the school and delivered a great treatise on a large number of patients who had undergone successful operations for vascular reconstruction. At the end of the lecture, a young student at the back of the room timidly asked, "Do you have any controls?" Well, the great surgeon drew himself up to his full height, hit the desk, and said, "Do you mean did I not operate on half of the patients?" The hall grew very quiet then. The voice at the back of the room very hesitantly replied, "Yes, that's what I had in mind." Then the visitor's fist really came down as he thundered, "Of course not. That would have doomed half of them to their death." God, it was quiet then, and one could scarcely hear the small voice ask, "Which half?"³

• …[I]f propaganda were truly doomed to a future in which it would always be nothing more than a technologically enhanced amplification of…information developed and disseminated by a central source, the future of democracy would be bleak indeed. However, the technology that has enhanced both the nature and dissemination of propaganda has also put its tools in many more rather than in fewer hands. … The new tools of technology are powerful indeed, but they are available to us all. In [the early 20th-century], the culture of information was a pyramid, with propaganda originating at the top and flowing down in a widening cascade from a single source. At least since the proliferation of the Internet and all that is associated with it beginning in the early 1990s, the culture of information has been collapsing, the pyramid flattening out. In the future, it will increasingly approach the intellectual geometry of a perfect plane…and in a flat world, propaganda…will finally become impossible because all available information will be available to everyone at all times. In this way, technology, not great thinkers and their great ideas, may create the apotheosis of democracy.⁴

  Well, that was way too optimistic. I have to admit that I thought much the same way in 2009, but the pyramid has been rebuilt since then.

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Notes:

1. James Hadley Chase, No Orchids for Miss Blandish (Avon Books, 1970).
2. George Orwell, "Raffles and Miss Blandish", The Orwell Foundation, 1944. Paragraphing suppressed.
3. Leon Gordis, Epidemiology (Second edition, 2000), p. 102.
4. Alan Axelrod, Selling the Great War: The Making of American Propaganda (2009), p. 226.

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Disclaimer: The opinions expressed in the above quotes represent the views of their original authors and do not necessarily represent the views or opinions of The Fallacy Files. The mere appearance of content on this site does not constitute an endorsement by The Fallacy Files or any of its affiliates or assignees.

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January 13th, 2023 (Permalink)

Guesstimate It

I've been banging the drum for over fifteen years in favor of the value of guesstimation to critical thinking. The idea behind guesstimation is to estimate some number quickly and easily based on what you already know without doing any research. Guesstimation is not just blind guessing, but educated guessing, that is, guessing based on what you know.

The goal of guesstimation is not to come up with a precise answer to a question: it's an estimate, after all. If you need an exact answer, then you'll have to research rather than estimate, but often you don't need a precise answer and a "ballpark" estimate will do. So, the goal of guesstimation is to use educated guessing to get an estimate that's "in the ballpark".

What's "in the ballpark"? This depends on what you're estimating and how precise an estimate you need. However, one way of defining the "ballpark" is in terms of orders of magnitude (OOMs), that is, tens, hundreds, thousands, millions, and so on. Unlike most puzzles or math problems, in guesstimation there is no right answer, though there are wrong ones. If a guesstimate is the right OOM, then that may be a good enough answer.

How can you learn to guesstimate? There's no algorithm for guesstimation, so the only way to learn to do it is to see examples of how it's done and try it yourself. That's what this entry is all about: you can try your hand at a guesstimation problem, then compare how you did it to how I did it. I'll provide some hints and suggestions along the way, but the main thing is to practice it yourself. As an added bonus, it's fun!

A guesstimate is not just a guess, or even just an educated guess, it's also an estimate. So, don't just try to immediately guess the answer; instead, use what you know to calculate the answer.

So, let's get started. Here's the question:

Guesstimate It: How many American women are currently of childbearing age?^*

Extra Credit: What percentage of the total population of the United States are women of childbearing age?

Hint 1

Hint 2

Hint 3

Hint 4

Guesstimate

Fact Check

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^* This problem was suggested by one from Saul X. Levmore & Elizabeth Early Cook's Super Strategies for Puzzles and Games (1981), pp. 57-58.

