Futility Closet book ad

Society

The Dancing Plague

http://commons.wikimedia.org/wiki/File:Dancingmania1.jpg

In July 1518, a woman named Frau Troffea stepped into a street in Strasbourg and began to dance. As onlookers gathered it became clear that she could not stop; after many hours of exertion she collapsed and slept briefly but then rose and again began the dance. After three exhausting days she was bundled into a wagon and taken to a shrine in the Vosges Mountains, but her example had had its effect. Within days more than 30 more people had begun to dance uncontrollably, and their numbers grew; according to one chronicle, within a month 400 people were dancing.

The fact of the plague is well attested; a manuscript chronicle in the city’s archives reads:

There’s been a strange epidemic lately
Going amongst the folk,
So that many in their madness
Began dancing,
Which they kept up day and night,
Without interruption,
Until they fell unconscious.
Many have died of it.

The sickness lasted until early September, when it passed away just as mysteriously. A number of explanations have been put forward, including convulsion brought on by ergot, a mold that flourishes on the stalks of damp rye. The most convincing was advanced by John Waller in his 2008 book A Time to Dance, A Time to Die: He found that a series of famines had preceded the dancing plague, spreading fear and anxiety through the city, and that a Christian church legend had told that a wrathful Saint Vitus would send down plagues of compulsive dancing on anyone who angered him. The dancing, Waller believes, was a “mass psychogenic illness” brought on by this belief.

Vanderbilt epidemiologist Timothy Jones says the plague is “of immense historical value”; it “tells us much about the extraordinary supernaturalism of late medieval people, but it also reveals the extremes to which fear and irrationality can lead us.”

“Socrates Among the Athenians”

socrates among the athenians

– Louis Phillips, Academe, February 1979

Rubbing Elbows

http://commons.wikimedia.org/wiki/File:Palais_Ferstel.jpg

Vienna’s Café Central was crowded with intellectuals at the turn of the 20th century, including Freud, Lenin, the Vienna Circle of logical positivists, and endless chessplayers.

When Victor Adler made the argument that war would provoke a revolution in Russia, Leopold Berchtold replied, “And who will lead this revolution? Perhaps Mr. Bronstein sitting over there at the Café Central?”

Mr. Bronstein was Leon Trotsky.

Social Studies

From Benoni Lanctot’s Chinese and English Phrase Book (1867), phrases for English-speaking employers of Chinese-Americans:

  • Can you get me a good boy?
  • He wants $8.00 per month.
  • He ought to be satisfied with $6.00.
  • When I find him useful, I will give him more.
  • I think he is very stupid.
  • Do you know how to count?
  • If you want to go out, you must ask me.
  • Come at seven every morning.
  • Go home at eight every night.
  • This lamp is not clean.
  • See that the money is weighed.
  • If there is any thing short, I will make him pay the difference.
  • Take this plate away.
  • Change this napkin.
  • Did you prepare any toast?
  • The tea is too strong.
  • Make me a pigeon pie.
  • Get a bottle of beer.
  • Please carve that capon.
  • Tell the cook to roast it better next time.
  • This wine glass is not clean.
  • The cook is very strange.
  • Sometimes he spoils the dishes.
  • Tell the cook to fry some pancakes.
  • Don’t burn them.
  • He did very bad last time.
  • I want to cut his wages.
  • This tea is very bad.
  • Get out of the way.
  • Don’t speak with me.
  • Who gives you permission?
  • Don’t be lazy.
  • You ought not to do so.
  • Pick this up.
  • This is nothing to you.
  • He is fit for nothing.
  • That belongs to me.
  • Carry it up stairs.
  • You ought to be contented.

Phrases for Chinese speakers:

  • Good morning sir.
  • When shall I begin?
  • I beg your pardon.
  • Lunch is on the table, sir.
  • I beg you to consider again.
  • It is my duty.
  • Sir, what will you have for dinner to-day?
  • You must excuse me.
  • You must not strike me.

