Half of Everything

If two people want to split up amicably, the easiest solution is to divide their assets equally, with each partner getting 0.5. But suppose that one partner goes to a lawyer who charges a fee f but promises to get more, by an amount m + f, leaving his client better off by the amount m. If this happens, then the second partner will get only 0.5 – m – f. If the second partner engages their own lawyer then the split is equal again, except that now the lawyers’ fees must be paid:

robin table

This is an example of the so-called prisoner’s dilemma: Both sides would be better off if they left the lawyers out of it, but if one engages a lawyer than the other had better do so as well.

Now suppose that each partner can choose the amount of lawyer time to buy, and that they get a payoff that’s proportional to the amount they spend. If one spends x on lawyers and the other spends y, each measured as a fraction of the total assets, then the first partner should receive an amount given by:

$\frac{x(1-x-y)}{x+y}$

An industrious divorcee can now use calculus to maximize this expression, varying x and keeping y constant. The optimum value of x turns out to be $\sqrt{y}-y$ . If my partner spends 9%, or 0.09, of our assets on lawyers, then I should spend $\sqrt{0.09}-0.09=0.21$ . Then my partner will get 0.21 of the assets, and I’ll get 0.49, and the lawyers get the rest.

Well, now what? Knowing all this, what’s our best course? If we could trust each other then we’d each pay a pittance on lawyers and get nearly 0.5 each. But I’m aware that if you pay a millionth and I pay a thousandth (still nearly a pittance), I’ll get nearly 99.9% of our assets. And simply resolving to outspend you won’t work: If you spend 0.36 then I should spend 0.24; I’ll come away with less than you, but this is the best I can do.

robin graph

“Looking at the graph of $x=\sqrt{y}-y$ , above, we (the author and reader) see that y = 0.25 gives us x = 0.25, and this gives us a sort of stability,” writes Anthony C. Robin in the Mathematical Gazette. “Neither partner can pull a fast one over the other, and it results in the assets being equally shared between us, them, and the lawyers. No doubt this is the reason why lawyers are so rich in our society!”

(Anthony C. Robin, “How Lawyers Make a Living,” Mathematical Gazette 88:512 [July 2004], 313-315.)

September 10, 2015September 9, 2015 | Science & Math · Society

Man Handling

date

In 1946, sociologist Mirra Komarovsky asked American undergraduate women whether they had “played dumb” on dates. Some of their responses:

I am engaged to a southern boy who doesn’t think too much of the woman’s intellect. In spite of myself, I play up to his theories because the less one knows and does, the more he does for you and thinks you “cute” into the bargain. … I allow him to explain things to me in great detail and to treat me as a child in financial matters.
When my date said that he considers Ravel’s Bolero the greatest piece of music ever written, I changed the subject because I knew I would talk down to him.
One of the nicest techniques is to spell long words incorrectly once in a while. My boyfriend seems to get a great kick out of it and writes back, “Honey, you certainly don’t know how to spell.”
Once I went sailing with a man who so obviously enjoyed the role of a protector that I told him I didn’t know how to sail. As it turned out he didn’t either. We got into a tough spot, and I was torn between a desire to get a hold of the boat and a fear to reveal that I had lied to him.
I am better in math than my fiancé. But while I let him explain politics to me, we never talk about math even though, being a math major, I could tell him some interesting things.
I was once at a work camp. The girls did the same work as the boys. If some girls worked better, the boys resented it fiercely. The director told one capable girl to slow down to keep peace in the group.
On dates I always go through the “I-don’t-care-anything-you-want-to-do” routine. It gets monotonous but boys fear girls who make decisions. They think such girls would make nagging wives.
I am a natural leader and, when in the company of girls, usually take the lead. That is why I am so active in college activities. But I know that men fear bossy women, and I always have to watch myself on dates not to assume the “executive” role. Once a boy walking to the theater with me took the wrong street. I knew a short cut but kept quiet.

In all, 60 percent said they had “concealed some academic honor, pretended ignorance of some subject, or allowed the man the last word in an intellectual discussion.” “And the funny part of it is that the man, I think, is not always so unsuspecting,” one said. “He may sense the truth and become uneasy in the relation. ‘Where do I stand? Is she laughing up her sleeve or did she mean this praise? Was she really impressed with that little speech of mine or did she only pretend to know nothing about politics?’ And once or twice I felt that the joke was on me: the boy saw through my wiles and felt contempt for me for stooping to such tricks.”

(Mirra Komarovsky, “Cultural Contradictions and Sex Roles,” American Journal of Sociology 52:3 [November 1946], 184-189.)

