A flea sits on one vertex of a regular tetrahedron. He hops continually from one vertex to another, resting for a minute between hops and choosing vertices without bias. Prove that, counting the first hop, we’d expect him to return to his starting point after four hops.
A notable detail from Alexander Morrison Stewart’s Camp, March and Battle-Field (1865): During the Battle of Malvern Hill, a terrified rabbit darted about the battlefield looking for safety until it came upon a Union regiment lying prone:
Ere the rabbit seemed aware, it had jumped into the midst of these men. It could go no farther, but presently nestled down beside a soldier, and tried to hide itself under his arm. As the man spread the skirt of his coat over the trembling fugitive, in order to insure it of all the protection in his power to bestow, he no doubt feelingly remembered how much himself then needed some higher protection, under the shadow of whose arm might be hidden his own defenceless head, from the fast-multiplying missiles of death, scattered in all directions.
It was not long, however, before the regiment was ordered up and forward. From the protection and safety granted, the timid creature had evidently acquired confidence in man — as the boys are wont to say, ‘Had been tamed.’ As the regiment moved forward to the front of the battle, it hopped along, tame, seemingly, as a kitten, close at the feet of the soldier who had bestowed the needed protection. Wherever the regiment afterwards went, during all the remaining part of that bloody day and terrible battle, the rabbit kept close beside its new friend.
“When night came on, and the rage of battle had ceased, it finally, unmolested and quietly, hopped away, in order to find some one of its old and familiar haunts.”
English chemist Septimus Piesse likened scents to music:
Odors seem to affect the olfactory nerves in certain definite degrees, as sounds act on the auditory nerves. There is, so to speak, an octave of smells, as there is an octave of tones; some perfumes accord, like the notes of an instrument. Thus almond, vanilla, heliotrope, and clematis, harmonize perfectly, each of them producing almost the same impression in a different degree. On the other hand, we have citron, lemon, orange peel, and verbena, forming a similarly associated octave of odors, in a higher key. The analogy is completed by those odors which we call half-scents, such as the rose, with rose-geranium for its semitone; ‘petit-grain’ and neroli, followed by orange-flower. With the aid of flowers already known, by mixing them in fixed proportions, we can obtain the perfume of almost all flowers.
Using an “odaphone,” or scale, on which harmonies and discords of odors might be studied, his London perfumery Piesse and Lubin produced some of the most important scents of the Victorian era, such as Ambergris (1873), Hungary Water (1873), Kiss Me Quick (1873), The Flower of the Day (1875), White Rose (1875), and Frangipanni (1880).
It had been thought that none of these had survived, but in 2011 two unopened bottles were discovered in the bow of the Mary Celestia, a Civil War blockade runner that had foundered off Bermuda in 1864. The bottles contained Bouquet Opoponax, one of the company’s most popular fragrances, and after analysis with a gas chromatograph, Germany’s Drom Fragrances managed to reproduce the scent in 2014.
“I was shocked at how fresh and floral it was and by the amount of citrus in it,” senior perfumer Jean-Claude Delville told the Star-Ledger. “When the fragrance has been sitting at the bottom of the ocean and aging for so many years you expect something that is oxidized or damaged,” he told CTVNews. “But my first impression was ‘wow’.”
Margaret Hamilton on the Wicked Witch of the West:
[There was] a feeling inside that you get. One word: skulduggery. She enjoyed every single minute of whatever she was doing, whether she was screaming or yelling about the fact that Dorothy had those slippers, or sending the monkeys after them all. And the other thing was her utter and complete frustration. She never got what she wanted. She didn’t want Dorothy and she didn’t want any of those other characters. She just wanted those slippers. And today, according to law, she probably would have had them. They were her sister’s, and she would have been in line to inherit them. But she didn’t get there fast enough.
(From Aljean Harmetz, The Making of The Wizard of Oz, 1977.)
We often think of consciousness as fundamentally involving self-awareness. A conscious decision is one I’m aware of making; a conscious memory is one I’m aware of having. It would seem that most complex behaviors require this state. But philosopher David Malet Armstrong points out:
If you have driven for a very long distance without a break, you may have had experience of a curious state of automatism, which can occur in these conditions. One can suddenly ‘come to’ and realize that one has driven for long distances without being aware of what one was doing, or, indeed, without being aware of anything. One has kept the car on the road, used the brake and the clutch perhaps, yet all without any awareness of what one was doing.
What’s going on here? “The driver in a state of automatism perceives, or is aware of, the road. If he did not, the car would be in a ditch. But he is not currently aware of his awareness of the road. He perceives the road, but he does not perceive his perceiving, or anything else that is going on in his mind.” He is driving, it would seem, without conscious awareness of what he’s doing; we seem to be able to perform complex mental processes without conscious experience.
(From D.M. Armstrong, The Nature of Mind, 1981.)
