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February 9th, 2026 (Permalink)

How to Lie With Notes 5: Death by Footnote1

The conspiracists work hard to give their written evidence the veneer of scholarship. The approach has been described as death by footnote2.

I take the title of this entry from the above passage from David Aaronovitch's book on conspiracy theories. Ironically and frustratingly, the second sentence is not noted, that is, there is no citation to a source, so there's no way to tell who described this "approach" as "death by footnote", which I would dearly like to know. Moreover, it's not as if the book has no notes―it has endnotes―so this is a ghost note of the second type, that is, a missing one3. Of course, Aaronovitch probably just couldn't remember where he heard or read the phrase, but he could have at least added a note explaining that.

In a magazine article published shortly before the book, and perhaps drawing on it, Aaronovitch wrote:

[Conspiracy theories] share certain features that make them work. These include…the use of apparently scholarly ways of laying out arguments (or "death by footnote")…. These characteristics help them to convince intelligent people of deeply unintelligent things.4

It's hard to tell from these two brief mentions what exactly Aaronovitch or his unnamed source meant by "death by footnote", though it's clear that it has something to do with conspiracy theorists (CTists) making a pretense to scholarship. There are many ways that pseudo-scholarship apes actual scholarship but, in this entry, I'll use the phrase "death by footnote" to refer to one particular practice, namely, loading up on notes. So, "death by footnote" is the opposite of ghost notes, that is, instead of too few notes there are too many.

Though Aaronovitch's topic in both the article and book is CTists, they're not the only guilty parties. For instance, the philosopher Roger Scruton describes a pseudo-philosophical book as follows: "Abundant footnotes, referring to out-of-the-way works in political theory, anthropology, biology, musicology, particle physics, etc., serve further to intimidate the reader, and the undergraduate, faced with the resulting text at the top of his reading list, is given no alternative but to parrot its terms….5"

While ghost notes and death by footnote seem mutually exclusive, they're not completely so. It's true that the first type of ghost notes―non-existent ones―are incompatible with excessive notes, since a work with no notes at all certainly can't have too many. However, the other type―missing notes, that is, notes that should be there but aren't―is compatible with an excess of notes. In fact, one way of concealing that a note is missing is to include so many other notes that it won't be noticed.

A good rule of thumb for scholarly works with notes is that the word count in the notes should never exceed that of the work itself. While such note bloat is not necessarily death by footnote, it's bad practice. If the notes are longer than the body of the work, then some of the material in the notes should either be incorporated into the text or made into a separate work. So, if you look at a page―assuming that you're looking at an old-fashioned paper book or journal article with footnotes―and more than half the page is taken up by notes, that's too many. However, death by footnote is not just a matter of having too many notes, but of using notes as a defense mechanism against criticism.

Notes:

  1. ↑ For previous entries in this series, see:
    1. Introduction, 10/23/2025
    2. Latin Abbreviations, 11/15/2025
    3. Anatomy of a Citation, 12/6/2025
    4. Ghost Notes, 1/3/2026
  2. ↑ David Aaronovitch, Voodoo Histories: The Role of the Conspiracy Theory in Shaping Modern History (2010), p. 13.
  3. ↑ See the previous entry in this series, that is, number IV, above.
  4. ↑ David Aaronovitch, "A Conspiracy-Theory Theory", The Wall Street Journal, 12/19/2009.
  5. ↑ Roger Scruton, Fools, Frauds and Firebrands: Thinkers of the New Left (2015), p. 190. The book that Scruton is describing is: Gilles Deleuze & Félix Guattari, A Thousand Plateaus: Capitalism and Schizophrenia (3rd edition, 1996). Cited by Scruton, in footnote 50, p. 189. I haven't read it and, from Scruton's description, I don't want to.
February 4th, 2026 (Permalink)

No Smoking in Pubic Places

"When I was only three, and still named Belle Miriam Silverman, I sang my first aria in pubic." Thus read the first sentence of the first printing of the first edition of an autobiographical work by the late opera singer, Beverly Sills1.

As I suspect you know, the word "pubic" refers to the part of the human body where the sexual organs are located2. "Pubic" is always an adjective, so the example sentence is ungrammatical, since the preposition "in" should be followed by a noun.

"Public" is both a noun and an adjective3. As a noun, it can refer to people as a whole, or the common people, as in the phrase "the public", or to those spaces that are open to the public, that is, places that are "in public". As an adjective, it modifies nouns that refer to public spaces, including physical places such as public parks as well as abstract spaces, such as public opinion.

