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June 5th, 2023 (Permalink)

More Junk Statistics

Former president Donald Trump is, of course, running for president, as is current governor of Florida, Ron DeSantis. Since DeSantis is popular with Republican voters, he's likely to be Trump's strongest opponent in the primary elections for the GOP's nomination. So, Trump has launched a series of attacks on DeSantis, including the following:

Surprise, Ron…was Third Worst in the Nation for COVID-19 Deaths (losing 86,294 People), Third Worst for Total Number of Cases, at 7,516,906. … For COVID Death Rates Per State, Ron, as Governor of Florida, did worse than New York.1

If you know anything at all about what happened in 2020-2022 in New York and Florida, then Trump's claim should strike you as implausible. In New York in 2020, thousands of patients infected with the coronavirus were moved from hospitals into nursing homes, the worst possible places for them since the elderly infirm are at much greater risk of serious illness and death than the general population2. Then, when the number of deaths in nursing homes predictably spiked, the state covered it up3. Thankfully, nothing like this happened in Florida, so there's every reason to think that its record in COVID-19 deaths should be superior to New York's, not worse.

So, where did Trump get these statistics? His statement lists no source for the numbers he gives, and I haven't been able to find one for them. According to the Centers for Disease Control and Prevention's (CDC) current data, Florida has had a total of 78,707 deaths attributed to Covid-19 since the beginning of 2020, which is less than what Trump claimed. In addition, New York state had a total of 80,611, which is over 2K more than Florida. Ranked by total deaths, Florida is not the "Third Worst"; New York is, with Florida just behind it as fourth worst.4

The CDC stopped tracking "cases" on the eleventh of last month when the so-called emergency officially ended5, so if Trump got the number of cases from the CDC it must have been before then. While it's possible that Florida's number of deaths actually declined in a month as a result of adjustment for over-counting, it's not likely, especially by over 7,500 deaths.

Even if Trump's numbers were correct, comparing the absolute numbers of deaths between states is an apples-to-oranges comparison, because different states have different-sized populations. In 2020, New York had a population just under 20 million, while Florida's was almost 22 million6, so the latter state should have a slightly larger number of deaths, every thing else being equal. Of course, everything else was not equal, and New York had a greater number of deaths despite a smaller population.

Population is also why both states ranked so high in terms of absolute numbers of deaths. In 2020, Florida was the third largest state in population, while New York was fourth. Thus, the numbers that Trump gave would make perfect sense simply based on population size, but we've seen that they're no longer accurate if they ever were.

Geographical entities that differ in population―such as states, cities, or countries―should not be compared in terms of absolute numbers. Instead, the proper basis for comparison is the rate―in this case, the death rate―since the rate takes the population into consideration.

Given the numbers of deaths and population given above, the death rate for Florida was 78,700/22,000,000 for a raw rate of .0358; these rates are usually given as deaths per 100K, which in this case is 358. New York's rate, in contrast, was 403 per 100K.

There's yet another problem with Trump's comparison: in addition to differences in size of population, New York and Florida differ in the age-distribution of their populations. Florida is a famous retirement destination so that its population tends to be older than that of other states, and Covid-19 is more likely to be fatal the older the patient is. So, the death rate should be adjusted to take age into account. Thankfully, the CDC has done this for us and the age-adjusted death rate for New York is 312 per 100K, making it the 18th worst state, whereas that for Florida is only 245 per 100K, which makes Florida the 17th best.4

The statistics given by Trump are junk because, even if they were right, they're useless for comparing how well the two states did with respect to Covid-19. And they're not right.


  1. Donald Trump, "Statement by Donald J. Trump, 45th President of the United States of America", Truth Social, 3/22/2023.
  2. Holmes Lybrand, "Fact checking Gov. Cuomo’s false claim about Covid-positive patients and nursing homes", CNN, 10/2/2020.
  3. See:
  4. "COVID Data Tracker", Centers for Disease Control and Prevention. Data through: May 27, 2023. Posted: June 1, 2023.
  5. Brenda Goodman, "The way the US government tracks Covid-19 is about to change", CNN, 5/5/2023. This change was a good thing since it was never clear what a "case" was. Simply testing positive for the coronavirus was often counted as a "case", even if the person never had any symptoms. Moreover, every test has false positives, so that some unknown percentage of those testing positive did not even have the virus.
  6. Ellen Kershner, "The 50 US States Ranked By Population", World Atlas, 6/12/2020.

June 2nd, 2023 (Permalink)

Soldier or Solider?

