Zipf’s Law
Image: Wikimedia Commons

In any language, the most frequently used word occurs about twice as often as the second most frequent word, three times as often as the third most frequent word, and so on.

In American English text, the word the occurs most frequently, accounting for nearly 7% of all word occurrences. The second most frequent word, of, accounts for slightly over 3.5% of words, and so on.

This pattern obtains even in non-natural languages like Esperanto. It’s named for American linguist George Kingsley Zipf, who popularized it.

12/24/2021 UPDATE: Apart from languages, the law is observed in measurements of the citations of scientific papers, web hits, copies of books sold, telephone calls, the magnitude of earthquakes, the diameter of moon craters, the intensity of solar flares, the intensity of wars, and the populations of cities. See this paper. (Thanks, Snehal.)

Image: Wikimedia Commons

Marco Polo noticed an interesting feature in the architecture of Hormuz: “The heat is tremendous, and on that account their houses are built with ventilators to catch the wind. These ventilators are placed on the side from which the wind comes, and they bring the wind down into the house to cool it. But for this the heat would be utterly unbearable.” This technique has been used for thousands of years, originally in ancient Iran and now throughout West Asia: By catching the prevailing wind and directing it through the interior of a house, the residents can greatly increase air circulation while avoiding the sun’s heat.

In 2005 tests using a wind tunnel, Vipac Engineering confirmed that windtowers are effective in reducing the impact of summer climate — and their passivity makes them valuable for energy conservation.

(Anne Coles and Peter Jackson, Windtower, 2007.)

Simplest Terms

English geographer Halford Mackinder’s 1914 paper “The Geographical Pivot of History” helped to found the study of geopolitics. In it, he described his Heartland Theory, in which the world’s land surface was divided into the “World-Island,” meaning Europe, Asia, and Africa; the “offshore islands,” including Britain and Japan; and the “outlying islands,” including the continents of North America, South America, and Australia. At the world’s center lies the Heartland, stretching from the Volga to the Yangtze and from the Himalayas to the Arctic.

In 1919 he reduced his theory to three startlingly stark statements:

Who rules East Europe commands the Heartland.

Who rules the Heartland commands the World Island.

Who rules the World Island commands the World.

He thought the “pivot area” was impregnable to attack by sea and thus capable of building a land power that could conquer the world.

“No mere academic theoretician, Mackinder injected his Heartland thesis into the 1919 Paris Peace Conference that followed World War I,” write Mark Monmonier and George Schnell in Map Appreciation. “He recommended buffer states in Eastern Europe to prevent any nation(s) from gaining control of the Heartland, especially through a German-Soviet alliance. The conference’s subsequent creation of independent states from territories that had been parts of Austria-Hungary, Germany, or Russia varied little from Mackinder’s proposal and included Estonia, Latvia, and Lithuania (along the Baltic Sea) and Poland, Czechoslovakia, and Yugoslavia (extending from the Baltic to the Adriatic).”

“The Black Patch”

Submitted by Randolph Hartley for Life magazine’s 1915 short story contest:

I wear a black patch over my left eye. It has aroused the curiosity of many; no one has suspected the horror that it hides.

Twenty years ago Bernard Vroom and I, fellow students at the University of Jena, were devotees at the feet of Professor Malhausen, the foremost optical surgeon of his time. Living, working, dreaming together, Vroom and I became almost as one intelligence in our passionate study of the anatomy of the eye. Vroom it was who advanced the theory that a living eye-ball might be transferred from the head of one man to the head of another. It was I who suggested, and arranged for, the operation, performed by Professor Malhausen, through which Vroom’s left eye became mine and my left eye became Vroom’s. Professor Malhausen’s monograph, published shortly afterward, describes the delicate operation in detail. The ultimate effects of the operation are my own story.

Very distinctly do I remember the final struggle for breath when the anesthetic was administered; and quite as vividly do I recall my return to consciousness, in a hospital cot, weakened by a six weeks’ illness with brain fever, which had followed the operation. Slowly but clearly my mind advanced through the process of self-identification, and memory brought me to the moment of my last conscious thought. With a mingled feeling of curiosity and dread I opened my eyes.

I opened my eyes and beheld two distinct and strongly contrasting scenes. One, which was visible most clearly when I employed only my right eye, was the bare hospital room in which I lay. The other, distinct to the left eye alone, was the deck of a ship, a stretch of blue sea, and in the distance a low, tropical coast that was to me totally unfamiliar.