Absentee Ballots

http://commons.wikimedia.org/wiki/File:Declaration_independence.jpg

Can one generation bind another, and all others, in succession forever? I think not. The Creator has made the earth for the living, not the dead. Rights and powers can only belong to persons, not to things, not to mere matter, unendowed with will. The dead are not even things. The particles of matter which composed their bodies, make part now of the bodies of other animals, vegetables, or minerals, of a thousand forms. To what then are attached the rights and powers they held while in the form of men? A generation may bind itself as long as its majority continues in life; when that has disappeared, another majority is in place, holds all the rights and powers their predecessors once held, and may change their laws and institutions to suit themselves. Nothing then is unchangeable but the inherent and unalienable rights of man.

– Thomas Jefferson, letter to Maj. John Cartwright, June 5, 1824

Tradition means giving votes to the most obscure of all classes — our ancestors. It is the democracy of the dead. Tradition refuses to submit to the small and arrogant oligarchy of those who merely happen to be walking around.

– G.K. Chesterton

Unquote

“[John] von Neumann gave me an interesting idea: that you don’t have to be responsible for the world that you’re in. So I have developed a very powerful sense of social irresponsibility as a result of von Neumann’s advice. It’s made me a very happy man ever since. But it was von Neumann who put the seed in that grew into my active irresponsibility!” — Richard Feynman

He expands on this in Christopher Sykes’ No Ordinary Genius (1994):

“I got the idea of ‘active irresponsibility’ in Los Alamos. We often went on walks, and one day I was with the great mathematician von Neumann and a few other people. I think Bethe and von Neumann were discussing some social problem that Bethe was very worried about. Von Neumann said, ‘I don’t feel any responsibility for all these social problems. Why should I? I’m born into the world, I didn’t make it.’ Something like that. Well, I’ve read von Neumann’s autobiography and it seems to me that he felt perpetually responsible, but at that moment this was a new idea to me, and I caught onto it. Around you all the time there are people telling you what your responsibilities are, and I thought it was kind of brave to be actively irresponsible. ‘Active’ because, like democracy, it takes eternal vigilance to maintain it — in a university you have to perpetually watch out, and be careful that you don’t do anything to help anybody!”

Hans Bethe:

“Feynman somehow was proud of being irresponsible. He concentrated on his science, and on enjoying life. There are some of us — including myself — who felt after the end of the Second World War that we had a great responsibility to explain atomic weapons, and to try and make the government do sensible things about atomic weapons. … Feynman didn’t want to have anything to do with it, and I think quite rightly. I think it would be quite wrong if all scientists worked on discharging their responsibility. You need some number of them, but it should only be a small fraction of the total number of scientists. Among the leading scientists, there should be some who do not feel responsible, and who only do what science is supposed to accomplish.”

Marvin Minsky:

“I must say I have a little of this sense of social irresponsibility, and Feynman was a great inspiration to me — I have done a good deal of it since. There are several reasons for a scientist to be irresponsible, and one of them I take very seriously: people say, ‘Are you sure you should be working on this? Can’t it be used for bad?’ Well, I have a strong feeling that good and bad are things to be thought about by people who understand better than I do the interactions among people, and the causes of suffering. The worst thing I can imagine is for somebody to ask me to decide whether a certain innovation is good or bad.”

Young American

Thomas Jefferson received the following letter on July 31, 1806:

To his Excelency Thomas Jefferson Esq.

Sir.

It is A Boy of 15 years Old Address to You the following lines. I feel A Strong regard for my Country’s welfair.

I think if I had A been Presendent at the time them opposen Set of People (I allude to the Brittish) appeared before Newyork I Should A been for rasing all the Naval force in the United States and opposed thire proceeding’s. My Father is an Englishman Born. Ever Sence I had an knowledge of Nation affaires I dispised them tirents as there are. I often read of the American War. I fear they Never will Come hear Again. I think if they Should I take up armes boy as I am in my Country’s Defence. If every one was as true to thier Country as me I think the Contest last war would not of been of so long Duration. Conquer or Die is my Wash Word.

A True American though a Youth

Huza to the Constetuon
Huza to the Repubeck
Huza Fredom Independence
Huza to all America.
PS. Sir Excuse the spelling.

Admittance

http://www.sxc.hu/photo/380514

After observing security measures at a number of organizations, University of California psychologist Robert Sommer reflected that a person’s status seems to be tied to his keyring:

key status formula

S is a person’s status within the organization, D is the number of doors he must open to perform his job, and K is the number of keys he carries. A janitor who can open 20 doors but must carry 20 keys has a status of 1; he’s outranked by a secretary who can open only two doors but can do it with a single key. A staff scientist who can open six doors or cupboards using two keys has status 3, and the lab director might open 15 doors with three keys, giving him a status score of 5.

