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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:
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:
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 . If my partner spends 9%, or 0.09, of our assets on lawyers, then I should spend . 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.
“Looking at the graph of , 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.)
“I have seen a thousand graves opened, and always perceived that whatever was gone, the teeth and the hair remained of those who had died with them. Is this not odd? They go the very first things in youth and yet last the longest in the dust.” — Lord Byron, letter to John Murray, Nov. 18, 1820
Another puzzle by Yakov Perelman:
“Two fathers gave their two sons some money. One gave his son 150 rubles and the other 100 rubles. When the two sons counted their finances, they found that together they had become richer by only 150 rubles. What is the explanation?”
“It is highly desirable for the spectators at a baseball game to hear what is transpiring on the playing field,” observed inventor James Sellers in 1959, “such as arguments at the bases between opposing players, and discussions between the umpires and players.”
Accordingly he patented an “apparatus for transmitting sound from a baseball field.” Each base is fitted with a hidden microphone, which sends its signal to the announcers’ PA system.
“The sounds on the playing field can thus be transmitted through the control booth to the public address system so that spectators in the grandstand may hear what is taking place on the playing field.”
“By transmitting the sounds from the playing field to the grandstand, the spectators feel that they are taking part in the game. Also, it enables the spectators to judge a play better as they can hear the baseball strike the glove or mitt of a player.”
In the backing vocals on “Paperback Writer” (1:02 above), John and George are singing “Frère Jacques.”
What do René Descartes, Joseph Haydn, and Oliver Cromwell have in common? All three lost their heads after death. In this week’s episode of the Futility Closet podcast, we’ll run down a list of notable corpses whose parts have gone wandering.
We’ll also hear readers chime in on John Lennon, knitting, diaries and Hitchcock, and puzzle over why a pilot would choose to land in a field of grazing livestock.
Sources for our feature on posthumously itinerant body parts:
Bess Lovejoy, Rest in Pieces: The Curious Fates of Famous Corpses, 2013.
Edith Sitwell, English Eccentrics, 1993.
Barney Snow’s documentary about Gerald and Linda Polley is Where Has Eternity Gone?
Douglas Martin, “Robert Shields, Wordy Diarist, Dies at 89,” New York Times, Oct. 29, 2007.
Listener Christine Fisher found Charles Thomas Samuels’ interview with Alfred Hitchcock in Sidney Gottlieb’s 2003 book Alfred Hitchcock: Interviews. It appeared originally in Samuels’ 1972 book Encountering Directors.
This week’s lateral thinking puzzle is from Kyle Hendrickson’s 1998 book Mental Fitness Puzzles.
Enter coupon code CLOSET at Harry’s and get $5 off their starter set of high-quality razors.
Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and all contributions are greatly appreciated. You can change or cancel your pledge at any time, and we’ve set up some rewards to help thank you for your support.
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Many thanks to Doug Ross for the music in this episode.
If you have any questions or comments you can reach us at email@example.com. Thanks for listening!
Painted on the east side of the Lani Nalu Plaza building in Honolulu, trompe-l’oeil artist John Pugh’s mural Mana Nalu (Power of the Wave) depicts Liliuokalani, the last monarch of the Hawaiian Islands, and surfing pioneer Duke Kahanamoku.
Pugh took a year and a half to create the image, working with 14 other artists. The whole scene is painted, including the wave, the skylight, the balcony, the urns, the children, and the staircase.
“After the mural was near completion,” Pugh writes, “a fire truck with crew stopped in the middle of traffic and jumped out to rescue the children in the mural. They got about 15 feet away and then doubled over laughing that they were fooled into an emergency response mode. I don’t think that there were any liability issues for a false report.”
“Experience never misleads; what you are misled by is only your judgment, and this misleads you by anticipating results from experience of a kind that is not produced by your experiments.” — Leonardo
The 11th Pennsylania infantry regiment was beginning its training at the fairground in West Chester, Pa., in 1861 when a local resident presented a wicker basket to one of the officers. In the basket was a 4-week-old black female terrier puppy. The dog, quickly named Sallie after a local beauty whom the soldiers admired, made hundreds of friends among the men and was adopted as the regiment’s official mascot.
“Sallie knew the drumroll announcing reveille,” writes James Robertson in The Untold Civil War. “She was first out of quarters to attend roll call. During drills, she latched on to a particular soldier and pranced alongside him throughout the exercise. At dress parade, the dog marched proudly beside the regimental colors. At encampments, she slept by the captain’s tent after strolling leisurely through the grounds on her own kind of inspection.”
She accompanied the regiment into battle at Cedar Mountain, Antietam, Fredericksburg, and Chancellorsville, standing stoutly on the front lines and barking ferociously at the enemy. In 1863 Abraham Lincoln tipped his hat to her as he reviewed the Army of the Potomac. On the first day’s fighting at Gettysburg, the regiment was driven back a mile from its original position and she was feared lost; she was discovered three days later standing guard over the wounded and the dead.
She survived, in fact, nearly to the end of the war. On Feb. 5, 1865, at the Battle of Hatcher’s Run during the Siege of Petersburg, men in the second wave of a Union attack found her dead on the battlefield, shot through the head. She had died instantly.
In 1890, the surviving veterans of the 11th Pennsylvania erected a monument at Gettysburg. From a distance it looks like other regimental memorials, a defiant soldier atop a marble pedestal. But on a ledge near the base of the monument lies a small bronze dog.