Bean Counting

We tend to think that some wrongs are so small that doing them makes no difference. If I keep my heater on during a power shortage, perhaps the shortage lasts a hundredth of a second longer than it would otherwise have done. I tell myself that this effect is too small to matter.

But imagine a village in which 100 tribesmen are eating lunch. 100 bandits descent on the village, and each bandit takes one tribesman’s lunch and eats it. The bandits leave, each having denied a tribesman an appreciable amount of pleasure.

The next week, hungry again, they descend on the village and tie up the tribesmen. At first they have some moral qualms about robbing them again, but then they notice that each tribesman’s lunch consists of 100 beans.

“The pleasure derived from one baked bean is below the discrimination threshold,” writes philosopher Jonathan Glover. “Instead of each bandit eating a single plateful as last week, each takes one bean from each plate. They leave after eating all the beans, pleased to have done no harm, as each has done no more than sub-threshold harm to each person.”

The outcome of the second raid is the same as that of the first, yet this time no tribesman has been “significantly” wronged by any bandit. Can we still say that some crimes are too small to matter?

(Jonathan Glover and M.J. Scott-Taggart, “It Makes No Difference Whether or Not I Do It,” Proceedings of the Aristotelian Society, Supplementary Volumes, 49 (1975), 171-209)

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 phenomenon 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 congestion at rush hour, but few with its emptiness 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)

Ready Made

In 1923 the Acme Code Company published a list of “phrase codes” for use in telegrams — customers could save money by substituting a five-letter code for a longer phrase in their messages. The list of codes was charmingly comprehensive:

BIINC What appliances have you for lifting heavy machinery?

URPXO For what use was the mixing machine intended?

CHOOG lard, in bladders

GAHGU cod-liver oil

GNUEK rubber, slightly moldy

HEHST clammy condition

ZOKIX unhealthy trees

ARPUK The person is an adventurer …

BUKSI Avoid arrest if possible

NARVO Do not part with the documents

OBYNX Escape at once

CULKE Bad as possibly can be

LYADI Arrived here with decks swept … encountered a hurricane

PYTUO Collided with an iceberg

YBDIG Plundered by natives

Similarly, George Holland Ackers’ Universal Yacht Signals (1847) includes signals for “Can I have … quarts of turtle soup?”, “Marmalade — orange unless specified,” and “I can strongly recommend my washerwoman.”

In Film Facts (2001), Patrick Robertson notes that Central Casting installed a Hollerith computer in 1935 to help with the casting of extras in Hollywood films. This meant subdividing humanity into tidy categories — lawyers, for instance, were classed as Shrewd, Dixie, Hawk-faced, Inquisitor and Benevolent. “When the new system was unveiled before the press, the operator was asked to produce ten Englishmen, 6ft tall, blue-eyed, possessed of full evening dress, and able to play polo. The cards of all 600 male dress extras were run through the machine to reveal that there were only two such paragons on the books of Central Casting.”

See Enjoy Your Stay.

Jury Duty

From Gábor J. Székely’s Paradoxes in Probability Theory and Mathematical Statistics, via Mark Chang’s Paradoxology of Scientific Inference:

A, B, C, D, and E make up a five-member jury. They’ll decide the guilt of a prisoner by a simple majority vote. The probability that A gives the wrong verdict is 5%; for B, C, and D it’s 10%; for E it’s 20%. When the five jurors vote independently, the probability that they’ll bring in the wrong verdict is about 1%. But if E (whose judgment is poorest) abandons his autonomy and echoes the vote of A (whose judgment is best), the chance of an error rises to 1.5%.

Even more surprisingly, if B, C, D, and E all follow A, then the chance of a bad verdict rises to 5%, five times worse than if they vote independently, even though A is nominally the best leader. Chang writes, “This paradox implies it is better to have your own opinion even if it is not as good as the leader’s opinion, in general.”

The Real Thing

Amanda Blake and David Cronin were engaged to be married while both were working for the Coca-Cola Company in Northampton, Mass., in 1985. Then Cronin left Coke to work for Pepsi.

Blake sued Coke for $600,000, alleging that her employer had told her that she must either break off the engagement, leave Coke, or convince Cronin to leave Pepsi. When she refused, she was fired.

“It made me sad that they didn’t trust me,” she said. “I was more sad than mad after all the hours and time I put in, and then they didn’t think twice about firing me.”

In 1987 they reached a settlement that was “satisfactory to all parties.”


“Not for life, but for school do we learn.” — Seneca the Younger

“Nothing in education is so astonishing as the amount of ignorance it accumulates in the form of inert facts.” — Henry Adams

“Just as eating contrary to the inclination is injurious to the health, study without desire spoils the memory, and it retains nothing that it takes in.” — Leonardo

“I believe that school makes complete fools of our young men, because they see and hear nothing of ordinary life there.” — Petronius

But to go to school in a summer morn,
Oh, it drives all joy away!
Under a cruel eye outworn,
The little ones spend the day —
In sighing and dismay.

