In illustrating his Just So Stories, Rudyard Kipling hid messages in the runic characters accompanying some drawings. The tusk above illustrates “How the First Letter Was Written”:

Left side: “This is the stori of Taffimai all ritten out on an old tusk. If u begin at the top left hand corner and go on to the right u can see for urself things as the happened.”

Right side: “The reason that I spell so queerli is becase there are not enough letters in the Runic alphabet for all the ourds that I ouant to use to u o beloved.”

Bottom (barely visible here): “This is the identical tusk on ouich the tale of Taffimai was ritten and etched bi the author.”

The initial “H” at the start of the “Cat That Walked by Himself” hides another message using the same characters: “I, Rudiard Kipling, drew this, but because there was no mutton bone in the house I faked the anatomi from memori.”

“Are these really Runic letters or just an alphabet that Kipling made up for fun?” asked Maj. B.J. Bewley in the Kipling Journal in January 1928. “I think the chief interest lies in the almost boyish pleasure the author plainly took in writing in these strange characters. He must have done it entirely for his own amusement.”

Double Duty

What’s unusual about this limerick?

There was a young lady of Riga,
Who went for a ride on a tiger,
They came back from their ride
With the lady inside
And a smile on the face of the tiger.

It remains a limerick when translated into Latin:

Puella Rigensis ridebat,
Quam tigris in tergo vehebat,
Externa profecta
Interna revecta,
Risusque cum tigre manebat.

Ronald Knox found that the same is true of this one:

There was a young man of Devizes,
Whose ears were of different sizes;
The one that was small
Was no use at all,
But the other won several prizes.

Visas erat; huic geminarum
Dispar modus auricularum:
Minor haec nihili;
Palma triplici
Iam fecerat altera clarum.

Asleep Awake

At age 13 Marie-Jean-Léon Lecoq, Marquis d’Hervey de Saint-Denys, discovered a rare talent: He could recognize a dream state while he was experiencing it, and could move and act lucidly within the dream. Eventually he filled 25 notebooks with descriptions and illustrations of his adventures in the dream world. These are now lost, but his 1867 book Les Rêves et les Moyens de Les Diriger describes some of his feats:

I change a porcelain vase into a rock-crystal fountain, from which I desire a cooling drink — and this immediately flows out through a golden tap. Some years ago I lost a particular ring whose loss I felt deeply. The memory of it comes to mind, and I should like to find it. I utter this wish, fixing my attention on a piece of coal that I pick up from the fireplace — and immediately the ring is on my finger. The dream continues in the same way until one of the apparitions I have called up charms and captivates me so much that I forget my magician’s role and plunge into a new, more realistic series of illusions.

Saint-Denys believed that almost anyone could learn to do this. One of his suggestions was to keep a dream diary and to make a daily habit of completing it. Like the rest of the student’s life, this habit would then itself become the raw material for his dreams — eventually he would dream of recording a dream. And if he noted the details of a dream he was recording, he would virtually be dreaming lucidly, having smuggled himself into his own slumbers.

Black and White

ebert chess problem

By Hilmar Ebert. White to mate in two moves.

Click for Answer

“Quiet Fun”

My son Augustus, in the street, one day,
Was feeling quite exceptionally merry.
A stranger asked him: “Can you tell me, pray,
The quickest way to Brompton Cemetery?”
“The quickest way? You bet I can!” said Gus,
And pushed the fellow underneath a bus.

— Harry Graham

True Colors

In the early 1900s, Prussian authorities forbade Danes living in North Frisia from raising the Danish flag, above.

So they bred flag-colored pigs, below. The “Danish protest pig” was probably developed by crossbreeding Jutlandian and Holsteinian marsh pigs, red individuals from the Angeln Saddleback breed, and Tamworth pigs from England. Only around 140 individuals exist worldwide, but Schleswig-Holstein is trying to preserve the breed for its cultural value.

