The Short of It

https://commons.wikimedia.org/wiki/File:Boycriedwolfbarlow.jpg

A boy, who kept watch on a flock of sheep, was heard from time to time to call out, ‘The Wolf! The Wolf!’ in mere sport. Scores of times, in this way, had he drawn the men in the fields from their work. But when they found it was a joke, they made up their minds that, should the boy call ‘Wolf’ once more, they would not stir to help him. The wolf, at last, did come. ‘The Wolf! The Wolf!’ shrieks out the boy, in great fear, but none will now heed his cries, and the wolf kills the boy, that he may feast on the sheep.

One knows not how to trust those who speak lies, though they may tell one the truth.

— From Lucy Aikin, Æsop’s Fables in Words of One Syllable, 1868

Back to Basics

When [Sir Richard Francis Burton] was in India he at one time got rather tired of the daily Mess, and living with men, and he thought he should like to learn the manners, customs, and habits of monkeys, so he collected forty monkeys of all kinds of ages, races, species, and he lived with them, and he used to call them by different offices. He had his doctor, his chaplain, his secretary, his aide-de-camp, his agent, and one tiny one, a very pretty, small, silky-looking monkey, he used to call his wife, and put pearls in her ears. His great amusement was to keep a kind of refectory for them, where they all sat down on chairs at meals, and the servants waited on them, and each had its bowl and plate, with the food and drinks proper for them. He sat at the head of the table, and the pretty little monkey sat by him in a high baby’s chair, with a little bar before it. He had a little whip on the table, with which he used to keep them in order when they had bad manners, which did sometimes occur, as they frequently used to get jealous of the little monkey, and try to claw her.

That’s from Isabel Burton’s Life of Captain Sir Richard F. Burton, 1898. In her own biography of Burton, A Rage to Live, Mary S. Lovell says that Burton learned to imitate the monkeys’ sounds and believed that they understood some of them. He compiled a list of 60 words, but it was lost an 1860 fire that destroyed nearly all his papers.

Locke’s Index

https://archive.org/details/gu_newmethodmaki00lock

Like many thinkers of his age, John Locke maintained a commonplace book, an intellectual scrapbook of ideas and quotations he’d found in his readings. In order to be useful, such a book needs an index, and Locke’s method is both concise (occupying only two pages) and flexible (accommodating new topics as they come up, without wasting pages in trying to anticipate them).

The index lists the letters of the alphabet, each accompanied by the five vowels. Then:

When I meet with any thing, that I think fit to put into my common-place-book, I first find a proper head. Suppose for example that the head be EPISTOLA. I look unto the index for the first letter and the following vowel which in this instance are E. i. If in the space marked E. i. there is any number that directs me to the page designed for words that begin with an E and whose first vowel after the initial letter is I, I must then write under the word Epistola in that page what I have to remark.

The result is a useful compromise: Each of the book’s pages is put to productive use without any need for an overarching plan, and the contents are kept accessible through a simple, expanding index that occupies only two pages. The whole project can grow in almost any direction, and when the pages are full then a new volume can be begun.

(Via the Public Domain Review.)

The Pizza Theorem

https://commons.wikimedia.org/wiki/File:Pizza_theorem_example.jpg
Images: Wikimedia Commons

If you’re sharing a pizza with another person, there’s no need to cut it into precisely equal slices. Make four cuts at equal angles through an arbitrary point and take alternate slices, and you’ll both get the same amount of pizza.

Larry Carter and Stan Wagon came up with this “proof without words”: Each piece in an odd-numbered sector corresponds to a congruent piece in an even-numbered sector, and vice versa.

Also: If a pizza has thickness a and radius z, then its volume is pi z z a.

(Larry Carter and Stan Wagon, “Proof Without Words: Fair Allocation of a Pizza,” Mathematics Magazine 67:4 [October 1994], 267-267.)

A Stand of Seats

high wycombe chair arch

High Wycombe, a town of furniture makers, historically celebrated important visitors with arches of chairs. The most famous marked the arrival of Prince Edward in 1880; three years earlier a similar arch had arrested Queen Victoria on her way from Windsor Castle to Hughenden to visit Lord Beaconsfield.