Obviously, Sills meant that she sang in public. The typographical error was corrected in subsequent printings.

"In public" is not the only common phrase that may be transmogrified by a missing "l". A recent newspaper article displayed a photograph with the following caption: "Legislation to ban marijuana smoking and vaping in pubic places was approved by the Senate Regulated Industries Committee on Tuesday.4" I, too, approve of that legislation, though it reminds me of an old joke: "Do you smoke after sex?" "I don't know, I never looked."5

In addition to "pubic places", another frequent offender is "pubic library", which sounds as if it's a collection of pornography. A search of Google Books turns up a large number of occurrences of this phrase, surprisingly, from publications for professional librarians. For instance, an issue of The Library World includes a reference to the "Kettering Pubic Library"6. I suspect that library journals are more prone to this particular misspelling only because they more frequently refer to public libraries than other publications.

Most of the easily confused word pairs examined in these entries are soundalikes, but "pubic" and "public" are lookalikes. I doubt that anyone would ever mistakenly say "pubic" when "public" is meant, or vice versa, but when proofreading it may be easy to miss the difference. At a passing glance, the two words look the same, perhaps because the "l" in "public" is next to the "b" and each have a long upward stroke.

I've seen "pubic" in place of "public" on more than one occasion prior to stumbling over the above example, but I don't recall ever seeing "public" in place of "pubic", so this appears to be a one-way error. Of course, it's possible that this asymmetry is due to the fact that "public" is a more common word than "pubic". Also, some omissions of the "l" are pubescent puns, and others may be prurient pranks. Perhaps Sills was the victim of a proofreader with an adolescent sense of humor.

None of my reference books lists "pubic" as a common misspelling of "public", which could be because it's uncommon or perhaps just that the authors of such works are squeamish or prudish.

Notes:

  1. ↑ Beverly Sills, Bubbles: A Self-Portrait (1976), p. 12; quoted by Rudolf Flesch in Lite English: Popular Words That Are OK to Use (1983), p. 72.
  2. ↑ "Pubic", The Britannica Dictionary, accessed: 2/1/2026.
  3. ↑ "Public", The Britannica Dictionary, accessed: 2/1/2026.
  4. ↑ Christine Sexton, "Smoking marijuana in public places is banned under a bill moving in the Florida Senate", The Apopka Voice, 1/20/2026.
  5. ↑ I mentioned this joke once previously; see: "Do you smoke after sex?", 2/14/2021.
  6. ↑ The Library World, Vol. VII, No. 73 (July, 1904), p. 10.
Puzzle
February 1st, 2026 (Permalink)

Spyhunters Vs. Spy

A spy has infiltrated the Agency for Counter-Terrorism (ACT). According to the agency's definition, a spy is someone who knows everyone in the agency by name but is known by name to no one else. An internal investigation by the agency's spyhunters has narrowed the suspects down to eight agents whom I will call only A through H to protect the seven innocent suspects.

The spyhunters interrogated the eight suspects in pairs, asking only whether they knew the other agent's name. While under interrogation, the agents were monitored by the most advanced deception-detection equipment available―equipment that is still classified as top secret―according to which each suspect interrogated told the truth.

Here are the answers elicited from the pairs of suspects when asked whether they knew each other's names:

A: "Yes"; B: "Yes".

C: "Yes"; D: "No".

E: "No"; F: "Yes".

G: "No"; H: "No".

Finally, after a short conference, the investigators called back into the interview room two of the agents, C and F, for further questioning. Asked if they knew each other's names, each replied:

C: "No"; F: "Yes".

Which suspect is the spy?

Extra Credit: Could there be more than one spy in the ACT? If not, why not?

* ↑ See: Anany & Maria Levitin, Algorithmic Puzzles (2011), pp. 8-9.

January 28th, 2026 (Permalink)

A Weighty Problem

There seems to be a theme to this month's entries, namely, numeracy or the lack thereof; this was not intentional but simply the result of what I've happened to notice recently. I suppose it's because I've started reading John Allen Paulos' latest book, Who's Counting?1, a collection of his columns of the same title for ABC News from 2000-2010, along with updates and some more recent writings2.

