A Logic Oddity

Opinion polls taken just before the 1980 election showed the Republican Ronald Reagan decisively ahead of the Democrat Jimmy Carter, with the other Republican in the race, John Anderson, a distant third. Those apprised of the poll results believed, with good reason:

— If a Republican wins the election, then if it’s not Reagan who wins it will be Anderson.
— A Republican will win the election.

Yet they did not have reason to believe

— If it’s not Reagan who wins, it will be Anderson.

— Vann McGee, “A Counterexample to Modus Ponens,” Journal of Philosophy, September 1985

Home Again

Unprepossessing English town names:

  • Bishop’s Itchington
  • Brokenborough
  • Great Snoring
  • Mockbeggar
  • Turners Puddle
  • Pett Bottom
  • Twelveheads
  • Ugley
  • Nether Wallop
  • Nasty
  • Wetwang
  • Blubberhouses
  • Yelling

Charles Dickens called the chipper-sounding Chelmsford “the dullest and most stupid spot on the face of the earth.”

Pi Squared

pi magic square

This curiosity was discovered by T.E. Lobeck. The square on the left is a conventional magic square — each row, column, and long diagonal totals 65. Replacing each number with the corresponding digit of pi (for example, replacing 17 with the 17th digit of pi, which is 2) yields the square on the right, in which the rows and columns yield equivalent sums.

A King’s Homework

http://commons.wikimedia.org/wiki/File:Edward_VI_of_England_c._1546.jpg

When Edward VI succeeded to the throne at age 9, William Thomas, clerk of the council, set him 85 questions on history and policy to answer at his leisure. “For though these be but questions, yet there is not so small an one among them, as will not administer matter of much discourse, worthy the argument and debating.” Samples:

  • Whether it is better for the commonwealth, that the power be in the nobility or in the people?
  • How easily a weak prince with good order may long be maintained, and how soon a mighty prince with little disorder may be destroyed?
  • What is the occasion of conspiracies?
  • Whether the people commonly desire the destruction of him that is in authority, and what moveth them so to do?
  • How flatterers are to be known and despised?
  • How dangerous it is to be author of a new matter?
  • Whether evil report lighteth not most commonly upon the reporter?
  • Whether a puissant prince ought to purchase amity with money, or with virtue and stoutness?
  • What is the cause of war?
  • Whether the country ought not always to be defended, the quarrel being right or wrong?
  • What danger it is to a prince, not to be revenged of an open injury?
  • Whether it be not necessary sometimes to feign folly?

Thomas closes by suggesting that Edward keep the questions to himself, since it is better “to keep the principal things of wisdom secret, till occasion require the utterance.”

Dead Letters

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

In a trance in 1926, medium Geraldine Cummins wrote out messages transmitted to her by a disembodied spirit who had died 1900 years earlier. Architect Frederick Bligh Bond transcribed, punctuated, and arranged the messages. When Bond published these in a newspaper, Cummins sued him. This raises an interesting legal question: Who holds the copyright?

In an extempore judgment, Justice J. Eve wrote that, although all parties agreed that “the true originator of all that is found in these documents is some being no longer inhabiting this world,” the medium’s “active cooperation” had helped to translate them into modern language. This might make her a joint author with the disembodied spirit, but “recognizing as I do that I have no jurisdiction extending to the sphere in which he moves,” he found that “authorship rests with this lady.”

Bond had claimed that the writing had no living author, that, in Eve’s words, “the authorship and copyright rest with some one already domiciled on the other side of the inevitable river.” But “That is a matter I must leave for solution by others more competent to decide it than I am. I can only look upon the matter as a terrestrial one, of the earth earthy, and I propose to deal with it on that footing. In my opinion the plaintiff has made out her case, and the copyright rests with her.”

Communiqué

http://commons.wikimedia.org/wiki/File:Arthur_Wellesley,_1st_Duke_of_Wellington.jpg

One day the elderly soldier [Arthur Wellesley, first Duke of Wellington] chanced on a small boy weeping bitterly and on asking the cause the child began to explain that he was going away to school next day … not waiting to hear more the Duke read him a severe lecture on his attitude, which was cowardly, unworthy of a gentleman and not at all the way to behave, etc. At last the little boy managed to explain he was not crying because he was going to school, but he was worried about his pet toad, as no one else seemed to care for it and he wouldn’t know how it was. The Duke, a just man, apologized to the child for having wronged him, and being human as well as just, took down the particulars and promised to report himself about this pet. In due course the little boy at school received a letter saying ‘Field-Marshal the Duke of Wellington presents his compliments to Master —– and has the pleasure to inform him that his toad is well.’

— G.W.E. Russell, Collections and Recollections, 1963

The Counterfeit Coin

You have nine coins and a balance scale. One of the coins is lighter than the others. Is it possible to identify it in only two weighings?

Click for Answer

The Carisbrooke Donkey

http://books.google.com/books?id=68YhAQAAIAAJ&printsec=frontcover#v=onepage&q&f=false

The well at Carisbrooke Castle on the Isle of Wight is 200 feet deep, so the residents raise water using an enormous wheel driven by a donkey, a practice that dates to at least 1690.

“While it is not claimed that the same individual donkey has drawn its water all of these years,” wrote a correspondent to American Machinist in 1904, “the claim is made that the duty of drawing water from this famous well descends from father to son, and is never shared outside this one royal family of donkeys.”

“One ass has been known to perform this service at Carisbrooke for fifty years, another for forty, a third for thirty, and a fourth had performed it for ten years at the time of the writer’s last visit,” wrote Caroline Bray in 1876. “The dates are marked down inside the door of the well-house.”

(“The donkey was continuing his labour and looking towards the well when the question was asked, ‘What is he looking at?’ ‘He is looking for the bucket,’ said the man; and, in fact, as soon as the bucket appeared the donkey stopped, and very deliberately walked out of the wheel to the place at which he stood at our entrance, knowing full well that he had done what was desired.”)

Gripping Pages

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

Mark Twain found it exasperating to compose a scrapbook using mucilage and glue. In order to “economize the profanity of this country,” in 1873 he patented a “self-pasting scrapbook” whose pages are already covered with adhesive — the user simply moistens a portion of the page to paste in each piece.

You know that when the average man wants to put something in his scrap book he can’t find his paste — then he swears; or if he finds it, it is dried so hard that it is only fit to eat — then he swears; if he uses mucilage it mingles with the ink, and next year he can’t read his scrap — the result is barrels and barrels of profanity. This can all be saved and devoted to other irritating things, where it will do more real and lasting good, simply by substituting my self-pasting Scrap Book for the old-fashioned one.

Twain called it “the only rational scrapbook the world has ever seen.” It proved to be his only profitable invention, selling still in 1912. One wag called it “a book to which readers could easily become attached.”