They’re all outranked by the president of the company, who never has to carry keys at all, since there’s always someone around to open doors for him. “With a K of zero and a high D,” Sommer concluded wryly, “his status rank in the company reaches infinity.”

(“Keys, Kings and Kompanies,” from The Worm Runner’s Digest 3:1 [March 1961], 52-54)

A Tall Tail

http://commons.wikimedia.org/wiki/File:Halley%27s_Comet_-_May_29_1910.jpg

As skywatchers prepared for the return of Halley’s comet in 1910, their excitement turned to trepidation when astronomer Camille Flammarion warned that cyanogen gas in the comet’s tail could poison the atmosphere. The New York Times reported growing alarm among astronomers and warned, “Prof. Flammarion is of the opinion that the cyanogen gas would impregnate the atmosphere and possibly snuff out all life on the planet.” The Washington Post quoted astronomer Henri Deslandres that the comet might cause torrential rains; his colleague D.J. McAdam warned that “Disease and death have frequently been ascribed to the admixture of cometary gases with the air.”

As the fateful date approached, an ad appeared in a South African newspaper: “Gentleman having secured several cylinders of oxygen and having bricked up a capacious room wishes to meet others who would share the expense for Wednesday night. Numbers strictly limited.” In Texas, salesmen went door to door selling “comet pills” and leather inhalers. In Germany, anxious residents began wearing comet hats and carrying comet umbrellas.

On the evening of May 18, as Earth passed into the comet’s tail, hundreds marched in a candlelight parade in San Juan, and prayer vigils were held in St. Petersburg churches and on the hilltops around Mexico City. In Lexington, Ky., excited citizens held all-night services, “praying and singing to prepare … [to] meet their doom.”

Nothing happened. Well, nearly nothing: In Towaco, N.J., two men had offered to pay $10 for the best description of the event as viewed from Walkman Mountain. When the town’s weary residents returned from their vigil, they found their chicken coops empty.

Swift Swords

http://commons.wikimedia.org/wiki/File:Alexander_von_Bensa_Das_Duell.jpg

Ben Franklin considered dueling a senseless practice, as “whichever is killed the point in dispute remains unsettled”:

To this purpose they have a pleasant little story here. A gentleman in a coffee-house desired another to sit further from him. ‘Why so?’ ‘Because, sir, you stink.’ ‘That is an affront, and you must fight me.’ ‘I will fight you if you insist upon it; but I do not see how that will mend the matter. For if you kill me, I shall stink too; and if I kill you, you will stink, if possible, worse than you do at present.’

(From a letter to Thomas Percival, July 17, 1784.)

Righteousness

The autobiography of the 12th-century Muslim poet Usama ibn Munqidh tells of an incident in which the invading Crusaders appealed for a doctor to treat some of their number who had fallen ill. The Muslims sent a doctor named Thabit, who returned after 10 days with this story:

They took me to see a knight who had an abscess on his leg, and a woman with consumption. I applied a poultice to the leg, and the abscess opened and began to heal. I prescribed a cleansing and refreshing diet for the woman. Then there appeared a Frankish doctor, who said: ‘This man has no idea how to cure these people!’ He turned to the knight and said: ‘Which would you prefer, to live with one leg or die with two?’ When the knight replied that he would prefer living with one leg, he sent for the strong man and a sharp axe. They arrived, and I stood by to watch. The doctor supported the leg on a block of wood, and said to the man: ‘Strike a mighty blow, and cut cleanly!’ … The marrow spurted out of the leg (after the second blow) and the patient died instantaneously. Then the doctor examined the woman and said: ‘She has a devil in her head who is in love with her. Cut her hair off!’ This was done, and she went back to eating her usual Frankish food … which made her illness worse. ‘The devil has got into her brain,’ pronounced the doctor. He took a razor and cut a cross on her head, and removed the brain so that the inside of the skull was laid bare … the woman died instantly. At this juncture I asked whether they had any further need of me, as they had none I came away, having learnt things about medical methods that I never knew before.

