For years Raymond Smullyan sought a “metaparadox,” a statement that is paradoxical if and only if it isn’t. He arrived at this:
Either this sentence is false, or (this sentence is paradoxical if and only if it isn’t).
He wrote, “I leave the proof to the reader.”
From Lewis Carroll:
I don’t know if you are fond of puzzles, or not. If you are, try this. … A gentleman (a nobleman let us say, to make it more interesting) had a sitting-room with only one window in it–a square window, 3 feet high and 3 feet wide. Now he had weak eyes, and the window gave too much light, so (don’t you like ‘so’ in a story?) he sent for the builder, and told him to alter it, so as only to give half the light. Only, he was to keep it square–he was to keep it 3 feet high–and he was to keep it 3 feet wide. How did he do it? Remember, he wasn’t allowed to use curtains, or shutters, or coloured glass, or anything of that sort.
In 1976, CUNY mathematician Robert Feinerman showed that the game of dreidel is fundamentally unfair.
Each player contributes one unit to the pot, and then all take turns spinning the top. Each spin produces one of four outcomes: the player does nothing, collects the entire pot, collects half the pot, or puts one unit into the pot. When a player collects the entire pot, then each player contributes one unit to form a new pot and play continues.
Feinerman found that, if Xn is the payoff on the nth spin and p is the number of players, the expected value of Xn is
Thus if there are more than two players, “the first player has an unfair advantage over the second player, who in turn has an unfair advantage over the third player, etc.”
Dreidel is booming nonetheless. A Major League Dreidel tournament has been held in New York City every Hanukkah since 2007. The official playing surface is called the Spinagogue, and the tournament slogan is “no gelt, no glory.”
(Robert Feinerman, “An Ancient Unfair Game,” American Mathematical Monthly 83:623-625.)
resipiscence
n. acknowledgment that one has been mistaken
At noon on the 12th of July, 1892, Mr. J.E. Muddock, the well-known novelist, then on his way home from Canada in the Sarna, threw into the icy Straits of Belle Isle a soda-water bottle containing a message, which, together with the bottle, is here shown. Exactly 485 days afterwards Mr. Muddock had a letter from Norway saying that his bottle had been picked up by a poor fisherman at the entrance to the Sogne Fiord, 2,500 miles in a straight line from the place where it was committed to the sea. Had it not been picked up it would have gone into the Arctic regions. This experiment was of real scientific value, since it was the means of settling certain matters relating to ocean currents.
— Strand, January 1898
A mosquito was heard to complain
That a chemist had poisoned his brain;
The cause of his sorrow
Was paradichloro-
Diphenyltrichloroethane.
— Anonymous
From a remarkably bad poem by English naturalist Edward Newman (fl. 1840):
First of walkers come the Earwigs,
Earwigs or FORFICULINA;
At the tail we find a weapon,
Very like a pair of pincers,
And with this ’tis said the Earwigs
Open and fold up the hind wings;
You may watch them and observe it;
I have never had the pleasure.
On July 30, 1915, the German submarine U-28 torpedoed the British steamer Iberian in the North Atlantic. Captain Georg Günther Freiherr von Forstner and his crew watched the ship sink rapidly under the waves, stern first. Then, a surprise:
When the steamer had disappeared for about 25 seconds it exploded at a depth which we could not know, but one thousand meters will be a safe guess. Shortly afterwards pieces of wreckage, among them a huge marine animal which made violent movements, were thrown out of the water, flying approximately 20 or 30 meters high.
At this moment we were six men on the bridge, myself, the two officers of the watch, the chief engineer, the navigator and the helmsman. We at once centered our attention upon this marvel of the seas. Unfortunately we had not time to take a photograph because the animal disappeared in the water after 10 or 15 seconds. It was about 20 meters long, looked like a giant crocodile, and had four powerful paddle-like limbs and a long pointed head.
“The explanation of this event seems easy to me,” von Forstner wrote. “The explosion of, or in, the sinking steamer caught the ‘undersea-crocodile,’ as we called it, and forced it out of the water.” When the story was attacked, von Forstner stood firm, declaring that he “would not give up a single meter of the length of the animal.” What was it? Who knows?
That the deliverance of the saints must take place some time before 1914 is manifest, since the deliverance of fleshly Israel, as we shall see, is appointed to take place at that time, and the angry nations will then be authoritatively commanded to be still, and will be made to recognize the power of Jehovah’s Anointed. Just how long before 1914 the last living members of the body of Christ will be glorified, we are not directly informed; but it certainly will not be until their work in the flesh is done; nor can we reasonably presume that they will long remain after that work is accomplished. With these two thoughts in mind, we can approximate the time of the deliverance.
— Charles Taze Russell, Studies in the Scriptures, 1908
That the deliverance of the saints must take place very soon after 1914 is manifest, since the deliverance of fleshly Israel, as we shall see, is appointed to take place at that time, and the angry nations will then be authoritatively commanded to be still, and will be made to recognize the power of Jehovah’s Anointed. Just how long after 1914 the last living members of the body of Christ will be glorified, we are not directly informed; but it certainly will not be until their work in the flesh is done; nor can we reasonably presume that they will long remain after that work is accomplished. With these two thoughts in mind, we can approximate the time of the deliverance.
— Charles Taze Russell, Thy Kingdom Come, 1916
In the late 1950s and early 1960s, the tiny town of Vernon in Florida’s panhandle gained a disturbing reputation for insurance fraud. Only 500 people lived in Vernon, but fully 10 percent of these (all men) reported they had lost arms, legs, and fingers. For a brief period this region of Florida accounted for two-thirds of all loss-of-limb claims in the United States.
“Somehow they always shoot off the parts they seem to need least,” noted one investigator. Another wrote, “To sit in your car on a sweltering summer evening on the main street of Nub City, watching anywhere from eight to a dozen cripples walking along the street, gives the place a ghoulish, eerie atmosphere.”
The trend lasted only a few years, and the allegations were never proven, but the town remained sensitive to its reputation for decades. In 1981 filmmaker Errol Morris was planning a documentary about Vernon (where, he said, the people “became a fraction of themselves to become whole financially”). According to Morris’ Web site, the film “had to be retooled when his subjects threatened to murder him.”
This looks a bit … direct, but it dates from 1882. James Williams needed a device that would destroy a burrowing animal and give an alarm so that it could be reset. His solution was a revolver attached to a treadle. Touché.
The patent abstract adds, “This invention may also be used in connection with a door or window, so as to kill any person or thing opening the door or window to which it is attached.” Evidently Williams had problems bigger than rodents.
