Yablo’s Paradox

All the statements below this one are false.
All the statements below this one are false.
All the statements below this one are false.
All the statements below this one are false.
All the statements below this one are false.
…

These statements can’t all be false, because that would make the first one true, a contradiction. But neither can any one of them be true, as a true statement would have to be followed by an infinity of false statements, and the falsity of any one of them implies the truth of some that follow. Thus there’s no consistent way to assign truth values to all the statements.

This is reminiscent of the well-known liar paradox (“This sentence is false”), except that none of the sentences above refers to itself. MIT philosopher Stephen Yablo uses it to show that circularity is not necessary to produce a paradox.

| Science & Math

“Evils of Railroads”

A canal stockholder’s argument against railways, from the Vincennes, Ind., Western Sun, July 24, 1830:

He saw what would be the effect of it; that it would set the whole world a-gadding. Twenty miles an hour, sir! Why, you will not be able to keep an apprentice-boy at his work: every Saturday evening he must take a trip to Ohio, to spend the Sabbath with his sweetheart. Grave plodding citizens will be flying about like comets. All local attachments must be at an end. It will encourage flightiness of intellect. Veracious people will turn into the most immeasurable liars; all their conceptions will be exaggerated by their magnificent notions of distance. ‘Only a hundred miles off! Tut, nonsense, I’ll step across, madam, and bring your fan!’ ‘Pray, sir, will you dine with me to-day at my little box at Alleghany?’ ‘Why, indeed, I don’t know — I shall be in town until twelve. Well, I shall be there; but you must let me off in time for the theatre.’ And then, sir, there will be barrels of pork, and cargoes of flour, and chaldrons of coals, and even lead and whiskey, and such like sober things, that have always been used to sober travelling, whisking away like a set of skyrockets. It will upset all the gravity of the nation. If two gentlemen have an affair of honour, they have only to steal off to the Rocky Mountains, and there no jurisdiction can touch them. And then, sir, think of flying for debt! A set of bailiffs, mounted on bomb-shells, would not overtake an absconded debtor — only give him a fair start. Upon the whole, sir, it is a pestilential, topsy-turvy, harum-scarum whirligig. Give me the old, solemn, straightforward, regular Dutch canal — three miles an hour for expresses, and two for jog-and-trot journeys — with a yoke of oxen for a heavy load! I go for beasts of burthen: it is more primitive and scriptural, and suits a moral and religious people better. None of your hop-skip-and-jump whimsies for me.

| History · Society · Technology

Public Servant

During the War of 1812, the Declaration of Independence hung in the office of Stephen Pleasonton, an auditor in the State Department. When word came that the British might march on Washington, Secretary of State James Monroe ordered Pleasonton to safeguard the department’s important books and papers, so Pleasonton ordered linen bags made and began filling them with documents.

As he was doing this, Secretary of War John Armstrong Jr. passed through the building and remarked that the alarm was unnecessary; he did not believe that the British planned to attack the city.

“Had he followed the advice of the Secretary of War, an irreparable loss would have been sustained,” noted the New York Times in 1905. “For the papers which Mr. Pleasonton had placed in the coarse linen bags comprised the secret journals of Congress, then not published; the correspondence of Gen. Washington, his commission, resigned at the close of the war; the correspondence of Gen. Greene and other officers of the Revolution, a well as laws, treaties, and correspondence of the Department of State, from the adoption of the Constitution down to that time.”

Pleasonton had the bags carted to a grist mill on the Virginia side of the Potomac. As he was leaving his office, he caught sight of the Declaration hanging on his wall. He took it down, cut it out of its frame, and carried it away with the other papers.

Feeling that even the grist mill was too vulnerable, Pleasonton removed the bags a further 35 miles to Leesville, where he stored them in an empty house. “Worn out with his labors, Mr. Pleasonton states in a letter, he retired early to bed that night and slept soundly. Next morning he was informed by the people of the little tavern where he had stayed that evening that they had seen during the night, the same being the 24th of August, a large fire in the direction of Washington, which proved to be the light from the public buildings, which the enemy had set on fire and burned to the ground.”

| History

In a Word

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

transpicuous
adj. transparent

In 1922, magician Harry Price published “Cold Light on Spiritualistic Phenomena” in the Journal of the Society for Psychical Research, showing that so-called “spirit photographs” could be created using simple double exposures. In support of the exposé, Harry Houdini had himself photographed with Abraham Lincoln.

| Language · Society · Technology

Cool Shoes

http://www.google.com/patents/about?id=DgMfAAAAEBAJ

Israel Siegel’s “gravity-powered shoe air conditioner,” patented in 1994, fits bellows into the heel of each of a pair of shoes, so that the natural act of walking pumps a refrigerant through two networks of heat exchange coils, one operating as a heat-absorbing evaporator and the other as a heat-delivering condenser.