Cardiology

In other words, this is the day on which those charming little missives, ycleped Valentines, cross and intercross each other at every street and turning. The weary and all for-spent twopenny postman sinks beneath a load of delicate embarrassments, not his own. It is scarcely credible to what an extent this ephemeral courtship is carried on in this loving town, to the great enrichment of porters, and detriment of knockers and bell-wires. In these little visual interpretations, no emblem is so common as the heart,–that little three-cornered exponent of all our hopes and fears,–the bestuck and bleeding heart; it is twisted and tortured into more allegories and affectations than an opera-hat. What authority we have in history or mythology for placing the head-quarters and metropolis of god Cupid in this anatomical seat rather than in any other, is not very clear; but we have got it, and it will serve as well as any other thing. Else we might easily imagine, upon some other system which might have prevailed for any thing which our pathology knows to the contrary, a lover addressing his mistress, in perfect simplicity of feeling, ‘Madam, my liver and fortune are entirely at your disposal;’ or putting a delicate question, ‘Amanda, have you a midriff to bestow?’ But custom has settled these things, and awarded the seat of sentiment to the aforesaid triangle, while its less fortunate neighbours wait at animal and anatomical distance.

– Charles Lamb, Essays of Elia, 1823

A mathematical valentine:

http://commons.wikimedia.org/wiki/File:Heart3D.png

Justice Confused

Suppose that a house is robbed and police find a strand of the burglar’s hair at the scene of the crime. A suspect is in custody, and tests show that the strand matches his hair. A forensic scientist testifies that the chance of a random person producing such a match is 1/2000. Does this mean that there’s a 1999/2000 chance that the suspect is guilty?

No, it doesn’t. In a city of 5 million there will be 1/2000 × 5,000,000 = 2,500 people who produce a match, so on the basis of this evidence alone the probability that the suspect is guilty is only 1/2500.

In a 1987 article, William Thomson and Edward Schumann dubbed this “prosecutor’s fallacy.” Unfortunately, it’s matched by the “defense attorney’s fallacy,” which holds that the hair-match evidence is worthless because it increases the likelihood of the suspect’s guilt by a negligible amount, 1/2500. In fact it drastically narrows the range of possible suspects, from 5 million to 2,500, while failing to exclude the defendant, hardly cause for confidence.

Worryingly, Thompson and Schumann found an experienced prosecutor who insisted that if a defendant and a perpetrator match on a blood type found in 10 percent of the population, then there’s a 10 percent chance that the defendant would have this blood type if he were innocent and hence a 90 percent chance that he’s guilty. “If a prosecutor falls victim to this error,” they write, “it is possible that jurors do as well.”

(William C. Thompson and Edward L. Schumann, “Interpretation of Statistical Evidence in Criminal Trials,” Law and Human Behavior, 11:3 [September 1987], 167-187)

Fixing Dates

In 1899, British statistician Moses B. Cotsworth noted that recordkeeping could be greatly simplified if each month contained a uniform number of whole weeks. He proposed an “international fixed calendar” containing 13 months of 28 days each:

international fixed calendar

This makes everything easier. The 26th of every month falls reliably on a Thursday, for example, and statistical comparisons between months are made more accurate, as each month contains four tidy weeks with four weekends. (Unfortunately for the superstitious, every one of the 13 months contains a Friday the 13th.) A new month, called Sol, would be wedged between June and July, and an extra day, “Year Day,” would be added at the end of the year, but it would be independent of any month (as would Leap Day).

In 1922 the League of Nations chose Cotsworth’s plan as the most promising of 130 proposed calendar reforms, but the public, as always, resisted the unfamiliar, and by 1937 the International Fixed Calendar League had closed its doors. It left one curious legacy, though: George Eastman, the founder of Eastman Kodak, was so pleased with Cotsworth’s scheme that he adopted it as his company’s official calendar — and it remained so until 1989.