Look closely at the following recent headlines:

Colorado solider among 3 killed in collision of U.S. Army helicopters in Alaska1

Michigan solider killed in Colorado shooting returning home with special procession2

What is a solider? I think whoever typed these headlines meant "soldier". I've seen this misspelling several times over the years, and it only took a few minutes of searching for "solider" on the web to find the first headline above, so this is a frequent error.

Misspelling "soldier" as "solider" is due to overly-rapid typing resulting in the transposing of adjacent letters. Or, at least I assume that's the reason; I hope nobody thinks that "soldier" is actually spelled this way. Since "solider" is a genuine if uncommon English word, many spell-checking programs will not catch the switch. In addition, the two words look alike at a quick glance, so that it's easy for a human writer or editor not to notice the transposition.

While similar to the eye, "soldier" and "solider" could scarcely be more different in meaning. "Soldier" is, of course, a noun referring to a member of the army, whereas "solider" is the rather rare comparative form of the adjective "solid", meaning "more solid". Given this grammatical difference, grammar checking programs may be able to detect the mistake of typing one word for the other.

Despite its frequency, none of the reference books I usually consult includes this error. The most recent of these books is from a dozen years ago, and most are twenty years old or more, which made me wonder whether this mistake has become more common with the invention of spell-checking programs. Google's Ngram Viewer, which allows you to chart the prevalence of a word or phrase in Google's book corpus, shows a slow rise in the occurrences of "solider" from 1800 to 1900, then a plateau until the late 1990s, at which point the number starts sharply rising until it peaks in 20173. I checked a few of these occurrences and all were clearly misspellings of "soldier", even in the titles of books! I can imagine no reason for this state of affairs other than the rise of automated spell-checkers, and a resulting decline in careful copyediting. So, this is exactly the kind of misspelling you should watch out for since the spell-checker in your computer is not likely to catch it.


  1. The Associated Press, "Colorado solider among 3 killed in collision of U.S. Army helicopters in Alaska", The Denver Post, 5/1/2023. In case this headline is edited, you can view it at: Archived version of above page, Internet Archive Wayback Machine, 5/1/2023.
  2. Caitlyn French, "Michigan soldier killed in Colorado shooting returning home with special procession", M Live, 4/7/2023. The headline has since been corrected, but the misspelling lives on in its URL.
  3. "Solider", Google Books Ngram Viewer, accessed: 6/2/2023.

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Recommended Reading
May 31st, 2023 (Permalink)

Freedom of the Press & the Two Minutes Hate

The first recommended reading this month is a preface by George Orwell to his novel Animal Farm that, for some reason, was not included when the book was published. Instead, the preface was lost for decades and only rediscovered in 19711. Animal Farm was finished in early 1944, during World War Two, and Orwell spent the next year and a half trying to get it published. The following preface explains why he had so much difficulty finding a publisher. It's worth reading today because, though the details are different, the general situation is so familiar to us. Change the examples and it could have been written yesterday.


  1. Bernard Crick, "How the essay came to be written", The New York Times, 10/8/1972.
  2. According to Dorian Lynskey, "[Peter] Smollett was almost certainly the man who advised Jonathan Cape [the publisher] to drop Animal Farm when he was head of Soviet relations at the Ministry of Information." In the last year of his life, Orwell informed the British government's Information Research Department that Smollett was "some kind of Russian agent". In 1980, after his death, it was revealed that Smollett had indeed been a Soviet agent. See: The Ministry of Truth: The Biography of George Orwell's 1984 (2019), p. 204. See also: Peter Foges, "My Spy", Lapham's Quarterly, 1/14/2016.
  3. Orwell's ellipsis.
  4. Is this still true?
  5. George Orwell, Nineteen Eighty-Four (1949), chapter 1.
  6. Erica Byfield & Checkey Beckford, "Bellevue Worker in Citi Bike Fight Video Has Receipts Showing She Rented It: Lawyer", NBC New York, 5/19/2023.
  7. See: "Get to know Citi Bike", Citibike, accessed: 5/30/2023.
  8. See: Medice, Cura Te Ipsum, 6/1/2019.

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.

May 28th, 2023 (Permalink)

Psychic Reading?

