## Practical Math

Sample questions from L. Johnson’s 1864 textbook Elementary Arithmetic Designed for Beginners, used in North Carolina during the Civil War:

1. A Confederate soldier captured 8 Yankees each day for 9 successive days; how many did he capture in all?
2. If one Confederate soldier kill 90 Yankees how many Yankees can 10 Confederate soldiers kill?
3. If one Confederate soldier can whip 7 Yankees, how many soldiers can whip 49 Yankees?

Students were also asked to imagine rolling cannonballs out of their bedrooms and dividing Confederate soldiers into squads and companies. Let’s hope they didn’t take field trips.

## Logic and Belief

A syllogism is a logical argument in which a conclusion is inferred from a set of premises:

All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.

The conclusion can be valid without actually stating a true fact; to be valid it just needs to follow logically from the premises. Which of these syllogisms are valid?

No cigarettes are inexpensive.
Therefore, some addictive things are not cigarettes.

Some cigarettes are inexpensive.
Therefore, some cigarettes are not addictive.

In fact both of them are valid. But, interestingly, here the first conclusion seems plausible, while the second does not. That shouldn’t matter, but it does: When Plymouth Polytechnic psychologist J. St. B.T. Evans presented a set of these arguments to subjects in 1983, he found a substantial “belief bias” — the subjects tended to judge the believable conclusions to be valid more than the unbelievable ones. If the conclusion was believable, 92% of the subjects accepted it, regardless of its validity. If the conclusion was unbelievable, 46% accepted it if it was valid, 8% if it was invalid.

Evans wrote, “These findings not only provide a challenge for existing models of syllogistic reasoning but also raise broader questions about people’s rational competence to generate and assess logical arguments in real life, whenever they have clear a priori beliefs about the subject under discussion.”

(J. St. B.T. Evans et al., “On the Conflict Between Logic and Belief in Syllogistic Reasoning,” Memory & Cognition, 11(3), 295-306.)

## Podcast Episode 80: ‘Black Like Me’: Race Realities Under Jim Crow

In 1959, Texas journalist John Howard Griffin darkened his skin and lived for six weeks as a black man in the segregated South. In this week’s episode of the Futility Closet podcast we’ll describe his harrowing experience and what it taught him about the true state of race relations in America.

We’ll also ponder crescent moons, German submarines, and griffins in India and puzzle over why a man would be arrested for winning a prize at a county fair.

Sources for our feature on John Howard Griffin:

John Howard Griffin, Black Like Me, 1961.

Robert Bonazzi, Man in the Mirror: John Howard Griffin and the Story of Black Like Me, 2010.

Maurice Dolbier, “Blinding Disguise in South,” Miami News, Oct. 15, 1961.

Jerome Weeks, “‘Black Like Me’ Just One of Many Roles for John Howard Griffin,” Dallas Morning News, Sept. 19, 1997.

H.W. Quick, “He Finds Bias Blighting North, South,” Milwaukee Sentinel, Jan. 16, 1964.

Karen De Witt, “Oppressor Shown What Being Oppressed Is Like,” Ottawa Citizen, Nov. 1, 1977.

Ray Sprigle, In the Land of Jim Crow, 1949.

Lucile Torkelson, “Writer Crosses the Race Barrier,” Milwaukee Sentinel, Oct. 29, 1969.

Research questions:

Here’s the image of the star and crescent:

And here are the sources I’ve found that describe the German submarine rescue:

Wolfgang Frank, The Sea Wolves, 1955.

Arch Whitehouse, Subs and Submariners, 1961.

Jacques Yves Cousteau, Captain Cousteau’s Underwater Treasury, 1959.

This week’s lateral thinking puzzle was contributed by listener Lawrence Miller.

You can listen using the player above, download this episode directly, or subscribe on iTunes or via the RSS feed at http://feedpress.me/futilitycloset.

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.

You can also make a one-time donation via the Donate button in the sidebar of the Futility Closet website.

Enter coupon code CLOSET at Harry’s and get \$5 off their starter set of high-quality razors!

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at podcast@futilitycloset.com. Thanks for listening!

## Unquote

“Murder is a crime. Describing murder is not. Sex is not a crime. Describing sex is.” — Gershon Legman

## Podcast Episode 73: The Tichborne Claimant

In 1854, English aristocrat Roger Tichborne disappeared at sea. Twelve years later, a butcher from Wagga Wagga, Australia, claimed he was the long-lost heir. In this week’s episode of the Futility Closet podcast, we’ll tell the sensational story of the Tichborne claimant, which Mark Twain called “the most intricate and fascinating and marvelous real-life romance that has ever been played upon the world’s stage.”

We’ll also puzzle over why family businesses are often more successful in Japan than in other countries.

Sources for our feature on the Tichborne claimant:

Rohan McWilliam, The Tichborne Claimant: A Victorian Sensation, 2007.

Robyn Annear, The Man Who Lost Himself: The Unbelievable Story of the Tichborne Claimant, 2011.

This week’s lateral thinking puzzle is from Paul Sloane and Des MacHale’s 2014 book Remarkable Lateral Thinking Puzzles. There’s a fuller explanation (with spoilers!) in Dan Lewis’ Now I Know newsletter.

You can listen using the player above, download this episode directly, or subscribe on iTunes or via the RSS feed at http://feedpress.me/futilitycloset.

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.

You can also make a one-time donation via the Donate button in the sidebar of the Futility Closet website.

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at podcast@futilitycloset.com. Thanks for listening!

## 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 – mf. 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:

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

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.

“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.)

## Man Handling

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.)

## In a Word

thersitical

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.’