“It was made up of chairs of all kinds, and bore the words, ‘Long Live the Queen,'” read the Annual Register. “Her Majesty’s attention was specially attracted by this curious structure, and the Royal carriage was stopped that its occupants might have a better view.”

Twice-Told Tale

In 1986 the Los Angeles Times received a peculiar 167-page novel from Lawrence Levine of St. Augustine, Fla. Titled Dr. Awkward & Olson in Oslo, it began “Tacit, I hate gas (aroma of evil), masonry …” It ended “No, Sam — live foam or a sage Tahiti CAT!” And the very middle read “I deplore media, rats, gals, a tar bag and a maniac Dr. Awkward ‘Cain,’ a mad nag, a brat, a slag star. Ai! Demerol, pedicular addenda, Edgar!”

Working four hours a day for five months, Levine had composed a novel that was one long palindrome, 31,594 words.

“There were lessons in trial and error, in logic, in vocabulary, in syntactics, and a wide-ranging lexical development that I never thought possible,” Levine revealed elsewhere. “I wrote the novel because to my knowledge no other person had ever composed an equal nonesuch. I decided, as it were, to be the first.”

The Times responded, “The world needs more Levines — playful eccentrics determined to scale the heights where no one has gone before, even if getting there isn’t much of an accomplishment. Or, as the metaphysicians say, ‘No lemons, no melon.'”

Franklin’s Magickest Square

http://books.google.com/books?id=yE0YAQAAIAAJ&pg=PA293

When a friend showed him a 16 × 16 magic square devised by Michel Stifelius, Ben Franklin went home and composed the square above, “not willing to be outdone.” An admirer describes its properties:

1. The sum of the sixteen numbers in each column or row, vertical or horizontal, is 2,056. — 2. Every half column, vertical or horizontal, makes 1,028, or just one half of the same sum, 2,056. — 3. Any half vertical row added to any half horizontal, makes 2,056. — 4. Half a diagonal ascending added to half a diagonal descending, makes 2,056, taking these half diagonals from the ends of any side of the square to the middle of it, and so reckoning them either upward, or downward, or sideways. — 5. The same with all the parallels to the half diagonals, as many as can be drawn in the great square: for any two of them being directed upward and downward, from the place where they begin to that where they end, make the sum 2,056; thus, for example, from 64 up to 52, then 77 down to 65, or from 194 up to 204, and from 181 down to 191; nine of these bent rows may be made from each side. — 6. The four corner numbers in the great square added to the four central ones, make 1,028, the half of any column. — 7. If the great square be divided into four, the diagonals of the little squares united, make, each, 2,056. — 8. The same number arises from the diagonals of an eight sided square taken from any part of the great square. — 9. If a square hole, equal in breadth to four of the little squares or cells, be cut in a paper, through which any of the sixteen little cells may be seen, and the paper be laid on the great square, the sum of all the sixteen numbers seen through the hole is always equal to 2,056.

Franklin wrote, “This I sent to our friend the next morning, who, after some days, sent it back in a letter with these words: ‘I return to thee thy astonishing or most stupendous piece of the magical square, in which’ — but the compliment is too extravagant, and therefore, for his sake as well as my own, I ought not to repeat it. Nor is it necessary; for I make no question but you will readily allow this square of 16 to be the most magically magical of any magic square ever made by any magician.”

(“Clavis,” “Magic Squares,” The Mirror of Literature, Amusement, and Instruction 4:109 [Oct. 23, 1824], 293-294.) (Thanks, Walker.)

12/21/2020 UPDATE: The square appeared originally in 1767 in James Ferguson’s Tables and Tracts, Relative to Several Arts and Sciences and was reprinted a year later in the Gentleman’s Magazine. Only the second publication credits Franklin. I don’t have a date for Franklin’s purported composition, so I don’t know what to make of this. (Thanks, Tom.)

A Nursery Sonnet

In 2000, mathematician Mike Keith rearranged the letters in Shakespeare’s Sonnet 143 to tell a familiar story:

Lo, as a careful huswife runs to catch
One of her feathered creatures broke away,
Sets down her babe and makes all swift dispatch
In pursuit of the thing she would have stay,
Whilst her neglected child holds her in chase,
Cries to catch her whose busy care is bent
To follow that which flies before her face,
Not prizing her poor infant’s discontent:
So run’st thou after that which flies from thee,
Whilst I, thy babe, chase thee afar behind;
But if thou catch thy hope turn back to me,
And play the mother’s part: kiss me, be kind.
So will I pray that thou mayst have thy Will,
If thou turn back and my loud crying still.

