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April 5th, 2021 (Permalink)

A Chinese Family Problem

One unfortunate effect of the one-child policy in China was to produce an imbalance of men to women, because so many couples wanted a boy more than a girl. As a result, after several years of the policy there were more young men in China than young women, meaning that many young Chinese men would have to live without a wife.

In order to correct this imbalance, a government bureaucrat in the same agency that had devised the one-child policy proposed a solution. The policy would be revised to say that couples could have as many girls as they wished, but must stop having children after one boy.

"Clearly," argued the bureaucrat, "this revised policy will correct the imbalance between the sexes. There will be families of one boy, one girl and a boy, two girls and a boy, three girls and a boy, and so on. Since Chinese parents want most of all to have a boy, they will keep having babies until they get one, thus producing more girls than boys. In just a few years, the imbalance will disappear!"

Assuming that the Chinese people obey the new policy as written, will it redress the imbalance in a few years?

April 2nd, 2021 (Permalink)

2020 Hindsight, Part 2

Last month, we looked at a "prediction" of the coronavirus epidemic attributed to Nostradamus, which turned out to be a retrodiction created after the epidemic had got underway1. This month, let's look at some predictions of the events of last year attributed to Nostradamus that were published before the year started. How accurate were such predictions, and did the famed seer foresee the most important event of the year, namely, the coronavirus epidemic?

On the last day of 2019, the British tabloid newspaper Express published an article with the five top predictions for 2020 from the Nostradamus2020.com website2. Here they are in the order given by the article:

  1. Trump wins re-election: I suppose that some of Trump's supporters, and perhaps even the man himself, would claim that he really did win so that the prediction came true. Had Trump read and believed this when he claimed that he won? Of the five prognostications, this is the only one for which the newspaper article supplies a quatrain:
    The exiles because of anger and intestine hatred
    Will bring a great conspiracy to bear against the King
    Secretly they will place enemies as a threat,
    And his own old ones against them sedition.3

    This is a loose translation of Nostradamus' quatrain I-13:

    Les exilés par ire, haine intestine,
    Feront au Roi grand conjuration:
    Secret mettront ennemis par la mine,
    Et ses vieux siens contre eux sédition.4

    Of course, this quatrain doesn't predict anything about Trump or anyone else being re-elected. Instead, it predicts a plot against some unnamed King. Maybe Trump would have liked to be king, but he was only president. Nostradamus lived during the time period when there were still kings with real power, so there's no reason to think that he was using the word figuratively. Other than that, there's no indication of when the prediction is supposed to come true, nor any details that apply to Trump rather than some real king. Now, if it had predicted a conspiracy against the "great orange man", I would be impressed.

    Furthermore, at the time that this article was published, there was already a conspiracy aimed at impeaching Trump and removing him from the presidency that had been going on since before his election. So, even assuming that "the King" refers to Trump and not Elvis Presley, this is not a prediction, but an attempt to apply the quatrain to an event that was ongoing.

    A test of such a vaguely-written prophecy is how it was interpreted prior to the supposed event that fulfilled it. In this case, an early Nostradamus interpreter named Étienne Jaubert5, interpreted it as referring to the conspiracy of Amboise, which occurred in 15606. While Nostradamus lived until 1566, this quatrain is the thirteenth in the first book of "centuries"―collections of a hundred quatrains―so it was probably printed in the first edition of 1555, five years prior to the conspiracy.

    Another interpreter, Henry C. Roberts, wrote the following about this quatrain: "The progress of the Italian conspiracy is indicated―the rise of a fifth column rife with internal dissensions, culminating with a plot against King Victor Emmanuel.7" This is itself ambiguous since there were three kings of that name, but given that Roberts interpreted the two previous quatrains to be about the rise of fascism in Italy, he may have been referring to the third one8.

    In any case, the poem is so vaguely worded that it can be interpreted to apply to almost any plot against a king, but not to the re-election of President Trump.

