One more chess curiosity by T.R. Dawson: How can White mate in two half moves?
The answer is to play the first half of Bg1-f2, and the second half of Bf1-g2, thus getting the white bishop from g1 to g2 and giving mate.
A fair-minded reader might ask why Black can’t pull the same trick, transferring his bishop from b8 to b7 to block the check. The answer, Dawson argues, is that some of the constituent moves are illegal: Black can’t combine Bb8-c7 and Bc8-b7 because a bishop on c8 would put the white king in an unreal check on h3; and he can’t combine Bb8-a7 and Ba8-b7 because a8 is occupied.
A memory of Lewis Carroll by Lionel A. Tollemache:
He was, indeed, addicted to mathematical and sometimes to ethical paradoxes. The following specimen was propounded by him in my presence. Suppose that I toss up a coin on the condition that, if I throw heads once, I am to receive 1d.; if twice in succession, 2d.; if thrice, 4d.; and so on, doubling for each successful toss: what is the value of my prospects? The amazing reply is that it amounts to infinity; for, as the profit attached to each successful toss increases in exact proportion as the chance of success diminishes, the value (so to say) of each toss will be identical, being in fact, 1/2d.; so that the value of an infinite number of tosses is an infinite number of half-pence. Yet, in fact, would any one give me sixpence for my prospect? This, concluded Dodgson, shows how far our conduct is from being determined by logic.
Actually this curiosity was first noted by Nicholas Bernoulli; Carroll would have met it in his studies of probability. Tollemache wrote, “The only comment that I will offer on his astounding paradox is that, in order to bring out his result, we must suppose a somewhat monotonous eternity to be consumed in the tossing process.”
(Lionel A. Tollemache, “Reminiscences of ‘Lewis Carroll,'” Literature, Feb. 5, 1898.)
In 1879 a ghastly crime gripped England: A London maid had dismembered her employer and then assumed her identity for two weeks, wearing her clothes and jewelry and selling her belongings. In this week’s episode of the Futility Closet podcast we’ll describe the murder of Julia Thomas and its surprising modern postscript.
We’ll also discover the unlikely origins of a Mary Poppins character and puzzle over a penguin in a canoe.
Park Road, Richmond, today. At left is the site of the former Mayfield Cottages, where the murder took place. At center is the home of naturalist Sir David Attenborough. At right is the site of the former Hole in the Wall pub. Thomas’ skull was discovered in 2010 at the site of the pub’s stables.
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Many thanks to Doug Ross for the music in this episode.
In 1976, Australian monkey trainer Alex Brackstone declared his four-hectare property northeast of Adelaide to be the independent Province of Bumbunga and named himself its governor-general. He was concerned that Australia was drifting toward republicanism and wanted to be sure that at least a part of the continent would always be loyal to the British Crown.
To underscore his devotion to the queen he drew a huge scale model of Great Britain using strawberry plants. He planned to sprinkle each county with authentic soil imported from Britain, but customs authorities put a stop to that, and the strawberries eventually died in a drought. Full points for effort, though.
Related: In her 1981 book The Emperor of the United States of America, Catherine Caufield says that British eccentric John Alington laid out a giant street map of London on the grounds of his estate at Letchworth, to rehearse his laborers who were traveling there to see the Great Exhibition. This article repeats the story, noting that Alington was greatly taken with giant maps: “In 1855, he had a reproduction of the fortifications of Sebastopol built so his workers could better understand the progress of the Crimean War. He also had a pond remodelled into a map of the world, which the men toured in rowboats as he lectured them in geography.” I haven’t been able to confirm this elsewhere, though.
Suppose some 2n points in the plane are chosen so that no three are collinear, and then half are colored red and half blue. Will it always be possible to connect each red point with a blue one, in pairs, so that none of the connecting lines intersect?
Yes. Since n is finite, there are a limited number of ways to make the pairings. And for each way of making them, the lengths of the n segments add up to some total amount.
