A curious chess puzzle by T.R. Dawson. White is to mate in four moves, with the stipulation that white men that are guarded may not move.
This seems immediately impossible. The two rooks guard one another, and one of them guards the king. And moving the pawn will place it under the king’s protection, leaving White completely frozen. How can he proceed?
A spelling net is the pattern made when one writes down one instance of each unique letter that appears in a word and then connects these letters with lines, spelling out the word. For instance, the spelling net for VIVID is made by writing down the letters V, I, and D and drawing a line from V to I, I to V, V to I, and I to D.
Different words produce different spelling nets, of course, but every spelling net is an example of a graph, a collection of points connected by lines. A graph is said to be non-planar if some of the lines must cross; in the case of the spelling net, this means that no matter how we arrange the letters on the page, when we connect them in order we find that at least two of the lines must cross.
A word with a non-planar spelling net is called an eodermdrome, an ungainly name that itself illustrates the idea. The unique letters in EODERMDROME are E, O, D, R, and M. Write these down and run a pen among them, spelling out the word. You’ll find that no matter how the letters are arranged, it’s never possible to complete the task without at least two of the lines crossing:
Ross Eckler sought all the eodermdromes in Webster’s second and third editions; another example he found is SUPERSATURATES:
Since spelling nets are graphs, they can be studied with the tools of graph theory, the mathematical study of such networks. One result from that discipline says that a graph is non-planar if and only if it can be reduced to one of the two patterns marked K5 and K(3, 3) above. Since both EODERMDROME and SUPERSATURATES contain these forbidden graphs, both are non-planar.
A good article describing recreational eodermdrome hunting, by computer scientists Gary S. Bloom, John W. Kennedy, and Peter J. Wexler, is here. One warning: They note that, with some linguistic flexibility, the word eodermdrome can be interpreted to mean “a course on which to go to be made miserable.”
Vincent Gigante, head of the Genovese crime family from 1981 to 2005, feigned mental illness for 30 years in order to throw law enforcement authorities off his trail. Beginning in the 1960s he could regularly be seen shuffling around his Greenwich Village neighborhood in pajamas, a bathrobe, and slippers, mumbling to himself, and quietly playing pinochle at a local club. His lawyers and relatives insisted he had become mentally disabled, with an IQ of 69 to 72.
But informants told the FBI that during this time he was really leading the wealthiest and most powerful crime family in the nation and a dominant force in the New York mob.
At arraignments he appeared in pajamas, and psychiatrists testified that he had been confined 28 times for hallucinations and “dementia rooted in organic brain damage.” “He was probably the most clever organized-crime figure I have ever seen,” former FBI supervisor John S. Pritchard told the New York Times. Mob rival John Gotti called him “crazy like a fox.”
It wasn’t until April 2003, in exchange for a plea deal, that he acknowledged that the whole thing had been a con to delay his racketeering trial. His lawyer said, “I think you get to a point in life — I think everyone does — where you become too old and too sick and too tired to fight.” He died in prison in 2005.
“I would have praised you more if you had praised me less.” — Louis XIV, to poet Nicolas Boileau-Despréaux, after a fulsomely flattering verse
The three corners of any triangle ABC define a circle that surrounds it, called its circumcircle. And for any point P on this circle, the three points closest to P on lines AB, AC, and BC are collinear.
The converse is also true: Given a point P and three lines no two of which are parallel, if the closest points to P on each of the lines are collinear, then P lies on the circumcircle of the triangle formed by the lines.
This discovery is named for Robert Simson, though, as often happens, it was first published by someone else — William Wallace in 1797.
In 1976 a television crew discovered a mummified corpse in a California funhouse. Unbelievably, an investigation revealed that it belonged to an Oklahoma outlaw who had been shot by sheriff’s deputies in 1911 and whose remains had been traveling the country ever since. In this week’s episode of the Futility Closet podcast we’ll trace the postmortem odyssey of Elmer McCurdy, “the bandit who wouldn’t give up.”
We’ll also reflect on a Dutch artist’s disappearance and puzzle over some mysterious hospital deaths.