  2. Earthquakes: There are earthquakes every year somewhere, but the website made a surprisingly precise claim:
    The prophet announced the occurrence of a strong earthquake in the future that will lead to the sinking of the entire state of California under the ocean's water. Nostradamus foretold a great earthquake in 2020, in America. In the New World (the West Lands), California seems to be the logical guess. This will happen next time Mercury is retrograde in Cancer (between June 18 and July 12).2

    Though its politicians seem intent on destroying it, the last I heard California was still there. How the website interpreters came up with such a precise prediction, I've no idea. Usually, Nostradamus had more sense than to make falsifiable prophecies. Fortunately for Californians, the Nostradamus interpreters were wrong again.

  3. The United Kingdom will gain a king. The last I checked, it still has a queen.
  4. Major war: Whatever you can say against 2020, you can't say this.
  5. Kim Jong-Un gone: Unfortunately, the dictator is still dictating.

So, that's zero for five, and no mention of an epidemic. Of course, these predictions are only Nostradamus as interpreted by his modern followers. This is convenient for him, since he's never to blame for a failed prediction; instead, it's the fault of whoever misinterpreted his vague and ambiguous doggerel.


  1. 2020 Hindsight, 3/10/2021.
  2. Ciaran McGrath, "Trump re-elected, Kim Jong-Un out―& King William? Nostradamus predictions 2020 Revealed", Express, 12/31/2019. Unsurprisingly, the website is no longer available, but you can see the Wayback Machine's cache of its main page here: "Nostradamus Predictions for 2020", Internet Archive, 12/8/2019.
  3. This is Edgar Leoni's translation, see: Nostradamus and His Prophecies (1982), p. 135.
  4. See: Leoni, op. cit., p. 134.
  5. For Jaubert, see: Leoni, op. cit., pp. 62-63. Leoni finds this interpretation credible, but adds: "The wording, however, is sufficiently general that the quatrain may fit other palace plots of history as well. (p. 572)" The aptly-named Erika Cheetham also adopted Jaubert's interpretation, see: The Prophecies of Nostradamus, translated, edited & introduced by Erika Cheetham (1981). She translated the quatrain as follows:
    Through anger and internal hatreds,
    The exiles will hatch a great plot against the king.
    Secretly they will place enemies as a threat,
    And his own old (adherents) will find sedition against them.
  6. Editors, "Conspiracy of Amboise", Encyclopaedia Britannica, accessed: 3/12/2021.
  7. The Complete Prophecies of Nostradamus, translated, edited, and interpreted by Henry C. Roberts (New Revised Edition, 1982).
  8. Editors, "Victor Emmanuel III", Encyclopaedia Britannica, accessed: 3/12/2021.

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Recommended Reading
March 31st, 2021 (Permalink)

The Bad News Bearers & Pandemic Pessimism

  1. The report is here: Bruce Sacerdote, Ranjan Sehgal & Molly Cook, "Why Is All COVID-19 News Bad News?", NBER Working Paper No. 28110, 11/2020
  2. See:

March 26th, 2021 (Permalink)

How many COVID-19 patients are hospitalized?

Before reading further, please consider the question asked by the title of this entry. I don't expect you to know the answer exactly without doing research, which I also don't expect you to do. Instead, just guess a percentage that you think is within, say, five percentage points in either direction of the true answer.

Last year, we saw from a couple of surveys that, despite the news media's single-minded coverage of the coronavirus―or, perhaps, because of it―people grossly overestimate the risks of dying from COVID-191. The question that forms the title of this entry is from a survey conducted by the same group that did one of those we already looked at2, namely, the venerable Gallup organization.

I hope that you were brave enough to guess the answer to the question, because here's an excerpt from the researchers' report that reveals the correct answer:

The U.S. public is…deeply misinformed about the severity of the virus for the average infected person. In December, we asked, "What percentage of people who have been infected by the coronavirus needed to be hospitalized?" The correct answer is not precisely known, but it is highly likely to be between 1% and 5% according to the best available estimates, and it is unlikely to be much higher or lower. … Less than one in five U.S. adults (18%) give a correct answer of between 1 and 5%. Many adults (35%) say that at least half of infected people need hospitalization. If that were true, the millions of resulting patients would have overwhelmed hospitals throughout the pandemic.3

If you're answer was correct, or closer to correct than most people's, then congratulations. If not then you're in good, or at least numerous, company.

