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Image: Wikimedia Commons

In 1964, sociolinguist William Labov ran a revealing experiment in three New York department stores, Saks Fifth Avenue, Macy’s, and S. Klein. Of the three, Saks generally commanded the highest prestige and S. Klein the lowest. Labov had found that one marker of social stratification in the city was the pronunciation of the letter R, and he wanted to see whether this was reflected in the speech of the salespeople at the various stores.

He did this by approaching a salesperson in each store and asking directions to a department on the fourth floor. When the salesperson told him “Fourth floor,” he leaned forward and said, “Excuse me?” This forced the person to say the phrase “Fourth floor” again, this time rather self-consciously.

As expected, Labov found that salespeople at the upscale Saks tended to pronounce their Rs, while those at the lower-priced Klein tended to the broader New York pronunciation “fawth flaw.” But when asked to repeat the phrase, those at Macy’s and Klein’s tended to amend their pronunciation to sound more “classy.”

“How can we account for the differences between Saks and Macy’s?” Labov wrote. “I think we can say this: the shift from the influence of the New England prestige pattern [r-less] to the mid-Western prestige pattern [r-full] is felt most completely at Saks. The young people at Saks are under the influence of the r-pronouncing pattern, and the older ones are not. At Macy’s there is less sensitivity to the effect among a large number of younger speakers who are completely immersed in the New York City linguistic tradition. The stockboys, the young salesgirls, are not as yet fully aware of the prestige attached to r-pronunciation. On the other hand, the older people at Macy’s tend to adopt this pronunciation: very few of them rely upon the older pattern of prestige pronunciation which supports the r-less tendency of older Saks sales people.”

In separate interviews Labov found that two thirds of New Yorkers felt that outsiders disliked the city accent. “They think we’re all murderers,” one man told him. A woman said, “To be recognized as a New Yorker — that would be a terrible slap in the face.”

(William Labov, The Social Stratification of English in New York City, 2006.)

| Language · Society

Triples

A brainteaser from the Soviet science magazine Kvant, via Quantum, January/February 1991:

Bobby found the sum of three consecutive integers, then of the next three consecutive integers, then multiplied these two sums together. Could the product have been 111,111,111?

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| Puzzles

Tale Spinner

William Wallace Cook (1867-1933) claimed to have worn out 25 typewriters in as many years turning out hundreds of nickel and dime novels, all of them written in the same format, 40,000 words divided into 16 chapters of five single-spaced pages each. At the end of his career he published his system for generating plots, billed as “Plotto, an invention which reduces literature to an exact science.”

The “invention” is really a list of story ideas, all molded to Cook’s basic notion of a plot: “Purpose, opposed by Obstacle, yields Conflict.” The protagonist wants to find happiness in love and courtship, married life, or enterprise; he encounters a conflict and must reach a resolution. What makes the book fun is the absurd specificity of some of the ideas. Here’s an example:

1367
(b) (1083)(1287)
A has invented a life preserver for the use of shipwrecked persons*
A, in order to prove the value of the life preserver he has invented, dons the rubber suit, inflates it and secretly, by night, drops overboard from a steamer on the high seas.** (1414b) (1419b)

The numbers refer to elements that might be varied, to related plots, and to character types that might figure in the story. Varying the combinations might produce several million different stories. This is certainly formulaic, but, Cook said, “There are any number of highbrow authors who will ridicule this invention in public and use it in private.” (In fact both Alfred Hitchcock and Erle Stanley Gardner admitted in interviews that they’d read the book, which went through multiple editions.)

The numbered master list gives 1,462 plots, all linked with character symbols and apparently all thought up by the author. The full text is on the Internet Archive.

| Literature

More Magic

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Albrecht Dürer’s 1514 engraving Melencolia I includes this famous magic square: The magic sum of 34 can be reached by adding the numbers in any row, column, diagonal, or quadrant; the four center squares; the four corner squares; the four numbers clockwise from the corners; or the four counterclockwise.