In 1581, using a “shewstone,” or crystal, astrologer John Dee and seer Edward Kelley set out to discover knowledge that couldn’t be gleaned from books or experimentation.
They succeeded: Angels gave them the “Celestial Speech,” the language that God used to create the world and taught to Adam, who lost it in his fall from paradise.
After transmitting the 21-letter alphabet above, Dee said, the angels sent him a series of texts, some with translations, that formed the basis for a vocabulary.
Some features of “Enochian” suggest that Dee was “speaking in tongues” while transcribing the language, while others show suspicious similarities to English grammar and syntax. But then, Dee maintained that modern languages arose through Adam’s attempts to reconstruct the language he had lost.
“No language has a stranger history than the Enochian language,” wrote Australian linguist Donald Laycock, who studied the curious system. “Perhaps strangest of all is that we still do not know whether it is a natural language or an invented language — or whether it is, perhaps, the language of the angels, as its originators believed.”
In 1872 Francis Galton reflected that congregations throughout Britain pray every Sunday for the health of the British royal family. If prayer has tangible effects, he wondered, shouldn’t all this concentrated well-wishing result in greater health for its objects? He compared the longevity of royalty to clergy, lawyers, doctors, aristocracy and gentry, as well as other professions, and found that
[t]he sovereigns are literally the shortest lived of all who have the advantage of affluence. The prayer has therefore no efficacy, unless the very questionable hypothesis be raised, that the conditions of royal life may naturally be yet more fatal, and that their influence is partly, though incompletely, neutralized by the effects of public prayers.
He noted also that missionaries are not vouchsafed a long life, despite their pious purpose; that banks that open their proceedings with prayers don’t seem to receive any benefit from doing so; and that insurance companies don’t offer annuities at lower rates to the devout than to the profane. Certainly men may profess to commune in their hearts with God, he wrote, but “it is equally certain that similar benefits are not excluded from those who on conscientious grounds are sceptical as to the reality of a power of communion.”
(Francis Galton, “Statistical Inquiries Into the Efficacy of Prayer,” Fortnightly Review 12 [1872], 125-35.)
During a visit to the Colt firearms factory in Connecticut in 1995, English sculptor Cornelia Parker was captivated by the recognizably gun-shaped casts of metal produced early in the manufacturing process. As blank casts they had none of the capacities of working weapons, but “in one further step, a hole drilled, a surface filed, they would technically become firearms.”
Fascinated by this transition, “I asked the foreman if I could possibly have a pair of guns at this early stage in the production, and if he could give them the same finish that they’d get at the end of the process,” she wrote later. “Amazingly, he agreed, and they became Embryo Firearms, conflating the idea of birth and death in the same object.”
Ironically, as she was leaving America, customs officials discovered the casts in her luggage and “an argument ensued that perfectly reflected the questions raised by Parker’s work,” writes Jessica Morgan in Cornelia Parker (2000). “The American Customs department insisted that Embryo Guns were weapons, while the police department, in Parker’s defense, argued that they were harmless metal forms and Parker was released from questioning.”
In 1966, a group of teenagers in the town of Paulding, on Michigan’s Upper Peninsula, reported seeing a ghostly light in a valley nearby. Locals claimed that the light, which appears every night when viewed from a precise location, was the lantern of a ghostly railroad brakeman who had been killed trying to warn an oncoming train of railway cars stopped on the track.
A more prosaic explanation is that the specter is produced by the headlights of cars traveling on US 45, about 5 miles away. In 2010, a group of student engineers from Michigan Tech studied the light with a telescope and distinguished individual vehicles and even an Adopt a Highway sign. They were able to produce the effect themselves by driving a car along the suspected stretch of highway. It’s thought that an inversion layer may create a volume of unusually stable air that accounts for the lights’ visibility at such a distance.
That didn’t end the ghost theory, though. “We’ve been told we haven’t seen the real Paulding Light,” Ph.D. candidate Jeremy Bos told Michigan Tech News in 2010. “I’ve been out there 15 times, hours at a time, in the heat, the cold, and the rain. It’s always the same. We were there Monday with a man who saw the headlights on our computer, and he refused to believe it.”
“No matter what, some people will believe what they want to believe.”