August 28, 2015August 27, 2015 | Society

In a Word

thersitical
adj. abusive, foul-mouthed, reviling

In his Recollections of the Civil War, Charles Anderson Dana called Union general Andrew Atkinson Humphreys “one of the loudest swearers that I ever knew.” “The men of distinguished and brilliant profanity in the war were General Sherman and General Humphreys — I could not mention any others that could be classed with them. General Logan also was a strong swearer, but he was not a West Pointer: he was a civilian. Sherman and Humphreys would swear to make everything blue when some dispatch had not been delivered correctly or they were provoked.”

In Rex v. Sparling (1722), a leather dresser named James Sparling was alleged in the course of 10 days to “profanely swear fifty-four oaths, and profanely curse one hundred and sixty curses, contra formam statuti.” His conviction was overturned because the charge sheet had failed to list them. “For what is a profane oath or curse is a matter of law, and ought not to be left to the judgment of the witness … it is a matter of great dispute among the learned, what are oaths and what curses.”

When in 1985 a man named Callahan called a California highway patrolman a “fucking asshole,” California Court of Appeal Justice Gerald Brown referred to this phrase as the “Callahan epithet” to avoid having to repeat it continuously, “which arguably would assist its passage into parlor parlance.” And he reversed Callahan’s conviction:

A land as diverse as ours must expect and tolerate an infinite variety of expression. What is vulgar to one may be lyric to another. Some people spew four-letter words as their common speech such as to devalue its currency; their repetition dulls the senses; Billingsgate thus becomes commonplace. Not everyone can be a Daniel Webster, a William Jennings Bryan or a Joseph A. Ball. …

Fifty years ago the words ‘damn’ and ‘hell’ were as shocking to the sensibilities of some people as the Callahan epithet is to others today. The first word in Callahan’s epithet has many meanings. When speaking about coitus, not everyone can be an F.E. Smith (later Earl of Birkenhead) who, in his speech in 1920 in the House of Commons on the Matrimonial Causes Act, referred to ‘that bond by which nature in its ingenious telepathy has contrived to secure and render agreeable the perpetuation of the species.’

August 27, 2015August 26, 2015 | Crime · Language · Society

Spirit Reading

During Prohibition, an enforcement agent had a tough job: If he infiltrated a speakeasy and ordered a drink to confirm that it was alcoholic, his oral testimony could easily be attacked in court, and, ironically, once he admitted that he drank alcohol regularly then defense attorneys could question his reliability.

Robert Tetro patented this solution in 1930. Instead of drinking your drink, you’d discreetly clip a tube over the rim of the glass, reach into your pocket and squeeze a bulb, drawing off a sample. Then you’d pay your tab and leave. If the sample proved alcoholic then the feds could raid the place, which had no warning that it was under surveillance. And now the authorities had physical proof that alcohol was being served.

In the patent application, Tetro says his invention “has been used to a considerable extent, proving its value.” He was based in Michigan; I don’t know how widely it was used.

August 26, 2015July 1, 2017 | Crime · Society · Technology

Fair Play

An extraordinary scene took place on Saturday last at a small village within three miles of Middleton. A half-witted fellow named James Driscott had cruelly ill-used his donkey. He was told by several of the villagers that he would be brought up before the magistrates and severely punished; but his informants said that if he consented to do penance for his inhuman conduct, no information should be laid against him. Discott gladly agreed to the proposed terms. The donkey was placed in the cart, and its owner, with the collar round his neck, was constrained to drag his four-footed servant through the village. The scene is described by a local reporter as being the most laughter-moving one he had ever witnessed.

— Illustrated Police News, Jan. 22, 1876

August 11, 2015August 8, 2015 | Crime · Oddities · Society

Reflections

More maxims of La Rochefoucauld:

“Those who are deceived by our Cunning don’t appear near so ridiculous to us, as we seem to ourselves, when deceived by the Cunning of others.”
“The World oftner rewards the Appearance of Merit than Merit itself.”
“The Calm, or Disquiet, of our Temper depends not so much on Affairs of Moment; as on an agreeable, or disagreeable, Disposition of the Trifles that daily occur.”
“In Misfortunes we often mistake Dejection for Constancy; and we bear them, without daring to look on them; as Cowards suffer themselves to be kill’d, without Resistance.”
“How brilliant soever an Action may be, it ought not to pass for Great when it is not the Effect of a Great Design.”
“There are Crimes which become innocent, and even glorious, thro their Splendor, Number, and Excess: Hence it is, that public theft is call’d Address; and to seize on Provinces unjustly, to make Conquests.”
“‘Tis easier to appear worthy of the Employments we have not, than of those we have.”
“‘Tis difficult to love those we don’t esteem; but ’tis no less difficult to love those we esteem much more than ourselves.”
“Every body speaks well of his Heart, but no body dares speak well of his Head.”
“Flattery is a sort of bad Money to which our Vanity gives Currency.”
“Those who are incapable of great Crimes don’t readily suspect others of them.”
“Fortune breaks us of many Faults, which Reason cannot.”
“We easily excuse in our Friends the Faults that don’t affect us.”
“None are so happy, or unhappy, as they imagine.”