Paulos is, of course, responsible for highlighting the problem of mathematical illiteracy, as well as popularizing the word "innumeracy" for it through his book of that title3. Here's a problem from the recent book taken from a test that Paulos proposes be given to presidential candidates to test their numeracy:

A model car, an exact replica of a real one in scale, weight, material, and so on, is 6 inches (1/2 foot) long, and the real car is 15 feet long, 30 times as long. …[I]f the model car weighs 4 pounds, what does the real car weigh?4

As Paulos mentions, this is a problem in scaling: "Problems and surprises arise as we move from the small to the large since social phenomena generally do not scale upward in a regular or proportional manner.5" Even if you're not planning to run for president, I suggest giving the problem a try. When you've finished, click on the button below to see the solution.

Notes:

  1. ↑ John Allen Paulos, Who's Counting?: Uniting Numbers and Narratives with Stories from Pop Culture, Puzzles, Politics, and More (2022). I mentioned this as a "New Book" when it came out; see: Who's Counting? John Allen Paulos!, 9/15/2022.
  2. ↑ Ibid., p. xii.
  3. ↑ John Allen Paulos, Innumeracy: Mathematical Illiteracy and its Consequences (1988).
  4. ↑ Ibid., p. 8. There was a "Who's Counting?" column with a similar but different test than the one in the book; here's the first page: "A Proposed Math Quiz for Presidential Candidates", ABC News, 12/2/2003; I can't find the remaining pages.
  5. ↑ Ibid., p. 7.
  6. ↑ Ibid., p. 9. If you got the wrong answer or didn't know how to go about doing the math, here's a short and reasonably easy to understand tutorial on scaling: "Scaling Rules!", The University of Utah, accessed: 1/27/2026.
  7. ↑ That's United States tons, also known as "short" tons, which are 2K pounds. "Ton" is ambiguous; see: "Ton", Britannica, accessed: 1/28/2026.
  8. ↑ "Heaviest car", Guinness World Records, accessed: 1/25/2026.
  9. ↑ Alexus Bazen, et al., "How Much Does the Average Car Weigh? 2026", Consumer Affairs, 2/1/2024.
January 20th, 2026 (Permalink)

The Strange Case of the Nine-Piece Pizza

I recently purchased a "take and bake" pizza, that is, one that is made in the store and then sold to a customer to take home and bake. As is usual, the packaging on the pizza included a standardized nutrition information label, according to which a serving size was "about" one-ninth of the total pizza―I mean the label is usual; the serving size was unusual.

Nine, in this context, is an "odd" number in every sense of the word. The natural way to divide a pizza, assuming that it is circular in shape, is to cut along the pie's diameter. The effect of such a cut is to divide the circle into two equal pieces, and subsequent cuts along a diameter will further divide each of two pieces into two smaller, not necessarily equal, pieces. Thus, a series of such cuts will produce two, four, six, eight, ten, and so on, pieces. What is the pattern here?

This is not a hard riddle: cutting a circle along a diameter a number of times always produces an even number of pieces. Nine is not an even number, so cutting a pizza in the usual way would never produce nine pieces. You could cut the pizza into eight pieces then cut one of those pieces in half, but the resulting slices would be quite unequal. Alternatively, it would be possible to cut the pizza into nine equal pieces by cutting along the pie's radii, perhaps using a protractor, but who's going to do that?

Why does the nutrition label use an odd number of slices for the serving size? As a result of that choice, all of the nutrition information―such as calories, amount of sodium, total carbohydrates, etc.―is based on a piece of a size that no one is likely to eat. Of course, it would be possible to multiply each of the data points given on the label by nine and then divide by the actual number of pieces into which the pizza is cut, but who would do such a thing? Probably the same person who would use a protractor to divide a pizza. For anyone else, the information on the label is practically useless.

Putting aside the odd number of servings, which is perhaps specific to this particular brand or size of pizza, there's a more general problem with the nutrition label: it says that each serving of pizza has 330 calories, 35 milligrams of cholesterol, 830 milligrams of sodium, and so on. Yet, even if you carefully carved the pie into nine equal pieces, some pieces will have more pepperoni slices than others, some less cheese, and so on. As a result, the information on the label is at best approximate, but the only indication of this fact is the word "about" before the serving size.

Given a serving of "about" one-ninth of the pizza, with more or less pepperoni, cheese, and tomato sauce than other servings, the calories of each piece would be about 300, its cholesterol content about 30 milligrams, its amount of sodium about 800 milligrams, and so forth. Combine the label's over-precision* with the odd serving size and the result is misleading nutrition information. Is misleading information better or worse than no information at all?