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January 9th, 2023 (Permalink)

"Emerging Evidence"

Earlier this month, an article in The New York Post claimed: "The USDA recommends drinking eight to 10 glasses of water per day…"¹. An earlier Post article, which is virtually an ad for Evian water, attributed the same recommendation to the same agency², and perhaps is the source of this month's claim.

I've heard the same advice since I was a child, though not attributed to the United States Department of Agriculture (USDA) as far as I recall. The recommendation was always specifically eight glasses, not nine or ten, and specifically water, not other beverages. Even when I was young this seemed absurd to me: was I supposed to drink eight glasses of water in addition to the glasses of milk, orange juice, RC cola, and Shasta root beer I drank? If I had done so, I would have never left the bathroom.

This entry is not a history of the advice to drink eight glasses of water a day, but I did discover that the recommendation is at least a hundred years old. An article in Everygirl's Magazine of March, 1924 asserts: "Most people interested in experiments of the right way to live say that the body requires about eight glasses of water each day³." So, the advice was already well-established when the article was published, and the USDA was not mentioned.

The traditional recommendation is vague in at least two ways: how much is a "glass", and does the water have to be plain or can it be consumed in other beverages or even food? Drinking glasses range in size from shot glasses, which hold only a fluid ounce or two, to pint beer glasses that hold sixteen ounces. Some recent versions specify eight-ounce glasses, and the recommendation is referred to as the "8×8 rule"⁴, which amounts to 64 ounces or a half gallon. That's a lot, especially if it's in addition to other beverages consumed in a day.

Eight ounces is a standard cup, so why not express the rule in terms of eight cups a day? Of course, "cup" is ambiguous―is it a coffee cup or a measuring cup?―but the rule could make it clear that it's the standard eight-ounce measurement rather than the vessel from which it is consumed.

Surprisingly, The Post itself reported late last year on a study concluding that the rule was incorrect⁵. Moreover, the USDA's most recent version of "Dietary Guidelines for Americans" makes no recommendation as to how much water or other fluids Americans should consume⁶.

The Post's article seems to have been mostly cribbed from an NBC News report⁷, but the NBC version makes no mention of the alleged USDA recommendation. Instead, it attributes the following precise recommendation to the "National Academies of Medicine": eight eight-ounce cups of "fluid" daily. As far as I can tell, there is no National Academies of Medicine, though there are National Academies, and one of them is the National Academy, singular, of Medicine (NAM). However, the NAM's report on Dietary Reference Intakes lists 3.7 liters of water daily for men and 2.7 for women, which translates to over fifteen eight-ounce cups for men and over eleven for women! However, the report also states:

All sources can contribute to total water needs: beverages (including tea, coffee, juices, sodas, and drinking water) and moisture found in foods. Moisture in food accounts for about 20% of total water intake. Thirst and consumption of beverages at meals are adequate to maintain hydration.⁸

So, you don't actually have to drink any plain water at all to stay hydrated, since most beverages are 90% water or more, and many foods contain water. Moreover, your body will signal you if it needs water by making you thirsty, so that most people don't need to be sweating about how much water they're consuming.

Despite these facts, the scary headline of the Post article suggests that you're more likely to die if you don't drink enough water:

Drink up: Large study finds that not consuming enough water increases risk of death by 20%¹

As is typical of these kind of studies that make their way into the headlines, this is an observational study, as opposed to an experimental one. The study finds "links", "associations", and correlations that "suggest" but don't prove things. Such studies are at best preliminary ones that should lead to experiments, but all too often do not.

As I've mentioned before⁹, many health and science news articles begin and often end as news releases, and this one is no exception. The author of the press release is careful not to suggest that the study establishes causation:

The findings don’t prove a causal effect, the researchers noted. Randomized, controlled trials are necessary to determine if optimal hydration can promote healthy aging, prevent disease, and lead to a longer life. However, the associations can still inform clinical practice and guide personal health behavior.¹⁰

Well, they can, but so can your daily horoscope. It probably won't hurt to drink more fluids―at least if you don't overdo it―but without evidence of causation there's no reason to think it will do any good.

