A Hidden Economy

During the American Civil War, enemy soldiers would sometimes meet to barter. Tobacco was hard to get in the North, and coffee was scarce in the South, so, where it could be done safely, soldiers would meet between the lines to trade.

In some cases this was done across distances. If a river or lake separated the lines, a tiny boat would be laden with commodities and sent to the other side, where it would be unloaded and filled with exchange cargoes, as agreed on by shouting and signaling across the water. On the Rappahannock early in 1863 a group of New Jersey soldiers received a shipment “by miniature boat six inches long.” It carried this note:

Gents U.S. Army

We send you some tobacco by our Packet. Send us some coffee in return. Also a deck of cards if you have them, and we will send you more tobacco. Send us any late papers if you have them.

Jas. O. Parker
Co. H. 17th Regt. Miss. Vols.

Alfred S. Roe, who served in a New York artillery unit, recalled that near Petersburg in the winter of 1864, “a certain canine of strictly impartial sentiments” was “taught to respond to a whistle from either side. Thus with a can of coffee suspended from his neck he would amble over to the Johnnies, and when they had replaced coffee with tobacco he would return in obedience to Union signals, intent only on the food reward both sides gave him.”

(From Bell I. Wiley, The Life of Billy Yank: The Common Soldier of the Union, 1952.)

A Southern Education

Sentence completion exercises from Levi Branson’s First Book in Composition, 1863:

_______ is a Confederate State.

Gen. _______ reduced Fort Sumter.

South Carolina is the greatest _______ country in the Confederate States.

Louisiana raises more _______ than any other State in the Confederacy.

Abraham Lincoln led _______ people into war.

Jefferson Davis defended _______ country bravely, and deserves great applause for _______ patriotism.

General Stuart _______ started in pursuit; he _______ overtook the enemy, _______ led on the attack in person, and gained a complete victory.

General Lee defeated the Yankees, _______ his army was much smaller _______ theirs.

I saw the Confederate flag _______ from the City Hall.

From Marinda Branson Moore’s Dixie Speller, 1864:

It makes us sad to hear the booming of cannon in time of war. We think of our dear friends who are in the army, and fear they may be killed.

War is a sad thing, and those who bring it about will have much to answer for.

Some people lay all the blame at the door of the rulers of the nation. In some countries this is true, but in our country it is not so. The people elect their own rulers, and they should not choose bad men. If the rulers in the United States had been good Christian men, the present war would not have come upon us.

The people sent bad men to Congress, and they were not willing to make just laws, but were selfish, and made laws to suit themselves.

The Bible says “When the wicked bear rule the nation mourneth, but when the righteous are in authority, the people rejoice.”

People often do wrong, and when trouble comes upon them, they say God sent it.

God has made good laws for man, and if we do right we will be happy; but sin will always bring trouble.

Let every boy learn this lesson, and when he is a man, let him not vote for a bad man to fill an office of trust. — Then the men who wish to be in office will strive to be good, and the nation will be happy.

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

No addictive things are inexpensive.
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

john howard griffin

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.

See full show notes …

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.

See full show notes …

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:

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:


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.)

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.)