— William Blake, The Schoolboy

“The only thing I ever learned in school that did me any good in after life was that if you spit on a pencil eraser, it will erase ink.” — Dorothy Parker

The pupils of St. Cassian, a schoolmaster, stabbed him to death with their pens.

Legal Vision

In May 1954, 12-year-old M. Paul Claussen Jr. of Alexandria, Va., sent a letter to Felix Frankfurter saying that he was interested in “going into the law as a career” and requested the jurist’s advice as to “some ways to start preparing myself while still in junior high school.” He received this reply:

My Dear Paul:

No one can be a truly competent lawyer unless he is a cultivated man. If I were you, I would forget all about any technical preparation for the law. The best way to prepare for the law is to come to the study of the law as a well-read person. Thus alone can one acquire the capacity to use the English language on paper and in speech and with the habits of clear thinking which only a truly liberal education can give. No less important for a lawyer is the cultivation of the imaginative faculties by reading poetry, seeing great paintings, in the original or in easily available reproductions, and listening to great music. Stock your mind with the deposit of much good reading, and widen and deepen your feelings by experiencing vicariously as much as possible the wonderful mysteries of the universe, and forget about your future career.

With good wishes,

Sincerely yours,

Felix Frankfurter

Moving Language

Writing in Word Ways in May 1975, David Silverman noted that the phrase LEFT TURN FROM THIS LANE ONLY, stenciled in the leftmost traffic lane at various U.S. intersections, was ambiguous — and that both meanings had been struck down, in contested court cases in Arizona and California.

In one case, the motorist had driven straight ahead rather than turning, which the prosecutor said was illegal. The motorist returned that this wasn’t so — LEFT TURN FROM THIS LANE ONLY meant that it would be illegal to make a left turn from any other lane, but it didn’t require that a left turn be made from this one. “If the city had meant my failure to turn to be illegal, they should have written FROM THIS LANE, ONLY A LEFT TURN.”

In the other case, the motorist had made a left turn from the lane to the right of one marked LEFT TURN FROM THIS LANE ONLY. He argued that this was legal — the marking required drivers in the leftmost lane to turn left, but imposed no requirement on the other lanes. “Had the city wanted to make my turn illegal the marking should have been LEFT TURN ONLY FROM THIS LANE.”

Both motorists were found not guilty. Perhaps because of such confusion, Silverman noted, most intersections had lately begun to use unambiguous arrows: “One good picture is worth ten thousand signs reading LEFT TURN IF AND ONLY IF FROM THIS LANE.”


An episode from the sinking of the Titanic, from the testimony of passenger Mary Smith:

When the first boat was lowered from the left-hand side I refused to get in, and they did not urge me particularly; in the second boat they kept calling for one more lady to fill it, and my husband insisted that I get in it, my friend having gotten in. I refused unless he would go with me. In the meantime Capt. Smith was standing with a megaphone on deck. I approached him and told him I was alone, and asked if my husband might be allowed to go in the boat with me. He ignored me personally, but shouted again through big megaphone, ‘Women and children first.’ My husband said, ‘Never mind, captain, about that; I will see that she gets in the boat.’ He then said, ‘I never expected to ask you to obey, but this is one time you must; it is only a matter of form to have women and children first. The boat is thoroughly equipped, and everyone on her will be saved.’ I asked him if that was absolutely honest, and he said, ‘Yes.’ I felt some better then, because I had absolute confidence in what he said. He kissed me good-by and placed me in the lifeboat with the assistance of an officer. As the boat was being lowered he yelled from the deck, ‘Keep your hands in your pockets; it is very cold weather.’ That was the last I saw of him; and now I remember the many husbands that turned their backs as that small boat was lowered, the women blissfully innocent of their husbands’ peril, and said good-by with the expectation of seeing them within the next hour or two.

Bedroom steward Alfred Crawford was helping ladies into a port-side lifeboat when Isidor Straus, co-owner of Macy’s department store, arrived with his wife, Ida. “She made an attempt to get into the boat first. She had placed her maid in the boat previous to that. She handed her maid a rug, and she stepped back and clung to her husband and said, ‘We have been together all these years. Where you go I go.'” The two were last seen sitting side by side in chairs on the deck.

See Leaving.


Suppose we agree that everyone has a right to life, but that a person forfeits this right when he threatens the life of another — in that case it’s permissible to kill him.

Now consider three people, A, B, and C. A aims a gun at B, B aims a gun at C, and C aims a gun at A. When A takes aim, he’s threatening another person, so he loses his own right to life. Normally in that case C would be justified in killing him, since this defends B. But B is aiming at C, which means he forfeits his own right to life … which means that A can kill him, and that C can’t kill A.

There seems no way to resolve this under the rules we’ve laid out. “Each actor has a right to life if he or she lacks a right to life and lacks a right to life if he or she has a right to life,” wrote University of Tulsa law professor Russell Christopher, who offered the puzzle in 1998. He uses it to suggest that subjective factors such as motive, belief, and knowledge must be considered when making these judgments.

(Russell Christopher, “Self-Defense and Defense of Others,” Philosophy & Public Affairs, Spring 1998)

See The Bystander Paradox.