So, why are we so badly misinformed despite months of constant coverage by the news media? According to the study authors:

People's "information diet" plays a crucial role here. In the first and second rounds of our survey…, we found that those who get their news primarily from social media had the most erroneous perception of the risk of death by age.3

Which is why I call them "anti-social media". However, that doesn't mean that the traditional news media have done a good job of informing us.

As was true of the previous Gallup survey, this one was not based on a random probability sample of the population, but on a large panel recruited from the internet. For that reason, such statistical tools as the margin of error are inapplicable. Also, despite the large size of the sample, we should be on our guard against the possibility that it is unrepresentative of the whole population. However, the survey's results are consistent with the other surveys I've seen, as well as with my informal sense that the news media have been consistently exaggerating the risks of COVID-19.


  1. Survey Says, 8/23/2020
  2. Survey Says & How to Read Scientific Research, 9/27/2020
  3. Jonathan Rothwell & Sonal Desai, "How misinformation is distorting COVID policies and behaviors", The Brookings Institution, 12/22/2020

March 18th, 2021 (Permalink)

Parity or Parody

One problem with spellchecking programs is that they won't catch a misspelling of a word if it spells a different word that's found in the program's dictionary. As a result, an over-reliance on spellcheckers can lead to the perverse result that certain spelling errors become more common. For instance, the common misspelling of "led" as "lead" won't be caught by spellcheckers1.

Here's another example I recently came across:

On the parity in college basketball today:

"You see it around the country where teams beat teams that maybe they weren't expected [to beat]. However, I'd also tell you there's a lot of guys who-the parody is just so evenly spread out in college basketball, besides maybe the top eight, nine teams in the country, anywhere between 30-250 in the country is pretty evenly spread out. There's not that much difference anymore. You can win the national championship at any school, you can go to the NBA from any school, you can be on TV from any school. So, the days where you can only go to a certain group―not anymore, that's why the talent is spread out so much, and that's why there is so much parody in college basketball."2

"Parity" means "equality", though it's most often used with specific technical meanings in mathematics, physics, and economics3. "Parody", in contrast, is a type of satire involving exaggerated, usually intentionally humorous, imitation4. Clearly, what the person quoted above was talking about was a rough equality in ability among college basketball teams.

What makes this a particularly odd example is that the word "parity" is correctly spelled in the introduction to the quote, but misspelled as "parody" twice within it. Moreover, it appears to be a quote of spoken words, in which case the misspellings were introduced by whoever transcribed those words rather than the speaker. Given that the two spoken words are near homophones, this mistake is probably most likely to happen in such transcribed speech.

I don't know how common this "parity"/"parody" confusion is, but I've seen two additional examples of it recently. I checked a number of reference works that list easily confused pairs of words5, but none listed "parity" and "parody". In any case, this is a mistake worth watching out for, especially since your spellchecker won't save you.


  1. See: Get the "Lead" Out, 2/5/2007.
  2. "Post-Game Quotes: Men's Basketball Vs. Prairie View", Georgia Tech, accessed: 3/16/2021.
  3. See: "Parity", Cambridge Dictionary, accessed: 3/18/2021.
  4. See: "Parody", Cambridge Dictionary, accessed: 3/18/2021.
  5. Some of the works consulted:
    • Harry Blamires, The Cassell Guide to Common Errors in English (1997)
    • Bill Bryson, Bryson's Dictionary of Troublesome Words (2002)
    • Adrian Room, The Penguin Dictionary of Confusibles (1980)
    • Harry Shaw, Dictionary of Problem Words and Expressions (Revised Edition, 1987)

March 10th, 2021 (Permalink)

2020 Hindsight

One thing you might expect of a supposed seer, such as the famous Nostradamus, is that he should have predicted events before they happen. For instance, there's no doubt that the most important event of 2020 was the coronavirus epidemic; did Nostradamus foresee it? The following was attributed to him on Nitwitter:

Nostradamus wrote in the year 1551 this! There will be a twin year (2020) from which will arise a queen (corona) who will come from the east (China) and who will spread a plague (virus) in the darkness of night, on a country with 7 hills (Italy) and will transform the twilight of men into dust (death), to destroy and ruin the world. It will be the end of the world economy as you know it.1