Ride Sharing

You and I have to travel from Startville to Endville, but we have only one bicycle between us. So we decide to leapfrog: We’ll leave Startville at the same time, you walking and I riding. I’ll ride for 1 mile, and then I’ll leave the bicycle at the side of the road and continue on foot. When you reach the bike you’ll ride it for 1 mile, passing me at some point, then leave the bike and continue walking. And so on — we’ll continue in this way until we’ve both reached the destination.

Will this save any time? You say yes: Each of us is riding for part of the distance, and riding is faster than walking, so using the bike must increase our average speed.

I say no: One or the other of us is always walking; ultimately every inch of the distance between Startville and Endville is traversed by someone on foot. So the total time is unchanged — leapfrogging with the bike is no better than walking the whole distance on foot.

Who’s right?

Click for Answer

Love Walks In

Personal ads from the New York Herald in the 1860s:

IF THE LADY WHO, FROM AN OMNIBUS, SMILED on a gentleman with a bunch of bananas in his hand, as he crossed Wall street, corner of Broadway, will address X., box 6,735 Post office, she will confer a favor. (March 21, 1866)

ON WEDNESDAY AFTERNOON A LADY WITH black silk quilted hat walked nearly side by side with a gentleman in a drab overcoat from Tenth to Fourteenth street, in Broadway. Both were annoyed by the wind and dust. Her smile has haunted him ever since. Will she send her address to Carl, Union square Post office? (March 8, 1861)

BOOTH’S THEATRE, THURSDAY EVENING, 11TH. Will the lady who met the gent’s gaze through an opera glass and smiled please address, in confidence, Harry Wilton, Herald office? (March 13, 1869)

A YEAR AGO LAST SEPTEMBER OR OCTOBER TWO ladies with a child were travelling on the Hudson River cars, one of whom offered a seat to a middle aged gentleman, with light whiskers or goatee, slightly gray, who kindly pointed out to her the red leaved trees, and said he had a number of them on his place, and made himself otherwise agreeable; and when she was leaving him (ten miles this side of where he stopped) gave her a parting embrace, which she has never been able to forget. If the gentleman has any recollection of the circumstance he will greatly oblige by addressing a note to Lena Bigelow, Madison square Post office, giving some description of the lady, also name of the paper he gave her. (Jan. 25, 1862)

In a Word

adj. having large ears

adj. large-headed

adj. long-necked

adj. having a large belly

adj. having long feet

adj. “That resembles the Sciapodes; having very large feet.”

Making Pi

We’ve mentioned before that you can estimate π by dropping needles on the floor. (Reader Steven Karp also directed me to this remarkable solution, from Daniel A. Klain and Gian-Carlo Rota’s Introduction to Geometric Probability [1997].)

Here’s a related curiosity. If a circle of diameter L is placed at random on a pattern of circles of unit diameter, which are arranged hexagonally with centers C apart, then the probability that the placed circle will fall entirely inside one of the fixed circles is

circle and scissel pi estimate 1

If we put k = C/(1 – L), we get

circle and scissel pi estimate 1

And a frequency estimate of P will give us an estimate of π.

Remarkably, in 1933 A.L. Clarke actually tried this. In Scripta Mathematica, N.T. Gridgeman writes:

His circle was a ball-bearing, and his scissel a steel plate. Contacts between the falling ball and the plate were electrically transformed into earphone clicks, which virtually eliminated doubtful hits. With student help, a thousand man-hours went into the accumulation of N = 250,000. The k was about 8/5, and the final ‘estimate’ of π was 3.143, to which was appended a physical error of ±0.005.

“This is more or less the zenith of accuracy and precision,” Gridgeman writes. “It could not be bettered by any reasonable increase in N — even if the physical error could be reduced, hundreds of millions of falls would be needed to establish a third decimal place with confidence.”

(N.T. Gridgeman, “Geometric Probability and the Number π,” Scripta Mathematica 25:3 [November 1960], 183-195.)

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