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March 8th, 2026 (Permalink)

How to Lie With Notes 6: The Phantom Reference Menace

In previous entries¹, we've looked at how scholarly works―or non-scholarly works trying to pass as scholarly―can have too few notes or too many. Now, it's time to turn to the ways in which individual notes can mislead.

We tend to rely on the notes of a scholarly work to support its claims, but they don't always do so. Few of us check notes, and even those of us who sometimes do so don't check them all. Many books that include notes often have too many to check, so misleading notes may go unrecognized, which just encourages those who resort to them.

A phantom reference is not a ghost note, which is a non-existent note, but an existing note that cites a non-existent work. While there probably were cases of phantom references in the mountain of pre-21st century literature, I expect that citations to non-existent works were uncommon until recently. A previous entry discussed a phantom reference from this century―in fact, a quite recent one―but one that appears to have resulted from a typographical error in the citation².

In the current century, phantom references are becoming a more serious problem, especially with the rising use of so-called artificial intelligence ("AI"). "AI" programs have a tendency to cook up references to non-existent articles and books³, which is called "hallucinating", and some humans use such hallucinations without bothering to check them. Why "AI" does this is an interesting question, but one that is beyond the concern of this entry. However, we don't need to know "why", we just need to know "that" it does so, and take steps to avoid falling into the trap of accepting such hallucinated references.

Ultimately, the responsibility is on the human author if such fake citations make their way into a published work. If you use "AI" to draft an article or book for you, or just the references for one, it's up to you to check that those references are for real⁴. One reason that the phantom reference has become such a growing menace to 21st-century scholarship is that it can always be blamed on the "AI". In the past, a note to a fake work would have likely been a career killer for a scholar. Using manufactured citations is as much scholarly malpractice as plagiarism, and should be punished as severely.

Another basis for the rise in phantom references is the slighly less egregious practice of copying references from other works⁵. Once a non-existent source is cited in the notes of one author's work, other authors may beef up their references by simply copying those citations without checking them for authenticity. If an "AI" generated hallucination is hiding in that work's notes, it is likely to spread through other works like a virus. In the past, this may have been a relatively harmless practice since phantom notes were uncommon, but it always violated the principle that references should be to works that are used as sources: obviously, you can't have used a non-existent work as a source. Moreover, copying sources from related works is a pseudo-scholarly practice that makes it look like the author has done more research than the reality. It's lazy, as well.

Finally, at the risk of repeating myself, it's more important than ever for readers to randomly check at least a few notes in current research papers and scholarly works before relying on them. The phantom reference problem is likely to get worse as more researchers use "AI" to help them quickly and easily produce publishable articles.

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Notes: I've intentionally included one phantom reference in the following notes: see if you can find it.

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
   5. Death by Footnote, 2/9/2026
2. ↑ See: Striking a False Note, 7/16/2025. The current entry is partly based on this previous one; in fact, it was writing this earlier entry that got me thinking about the various types of misleading notes, and thus led to this series.
3. ↑ Nayeem Islam, "The Fabrication Problem: How AI Models Generate Fake Citations, URLs, and References", Medium, 6/12/2025.
4. ↑ Cf. J. Van der Geer, et al., "The art of writing a scientific article", The Journal of Science Communication (2000) 163 (2), pp. 51-59.
5. ↑ See: Victoria Stern, "The 'phantom reference:' How a made-up article got almost 400 citations", Retraction Watch, 11/14/2017.

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March 5th, 2026 (Corrected: 3/6/2026) (Permalink)

An Unmitigated Mistake

There are two problems with the following headline:

Marine reserves help mitigate against climate change, say scientists¹

When I first saw it, I wondered what the Marine Corps Reserve could possibly do about climate change. Then, I read the article beneath the headline and discovered that its first two words referred to ocean sanctuaries for sea life, not amphibious soldiers.

So, the first problem with the headline is that "marine reserves", especially with a capital "M", is ambiguous. Later in the article, we learn that such a reserve is referred to by the bureaucratic phrase "Marine Protected Area", or "MPA" for short. Thus, the ambiguity in the headline could have been avoided by rewording it: "Marine Protected Areas help mitigate against climate change, say scientists".

Can you see the second problem? "To mitigate" is a transitive verb meaning to lessen the severity of something―usually a problem or punishment². It's most commonly found in legal contexts in such phrases as "mitigating circumstances", which should lessen the punishment for an offense. The negative form "unmitigated" occurs in such hackneyed phrases as "unmitigated disaster", meaning a disaster without mitigating circumstances. Since "mitigate" is a transitive verb, there's no need for a preposition such as "against" to connect it to its object. If the article's writer really meant "mitigate", the headline should have left out "against".

However, it's likely that the writer was confusing "mitigate" with the similar-looking "militate", a rare word most often found in the phrase "militate against". "To militate" is an intransitive verb meaning to act vigorously in a positive or negative way³, and it takes a preposition to indicate whether the act is for or against something. So, the headline could have been worded: "Marine reserves help militate against climate change, say scientists". The erroneous "against" appears to have been introduced in the press release for the study paper, whose title uses "mitigate" correctly: "Marine reserves can mitigate and promote adaptation to climate change"⁴.

