In 1857 The Leisure Hour tried to imagine life in London a century in the future, that is, in 1957. Many of the predictions seem sadly optimistic (for instance, the eradication of crime), but one in particular stands out:

I observed that from each of these district shops innumerable electric wires branched off in all directions, communicating with several houses in the district to which it belonged. Thus, no sooner did a house-keeper stand in need of any article than she could despatch the order instantaneously along the wire, and receive the goods by the very first railway carriage that happened to pass the store. Thus, she saved her time, and she lost no money, because all chaffering and cheapening, and that fencing between buyer and seller, which was once deemed a pleasure, had been long voted a disgraceful, demoralizing nuisance, and was done away with.

You can read the whole thing at the Public Domain Review.

Spy Kids

Barbie typewriters, sold worldwide by Mattel, have an undocumented built-in cryptographic capability. Pressing SHIFT and LOCK in combination with a particular trio of keys will engage any of four monoalphabetic substitution ciphers — once the feature is engaged, a keyed message will be printed in a transposed alphabet. Pressing a different combination of keys will put the machine into “decoding mode,” where keying a transposed message will print the deciphered text. So the same machine can be used to code and decode a message.

Details are at the Crypto Museum. These things were marketed to 5-year-olds. What else don’t we know about?

(Thanks, David.)


In the Middle Ages, when schoolchildren spelled a one-letter word, they would indicate this with the Latin phrase per se (“by itself”) — so students learning to read would say “D-O-G, dog” but “A per se, a,” meaning “A by itself, [the word] a.”

When the alphabet was printed, the symbol & was customarily added at the end, and the reader would say, “& per se, and.”

After many years of hasty slurring, this left us with the word ampersand.

(Thanks, David.)

Area Magic Squares

On December 30 William Walkington sent this greeting to a circle of magic-square enthusiasts — it’s a traditional magic square (each row, column, and diagonal sums to 15), but the geometric area of each cell corresponds to its number.

He added, “The areas are approximate, and I don’t know if it is possible to obtain the correct areas with 2 vertically slanted straight lines through the square. Perhaps someone will be able to work this out in 2017?”

It’s only January 19, and the answer is already yes — Walter Trump has produced a “third-order linear area magic square” using the numbers 5-13:

There are many further developments, which have opened new questions and challenges, as these discoveries tend to do — see William’s blog post for more information.

(Thanks, William.)

Turning Keys

Most piano music is written with the melody in the right hand, which seems unfair to left-handers. In 1998 left-handed Chris Seed determined to do something about it: He remortgaged his house and spent £28,000 on a “reversed” instrument built by Dutch fortepiano makers Poletti and Tuinman.

“At first Seed found it far harder to learn to play the instrument than he’d expected,” reports Rik Smits in The Puzzle of Left-Handedness. “It seemed as if he’d have to begin learning again from scratch. But once he got going, Seed’s brain turned out to be perfectly capable of converting everything he’d ever learned into a left-handed playing technique. Exactly what he’d hoped happened: all the pieces of the puzzle fell into place more or less automatically. Seed became at least as good a pianist as he was on a conventional piano and eventually he felt real delight in playing ‘as God intended.'”

Seed told the BBC, “The piano has transformed my playing, and I hope it will set a precedent for a future of left-handed pianists and uncover a whole new wealth of talent in the world of music.”

The Harcourt Interpolation

Here are two transcriptions of a speech by Home Secretary Sir William Harcourt, reprinted in the London Times on Jan. 23, 1882. At left is the column as it originally appeared; at right is the same speech in a hastily issued replacement edition. What’s the difference between them?

In the column on the left, about midway down, a disgruntled compositor has inserted the line “The speaker then said he felt inclined for a bit of fucking.”

The paper issued an apology and suppressed the offending edition as well as it could, but that only increased public interest, driving the price of a copy up from threepence to £5 in some areas (it would reach £100 by the 1990s). The Times’ quarterly index recorded the offense:

Harcourt (Sir W.) at Burton on Trent, 23 j 7 c
———Gross Line Maliciously Interpolated in a
Few Copies only of the Issue, 23 j 7 d — 27 j 9 f

The paper tried to rise above all this, but it made a new rule: If you sack a compositor, get him off the premises immediately.

(Thanks, Alejandro.)

Watching the Detectives

Police exist, and sometimes they scrutinize other members of the constabulary. We might say Police police police. If the observed officers are already being observed by a third set of officers, then we could say Police police police police police, that is, “Police observe police [whom] police police.”

The trouble is that if you say this sentence, “Police police police police police,” to an innocent friend, she might take you to mean “Police [whom] police police … police police.” Police police police police police has one verb, police, and two noun phrases, Police and police police police, and without some guidance there’s no way to tell which noun phrase is intended to begin and which to end the sentence.

It gets worse. Suppose we add two more polices: Police police police police police police police. Now do we mean “Police [whom] police observe observe police [whom] police observe”? Or “Police observe police [whom] police whom police observe observe”? Or something else again?

In general, McGill University mathematician Joachim Lambek finds that if police is repeated 2n + 1 times (n ≥ 1), then the numbers of ways in which the sentence can be parsed is  \frac{1}{\left ( n + 1 \right )}\binom{2n}{n} , the (n + 1)st Catalan number.

Buffalo have their own troubles.

(J. Lambek, “Counting Ambiguous Meanings,” Mathematical Intelligencer 30:2 [March 2008], 4.)

The Mengenlehreuhr

Further to Saturday’s triangular clock post, reader Folkard Wohlgemuth points out that a “set theory clock” has been operating publicly in Berlin for more than 40 years. Since 1995 it has stood in Budapester Straße in front of Europa-Center.

The circular light at the top blinks on or off once per second. Each cell in the top row represents five hours; each in the second row represents one hour; each in the third row represents five minutes (for ease of reading, the cells denoting 15, 30, and 45 minutes past the hour are red); and each cell in the bottom row represents one minute. So the photo above was taken at (5 × 2) + (0 × 1) hours and (6 × 5) + (1 × 1) minutes past midnight, or 10:31 a.m.

Online simulators display the current time in the clock’s format in Flash and Javascript.

If that’s not interesting enough, apparently the clock is a key to the solution of Kryptos, the enigmatic sculpture that stands on the grounds of the CIA in Langley, Va. In 2010 and 2014 sculptor Jim Sanborn revealed to the New York Times that two adjacent words in the unsolved fourth section of the cipher there read BERLIN CLOCK.

When asked whether this was a reference to the Mengenlehreuhr, he said, “You’d better delve into that particular clock.”