Perplexed and vaguely afraid, I begged the nurse to send at once for Vroom. She explained gently that Vroom had recovered quickly, and that, although deeply distressed over leaving me, he had sailed for Egypt, a fortnight since, on a scientific mission. In a flash the truth came to me overwhelmingly. The severing of the optic nerve had not destroyed the sympathy between Vroom’s two eyes. With Vroom’s left eye, now physically mine, I was beholding that which Vroom beheld with his right. The magnitude of the discovery and its potentialities stunned me. I dared not tell Professor Malhausen for fear of being thought insane. For the same reason I have held the secret until now.

On the second day of double-vision my left eye revealed a gorgeous picture of the port and city of Alexandria — and of a woman. Evidently she and Vroom were standing close together at the ship’s rail. I saw on her face an expression that I had never seen on woman’s before. I thrilled with exultation. Then suddenly I went cold. The look was for Vroom, not for me. I had found a love that was not mine, a love to which every atom of my being responded, and it was to be my portion to behold on my loved one’s face, by day and by night, the manifestation of her love for another man.

From that moment on I lived in the world that was revealed to me by my left eye. My right was employed only when I set down in my diary the impressions and experiences of this other life. The record was chiefly of the woman, whose name I never knew. The final entry, unfinished, describes the evidences that I saw of her marriage to Vroom in the English Garrison Church at Cairo. I could write no more. A jealousy so sane and so well founded, so amply fed by new fuel every new moment that it was the acme of torture, possessed me. I was truly insane, but with a true vision, and to me was given the weapon of extreme cunning that insanity provides. I convinced Professor Malhausen that my left eye was sightless, and by simulating calmness and strength I gained my discharge from the hospital. The next day I sailed from Bremen for Port Said.

Upon reaching Cairo I had, naturally, no difficulty in finding my way through the already familiar streets, to the Eden Palace Hotel, and to the very door of Vroom’s apartment, overlooking the Esbekieh Gardens. Without plan, save for the instant sight of her I loved, I opened the door. Vroom stood there facing me, a revolver in his hand.

“You did not consider,” he said calmly, “that my left eye also is sympathetic; that I have followed every movement of yours; that I am acquainted with your errand through the entries in your diary, which I read line by line as you wrote. You shall not see her. I have sent her far away.”

I rushed upon him in a frenzy. His revolver clicked but missed fire. I bore him backward over a divan, my hands at his throat. His eyes grew big as I strangled him. And into my left eye came a vision of my own face, as Vroom saw it, distorted by the lust of murder. He died with that picture fixed in his own eye, and upon the retina of the eye that once was his, and is now mine, that fearful picture of my face was fixed, to remain until my death.

I wear a black patch over my left eye. I dare not look upon the horror that it hides.


“There’s nothing more boring on this earth than to have to read the description of an Italian journey, except maybe to have to write one — and the writer can only make it halfway bearable by speaking as little as possible of Italy itself.” — Heinrich Heine

Concealed Shoes
Image: Wikimedia Commons

England’s Northampton Museum maintains a Concealed Shoe Index that documents the discovery of shoes hidden in the structure of buildings, 1900 of them as of 2012.

This seems to have been a tradition that was once widespread and that died out relatively recently — the first such shoe was discovered behind the choirstalls in Winchester Cathedral, which were installed in 1308, and almost half are from the 19th century. Most have been worn, and about half belonged to children.

Why did people do this? The shoes may have been a fertility charm, or offerings to a household deity, or protections against evil spirits. But the practice was evidently once very popular — concealed shoes have been found in Europe, North America, and Australia, and in many types of buildings: workhouses, factories, public houses, country cottages, town houses, manor houses, hospitals, and two Oxford colleges, St John’s and Queen’s.


On the second day of Apollo 16’s trip to the moon in 1972, command module pilot Ken Mattingly lost his wedding ring. “It just floated off somewhere, and none of us could find it,” lunar module pilot Charlie Duke told Wired in 2016.

Mattingly looked for it intermittently over the ensuing week, with no luck. By the eighth day, Duke and Commander John Young had visited the moon and rejoined him, but there was still no sign of the ring.

But during a spacewalk the following day, Mattingly was just heading back toward the open hatch when Duke said, “Look at that!” The ring was floating just outside the hatch. “I grabbed it,” he said, “and we put it in the pocket. We had the chances of a gazillion to one.”

Duke said later, “You plan and plan and plan but the unexpected always jumps up and bites you.”

(From Ben Evans, Foothold in the Heavens: The Seventies, 2010.)