Both the NBC and Post articles include the following quote from the study's lead author: "Emerging evidence from our and other studies indicate [sic] that adding consistent good hydration to healthy lifestyle choices may slow down the aging process." We've seen "emerging science", "emerging research", and "emerging data" before¹¹; now we can add "emerging evidence", which is evidence that has not yet emerged. My advice is to wait until the evidence has fully emerged before worrying about how much water you should drink.

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Notes:

1. Jeanette Settembre, "Drink up: Large study finds that not consuming enough water increases risk of death by 20%", The New York Post, 1/2/2023.
2. SWNS, "Most adults admit they don’t drink nearly enough water every day", The New York Post, 9/3/2020.
3. Dorothy Nye, "Playing the Game of Health", Everygirl's Magazine, 3/1924.
4. Hrefna Palsdottir, "Drink 8 Glasses of Water a Day: Fact or Fiction?", Healthline, 10/12/2020.
5. Adriana Diaz, "The rule you need eight glasses of water a day is nonsense: study", The New York Post, 11/3/2022.
6. "Dietary Guidelines for Americans, 2020-2025", United States Department of Agriculture, accessed: 1/8/2023.
7. Aria Bendix, "Poor hydration may be linked to early aging and chronic disease, a 25-year study finds", NBC News, 1/2/2023.
8. See: "Chapter 4: Water", in: "Dietary Reference Intakes for Water, Potassium, Sodium, Chloride, and Sulfate", National Academies, accessed: 1/8/2023.
9. See: "Do you smoke after sex?", 2/14/2021.
10. "Good hydration linked to healthy aging", National Heart, Lung, and Blood Institute, 1/2/2023.
11. See:
    • "Emerging" Science, 3/26/2006
    • "Emerging Research", 6/18/2009
    • "Emerging Data", 8/7/2017

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Disclaimer: The information in this entry is not intended or implied to be a substitute for professional medical advice, diagnosis or treatment. All content, including text, graphics, and jokes, is for general information purposes only. Please don't sue me.

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January 2nd, 2023 (Permalink)

Prophecy or Prophesy?

Speaking of prophecy, as I was last year, here's an example from a book I recently read of a common mistake: "…[C]rude historical determinism is mostly a self-fulfilling prophesy…"¹. The two words "prophecy" and "prophesy" are obviously related, both having to do with predicting the future, but the first is the noun form and the latter is a verb. "To prophesy" is to predict the future, and the prediction that results is a "prophecy". So, the example sentence should have read: "historical determinism is…a self-fulfilling" prophecy.

I've seen this mistake frequently enough that it was already in my mental spell-checker², and most of the books on usage that I regularly consult mention it³. For those reasons, it seems to be a common misspelling.

In my experience, the misspelling seems to go mainly in one direction, that is, from "prophecy" to "prophesy". It may be that people are unsure how the former word is spelled, since the "c" is pronounced as an "s", but spelling it as it's pronounced produces a different word.

Since "prophecy" and "prophesy" are both English words, but different parts of speech, you might expect that a spell checker would not detect the substitution of one for the other, but a grammar checker should. I tried the example sentence in several programs and a few did indeed catch the mistake and suggest the correct spelling, but as many others missed it. So, you might want to check your own checker to see whether it will catch this error; if not, you can commit it to the checker in your head.

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Notes:

1. Yunte Huang, Charlie Chan: The Untold Story of the Honorable Detective and His Rendezvous With American History (2010), p. 152.
2. Another recent example is: W. Joseph Campbell, Lost in a Gallup: Polling Failure in U.S. Presidential Elections (2020), p. 239.
3. Here, in alphabetical order by author's last name, are the books:
   • Bill Bryson, Bryson's Dictionary of Troublesome Words: A Writer's Guide to Getting It Right (2002)
   • Robert J. Gula, Precision: A Reference Handbook for Writers (1980), p. 220
   • Porter G. Perrin, Reference Handbook of Grammar & Usage (1972)
   • Harry Shaw, Dictionary of Problem Words and Expressions (Revised edition, 1987)
   • Bill Walsh, Lapsing Into a Comma: A Curmudgeon's Guide to the Many Things That Can Go Wrong in Print―and How to Avoid Them (2002), p. 195

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