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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.


"Did you steal the money?"


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?

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

Notes & Quotes
January 15th, 2023 (Permalink)

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


  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.

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.

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?

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

Weird Science Fantasy
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.


  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:

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.

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.


  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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December 31st, 2022 (Permalink)

When Prophecy Fails, 2022 Edition

It's that time of year again: time to reflect back on what happened in the last 365 days, and count ourselves lucky that Nostradamus was wrong once again1. As bad as the year was, it could have been worse―a lot worse. Here is what happened this year according to Nostradamus, or more accurately, "Nostradamus", that is, someone passing off his or her predictions as those of the famed "seer". Let's start with some of the more reasonable predictions:

Now, let's move on to the more colorful and risky predictions2:

As is usual for such prophecies, not only did the predicted events fail to occur, but the interesting and surprising events of the year make no appearance. Where is the Russian invasion of the Ukraine? The end of the pandemic? Elon Musk buying Twitter? The overturning of Roe v. Wade? The Red Wave that turned into a ripple? The Big Freeze of December? Donald Trump selling superhero trading cards of himself9? Well, that last one's a little implausible, so I can see why "Nostradamus" went with the robot war.

One reason why I write about these silly predictions is that the tabloids that publish them never look back at the failures of their prophets. However, in an article published just a few days ago, the British tabloid newspaper Mirror claims that three prophecies of Nostradamus came true this year10:

  1. Inflation: First of all, why wasn't this alleged prediction mentioned last year, instead of after it was fulfilled? It's pretty easy to predict something if you wait until after it has already happened. The "prediction" was based on the following:
    No abbots, monks, no novices to learn;
    Honey shall cost far more than candle-wax
    So high the price of wheat, that man is stirred
    His fellow man to eat in his despair.

    This is not a single quatrain but halves of two put together. The first two lines are from I.xliv and the remainder from II.lxxv. Neither quatrain has a date attached to it, so it's an open-ended, unfalsifiable prediction11 which can be expected to come true many times. There's no reason to think it predicts this year's inflation as opposed to any other period of high prices in the last half a millennium. In fact, as even the tabloid writer remarks: "…[T]he prediction of cannibalism due to extortionate living costs is one that is yet to come true." Well, there's always next year12.

  2. Global Warming: The author of this article claims that droughts and heat waves this year were due to global warming, and that Nostradamus predicted them. Putting aside the notion that specific weather events can be attributed to climate change, the allegedly correct prediction is based on the quatrain II.iii:
    Like the sun the head shall sear the shining sea:
    The Black Sea’s living fish shall all but boil.
    When Rhodes and Genoa half-starved shall be
    The local folk to cut them up shall toil.

    This is a creative translation of the same quatrain that supposedly predicts either a comet or a nuclear bomb exploding over the Mediterranean Sea13. The word that is here translated as "Black Sea" is "Negroponte", which is a name for the Greek island of Euboea14, which is not in the Black Sea. I suppose that the translator saw "Negro-", which does mean "black", and jumped to the conclusion that "Negroponte" referred to the Black Sea. Be that as it may, if global warming ever gets so bad that it half-boils fish in the sea, we're in big trouble.

  3. The Death of the Queen: 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 book15.

That's all for this year. For next year, prepare for more droughts, floods, riots, a new new Pope, and the promised cannibalism. After this year, it sounds positively restful.


  1. Previous weblog entries on Nostradamus:
    1. Check it Out, 9/22/2003
    2. Book Review: Comet of Nostradamus, 8/6/2004
    3. 2020 Hindsight, 3/10/2021
    4. 2020 Hindsight, Part 2, 4/2/2021
    5. 2020 Hindsight, Part 3, 5/2/2021
    6. When Prophecy Fails: 2021 Edition, 12/31/2021
  2. "Chilling Nostradamus Predictions 2022", Wise Horoscope, archived: 10/19/2021. This is from the Internet Archive as the original page is no longer available.
  3. Here are the scares:
  4. Patrick Knox, "Bad New Year: Nostradamus’ seven chilling 2022 predictions: From death of Kim Jong-un to war in Europe and collapse of EU", The Sun, 12/27/2021.
  5. Edgar Leoni, Nostradamus and His Prophecies (1982).
  6. See Rule 10 in: How to be a prophet for fun and profit, 6/26/2022.
  7. See: Did Nostradamus predict the Russian invasion of Ukraine?, 3/6/2022.
  8. "Nostradamus predictions 2023: World War III, Mars landing, celestial fire and much more", Times Now, 9/16/2022.
  9. Alex Kasprak, "Is Trump Selling Digital Trading Cards Featuring Himself in Superhero Garb?", Snopes, 12/15/2022.
  10. Charlotte Hawes, "Nostradamus' prophecies that came true this year―from 2022 inflation to Queen's death", Mirror, 12/27/2022.
  11. See Rule 1 in: How to be a prophet for fun and profit, 6/26/2022.
  12. Charlotte Hawes, "Nostradamus' chilling predictions for 2023―from cannibals to a disaster on Mars", Mirror, 12/27/2022.
  13. See: Through the Looking Glass, Darkly, 2/7/2009
  14. Jeff Wallenfeldt, et al., "Euboea", Encyclopaedia Britannica, accessed: 12/31/2022.
  15. Kieren Williams, "Nostradamus tops charts with book of prophecies after predicting Queen's death", Mirror, 9/16/2022.

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