Two for One

Longfellow thought that Dante Gabriel Rossetti, the Victorian poet and painter, was two different people. On leaving Rossetti’s house he said, “I have been very glad to meet you, Mr. Rossetti, and should like to have met your brother also. Pray tell him how much I admire his beautiful poem, ‘The Blessed Damozel.'”

In Philosophical Troubles, Saul A. Kripke offers a related puzzle. Peter believes that politicians never have musical talent. He knows of Paderewski, the great pianist and composer, and he has heard of Paderewski the Polish statesman, but he does not know that they are the same person. Does Peter believe that Paderewski had musical talent?

An Ancient Mystery

Around 1275, a native culture known as the Gallina vanished from northern New Mexico. And almost every Gallina skeleton ever found has been that of someone brutally murdered. No one knows why.

“[Someone] was just killing them, case after case, every single time,” U.S. Forest Service archaeologist Tony Largaespada told National Geographic News in 2007.

Seven skeletons found in a remote canyon paint a typical picture — one had a fractured skull, forearm, jaw, thighbone, pelvis, and several broken ribs; another bore cut marks on the upper arm that suggested blows from an ax. A 2-year-old child had had its skull crushed.

In other cases the victims’ necks have been broken, and the bodies are commonly thrown into a house, which is then burned to the ground.

Possibly this was a genocide, or possibly internecine conflict within the Gallina. Either could have been exacerbated by a drought that is known to have gripped the area around this time. But, so far, no one knows the reason.

Black and White

st. maurice chess problem

By Charles Ephrem St. Maurice. White to mate in two moves.

Click for Answer

“Come Wade, Dear Maid”

Cynthia Knight published this dialogue in the Journal of Recreational Linguistics in 1984 — apart from the italicized words, it’s composed entirely from two-letter state postal abbreviations:


MS. INGA LANE, paid cook
NEAL DEMSKY, lame vandal
PA (akin), many-decade lama


Arid moor
Arcade game near Marineland
Concorde de la Mode




Pail, cane, alpaca

NEAL: Decoct, maid! Almond wine! Deal?

INGA (in coma): Ma! Papa! Come near me! Alms!

NEAL (florid): Mine meal! Moil, Inga!

INGA (in pain): Demand in vain!

NEAL aria, or pavane
NEAL lams

INGA (in code): Deny; hide mail; scar me! Oh, inky condor, come! Oh, mend me!

PA came

PA: Hi, Inga. Come ride; wide lane? Mom’s game.

INGA (wail): Candor, OK? Pact?

(“Who can finish this absorbing story?”)

Popularity Contest

popularity contest

Your friends probably have more friends than you do.

The diagram above shows friendships among eight high school girls. The first number in each circle is the girl’s number of friends; the second is the mean number of friends that her friends have. Only Sue and Alice have more friends than their friends do on average, but their popularity, by its very nature, will impress an inordinate number of people, leaving more feeling inadequate by comparison.

“Those with 40 friends show up in each of 40 individual friendship networks and thus can make 40 people feel relatively deprived,” writes SUNY sociologist Scott Feld, “while those with only one friend show up in only one friendship network and can make only that one person feel relatively advantaged.” In general, he finds, in a given network the mean number of friends of friends is always greater than the mean number of friends of individuals. But understanding this phenomenon “should help people to understand that their position is relatively much better than their personal experiences have led them to believe.”

The same principle leads college students to feel that the mean class size is larger than it really is, and all of us to experience restaurants, parks, and beaches as more crowded than they really are. A highway impresses thousands with its crowdedness at rush hour, but few with its openness at midnight. So we tend to think of it as busier than it really is.

(Scott L. Feld, “Why Your Friends Have More Friends Than You Do,” American Journal of Sociology, 96:6, 1464-1477)

In a Word

n. a person who has the least possible faith in something

The Two Cultures

In 1855 American publisher James T. Fields made the mistake of taking William Thackeray to a dull scientific lecture:

During his second visit to Boston I was asked to invite him to attend an evening meeting of a scientific club, which was to be held at the house of a distinguished member. I was very reluctant to ask him to be present, for I knew he could be easily bored, and I was fearful that a prosy essay or geological speech might ensue, and I knew he would be exasperated with me, even although I were the innocent cause of his affliction. My worst fears were realized. We had hardly got seated, before a dull, bilious-looking old gentleman rose, and applied his auger with such pertinacity that we were all bored nearly to distraction. I dared not look at Thackeray, but I felt that his eye was upon me. My distress may be imagined, when he got up quite deliberately from the prominent place where a chair had been set for him, and made his exit very noiselessly into a small anteroom leading into the larger room, and in which no one was sitting. The small apartment was dimly lighted, but he knew that I knew he was there. Then commenced a series of pantomimic feats impossible to describe adequately. He threw an imaginary person (myself, of course) upon the floor, and proceeded to stab him several times with a paper-folder which he caught up for the purpose. After disposing of his victim in this way, he was not satisfied, for the dull lecture still went on in the other room, and he fired an imaginary revolver several times at an imaginary head. Still, the droning speaker proceeded with his frozen subject (it was something about the Arctic regions, if I remember rightly), and now began the greatest pantomimic scene of all, namely, murder by poison, after the manner in which the player King is disposed of in Hamlet. Thackeray had found a small phial on the mantel-shelf, and out of it he proceeded to pour the imaginary ‘juice of cursed hebenon’ into the imaginary porches of somebody’s ears. The whole thing was inimitably done, and I hoped nobody saw it but myself; but years afterwards a ponderous, fat-witted young man put the question squarely to me: ‘What was the matter with Mr. Thackeray that night the club met at M—-‘s house?’

A Losing Game

You and I each have a stack of coins. We agree to compare the coins atop our stacks and assign a reward according to the following rules:

  • If head-head appears, I win $9 from you.
  • If tail-tail appears, I win $1 from you.
  • If head-tail or tail-head appears, you win $5 from me.

After the first round each of us discards his top coin, revealing the next coin in the stack, and we evaluate this new outcome according to the same rules. And so on, working our way down through the stacks.

This seems fair. There are four possible outcomes, all equally likely, and the payouts appear to be weighted so that in the long run we’ll both break even. But in fact you can arrange your stack so as to win 80 cents per round on average, no matter what I do.

Let t represent the fraction of your coins that display heads. If my coins are all heads, then your gain is given by

GH = -9t + 5(1 – t) = -14t + 5.

If my coins are all tails, then your gain is

GT = +5t – 1(1 – t) = 6t – 1.

If we let GH = GT, we get t = 0.3, and you gain GH = GT = $0.80.

This result applies to an entire stack or to any intermediate segment, which means that it works even if my stack is a mix of heads and tails. If you arrange your stack so that 3/10 of the coins, randomly distributed in the stack, display heads, then in a long sequence of rounds you’ll win 80 cents per round, no matter how I arrange my own stack.

(From J.P. Marques de Sá, Chance: The Life of Games & the Game of Life, 2008.)

Apple Cheeks

Richard Tweddell III patented this “method and apparatus for molding fruits” in 1987. While fruit is growing on a plant, you enclose it in a transparent mold. As the fruit gets larger, it gradually fills the cavity “and in doing so conforms with remarkable fidelity to the internal details of the mold.” He sells it pretty well:

They can be caused to grow in the image of a particular person; in the shape of a different type of produce (e.g., a summer squash grown in the shape of an ear of corn); a fanciful shape such as a heart, or a bottle of pop; or other simple or even quite detailed shapes. A zucchini in the likeness of Clark Gable, for example, complete with mustache, would be no ordinary sight on the dinner table. Similarly, a Christmas tree ornament formed of a small, configured gourd is a very distinctive novelty.

Well, that’s true. Tweddell also suggests that turkey-shaped fruit might be enjoyed at Thanksgiving, or pumpkin-shaped fruit at Halloween. And “the invention also makes possible the concept of molding the logo of, say, a pickle company, directly into the side of a pickle itself.”

Planning Big

When Germany invaded the Soviet Union in 1941, it interrupted one of the most ambitious building projects in history. Situated near the Kremlin, the Palace of the Soviets would have commemorated the founding the U.S.S.R. with a 21,000-seat congress hall, 100 stories of administrative offices, and a crowning statue of Lenin 75 meters tall.

It would have been both the largest and the tallest building in the world. But only the foundation had been built when the war intervened, and the frame was disassembled for its steel. Construction never resumed, and in the 1960s the site was turned into an open-air swimming pool. This must symbolize something.