* ↑ See: Overprecision, 8/27/2022.

January 15th, 2026 (Permalink)

Innumeracy in the The New York Times

A recent article in The New York Times (NYT) on increased interest in the use of beef tallow in cooking now includes the following correction:

A correction was made on Jan. 10, 2026: An earlier version of this article misstated how much consumers spent on beef tallow in 2025. It was $9.9 million, not $900 million.*

So, the amount of spending was misstated by two orders of magnitude, or nearly a hundred times greater. This mistake would be of little interest if it weren't so large and made by the NYT.

How did it happen? I don't know, of course, but I suspect that a decimal point was misplaced by two digits. This article appeared in the "Dining" section of the newspaper, so perhaps it wasn't subjected to as careful editing as it would have been in a more prominent and important section.

Whether the absolute amount of money spent on tallow last year was nine or nine-hundred million dollars, that number doesn't tell us much without a point of comparison. Is that a big number or a small number? $10 million doesn't sound like a lot to me for the entire country, but I don't know anything about beef tallow sales. Was this more than was spent in 2024? If so, how much more? How does it compare with what was spent on lard or on vegetable oils? Without some such comparison, it's a meaningless number.

The article doesn't ask let alone answer any of the above questions, which is worse innumeracy than misplacing a decimal point, and harder to correct.

* ↑ Kim Severson, "Beef Tallow, Long a Health Pariah, Rises to the Top of the Food Pyramid", The New York Times, 1/10/2026, updated: 1/15/2026.

Puzzle
January 5th, 2026 (Permalink)

"Never Give a Sucker an Even Break"1

Montgomery "Three-Card Monty" Banks2 was sitting on his usual stool at the bar of his favorite local spot when a stranger sat down beside him. "Howdy," Monty began, "May I offer you a sporting proposition." The bartender, who knew Monty well, rolled his eyes but the stranger didn't notice. He just looked at Monty with raised eyebrows.

"I have right here some loose coins," Monty said while patting his pocket."I expect that you too may have some loose change. I suggest we play a little game. We'll each take a handful of coins out of our pockets and drop them in separate piles on the bar at the same time. Then, we'll count the coins in your pile and those in both piles to see if they're even or odd. If they match, you win and I'll pay for your drink; if they don't match, then you pay for mine."

The stranger frowned and looked confused.

"Looky, it's like this," Monty explained, "if the number of coins in your pile is even and the sum of the numbers of coins in both piles is even, you win and I pay for your drink. But if the sum of both piles is odd, you lose and pay for my drink. Same thing if the sum of your pile is odd: if it matches the sum of both piles, you win; if it don't match, you lose. Get it?"

The stranger nodded slowly.

"Now, I don't know how many coins you got in your pocket, and you don't know how many I got. So, there's no way either of us could know the sum of both, is there? Not only that but you don't have to put all your coins on the counter; you can put out any number you want to. There's no way I could know how many. And the number of coins in your pile is odd or even, and the sum of both piles is odd or even, and the payoff is the same. That's a fair bet, ain't it?"

The stranger nodded again.

At this point, Monty and the stranger played the game as described. I won't reveal what happened until later, but here's the question: Is Monty's game a fair bet for the other player, that is, does he have a 50-50 chance of winning?

Extra Credit: If it's not a fair bet, what is the probability that the other player will win?

Notes:

  1. ↑ This saying may have been coined by Wilson Mizner. "Who's Wilson Mizner?" well you may ask. This is why it's usually attributed to W. C. Fields―who titled one of his movies with it in 1936―in accordance with the principle "famous sayings need famous mouths." See: Ralph Keyes, "Nice Guys Finish Seventh": False Phrases, Spurious Sayings, and Familiar Misquotations (1993), pp. 20f, for the principle, and the same author's The Quote Verifier: Who Said What, Where, and When (2006), pp. 214f, for the saying.
  2. ↑ If you don't know Monty, he's a sharpster who always speaks the truth and nothing but the truth, but he doesn't always tell the whole truth. Also, he never uses sleight-of-hand or gimmicked coins. Monty doesn't manipulate coins; he manipulates minds. For previous puzzles involving Monty, see:
  3. ↑ "Parity", as applied to integers, refers to whether a number is odd or even. See: E. J. Borowski & J. M. Borwein, The Harper Collins Dictionary of Mathematics (1991).
  4. ↑ Leslie Charteris, "The Percentage Player", The Saint to the Rescue (1959).

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