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.)

First Things First

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In Languages and Their Speakers (1979), linguist Timothy Shopen shows how greetings and leave-takings can reflect a society’s cultural values. First he gives a typical American conversation in which one friend encounters another who is 15 minutes late for work:

Hello Ed!

— Hi! How are you?

Sorry, I’m in a hurry.

— Yeah, me too.

See you on Saturday.

The whole interaction lasts five seconds; it includes a greeting and a leave-taking, but there is no actual conversation between. Here’s the same interaction in the Maninka culture of West Africa:

Ah Sedou, you and the morning.

— Excellent. You and the morning.

Did you sleep in peace?

— Only peace.

Are the people of the household well?

— There is no trouble.

Are you well?

— Peace, praise Allah. Did you sleep well?

Praise Allah. You Kanté.

— Excellent. You Diarra.

Excellent.

— And the family?

I thank Allah. Is there peace?

— We are here.

How is your mother?

— No trouble.

And your cousin Fanta?

— Only peace. And your father?

Praise Allah. He greets you.

— Tell him I have heard it.

And your younger brother Amadou?

— He is well. And your uncle Sidi?

No trouble, Praise Allah …

Where are you going?

— I’m going to the market. And you?

My boss is waiting for me.

— O.K. then, I’ll see you later.

Yes, I’ll see you later. Greet the people of the household.

— They will hear it. Greet your father.

He will hear it.

— May your day pass well.

Amen. May the market go well.

— Amen. May we meet soon.

May that “soon” arrive in good stead.

“Time elapsed: 46 seconds,” Shopen writes. “It is more important to show respect for a friend or a kinsman than to be on time for work, and thus we have the example of Mamadou Diarra above, already fifteen minutes late for work and not hesitating to be even later in order to greet a friend in the proper manner. First things first, and there is no question for the Maninka people about what is most important.”

In a Word

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Image: Wikimedia Commons

obtest
v. to call heaven to witness; to protest against

proditor
n. a traitor; a betrayer

Is a union breaking the law if it posts a giant inflatable rat outside an employer’s facility? No, it’s not, according to a 2011 decision by the National Labor Relations Board. The Sheet Metal Workers’ Union had sought to dissuade a hospital from using non-union workers by stationing a 16-foot rat near the building’s entrance. The NLRB held that the “the use of the stationary Giant Rat (i) constituted peaceful and constitutionally protectable expression, (ii) did not involve confrontational conduct that would qualify as unlawful picketing, and (iii) did not qualify as nonpicketing conduct that was otherwise unlawfully coercive.”

The “rat collosi” are multiplying (gallery). Let’s hope they don’t stage an uprising themselves someday.

False Start

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The horse raced past the barn fell.

That’s a grammatically correct sentence. What does it mean? Most readers have to puzzle over it a bit before seeing the interpretation

The horse [that was] raced past the barn fell.

This is a “garden-path sentence” — the reader naturally assumes one interpretation and is confused to find that another had been intended. Further examples:

The old man the boat.

The government plans to raise taxes were defeated.

The cotton clothing is made of grows in Alabama.

I convinced her children are noisy.

Time flies like an arrow; fruit flies like a banana.

In writing, lexicographer Henry Fowler calls it “an obvious folly — so obvious that no one commits it wittingly except when surprise is designed to amuse. But writers are apt to forget that, if the false scent is there, it is no excuse to say they did not intend to lay it; it is their business to see that it is not there, and this requires more care than might be supposed.”

Legerdemain

Apart from being mathematically true, ONE + TWELVE = TWO + ELEVEN is also famously an anagram — the same group of letters appears on each side of the expression.

In numerical form (1 + 12 = 2 + 11) it’s both an anagram and a palindrome — the same numerals appear on either side of the equal sign, and in opposite order.

Expressed in Roman numerals (I + XII = II + XI) it remains an anagram and a palindrome — again, the same numerals appear on both sides, and in reverse order.

In a square font the equation remains the same when each character is turned upside down:

legerdemain 1

In Word Ways, contributor Anil points out a further coincidence: Write the original equation in a square font, turn it upside down, and twist the first plus sign 45 degrees to make a multiplication sign:

legerdemain 2

A similar trick works in Roman numerals: Start with the original expression, turn it upside down, and change the plus signs to minus. If IIX is taken as 8, then we get another valid expression:

I + XII = II + XI
IX + II = IIX + I
IX – II = IIX – I

(Anil, “One + Twelve = Two + Eleven,” Word Ways 35:4 [July 2012], 308. See also Spanagrams and Immortal Truth.)