This is unexpected — in 1999 mathematician Mike Keith programmed a computer to generate knights’ tours using Warnsdorff’s rule and then labeled the successive squares A, B, C, etc. to see whether any 8-letter words emerged. After about a million tours, he found two, UNSHAVEN and ARCHIVAL:
M T Q B W D O F E T W F G J Y H R C L O P G X C V E F Y X G T K U N S H A V E N S D U H U L I Z D K P S H Y B U D G Z K X M L S Q V G J I T M Z A R C H I V A L H E R C F I L A F C J W N I R M W D G J Y J A L Q B A D O P K B F I X E B K Z K B E P O J C N Q
After some further searching he also found PERORATE and EPIDURAL. See the link below for more results.
(Michael Keith, “Knight’s Tour Letter Squares,” Word Ways 32:3 [August 1999], 163-168.)
In Mary Shelley’s Frankenstein, we’re told explicitly that the creature is “gigantic”; at his birth at Ingolstadt he’s described as 8 feet tall. Where did Victor Frankenstein get a skeleton large enough for a giant?
For that matter, how does the creature clothe himself? He takes some “dress” of Victor’s to wear, yet he “exceeds the height of a man.” How is this possible?
(From John Sutherland, Frankenstein’s Brain, 2018. Dracula has his own puzzles.)
In 1825, impresario George Wombwell sponsored a fight between six bulldogs and a lion from his menagerie in the English market town of Warwick. Five hundred people assembled in a disused factory yard, and Wombwell arranged for the dogs to attack Nero three at a time, ignoring the pleas of a Quaker named Samuel Hoare, who asked “how thou wilt feel to see the noble animal thou hast so long protected, and which has been in part the means of supplying thee with the means of life, mangled and bleeding before thee?” The lion seemed indisposed to use its full strength against the first three dogs, swatting them away with his paws but never biting. After a 20-minute respite, Wombwell set the next three dogs upon him, and they pinned him to the floor. When a third round brought the same result, Wombwell conceded defeat for the lion, afraid that “the death of the animal must be the consequence of further punishment.”
In a second contest less than a week later, though, a Scottish-born lion known as Wallace fought back ferociously, holding one dog in his teeth and “deliberately walk[ing] around the stage with him as a cat would a mouse.” A second dog “died just a few seconds after he was taken out of the cage,” and a third remained in Wallace’s jaws until a keeper “threw a piece of raw flesh into the den.” A fourth was left in critical condition with “several of his ribs broken.”
The spectacle was widely condemned in the press and informed a new sensitivity regarding cruelty to animals. In 1838 one commentator remarked, “what dogs and lions can achieve in the arena of combat … having now been ascertained, let us hope that no closer approximation to the sanguinary games of the Roman amphitheatre may ever be attempted in Great Britain, nor her soil again polluted by a repetition of such spectacles.”
(Helen Cowie, “A Disgusting Exhibition of Brutality,” in Sarah Cockram and Andrew Wells, eds., Interspecies Interactions, 2018.)
You can ask Google to flip a coin for you.
You can add dice, or declare a constant to be added to the total, using the icons at the bottom.
Due to a miscommunication, Lt. Jack Brewster of the 3rd Royal Fusiliers started forward with his men to attack a German position in Ypres before the proper order had been given. He was last seen rushing toward the German trenches and was feared lost. In May 1915 Brewster’s parents were desperately seeking more information when they received an unexpected letter from a German sergeant named Egbert Wagner:
On 11th of this month, through God’s gracious guiding hand, I was led to discover your son, Lieutenant JA Brender [sic], 3rd Royal Fusiliers, in a shell hole, where he had been lying for two [three] days with a gun shot wound in the upper part of his thigh. Acting on the command of our Lord Jesus ‘Love your Enemies’ I bandaged him with the permission of our officer, and provided him with bread and wine. I had a lot of conversation with your dear son, whose condition visibly improved by evening. With eight of our brave Riflemen I arranged to get him conveyed, with the assistance of some medical staff, back from our front line position to the collecting center for wounded. There I handed over your dear son to the care of best and competent hands, and now carry out my promise given to your son, when we were lying so happily together in the shell-hole, in spite of the rain of bullets, that I would communicate his deliverance to his dear father. I offer you my earnest wish for peace and await your reply via Denmark.
Sergeant Egbert Wagner
He had forwarded it through his friend Axel Backhausen in Denmark. The family wrote back, asking Backhausen to convey their “great relief” to Wagner, who “must be a very good man. … We trust he may live to do other good work in the world for such men are badly needed in these terrible times.”
Brewster’s father added that friends had asked to see Wagner’s letter. “I hope you will forgive me for granting their requests,” he wrote. “I believe, in some cases, it will be used as a text for sermons next Sunday.”
(From Richard van Emden, Meeting the Enemy: The Human Face of the Great War, 2013.)