A Penny Saved

https://commons.wikimedia.org/wiki/File:Benjamin_Franklin_statue_at_National_Portrait_Gallery_IMG_4374.JPG

Ben Franklin’s “necessary hints to those that would be rich,” written around 1730:

  • The use of money is all the advantage there is in having money.
  • For six pounds a year you may have the use of one hundred pounds, provided you are a man of known prudence and honesty.
  • He that spends a groat a day idly, spends idly above six pounds a year, which is the price for the use of one hundred pounds.
  • He that wastes idly a groat’s worth of his time per day, one day with another, wastes the privilege of using one hundred pounds each day.
  • He that idly loses five shillings worth of time, loses five shillings, and might as prudently throw five shillings into the sea.
  • He that loses five shillings, not only loses that sum, but all the advantages that might be made by turning it in dealing, which, by the time that a young man becomes old, will amount to a considerable sum of money.
  • Again: he that sells upon credit, asks a price for what he sells equivalent to the principal and interest of his money for the time he is to be kept out of it; therefore, he that buys upon credit, pays interest for what he buys, and he that pays ready money, might let that money out to use: so that he that possesses any thing he has bought, pays interest for the use of it.
  • Yet, in buying goods, it is best to pay ready money, because he that sells upon credit expects to lose five per cent by bad debts; therefore he charges, on all he sells upon credit, an advance, that shall make up that deficiency.
  • Those who pay for what they buy upon credit, pay their share of this advance.
  • He that pays ready money, escapes, or may escape, that charge.
  • A penny sav’d is two-pence clear, A pin a day’s a groat a year.

Humility

From a letter from Benjamin Franklin to Samuel Mather, May 12, 1784:

You mention your being in your seventy-eighth year; I am in my seventy-ninth; we are grown old together. It is now more than sixty years since I left Boston, but I remember well both your father and grandfather, having heard them both in the pulpit and seen them in their houses. The last time I saw your father [Cotton Mather] was in the beginning of 1724, when I visited him after my first trip to Pennsylvania. He received me in his library, and on my taking leave showed me a shorter way out of the house through a narrow passage, which was crossed by a beam overhead. We were still talking as I withdrew, he accompanying me behind, and I turning partly towards him, when he said hastily, ‘Stoop, stoop!’ I did not understand him, till I felt my head hit against the beam. He was a man that never missed any occasion of giving instruction, and upon this he said to me, ‘You are young, and have the world before you; STOOP as you go through it, and you will miss many hard thumps.’ This advice, thus beat into my head, has frequently been of use to me; and I often think of it, when I see pride mortified, and misfortunes brought upon people by their carrying their heads too high.

B. Franklin.

Looking Up

Planetary economy will be a determining factor in the change of diet which the coming century must inevitably witness. Such a wasteful food as animal flesh cannot survive: and even apart from the moral necessity which will compel mankind, for its own preservation, to abandon the use of alcohol, the direct and indirect wastefulness of alcohol will make it impossible for beverages containing it to be tolerated. Very likely tobacco will follow it.

– T. Baron Russell, A Hundred Years Hence, 1905

Good Boy

An epitaph in the Pine Forest cemetery in Wilmington, N.C., reads:

“JIP” JONES
BORN SEPT. 24, 1894
DIED MAY 18, 1904

THIS WAS THE ONLY DOG WE EVER KNEW
THAT ATTENDED CHURCH EVERY SUNDAY

Actually, dogs commonly attended services in former times. Indeed, until the 19th century, they could be so numerous that churches employed “dog whippers” to remove unruly dogs during services. The Great Church of St. Bavo in Haarlem, the Netherlands, contains a carving of the hondenslager at work (above).

The 18th-century zoologist Carl Linnaeus used to attend mass with his dog Pompe. Linnaeus always left after an hour, regardless of whether the sermon was finished. It’s said that when he was sick Pompe would arrive at the service alone, stay for the customary hour, and depart.

“Heaven goes by favor,” wrote Mark Twain. “If it went by merit, you would stay out and your dog would go in.”