Prophecy is the most gratuitous form of error.1

On the last day of last year, in an entry on predictions for that year attributed to Nostradamus, I wrote:

A fellow named Mario Reading published a book on Nostradamus in 2006 which supposedly predicted that Queen Elizabeth II would die "circa 2022"―I write "supposedly" because I do not have this book and so am in no position to check it. Not that I doubt that he did make such a prediction, because it was a pretty safe bet given her advanced age. Moreover, the use of the word "circa" added a degree of vagueness to the prediction: if he had meant to predict that she would die this year, and only this year, then he would have written "in 2022". As it is, if she had died last year, or next year, he still could have claimed to have gotten the prediction right, as those years are "circa" 2022. So, at the very least, the prediction covered the years 2021-2023. While that's not quite a sure thing, if the prediction had failed we would simply have heard nothing about it. Sadly, Reading died in 2017, so he can't enjoy his fifteen minutes or the money from the spike in sales of his book.2

I have now obtained a copy of a later edition of Reading's book that was published in 20153. After a brief biographical note on its subject, the book is arranged chronologically in chapters ranging from 2001 to, believe it or not, 7074, when the world is supposed to end. Clearly, every chapter prior to 2015 is written with the benefit of hindsight, so that only with 2016 do the predictions get interesting.

Here's what Reading has to say about Queen Elizabeth II in the chapter on 2022: "The future King Charles III and his Princess Consort, the former Camilla Parker Bowles, will find themselves faced with a constitutional crisis on the death of Charles's mother, Queen Elizabeth II.4" In a later passage, he adds: "…Queen Elizabeth II will die, circa 2022, at the age of around ninety-six….5" So that is where the "circa" comes from, though the chapter heading would lead one to expect the event last year. As I noted in the comment quoted above, the success of this prediction was aided by the inexactness of "circa", and either 95 or 97 years of age would surely have counted as "around" 96.

As I mention in my entry on prophecy6, the more predictions a would-be prophet makes the greater the likelihood of a lucky hit. What's never mentioned in tabloid reporting is that Queen Elizabeth's death is just one of many predictions in the book for the years 2016-2022. How many of these did Reading/Nostradamus get right? That you haven't heard of any of them should tell you the answer: none.

Here's a list of Reading's failed predictions for the last seven years:

Date Prediction Page
2016 A "massive" flood in the Aegean Sea is so "catastrophic" that "no one on dry land will be safe". 195
2017 The Pope causes a scandal by forcing out his presumed successor. 203
The Pope defrocks a number of "schismatics". 210
Al-Qaeda attacks a U.S. naval base which is then "restored to Arab control". 213
2020 A new Pope. 224
2021 A biological terrorist attack on the French town of Agde. 228
A new volcanic island rises from the sea. 232
2022 The Church of England is disestablished. 235
King Charles III abdicates and Prince William becomes King 240

In addition to predicting many events that never happened in the years since the book was published, Reading/Nostradamus failed to predict the most important events that did happen. For example, where is the prediction of a worldwide pandemic in the years 2020-2022? One of the most important events, if not the most important, of those years is missing. Also, where is the invasion of Ukraine by Russia? Where is the election of Donald Trump in 2016 and of Joe Biden in 2020? Where is the return of inflation after a forty year absence?

Reading is likely to become the Jeane Dixon7 of the 21st century. Dixon, who was the best-known "psychic" of the last century, became famous because of one lucky hit―the assassination of President Kennedy―out of many hundreds of failed predictions.


  1. George Eliot, Middlemarch, chapter 10.
  2. When Prophecy Fails: 2022 Edition, 12/31/2022.
  3. Mario Reading, Nostradamus: The Complete Prophecies for the Future (2015). All page citations are to an electronic copy of this book.
  4. Reading, p. 234.
  5. Reading, p. 238.
  6. See Rule 5 in: How to be a Prophet for Fun and Profit, 6/26/2022.
  7. For more on Dixon, see: How to be a Prophet for Fun and Profit, 6/26/2022.

May 26th, 2023 (Permalink)


Q: I have a suggestion to add to your collection of fallacies. I'm not sure whether it's not completely contained in other fallacies but I didn't find a similar one. I call it the Pharisee Fallacy or Meta-Fallacy. It's kind of a reverse Fallacy Fallacy: Believing you are correct just because you haven't made any of the logical fallacies (or cognitive biases). This of course could be because we might well never have a complete list of all fallacies, or because our sources are just simply incorrect or because of some other factors.

The point of this fallacy is that knowing and following rules (in this case avoiding the logical fallacies) doesn't make you "good" (in this case correct). The rules are there to point out a flawed functioning of the human consciousness. But there is no need for rules if one's consciousness works well.