This is a good chance to practice your quote-checking skills: Before you do any research, is there anything about the alleged quote that arouses your skepticism? I notice three things, each of which requires at least some familiarity with Nostradamus' life or writings:

  1. The "tweet" claims that the alleged prophecy is from 1551, yet The Centuries, Nostradamus' famous prophetic book, was first published in 1555. He did produce yearly astrological almanacs starting in 1550, but they did not include prognostications until 15552.
  2. Nostradamus' prophecies were written in quatrains―that is, poems of four lines―and this doesn't seem to be even a translation of one, though it's possible that it might be a translation that didn't keep the poetic form.
  3. As I mentioned at the beginning of the month3, you should always keep a look-out for anachronisms in supposed quotes of historical figures such as Nostradamus. The last sentence of the alleged prophecy refers to "the world economy", but this is a modern notion, and there was no world economy in 1551. So, the apparent anachronism is a sign that either the prediction was written, or at least mistranslated, within the last century or so.

If you put these three reasons for doubt together with the improbability of someone from half-a-millenium ago predicting what happens today, you have the basis for some serious skepticism. But don't stop there: now is the time to start checking.

If you search the internet, you will soon find a number of fact-checking sites that have debunked the quote4: it's not Nostradamus, and it was almost certainly written last year after the epidemic started. Something similar happened nearly twenty years ago, when a phony Nostradamus quote circulated claiming to predict what happened on September eleventh5. Whenever an important event occurs and an after-the-fact "Nostradamus" prediction of it is produced, one should always suspect fakery.


  1. David Mikkelson, "Did Nostradamus Predict the COVID-19 Pandemic?", Snopes, 3/20/2020.
  2. Edgar Leoni, Nostradamus and His Prophecies (1982), pp. 42 & 54.
  3. How to Check Quotes, Part 5: Reliable Sources, 3/2/2021.
  4. In addition to the Snopes article linked in note 1, above, see also:
  5. Benjamin Radford, "Did Nostradamus Really Predict the 9/11 Terrorist Attacks?", Live Science, 9/11/2011.

March 4th, 2021 (Permalink)

Another Surprise Puzzle Prize at the Logicians' Club*

There are currently five members of the Logicians' Club, one of whom is the president. As you might expect, logicians love variables, so the five members are known only by the letters V, W, X, Y and Z, ranked by seniority. V is the most senior member of the club and, therefore, its president.

The club's treasury has swollen to $100 and, according to the bylaws of the club, the sum must be distributed to the current members whenever it hits that amount. The president, V, withdrew it from the club's bank account in the form of one-hundred silver dollars.

The following procedure for distributing the money to the membership was specified in the club's bylaws: The president, V, would decide upon and announce a distribution of the silver dollars among the five members. Then, a vote would be held immediately on V's plan so that the members have no time to consult with each other or negotiate agreements to share the money. If the plan receives a majority of the members' votes―including V's―then the coins will be distributed accordingly. However, if the plan receives half or fewer of the votes, then it is rejected and V loses eligibility. Should that happen, then W as the next most senior member of the club would come up with a new plan, and the above procedure would be repeated until a plan was accepted and the money distributed.

All members of the Logicians' Club are perfect logicians who are able to reason out all of the consequences of any plan. Moreover, the only thing they care about is maximizing the amount of money they personally receive; they do not care whether a distribution is fair, nor do they get emotional about it. They don't resent another member who receives a greater amount of money than they do, so long as they get the maximum amount they can in the situation. If the amount of money they would get from accepting the plan is no more than they would receive from rejecting it, then they will reject it.

How much money would Z receive under V's plan, and was that plan accepted by the club members?

* This puzzle is a sequel to the following one: A Surprise Puzzle Prize at the Logicians' Club, 11/5/2020. For earlier meetings of the club, see:

March 2nd, 2021 (Permalink)

How to Check Quotes, Part 5: Reliable Sources

As the final installment of this subseries on quote-checking*, here are some reliable sources and advice to help you check quotes:

* For earlier entries in the "How to Check Quotes" subseries, see:

  1. Four Types of Misleading Quote, 11/27/2020
  2. News Sources Vs. Familiar Quotations, 12/4/2020
  3. Rules of Thumb, 1/2/2021
  4. A Case Study, 2/4/2021

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