Images: Wikimedia Commons

During the Falklands War in 1982, the RAF airfield closest to the action was on Ascension Island near the equator, thousands of miles away. Tasked with destroying the runway at Port Stanley, the RAF organized a complicated relay in which 11 tankers accompanied a single bomber (mauve), refueling it and each other in midair to support its journey of 3,400 nautical miles to the target. The attacking Vulcan bomber was refueled four times on the way out and once on the way back, using more than 220,000 gallons of aviation fuel altogether.

At the time this was the longest-ranged bombing raid in history — the return journey alone took 16 hours. It put one crater in the runway, which was repaired within 24 hours, but it discouraged the Argentinians from using it more heavily.

See The Jeep Problem. (Thanks, Tom.)

Blind Spot

Given the premises No fruit-picker is a sailor and All Ruritanians are fruit-pickers, it’s fairly easy to deduce that No Ruritanian is a sailor. But what logical conclusion can be drawn from these premises?

All members of the cabinet are thieves.

No composer is a member of the cabinet.

Many people decide that no conclusion can be drawn. “Almost without exception that is the answer you will get, after some serious reflection, from intelligent people,” notes Massimo Piattelli-Palmarini in Inevitable Illusions.

But there is one: Some thieves are not composers (or There are thieves who are not composers). It’s logically impossible for the premises to be true and for this conclusion not to be true, and yet most people find the conclusion difficult to see.

Why? Princeton psychologist Philip Johnson-Laird thinks it’s because of the number and complexity of “mental models” that we have to build to elaborate our reasoning about such syllogisms. Unlike the case of the Ruritanian sailors, “The case of the cabinet ministers and composers requires … three distinct, and mentally separate, arrays of obligatory couplings: cabinet ministers and thieves, composers and cabinet ministers, and thieves and composers,” Piattelli-Palmarini explains.

“The result for all of us is a prohibitive difficulty in ‘seeing’ that there are necessarily false couplings between thieves and composers.”

01/04/2018 A number of readers have pointed out the existential fallacy in Johnson-Laird’s syllogism. Piattelli-Palmarini notes, “[O]ne has to avoid the situation in which these sets are empty. Rephrasing the premises as ‘all the ministers’ and ‘all the composers’ may aptly reinforce in the subjects the assumption that there are ministers and that there are composers. As the distinguished logician George Boolos of MIT has put it, the sentence ‘All deserters will be shot’ can be true also if there are, in fact, no deserters. In these cognitive tests, one wants to avoid such limited cases. For a further and accurate account of this problem, the reader is referred to Philip Johnson-Laird’s Mental Models, Chapter 6, and to his exchange with George Boolos in the journal Cognition in 1984.” (That’s Cognition 17:2, 181-182; Johnson-Laird’s reply is in 17:2, 183-184.)


In The Pleasures of Counting, T.W. Körner asks, “How long would you expect a paper reporting a crucial experiment in physics to be and how would you expect it to be written? Here in its entirety is a paper entitled ‘Interference Fringes With Feeble Light’ written by G.I. Taylor in 1909 (to be found in his collected works).”

It’s six paragraphs long.

A Bloody Bargain

During Henry Stanley’s 1886 Emin Pasha Relief Expedition to the interior of Africa, naturalist James S. Jameson allegedly paid a group of cannibals to kill and eat a young girl so that he sketch the act. According to his interpreter, Assad Farran, Jameson afterward took the sketches to his tent, finished them in watercolors, and then “showed these and many other sketches to all the chiefs.”

Jameson protested the accusation, but his own diary describes the killing:

I told him that people at home generally believed that these [accounts of cannibalism] were only ‘travellers’ tales,’ as they are called in our country, or, in other words, lies. He then said something to an Arab called Ali, seated next him, who turned round to me and said, ‘Give me a bit of cloth, and see.’ I sent my boy for six handkerchiefs, thinking it was all a joke, and that they were not in earnest, but presently a man appeared, leading a young girl of about ten years old by the hand, and I then witnessed the most horribly sickening sight I am ever likely to see in my life. He plunged a knife quickly into her breast twice, and she fell on her face, turning over on her side. Three men then ran forward and began to cut up the body of the girl; finally her head was cut off, and not a particle remained, each man taking his piece away down to the river to wash it. The most extraordinary thing was that the girl never uttered a sound, nor struggled, until she fell.

In his 1889 account of the expedition, Heroes of the Dark Continent, James William Buel presents the images above as copies of Jameson’s sketches.

Another of Stanley’s men claimed that Jameson had spoken freely of the incident at the time, and only realized “the seriousness” of his actions much later. “Life is very cheap in Central Africa,” he wrote. “Mr. Jameson forgot how differently this terrible thing would be regarded at home.”

Great and Small

michelangelo list

When the Seattle Art Museum presented an exhibition of Michelangelo’s early drawings in 2009, it included three menus that the sculptor had scrawled on the back of an envelope in 1518 — grocery lists for a servant.

Oregonian reviewer Steve Duin explained, “Because the servant he was sending to market was illiterate, Michelangelo illustrated the shopping lists — a herring, tortelli, two fennel soups, four anchovies and ‘a small quarter of a rough wine’ — with rushed (and all the more exquisite for it) caricatures in pen and ink.”

Related: In the 1490 manuscript below, Leonardo da Vinci tries to list successive doublings of 2 but mistakenly calculates 213 as 8092:

“Unmistakable this is a miscalculation of Leonardo and not of some sloppy copyists, as it was found in the original (mirrored) manuscript of da Vinci himself,” notes Ghent University computer scientist Peter Dawyndt. “That it was only discovered right now, five hundred years after da Vinci’s death, is probably due to the late discovery of the manuscript, barely fifty years ago.”

(Thanks, Peter.)

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In the February 2003 issue of Word Ways, Dave Morice nominates PEPPERTREE as the “holy grail” of wordplay. PEPPERTREE is a “pyramid word” — it contains 1 T, 2 Rs, 3 Ps, and 4 Es:

peppertree - 1

But it contains two shorter pyramid words, PEPPER and PEP:

peppertree - 2


  • All the letters in PEPPERTREE can be typed on the top row of a typewriter.
  • PEPPERTREE’s vowels are drawn from the first half of the alphabet, its consonants from the second. The vowels occupy odd-numbered positions in the alphabet, the consonants even.
  • Written in capitals, all the letters in PEPPERTREE contain vertical lines. Half contain curves and half don’t; half contain closed spaces and half don’t.
  • In lowercase each letter has one line and one curve.
  • E appears 4 times and T once; if A = 1, B = 2, etc., then E + E + E + E = T.
  • The PEPPERTREE is an EVERGREEN, and each of these words contains the letter E, its only vowel, four times.

Altogether, Morice lists 26 ways in which PEPPERTREE is notable for its letters, pronunciation, and meaning, making it “an evergreen of the most alphabetic kind.” The whole list is here.

(Dave Morice, “Peppertree: The Logological Holy Grail,” Word Ways 36:1 [February 2003], 3-5.)


The Austrian painter Johannes Gumpp is remembered for only two works.

Both are self-portraits in which his back is turned to the viewer.