I believe the way to infallibility is not through keeping a tab on each and every fallacy but through being more conscious: not lying to ourselves; letting our inner, deepest, unconscious thoughts register so that we see the intention of our more surface level, conscious thoughts.

It might seem like I'm against collecting fallacies, but I hope it's clear that I don't believe being conscious in such a deep level is easy to do and therefore I think that having a list of fallacies is a good way to remind us of the level of consciousness we should strive for again and again.―Márton Kenessey

A: You're correct that, as a general rule, it does not follow from the fact that an argument does not commit one of the named fallacies that it is, thereby, a "good" argument. To be good, an argument needs to start with true premisses and use cogent reasoning to reach a conclusion. In other words, there are two main ways that an argument can go wrong: either the reasoning is uncogent or at least one premiss is false. If you start from a false premiss, even the best reasoning may lead you astray.

Logical fallacies are concerned primarily with the cogency of reasoning, and cogency isn't everything: good arguments are also sound. If an argument does not commit any fallacy then it may be cogent, but if it has even one false premiss then it is unsound. The truth or falsity of premisses is not generally a question for logic, but for other sciences. So, the fact that an argument does not commit a fallacy may suggest that it is cogent, but it would still be a bad argument if it has one or more false premisses.

For the above reasons, it would be a mistake to claim that an argument must be good because it doesn't commit any of the known fallacies. However, it doesn't seem to be a common claim and, therefore, not the sort of bad argument worthy of a named fallacy. At least, I don't recall ever seeing an example of this type of argument―if anyone knows of one, please let me know. In any case, you are correct that there is no such fallacy in the Fallacy Files Taxonomy, and I would hesitate to add it until I see some evidence that it is common.

As to your claims about consciousness, psychological research shows that it's normal for people to make certain types of error. These errors include traditional logical fallacies and the more recently identified cognitive biases. So, even perfect consciousness of the workings of one's own mind would not be enough to avoid bad reasoning.

How do you know whether your consciousness works well if you don't know what mistakes it might make? I agree that being aware of one's own thinking and honest with oneself is a necessary part of good if not infallible reasoning, but it's not sufficient. You also need to know what biases to look out for and what pitfalls to avoid, and the only way to do that is to learn how to recognize them.

Infallibility is, I think, an unattainable goal, but what is attainable is improvement, and knowing about logical fallacies is one way to attain it.

May 18th, 2023 (Permalink)

Junk Statistics

In a recent episode of her show, Megyn Kelly claimed:

There are millions of [pedophiles] in the United States. Millions. There are about a million in custody, and something like ten to forty percent of pedophiles get caught; the vast majority do not get caught.1

I'm sorry to be the bearer of good news, but there are less than two million people incarcerated in the U. S.2 If about a million pedophiles were in custody, that would mean that more than half of those inmates were incarcerated for sex crimes against children, which is highly unlikely.

So, how many pedophiles are incarcerated in the United States? It's not easy to find this statistic, especially since people in jail and prison are not categorized as "pedophiles" as far as I know, and pedophilia is not itself a crime. Moreover, sexual crimes against children are often lumped in with adult rape and other crimes under labels such as "sex crimes". That said, I did find a statistical break down in terms of type of offense which indicates that 12% of the federal prison population is imprisoned for "sex offenses"3. I think it's safe to assume that the percentage of inmates incarcerated for sex-related crimes in state prisons and local jails is similar. Of course, since that percentage includes sex crimes against adults, at best it sets an upper limit on the percentage of those imprisoned for pedophilia-related offenses.

Let's be generous to Kelly and assume that 12% of the people incarcerated in the U. S. are there for sex crimes against children: that means that the number of pedophiles in custody is around 200K, not a million. Let's also be generous by assuming that only 10%, instead of 40%, of pedophiles are incarcerated; that would mean that there are about two million total. I suppose that means there are millions of pedophiles in America, as Kelly claimed, but barely. However, to get up to two million we had to assume that all sex offenses involved children, and we know that's not true. We also assumed that only ten percent of pedophiles are in custody, which was the lowest percentage given by Kelly―where did she get that?

So, even if we bend over backwards to be fair to Kelly, it seems unlikely that there are "millions" of pedophiles "prowling schools and kids' clubs and kids' charities right now" as she goes on to say1. Of course, even a million pedophiles is worrisome, but let's not get hysterical and scare parents into withdrawing their children from schools or clubs for fear of prowling child molesters.

Where did Kelly get the statistic that a million pedophiles are in custody? I don't know the answer, but she probably got it from an activist group. I suspect that it's a "Goldilocks number", that is, one that is big enough to frighten people but not so big that it attracts skeptical scrutiny4.