Depending on how these networks are arranged, the shoe can serve as a foot cooler or a foot warmer.

| Technology

Finding Mates

A remarkable spelling trick by American magician Howard Adams:

From a deck of cards choose five cards and their mates. A card’s mate is the card of the same value and color; for example, the mate of the five of clubs is the five of spades.

Arrange the cards in the order ABCDEabcde, where ABCDE are the chosen cards and abcde are the mates. Cut this packet as many times as you like, then deal five cards onto the table, reversing their order. Place the remaining five cards beside them in a second pile.

Now spell the phrase LAST TWO CARDS MATCH. As you say “L,” choose either pile at random and transfer a card from the top to the bottom. Do the same for A, S, and T. Now remove the top card from each pile and set them aside as a pair.

Perform the same procedure as you spell TWO, CARDS, and MATCH. When you’re finished, two cards will remain on the table. Not only do these cards match, but so do each of the other pairs!

| Science & Math

Overdue

In May 1919, Canadian flying ace Mansell Richard James won an air race from Atlantic City to Boston in a $1,000 competition sponsored by the Boston Globe.

At 11 a.m. on May 29 he departed Boston to return to Atlantic City.

At 12:30 p.m. a group of picknicking schoolchildren saw his Sopwith Camel flying smoothly southward over Hancock, Ct., at an altitude of about 5,000 feet.

He was never seen again. Despite numerous rewards and extensive searching, no trace of James has ever been found.

| Oddities

Close Enough

http://commons.wikimedia.org/wiki/File:Livermore_public_library_in_2010.jpg
Image: Wikimedia Commons

In 2004, Livermore, Calif., paid Miami artist Maria Alquilar $40,000 to create a ceramic mural outside its new library. Its pride was short-lived: The mural misspelled the names of 10 of the 175 historical figures it honored:

Nefertite
Thesues
Michaelangelo
Shakespere
Clara Schuman
Paul Gaugan
Vincent Van Gough
Albert Eistein

German chemist Otto Beckmann’s name was spelled Beckman, and Italian sculptor Luca Della Robbia’s name was spelled Luca Della Robia.

“The most egregious is Einstein,” library director Susan Gallinger told the San Francisco Chronicle. “That’s the worst one.” Livermore is home to the Lawrence Livermore National Laboratory.

Unfortunately, California state law bars the city from removing or changing public art without the creator’s consent, so the city council had to pay Alquilar an additional $6,000 to correct the errors.

The artist was unapologetic. “The people that are into humanities, and are into Blake’s concept of enlightenment, they are not looking at the words,” she told the Associated Press. “In their mind, the words register correctly.”

| Art · Language

The Time Store

http://commons.wikimedia.org/wiki/File:LaborNote.JPG

Anarchist Josiah Warren believed that the only just measure of a product’s value was the amount of labor that went into producing it. Charging more than this was “cannibalism” — interest, rent, and profit were state-sanctioned usury. Accordingly, he proposed a system where goods would be traded explicitly on this basis — “he who employs five or ten hours of his time, in the service of another, receives five or ten hours labour of the other in return.”

As an experiment, Warren opened a “time store” at the corner of Fifth and Elm Streets in Cincinnati in 1827. He priced all the goods at the amount he had paid for them, plus a small surcharge to cover overhead (his books were available for inspection at the back of the store), and customers could buy goods using “labor notes” — promises to perform labor, like the one above. As he accumulated notes, Warren would redeem those that he could use and endorse the rest, using them to buy more goods, following a list of their average cost in labor. In this way he set up a small economy among like-minded citizens in Cincinnati — each received fair compensation for his labors, but none could gouge another merely because “the market would bear it.”

In like spirit, Warren charged for his own time in running the store, using a clock — if it took him half an hour to help a customer buy groceries, 25 cents would be added to the customer’s bill. “This arrangement sweeps away at once all the higgling and chaffering about prices, so disgusting in the present system, but which is inseparably connected with it,” he explained in his 1852 book Equitable Commerce.

The store operated successfully for three years, with such low prices that the competitor on the next corner asked Warren’s help in coverting his own store to Warren’s system. Warren closed the time store voluntarily in May 1830 — because, according to one account, he felt he had no claim to the increase in value of the land on which it stood.

| Society