The gal named Mary shuffles through the house —
But view her as she strokes her frisky lamb,
Whose brow is whiter than a snowy mouse,
Fleece chalky as French cliffs of epigram
Each place she’d bathe, attain or hie without
(To parish church or at the stuffy crypt),
The lamb’s instinct did follow her about
(So close around that twice she nearly tripped).
Back to her class that zany lamb would fly
And cause a hubbub (then they fetched it in);
It whacked the inkwell, overturn’d the pie,
Though this was chief and total public sin.
“Anoint this lofty one,” the brats then cried,
“For now it’s certain: school is rather fried!”

(Michael Keith, “Another Mary Sonnet,” Word Ways 33:3 [August 2000], 233.)

Old Booty’s Ghost

https://books.google.com/books?id=fKByQxeCmREC

A striking tale from the 18th century: It’s said that around 1687 a group of English mariners on the Italian coast were surprised to see “two men run by us with amazing swiftness”:

Captain Barnaby says, ‘Lord bless me, the foremost man looks like next door neighbour, old Booty;’ but said he did not know the other behind. Booty was dressed in grey clothes, and the one behind him in black; we saw them run into the burning mountain in the midst of the flames! on which we heard a terrible noise, too horrible to be described.

When they returned to Gravesend, Captain Barnaby’s wife said, “My dear, I have got some news to tell you; old Booty is dead.” Barnaby swore an oath and said, “We all saw him run into Hell!”

As the story goes, when word of this allegation reached Booty’s widow, she sued Barnaby for a thousand pounds. The punchline is that Booty’s appearance on the volcano was shown to have occurred within two minutes of his death, and when his coat was exhibited in the courtroom, 12 sailors swore that its buttons matched those of the fleeing man.

The Judge then said, ‘Lord grant I may never see the sight that you have seen; one, two, or three may be mistaken, but twenty or thirty cannot.’ So the widow lost her cause.

According to folklorist Jeremy Harte, this story appeared in print at least 19 times between the 1770s and the 1830s. It seems to have started among the dockyards of the lower Thames, where in one early version Booty was an unscrupulous contractor who had supplied the navy with adulterated beer — and his damnation was “a matter of just retribution for the sin he had committed.”

(Jeremy Harte, “Into the Burning Mountain: Legend, Literature, and Law in Booty v. Barnaby,” Folklore 125:3 [December 2014], 322-338.)

Another First

Jules Verne’s 1882 novel La Jangada tells the story of Joam Dacosta, a Brazilian man wrongly accused of theft and murder. In Book Two his friends struggle to save him by solving a cryptogram, whose last paragraph is given in the text:

Phyjslyddqfdzxgasgzzqqehxgkfndrxujugiocytdxvksbxhhuypo
hdvyrymhuhpuydkjoxphetozsletnpmvffovpdpajxhyynojyggayme
qynfuqlnmvlyfgsuzmqiztlbqgyugsqeubvnrcredgruzblrmxyuhqhp
zdrrgcrohepqxufivvrplphonthvddqfhqsntzhhhnfepmqkyuuexktog
zgkyuumfvijdqdpzjqsykrplxhxqrymvklohhhotozvdksppsuvjhd.

In the end this works out to:

Le véritable auteur du vol des diamants et de l’assassinat des soldats qui escortaient le convoi, commis dans la nuit du vingt-deux janvier mil huit cent vingt-six, n’est donc pas Joam Dacosta, injustement condamné à mort; c’est moi, le misérable employé de l’administration du district diamantin; oui, moi seul, qui signe de mon vrai nom, Ortega.

In the article linked below, Miami University mathematician Frederick Gass explains rigorously how the cipher might be solved. In the novel, Judge Jarriquez has a brainstorm: He learns that the writer might have been named Ortega, guesses that the declaration might end with that signature, and works out the rest from there.

“By virtue of this solution, Jules Verne is credited with the first published exposition of the probable word method for Gronsfeld ciphers.”

(Frederick Gass, “Solving a Jules Verne Cryptogram,” Mathematics Magazine 59:1 [February 1986], 3-11.)