Box Scores

http://commons.wikimedia.org/wiki/File:Family_watching_television_1958.jpg

“It is probable that television drama of high caliber and produced by first-rate artists will materially raise the level of dramatic taste of the nation.” — RCA president David Sarnoff, 1939

“Television? The word is half Greek and half Latin. No good can come of it.” — Manchester Guardian editor C.P. Scott, 1928

“Television won’t matter in your lifetime or mine.” — Rex Lambert, The Listener, 1936

“Television won’t last because people will soon get tired of staring at a plywood box every night.” — movie producer Darryl Zanuck, 1946

“Television won’t last. It’s a flash in the pan.” — BBC school broadcasting director Mary Somerville, 1948

“How can you put out a meaningful drama or documentary that is adult, incisive, probing, when every fifteen minutes the proceedings are interrupted by twelve dancing rabbits with toilet paper?” — Rod Serling, 1974

“I hate television. I hate it as much as peanuts. But I can’t stop eating peanuts.” — Orson Welles, 1956

Skin Deep

During the filming of Planet of the Apes in 1967, Charlton Heston noted “an instinctive segregation on the set. Not only would the apes eat together, but the chimpanzees ate with the chimpanzees, the gorillas ate with the gorillas, the orangutans ate with the orangutans, and the humans would eat off by themselves. It was quite spooky.”

James Franciscus noticed the same thing filming Beneath the Planet of the Apes in 1969. “During lunch I looked up and realized, ‘My God, here is the universe,’ because at one table were all the orangutans eating, at another table were the apes, and at another table were the humans. The orangutan characters would not eat or mix with the ape characters, and the humans wouldn’t sit down and eat with any one of them.

“I remember saying, ‘Look around — do you realize what’s happening here? This is a little isolated microcosm of probably what’s bugging the whole world. Call it prejudice or whatever you want to call it. Whatever’s different is to be shunned or it’s frightening or so forth.’ Nobody was intermingling, even though they were all humans underneath the masks. The masks were enough to bring out our own little genetic natures of fear and prejudice. It was startling.”

(From Joe Russo and Larry Landsman, Planet of the Apes Revisited, 2001.)

Addition and Subtraction

http://commons.wikimedia.org/wiki/File:United_States_Capitol_-_west_front_edit.jpg

In Mathematical Applications of Political Science, University of Minnesota political scientist William Riker describes a worrisome voting paradox that unfolded in the U.S. House of Representatives in 1956. At issue was a bill calling for federal aid for school construction; an amendment was proposed that would have offered this aid only to states whose schools were integrated. The House was divided into three interest groups:

  • Republicans opposed federal aid in general but supported integration. They would have preferred no bill at all but favored the amended bill to the original.
  • Northern Democrats wanted the amended bill but would accept the original bill rather than have no bill at all.
  • Southern Democrats, whose schools were segregated, favored the original bill but would prefer to have no bill rather than accept the amendment.

education bill bloc preferences

Clearly the original bill would have passed, as the Democrats as a group preferred it to having no bill at all. But, following procedure, the House voted first on whether to accept the amendment, and here the Republicans and the northern Democrats combined to support it, since both preferred the amended bill to the original bill. The second vote addressed whether to accept the now-amended bill, and now the Republicans and the southern Democrats united to kill it, since both preferred no bill to the amended bill.

So the original bill was popular, and the proposed amendment was popular, but combining them led to the bill’s defeat. “As if it were not enough that the choice may depend on the voting order, this fact can be used to twist the outcome of the legislative process,” Riker writes. “It may be possible to create a voting paradox such that no action is taken by the legislature even though a proposed bill would have passed prior to the creation of the paradox. A legislator could introduce an amendment to create such a paradox, and if the voting order were just right, the amended proposal would then be defeated.”

Apportionment Paradoxes

http://commons.wikimedia.org/wiki/File:United_States_Capitol_-_west_front_edit.jpg

Until 1911, the U.S. House of Representatives grew along with the country. Accordingly, when the 1880 census showed an increase in population, C.W. Seaton, chief clerk of the census office, worked out apportionments for all House sizes between 275 and 350, in order to see which states would get the new seats.

He was in for a surprise. The method was straightforward: Take the total U.S. population and divide it by the proposed number of seats in the House, rounding all fractions down. This would dispose of most of the seats; any leftover seats would be awarded to the states whose fractional remainders had been highest. But Seaton discovered an oddity:

alabama paradox

If the House had 299 seats, Alabama would get 8 representatives (because its remainder, .646, was higher than that of Texas or Illinois). But if the House had 300 seats it would get only 7 (the extra representative would now go to Illinois, whose remainder had surpassed Alabama’s). The problem is that the “fair share” of a large state increases more quickly than that of a small state.