We survived a previous moral panic about pedophiles, namely, the so-called "satanic panic" of the 1980s5. However, hundreds of innocent people were incarcerated for nonexistent crimes, and thousands had their reputations permanently destroyed by false accusations. There are signs of a return of this panic6, and journalists such as Kelly should not contribute to it. Fighting the sexual abuse of children is a worthy cause, but let's fight it with the truth and not noble lies.


  1. "Megyn Kelly Fires Back After Charlize Theron Drag Queen Comments Backlash, and Reality of 'Grooming'", YouTube, 5/16/2023.
  2. "U.S. Jail Population Increased While Prison Population Decreased in 2021", Bureau of Justice Statistics, 12/20/2022.
  3. "Offenses", Bureau of Prisons, 5/6/2023.
  4. See: The Goldilocks Number, 1/23/2022.
  5. Alan Yuhas, "It’s Time to Revisit the Satanic Panic", The New York Times, 3/31/2021.
  6. See: The Return of a Moral Panic, 1/31/2022.

May 5th, 2023 (Permalink)

How to Solve a Problem*: Think Backwards

To get the most out of this entry, give the following puzzle a shot. Don't give up too easily, but don't worry if you can't solve it as I'll show you one way to do it later.

Puzzle: What Stays in Las Vegas

One hot summer evening, Larry decided to try his luck on the strip in Las Vegas. He doubled his money playing blackjack at The Alexandria casino, but then lost $50 on roulette. Feeling like his luck had run out there, he went to the casino next door, Carnival Carnaval. This time, Larry doubled his money playing craps, but lost $50 on a slot machine. Finally, Larry went to a casino down the street, Circus Maximus, where he doubled his money playing baccarat, but lost $50 on keno. Checking his pockets, he discovered that he was tapped out! He hadn't so much as a penny left. How much money did Larry start the evening with?

You might be able to solve this puzzle by trial and error, but it would be a long and tedious procedure. Alternatively, it could be solved with algebra, so don't complain that you never have occasion to use your high school algebra. However, if you don't remember your algebra very well, it can also be solved without algebra by solving it backwards, that is, by starting at the end and working back to the beginning.

Notice that what we're asked to discover is how much money Larry had at the beginning of the evening―that's our unknown―but we know that he ended up with nothing. A good rule of thumb for problem solving is to start with what you know; in this case, that's what Larry ended up with: $0. Therefore, it's a good idea to start at the end and work backwards. Let's give it a try.

The same thing happened to Larry in each of the three casinos he visited: he doubled the money he came in with then lost $50. In mathematical terms, if we let x represent the number of dollars he entered a casino with, then what he left with was 2x - 50 dollars. So, if he left the casino with y dollars, then 2x - 50 = y. Thus, if we know y, which is what Larry left a casino with, then we can figure out what he must have had when he entered.

We're told that Larry's visit to the last casino, Circus Maximus, cleaned him out. So, if losing $50 cleaned him out, then doubling his money must have left him with $50, which means that he entered the casino with half that, $25. That is, if the amount that he entered the casino with is x, then what he left with is 2x - 50 = 0. So, x = 25.

That takes care of the last step in the puzzle. What we do now is continue this process with the preceding steps. We just figured out that he had $25 when he left the second casino, Carnival Carnaval. So, the amount that resulted from doubling his money in that casino was $75, which means that he entered with half of that: $37.50.

As we've just seen, Larry exited the first casino, The Alexandria, with $37.50 in his pockets after losing $50, which means that he doubled his money to get $87.50. Thus, the amount that he entered the first casino with was half of that: $43.75, which is the solution to the puzzle.

Wasn't that easy? Once you know how to approach the puzzle―namely, from the end―it's just a matter of working step-by-step until you reach the solution.

Now that we have another tool in our problem-solving chest, here's another puzzle to practice on:

Puzzle: Tickets to Ride

Smith, Jones, and Robbins wanted to ride the new rollercoaster together, but tickets to the amusement park cost $24. The three friends each checked their pockets for cash but some came up short. So, Smith gave Jones and Robbins as many dollars as each had, but some of the friends were still short. Then, Jones gave Smith and Robbins as much as they already had, but some still didn't have enough for tickets. Finally, Robbins gave Smith and Jones as much as they already had, and each friend now had exactly enough for a ticket. How much money did each one originally have?

* For the previous entry in this series, see: How to Solve a Problem: Contraction, 4/6/2023

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