The phrase "mitigate against" seems to be a common error since most of my reference books warn against it⁵. One exception is Lite English by Rudolf Flesch⁶, who calls it "a very interesting case", and I agree. Flesch's book is a sort of reversal of the reference books on common errors in English that I cited in the preceding note in that he defends some uses that those books condemn. It's a glossary of words and phrases that he says are "OK to use no matter what" those he refers to as "purists" say, and he claims that science is on his side⁷―how "science" could possibly take sides in this dispute he fails to explain.

After explaining what "mitigate" and "militate" mean, here's what he has to say about the phrase "mitigate against":

The trouble is that the American people constantly mix up the two words. They say and write mitigate against when they mean militate against and they simply don't use the word militate at all.⁸

After an example of the use of the phrase "mitigate against" from the New York Times Magazine, he continues:

Twenty years ago the mistake would have been caught by the copyreader and if not, by the printer's proofreader. No longer. The Times is now riddled with misprints and mistakes of all kinds. I looked up this common mixup or idiom in all the dictionaries. Not a single one of them mentions this extremely common usage. … On the other hand, this "common mistake" is mentioned in virtually every book on English usage.

Despite referring to the phrase as a "mixup" and a "mistake", Flesch finally surrenders:

I'm afraid it's a lost battle. We might as well accept the fact that mitigate against is now an American idiom.

I think the main reason that "mitigate" and "militate" continue to be confused is that both words are unfamiliar and people don't know what they mean. Anyone who understands what "mitigate" means would never say "mitigate against", which is ungrammatical: would anyone ever write "lessen against"?

Here's a fast and filthy tip for remembering the difference between "militate" and "mitigate": "militate" is cognate with "military" and "militant", all of which descend from the Latin verb "militare", meaning to serve as a soldier⁹. So, to militate is to fight for or against something like a soldier. For "mitigate", just remember that to use it in the phrase "mitigate against" would be an unmitigated error.

"Mitigate against" is an "interesting case" for "non-purists" such as Flesch: according to "purist" Bill Bryson, "[m]itigate against often appears and is always wrong"¹⁰. How is it possible, according to Flesch, for something to be both common and an error? How common does an error in language use have to be before it no longer counts as an error? Does it have to be the majority of its uses? If so, we need research such as surveys or searches of language corpora^* into the commonness of uses such as "mitigate against" before we can even know whether it's an error.

Over forty years after Flesch raised the white flag, "mitigate against" is still widely recognized as a grammatical error, and all but one of the books I cited above was published after Flesch's¹¹. So, the "purists" are still militating against the barbarian hordes.

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Notes:

1. ↑ "Marine reserves help mitigate against climate change, say scientists", University of York, 6/5/2017. I found this example in: Ross & Kathryn Petras, That Doesn't Mean What You Think it Means: The 150 Most Commonly Misused Words and Their Tangled Histories (2018), under: "Mitigate/militate".
2. ↑ "Mitigate", The Britannica Dictionary, accessed: 3/5/2026.
3. ↑ "Militate", The Britannica Dictionary, accessed: 3/5/2026.
4. ↑ Callum M. Roberts, et al., "Marine reserves can mitigate and promote adaptation to climate change", PNAS 114 (24) 6167-6175, 6/5/2017.
5. ↑ In addition to the Petras' book listed in note 1, above, they are:
   • Harry Blamires, The Cassell Guide to Common Errors in English (1997)
   • Bill Bryson, Bryson's Dictionary of Troublesome Words: A Writer's Guide to Getting it Right (2002)
   • James Cochrane, Between You and I: A Little Book of Bad English (2005)
   • Michael Dummett, Grammar & Style for Examination Candidates and Others (1993)
   • Harry Shaw, Dictionary of Problem Words and Expressions (1987)
6. ↑ Rudolf Flesch, Lite English: Popular Words that are OK to Use (1983).
7. ↑ Ibid., "Preface".
8. ↑ Ibid., under "mitigate against". Subsequent quotes of Flesch are from this entry.
9. ↑ William & Mary Morris, Dictionary of Word and Phrase Origins (1962).
10. ↑ Under "militate, mitigate": see full citation under note 5, above.
11. ↑ See also: Merrill Perlman, "Mitigate and militate", Columbia Journalism Review, 5/1/2017.

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*↑ I made the mistake of relying on my imperfect knowledge of Latin and originally wrote "corpi" here instead of the correct plural of "corpus", which is "corpora". See: "Corpus", The Britannica Dictionary, accessed: 3/6/2026.

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March 3rd, 2026 (Permalink)

The Mystery of the Top Five

Every month, Victor Timm's Mystery Magazine conducts a survey of its readers to determine their most popular mystery writers. The list is ordered from one to five from favorite (1) to least liked (5). The same five writers, including Brand, made the list this month as last month, but each was in a different position. For instance, Christie rose in this month's rankings from last month. If you add together the digits of the positions from last month and this month, then the sum for Armstrong is seven, Christie's is eight, Doyle's is six, and Edwards' is five.

From the information above, can you determine the positions of the top five mystery writers for both months?

Hint

Solution

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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.

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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.

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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.

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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.

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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?

Solutions

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

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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.

Solution

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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.

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