Two Blows

Theodore Roosevelt’s wife and mother died in the same house on the same day, Valentine’s Day 1884. His wife had just given birth to their daughter Alice, and the pregnancy had hidden her kidney disease. He held her for two hours, had to be torn away to see his mother die of typhoid fever, then returned to his wife, who died in his arms.

In his diary he drew a large X and wrote, “The light has gone out of my life.” Then he fled west to grieve in private.

Cause for Alarm

Sherlock Holmes is walking through the valley of Reichenbach Fall. On a clifftop overhead, Moriarty has perched a boulder. When he pushes it, it will have a 90 percent chance of killing Holmes. Just as he is about to send it over the edge, Watson arrives at the clifftop. Watson can’t see Holmes, so he’s not able to push the boulder safely clear, but he reasons that it’s better to push the boulder in a random direction than to let Moriarty aim it carefully. So he pushes the boulder off the cliff in such a way that Holmes’ chance of dying is reduced to 10 percent.

Unfortunately the boulder crushes Holmes anyway. Watson’s push decreased the chance of Holmes’ death, but it also caused it.

What are we to make of this? Generally speaking, it seems true to say that Pre-emptive pushing prevents death by crushing. That is, Watson’s push was of the sort that made it less likely that Holmes would die — if the scenario were re-enacted many times, with the boulder pushed sometimes by Watson, sometimes by Moriarty, Watson-type pushes would result in fewer deaths. But it also seems true to say that Watson’s pushing the rock caused Holmes to die. But cause and prevent are antonyms. How can both of these statements be true?

(Christopher Read Hitchcock, “The Mishap at Reichenbach Fall: Singular vs. General Causation,” Philosophical Studies, June 1995.)

Black and White

By Francis Healey. White to mate in two moves.

Click for Answer

Half and Half

A bisecting arc is one that bisects the area of a given region. “What is the shortest bisecting arc of a circle?” Murray Klamkin asked D.J. Newman. Newman supposed that it was a diameter. “What is the shortest bisecting arc of a square?” Newman answered that it was an altitude through the center. Finally Klamkin asked, “And what is the shortest bisecting arc of an equilateral triangle?”

“By this time, Newman had suspected that I was setting him up (and I was) and almost was going to say the angle bisector,” Klamkin writes. “But he hesitated and said let me consider a chord parallel to the base and since this turns out to be shorter than an angle bisector, he gave this as his answer.”

Was he right?

Click for Answer

In a Word

v. to grow dark, to become night

Proizvolov’s Identity

List the first 2N positive integers (here let N = 4):

1, 2, 3, 4, 5, 6, 7, 8

Divide them arbitrarily into two groups of N numbers:

1, 4, 6, 7

2, 3, 5, 8

Arrange one group in ascending order, the other in descending order:

1, 4, 6, 7

8, 5, 3, 2

Now the sum of the absolute differences of these pairs will always equal N2:

| 1 – 8 | + | 4 – 5 | + | 6 – 3 | + | 7 – 2 | = 16 = N2

(Presented by Vyacheslav Proizvolov as a problem in the 1985 All-Union Soviet Student Olympiads.)

Pomp and Circumstance

Why do we hold graduation ceremonies? You don’t have to attend the ceremony to collect your degree; your education would be just as complete without it. Why do we maintain this seemingly needless ritual?

Philosopher Elijah Millgram argues that the ceremony provides a motivation to persist through an otherwise uninspiring mountain of work. Education is a “jam-yesterday-jam-tomorrow” good — we value it when it’s in our future or in our past, but the experience itself is often stressful, difficult, or boring. “On any given occasion, a student is likely to be plowing through a hard-to-read book, or writing a difficult paper, or trying not to doze off in lecture,” he writes. “The education is all these things, and is correctly understood to be a great (and an intrinsic) good; but it is hard to stay focused on its value just because one does not see it, moment to moment.”

The graduation ceremony, with its colors, music, and ritual, provides a highly visible “dummy goal” that helps to motivate students to complete their requirements. Without it, the vague prospect of “jam tomorrow” — the promised satisfaction of holding a degree — might be too little to spur some students to finish their studies. “If students had to make their own moment-to-moment decisions as to whether to read the book, or write the paper, or stay in the lecture, on the basis of its intangible contribution to their education,” Millgram writes, “they would be all too likely to put off the unpleasant tasks to some other time.”

(Elijah Millgram, “Virtue for Procrastinators,” in Chrisoula Andreou and Mark D. White, eds., The Thief of Time, 2010.)

Stage Fright

“Not to be born is, past all prizing, best,” wrote Sophocles. Does this mean that life is not worth living? For surely that judgment must be made from “inside” a lived life, whose subjective judgments are always open to question.

In four U.S. states a severely disabled child can sue a doctor for “wrongful life” for bringing him into the world. In 1980 the California Court of Appeal wrote:

The reality of the ‘wrongful-life’ concept is that such a plaintiff both exists and suffers, due to the negligence of others. It is neither necessary nor just to retreat into meditation on the mysteries of life. We need not be concerned with the fact that had defendants not been negligent, the plaintiff might not have come into existence at all. The certainty of genetic impairment is no longer a mystery. In addition, a reverent appreciation of life compels recognition that plaintiff, however impaired she may be, has come into existence as a living person with certain rights.

The rest of us, it seems, must find a way to be philosophical. After all, Lionel Tollemache wrote, “If there is more pain than pleasure in life, were not Hyder Ali and Napoleon, who put so many human sufferers out of existence, deserving of praise as beneficent heroes?”


In 1948 Melvin Wellman discovered this pretty anagram:


Lee Sallows discovered two similar specimens in Spanish:



These can be combined to make more:



See Also

Index entries in Thomas De Quincey’s Collected Writings, 1896:

Aldermen not necessarily gluttons
Anecdotes, on eating peas with a knife
Bed, early retirement to, of the Ancients
Christenings, Royal, often hurried
Coffee, atrocious in England
Cookery, English, the rudest of barbarous devices
Devonshire men good-looking
Fleas in Greece
Greece, Ancient, its people a nation of swindlers
Horses, weeping
Johnson, Dr, at dinner, an indecent spectacle
Leibnitz, died partly from the fear of not being murdered
Lisbon earthquake and its effect on the religion of Germany
Muffins, eating, a cause of suicide
Music, English obtuseness to good
Pig-grunting, mimicry of
Rhinoceros, first sale of a
Servants, England the paradise of household
Solon, what did he do for Homer?
Spitting, art of
Talk, too much in the world
Toothache, that terrific curse
Waterton’s adventure with a crocodile
Women, can die grandly

“If once a man indulges himself in murder, very soon he comes to think little of robbing; and from robbing he comes next to drinking and Sabbath-breaking, and from that to incivility and procrastination,” he wrote in Murder Considered as One of the Fine Arts. “Once begun upon this downward path, you never know where you are to stop. Many a man has dated his ruin from some murder or other that perhaps he thought little of at the time.”

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