In Power Play (1997), University of Toronto mathematician Ed Barbeau points out that there’s even more magic when we consider squares and cubes. Take the numbers in the first two and the last two rows:

16 + 3 + 2 + 13 + 5 + 10 + 11 + 8 = 9 + 6 + 7 + 12 + 4 + 15 + 14 + 1

162 + 32 + 22 + 132 + 52 + 102 + 112 + 82 = 92 + 62 + 72 + 122 + 42 + 152 + 142 + 12

Or alternate columns:

16 + 5 + 9 + 4 + 2 + 11 + 7 + 14 = 3 + 10 + 6 + 15 + 13 + 8 + 12 + 1

162 + 52 + 92 + 42 + 22 + 112 + 72 + 142 = 32 + 102 + 62 + 152 + 132 + 82 + 122 + 12

Most amazingly, if you compare the numbers on and off the diagonals, this works with both squares and cubes:

16 + 10 + 7 + 1 + 13 + 11 + 6 + 4 = 2 + 3 + 5 + 8 + 9 + 12 + 14 + 15

162 + 102 + 72 + 12 + 132 + 112 + 62 + 42 = 22 + 32 + 52 + 82 + 92 + 122 + 142 + 152

163 + 103 + 73 + 13 + 133 + 113 + 63 + 43 = 23 + 33 + 53 + 83 + 93 + 123 + 143 + 153

| Art · Science & Math

Unknowns

In his 2014 book Describing Gods, Graham Oppy presents the “divine liar” paradox, by SUNY philosopher Patrick Grim:

1. X believes that (1) is not true.

If we suppose that (1) is true, then this tells us that X believes that (1) is not true. But if an omniscient being believes that (1) is not true, then it follows that (1) is not true. So the assumption that (1) is true leads to a contradiction.

Suppose instead that (1) is not true. That is, suppose that it’s not the case that X believes that (1) is not true. If an omniscient being fails to believe that (1) is not true, then it’s not true that (1) is not true. So this alternative also leads to a contradiction.

But, on the assumption that there is an omniscient being X, either it’s the case that (1) is true or it’s the case that (1) is not true.

“So, on pain of contradiction,” Oppy explains, “we seem driven to the conclusion that there is no omniscient being X.”

(Also: Patrick Grim, “Some Neglected Problems of Omniscience,” American Philosophical Quarterly 20:3 [July 1983], 265-276.)

| Religion · Science & Math

Say It With Flowers

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The lost art of floriography assigned meanings to flowers so that lovers could exchange messages with “talking bouquets.” In his 1839 Language of Flowers, English journalist Frederic Shoberl rendered an entire verse by French poet Évariste de Parny as the combination of 16 flowers:

Aimer est un destin charmant,
C’est un bonheur qui nous enivre,
Et qui produit l’enchantement.
Avoir aimé, c’est ne plus vivre,
Hélas! c’est avoir acheté
Cette accablante vérité,
Que les serments sont un mensonge,
Que l’amour trompe tôt ou tard,
Que l’innocence n’est qu’un art,
Et que le bonheur n’est qu’un songe.

“It may be thus rendered: ‘To love is a pleasure, a happiness, which intoxicates; to love no longer, is to live no longer; it is to have bought this sad truth, that innocence is falsehood, that love is an art, and that happiness is a dream.'”

| Language · Poems

Pillow Verse

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English textile designer William Morris always said he wanted to dream a poem. When he finally did and was asked whether he could remember it, he said, “Only the first line, and it went like this: The moonlight slept on a treacle sea.”

Archbishop Edward Benson told Edmund Gosse that he dreamed he had been appointed poet laureate and found himself reciting this couplet to the queen:

Your latest atmosphere device
Is all composed of dust and lice.

And Sir John Squire confessed that when he dreamed the following lines they seemed impressive until he woke up:

There was a boy grew twenty inch, yes,
Twenty inch a year,
It might have made his mother flinch, but
She was quite a dear;
Yes, she was excellent,
And she was well content
To watch her offspring forge ahead in his
Peculiar sphere.

(From Stephen Brook, ed., The Oxford Book of Dreams, 1983. See Night Work.)

| Poems

Line Work

bilinski problem

Robert Bilinski proposed this problem in the April 2006 issue of Crux Mathematicorum. On square ABCD, two equilateral triangles are constructed, ABE internally and BCF externally, as shown. Prove that D, E, and F are collinear.

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| Puzzles

Unquote

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“It was the irony. It was the same irony that caused me to think, pause, and just inwardly chuckle, just momentarily, that, God, here are two guys further away from home … than two guys had ever been, but there are more people watching us than anybody else has ever watched two people before in history.” — Buzz Aldrin

| Quotations