Now, if an arrangement contains an intersection, this total length can be reduced by an appeal to the triangle inequality, which says that the sum of the lengths of any two sides of a triangle must be greater than the third side.
In the example above, if we reassign the connections as shown, the total length of the connecting segments is reduced, because c < a + b and f < d + e.
Hence the arrangement with the minimum total length must necessarily be free of intersections.
(A Putnam paper problem from 1979, via Ross Honsberger’s Mathematical Gems, 1985.)
A portrait of a Civil War field hospital in 1863, written by a Union colonel wounded at Port Hudson:
I never wish to see another such time as the 27th of May. The surgeons used a large Cotton Press for the butchering room & when I was carried into the building and looked about I could not help comparing the surgeons to fiends. It was dark & the building lighted partially with candles: all around on the ground lay the wounded men; some of them were shrieking, some cursing & swearing & some praying; in the middle of the room was some 10 or 12 tables just large enough to lay a man on; these were used as dissecting tables & they were covered with blood; near & around the tables stood the surgeons with blood all over them & by the side of the tables was a heap of feet, legs & arms. On one of these tables I was laid & being known as a Col. the Chief Surgeon of the Department was called (Sanger) and he felt of my mouth and then wanted to give me cloriform: this I refused to take & he took a pair of scissors & cut out the pieces of bone in my mouth: then gave me a drink of whiskey & had me laid away.
In 1918, after a half-century of medical advances, one federal surgeon looked back on the war:
We operated in old blood-stained and often pus-stained coats, the veterans of a hundred fights. … We used undisinfected instruments from undisinfected plush-lined cases, and still worse, used marine sponges which had been used in prior pus cases and had been only washed in tap water. If a sponge or an instrument fell on the floor it was washed and squeezed in a basin of tap water and used as if it were clean. Our silk to tie blood vessels was undisinfected. … The silk with which we sewed up all wounds was undisinfected. If there was any difficulty in threading the needle we moistened it with … bacteria-laden saliva, and rolled it between bacteria-infected fingers. We dressed the wounds with clean but undisinfected sheets, shirts, tablecloths, or other old soft linen rescued from the family ragbag. We had no sterilized gauze dressing, no gauze sponges. … We knew nothing about antiseptics and therefore used none.
In The Life of Billy Yank, historian Bell I. Wiley writes, “Little wonder that gangrene, tetanus and other complication were so frequent and that slight wounds often proved mortal.”
The Soviet Union took propaganda to a ludicrous extreme in the 1930s with the Maksim Gorki, a multimedia communications empire in the sky. With a wingspan of 206 feet and a takeoff weight of 42 tons, it was the largest land aircraft ever built at the time, requiring eight huge 900-horsepower engines to get aloft.
Aboard were a complete printing plant, capable of printing 10,000 copies per hour of an illustrated 12″ x 16″ newspaper, a photographic darkroom, and a high-speed radio apparatus and telegraph. On the ground, a projection room could cast movies onto a folding screen for up to 10,000 spectators through a window in the fuselage.
“The aircraft also contained a cafe, its own internal telephone exchange, and sleeping quarters and toilets,” notes James Gilbert in The World’s Worst Aircraft. “Four auxiliary engines were required to generate the power to run the huge loudspeakers that broadcast the Soviet message down upon the astonished peasants over which the aircraft flew, and at night to power a system of lights along the underside flashing slogans.” Whether anyone wanted to hear all this is another question.
In 1925, 20 years after completing his work on the airplane, Orville Wright patented a spring-propelled doll:
This invention relates to toys and more particularly to that type of toy in which any object, such as a doll, is projected through the air and caused to engage and to be supported by a swinging bar or other suitable supporting structure.
I don’t know the story behind it. Orville was 53 years old. Neither he nor Wilbur had any children, and their sister didn’t marry until the following year.
Perhaps he was tinkering just to tinker. “Isn’t it astonishing,” he once said, “that all these secrets have been preserved for so many years just so we could discover them!”