# Tally Sticks

Until 1826, the British Royal Treasury recognized notched sticks as proof of payment. In a practice that had begun in medieval times, a debt would be recorded on a “tally stick,” and then the stick would be split lengthwise, with the shorter portion, the “foil,” given to the debtor and the longer portion, the “stock,” held by the creditor. Because the two halves of the stick could be matched together, this gave both parties a record of the deal, and the valuable stock could then be traded on a secondary market.

Accumulated tally sticks might have given us a valuable record of British monetary transactions, but unfortunately most of them have been lost. In 1834, after the advent of paper ledgers, it was decided to burn 600 years of accumulated tally sticks in a coal-fired stove in the House of Lords. A chimney fire resulted, destroying most of the Palace of Westminster.

# In a Word

passeggiata
n. a leisurely walk

In the ancient world, distances were sometimes measured by pacing. Specialists known as bematists were employed for this purpose in both Egypt and Greece, and their accuracy could be startling: In his Naturalis Historia, Pliny the Elder notes that two bematists employed by Alexander the Great had measured the distance from Hecatompylos to Alexandria Areion on the Silk Road at 851 kilometers. The actual distance is 855 kilometers, a deviation of just 0.4 percent. In general, according to Pliny’s records, Alexander’s bematists showed a median deviation of just 2.8 percent from the true distances; a separate account by Strabo shows a median deviation of only 1.9 percent.

This accuracy suggests that the bematists may have been using an early odometer, such as one described by Heron of Alexandria, though the records don’t mention this.

12/30/2023 UPDATE: Reader Charlotte Fare has made a data visualization. (Thanks, Charlotte.)

# All Relative

In a position puzzle, a phrase is meant to be inferred from the position of words on a page. A familiar example is

```stand   take    to     takings.
I     you    throw      my
```

This can be read “I understand you undertake to overthrow my undertakings.”

“Sometimes the difficulty is increased by using letters and making them suggest words,” noted Household Words in 1882. It offered this example, adding, “This requires some little thought”:

What does it say?

# Mane Routine

Why didn’t this catch on? Jean Gronier’s “automatic hair-cutting machine,” patented in 1966, works “in accordance with a predetermined program; each program is designed for a particular person and is established once and for all with a view to obtaining repeatedly the same cut for the same head.”

“Here I am, bald at last,” wrote Jules Renard in 1894. “So much the better! What use to me was hair? It was not exactly an ornament, and I was the natural victim of all barbers, an ignoble breed, who exhaled into my face their disdain, or caressed me like a mistress, or patted my cheek like a parish priest.”

# Easy Street

The following was rather widely quoted a few years ago. It bothered one banker so much that he made a hasty trip to consult his neighbor, a college professor of mathematics. Assume we make a deposit of \$50 in a bank.

```    withdraw \$20.00 leaving \$30.00
now withdraw  15.00 leaving  15.00
now withdraw   9.00 leaving   6.00
now withdraw   6.00 leaving   0.00
------         ------
\$50.00         \$51.00
```

We now present our figures to the bank, showing the discrepancy, and demand the extra dollar. Repeat ten thousand times, and retire for a while.

— Cecil B. Read, “Mathematical Fallacies,” School Science and Mathematics, June 1933

# The Werewolf of Bedburg

In 1589, German farmer Peter Stumpp confessed that the devil had given him a belt that would give him “the likeness of a greedy, devouring wolf, strong and mighty, with eyes great and large, which in the night sparkled like fire, a mouth great and wide, with most sharp and cruel teeth, a huge body, and mighty paws.”

Over the course of 25 years, he said, he had killed and eaten 14 children, two pregnant women, and their fetuses.

The confession was extracted on the rack, but the magistrate didn’t care: Stumpp was broken, hobbled, beheaded, and burned.

# The Three Cups Problem

Here are three cups, one upside down.

Turning over exactly two cups with each move, can you turn all cups right-side-up in no more than six moves?

If it’s possible, show how; if it’s not, say why.

# Protocol

The late Mr. Dawson Damer — ‘Hippy’ Damer, afterwards Lord Portarlington — was one of the most deservedly popular men in London and a great favourite of Queen Victoria. The Prince of Wales gave a garden party at Marlborough House to his mother, and to this gathering ‘Hippy’ Damer came — but came very much under the influence of ‘la dive bouteille.’ Spying the Queen he went up to her offered his hand cordially and said: ‘Gad! How glad I am to see you! How well you’re looking! But, I say, do forgive me — your face is, of course, very familiar to me; but I can’t for the life of me recall your name!’ The Queen took in the situation at once, and as she cordially grasped the hand extended to her, said smiling: ‘Oh, never mind my name, Mr. Damer — I’m very glad to see you. Sit down and tell me all about yourself.’

— Julian Osgood Field, Uncensored Recollections, 1924

Below: “Her Majesty has been the recipient of some remarkably addressed envelopes,” reported the Strand in 1891.

# “Sonnet With a Different Letter at the End of Every Line”

O for a muse of fire, a sack of dough,
Or both! O promissory notes of woe!
One time in Santa Fe N.M.
Ol’ Winfield Townley Scott and I … But whoa.

One can exert oneself, ff,
Or architect a heaven like Rimbaud,
Or if that seems, how shall I say, de trop,
One can at least write sonnets, a propos
Of nothing save the do-re-mi-fa-sol
Of poetry itself. Is not the row
Of perfect rhymes, the terminal bon mot,
Obeisance enough to the Great O?

“Observe,” said Chairman Mao to Premier Chou,
“On voyage à Parnasse pour prendre les eaux.
On voyage comme poisson
, incog.”

— George Starbuck