Seaton called this the Alabama paradox. A related problem is the population paradox: If the method above had been used in 1901 to reallocate 386 seats in the House, Virginia would have lost a seat to Maine even though the ratio of their populations had increased from 2.67 to 2.68:

population paradox

Here, even though the size of the House has not changed, a fast-growing state receives fewer representatives than a slow-growing one.

In 1982 mathematicians Michel Balinski and Peyton Young showed that if each party gets one of the two numbers closest to its fair share of seats, then any system of apportionment will run into one of these paradoxes. The solution, it seems clear, is to start cutting legislators into pieces.

(These data are from Hannu Nurmi’s Voting Paradoxes and How to Deal With Them, 1999. Balinski and Young’s book is Fair Representation: Meeting the Ideal of One Man, One Vote.)

The Centipede Game

Before you are two piles of coins. One contains 4 coins and the other contains 1. If you like, you can keep the larger pile, give me the smaller, and end the game. Or you can pass both piles to me. In that case the size of each pile doubles and I’m given the same option — I can keep the larger pile and give you the smaller one, or I can pass both piles back to you, in which case they’ll double again.

We both know that the game will end after six rounds. At that point I’ll have the coins and will win 128 coins to your 32. You’d be better off stopping the game in round 5, when you’ll have 64 coins and I have 16. But, by similar reasoning, I’d prefer round 4 to round 5, and you’d prefer round 3 to round 4 … if we rely on each other to be purely rational, it seems your best opening move is to end the game at once and keep 4 coins. This is less than you’d make in round 6, but it appears that purely rational play will never reach that round.

In practice, interestingly, human beings don’t do this — almost no one stops at the first opportunity, even after several repetitions of the game. Why they do so is not clear — possibly they’re hoping that their opponent has not reasoned through the whole game, or perhaps they’re agreeing tacitly to cultivate the pot in hopes of being the first one to cash out abruptly; perhaps the satisfaction of anticipating such a victory makes the risk worthwhile.

In lab tests in 2009, economists Ignacio Palacios-Huerta and Oscar Volij found that only 3 percent of games between students ended in the first round, but 69 percent of games between chess players did so. This rose to 100 percent when the first player was a grandmaster. They conclude that the most important factor is common knowledge of the players’ rationality, rather than altruism or social preferences.

(Ignacio Palacios-Huerta and Oscar Volij, “Field Centipedes,” American Economic Review 99 (4): 1619–1635.)

The Little Man

In 1525, more than 100,000 German peasants demanded an end to serfdom and were massacred by the well-organized armies of the ruling class. After observing the ornate memorials with which the aristocrats congratulated themselves, Albrecht Dürer proposed a similarly baroque monument to the slain peasants:

Place a quadrangular stone block measuring ten feet in width and four feet in height on a quadrangular stone slab which measures twenty feet in length and one foot in height. On the four corners of the ledge place tied-up cows, sheep, pigs, etc. But on the four corners of the stone block place four baskets, filled with butter, eggs, onions, and herbs, or whatever you like. In the centre of this stone block place a second one, measuring seven feet in length and one foot in height. On top of this second block place a strong chest four feet high, measuring six and a half feet wide at the bottom and four feet wide at the top. Then place a kettle upside down on top of the chest. The kettle’s diameter should be four and a half feet at the rim and three feet at its bottom. Surmount the kettle with a cheese bowl which is half a foot high and two and a half feet in diameter at the bottom. Cover this bowl with a thick plate that protrudes beyond its rim. On the plate, place a keg of butter which is three feet high and two and a half feet in diameter at the bottom. Cover this bowl with a thick plate that protrudes beyond its rim. On the plate, place a keg of butter which is three feet high and has a diameter of a foot and a half at the bottom, and of only a foot at the top. Its spout should protrude beyond this. On the top of the butter keg, place a well-formed milk jug, two and a half feet high, and with a diameter which is one foot at its bulge, half a foot at its top, and is wider at its bottom. Into this jug put four rods branching into forks on top and extending five and a half feet in height, so that the rods will protrude by half a foot, and then hang peasants’ tool on it – like hoes, pitchforks, flails, etc. The rods are to be surmounted by a chicken basket, topped by a lard tub upon which sits an afflicted peasant with a sword stuck into his back.

What would that look like?

durer peasants memorial