August 5, 2015 | Literature · Society

No Answer

In 1890 the editor of the New York World invited Mark Twain to offer a message of holiday goodwill to its readers. He sent this:

It is my heart-warm and world-embracing Christmas hope and aspiration that all of us — the high, the low, the rich, the poor, the admired, the despised, the loved, the hated, the civilized, the savage — may eventually be gathered together in a heaven of everlasting rest and peace and bliss — except the inventor of the telephone.

Mark Twain
Hartford, Dec. 23

August 1, 2015 | Literature · Society

Taber Bills

In 1799, Massachusetts passed a law restricting private banking companies from issuing their own currency notes without the consent of the legislature. This was well intended: If unlimited paper money were allowed to circulate, the resulting inflation would play havoc with the finances of ordinary people.

Unfortunately, the result was that legitimate currency became harder and harder to find. In Maine, where only a single bank existed, people were increasingly desperate for currency, and so the Portland merchant John Taber began to circulate notes for 1, 2, 3, and 4 dollars, payable to the bearer in silver on demand, despite the law:

This worked for a while, propped up by Taber’s reputation. But Taber’s profligate son Daniel began to print bills for his own use as he needed them, and when Massachusetts repealed its law John Taber and Son were forced into bankruptcy.

When it was over, Taber approached his old partner Samuel Hussey, who owed him $60. Hussey invited him into his counting room, counted out the amount in Taber’s own now-worthless bills, and asked for a receipt.

Taber said nervously, “Now, thee knows, friend Hussey, this money is not good now.”

“Well, well, that is not my fault,” said Hussey. “Thee ought to have made it better.”

(From the Collections and Proceedings of the Maine Historical Society, 1898.)

July 11, 2015 | Society

Unquote

“Happiness, whether consisting in pleasure or virtue, or both, is more often found with those who are highly cultivated in their minds and in their character, and have only a moderate share of external goods, than among those who possess external goods to a useless extent but are deficient in higher qualities.” — Aristotle

“Money only appeals to selfishness and always tempts its owners irresistibly to abuse it. Can anyone imagine Moses, Jesus, or Gandhi armed with the money-bags of Carnegie?” — Albert Einstein, The World As I See It, 1949

Where wealth and freedom reign, contentment fails,
And honour sinks where commerce long prevails.

— Oliver Goldsmith, The Traveller, 1764

“The essence of philosophy is that a man should so live that his happiness shall depend as little as possible on external things.” – Epictetus

“The most necessary disposition to relish pleasures is to know how to be without them.” — Marquise de Lambert, A Mother’s Advice to Her Son, 1726

“It is preoccupation with possessions, more than anything else, that prevents us from living freely and nobly.” — Bertrand Russell

“Who is rich? He that is content. Who is that? Nobody.” — Benjamin Franklin

July 5, 2015 | Quotations · Society

Food Fight

W.S. Gilbert’s neighbor in the country was a partner in a firm that was famous for its relishes, pickles, jams, jellies, and preserves. He had been made a baronet but “had grown very touchy about the source of his wealth and his title,” recalled DeWolf Hopper, “and was rather a hoity-toity neighbor.”

One day Gilbert’s dogs killed some pheasants on the man’s property, and he wrote a curt note of protest to the author. Gilbert wrote back:

Dear Sir Alfred:

I am extremely sorry about the loss of your pheasants, and I am taking steps to prevent my dogs from trespassing on your preserves in the future.

Sincerely,

W.S. Gilbert

P.S. You will pardon my use of the word ‘preserves,’ won’t you?

In his 1927 autobiography, Hopper also recalls:

Someone once challenged Gilbert to make up a verse offhand riming the words ‘Timbuctoo’ and ‘cassowary’. He studied for a moment and recited:

If I were a cassowary in Timbuctoo,
I’d eat a missionary and his hymn book too.

June 18, 2015 | Literature · Society