Overtime

At Labuan, a British possession in North Borneo, there are only two English officials, Governor Leys and Lieut. Hamilton. The latter gentleman combines in himself the offices of colonial secretary, postmaster, treasurer, magistrate, inspector of police, inspector of the prison, chief commissioner of woods, colonial engineer, and master attendant. In these various capacities he corresponds from himself to himself in the most stately official style, and carefully copies and registers his numerous despatches.

Poverty Bay Herald, Feb. 24, 1888

Surprise Appearance

Suppose we put eight white and two black balls into a bag and then draw forth the balls one at a time. If we repeat this experiment many times, which draw is most likely to produce the first black ball?

Most people answer 4, but in fact the first black ball is most likely to appear on the very first draw:

surprise appearance table

By symmetry, the second black ball is most likely to appear on the final draw.

(A.E. Lawrence, “Playing With Probability,” Mathematical Gazette, vol. 53 [December 1969], 347-354.)

Early Adopter

http://commons.wikimedia.org/wiki/File:Samuel_L_Clemens,_1909.jpg

Mark Twain boasted both that “I was the first person in the world that ever had a telephone in his house” and that “I was the first person in the world to apply the type-machine to literature.” The latter may be true — Twain began experimenting with a Remington No. 2 typewriter in 1874. He reckoned that the book must have been Tom Sawyer; in fact it was probably Life on the Mississippi.

Other writers have been slower to adopt new technology. “This is a nervous letter,” wrote Flannery O’Connor to Cecil Dawkins in 1959. “I am congratulating you on the electric typewriter. It is very nice but I am not used to it yet. I keep thinking about all the electricity that is being wasted while I think what I am going to say next.”

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The Weight of the World

kinmont 8 natural handstands

In 1969 artist Robert Kinmont produced 8 Natural Handstands, a series of photographs of himself standing on his hands in various locations.

Each, he said, depicted an upside-down view of Atlas holding up the earth.

“This world,” wrote Thoreau, “is but canvas to our imaginations.”

Public Enemy

In his 1880 autobiography, Henry Armitt Brown recalls a strange incident from his student days. While a law student in November 1865, he had gone to bed one midnight and dreamed that he was lying on the cobblestones of a narrow street, held down by a “low-browed, thick-set man” who was bent on killing him. He threw the man off and bit at his throat, but the man smiled and brought out a bright hatchet. Brown’s friends leaped to his aid, but as they did so “I saw the hatchet flash above my head and felt instantly a dull blow on the forehead.” He tasted blood and seemed to hover in the air over his own body, where he could see “the hatchet sticking in the head, and the ghastliness of death gradually spreading over the face.”

The following morning, as they walked to school, a friend of his remarked that he’d had a strange dream that night. “I fell asleep about twelve and immediately dreamed that I was passing through a narrow street, when I heard noises and cries of murder. Hurrying in the direction of the noise, I saw you lying on your back fighting with a rough laboring man, who held you down. I rushed forward, but as I reached you he struck you on the head with a hatchet, and killed you instantly.” At Brown’s inquiry he described the murderer as “a thick-set man, in a flannel shirt and rough trousers: his hair was uncombed, and his beard was grizzly and of a few days’ growth.”

A week later Brown called at a friend’s house in New Jersey:

‘My husband,’ said his wife to me, ‘had such a horrid dream about you the other night. He dreamed that a man killed you in a street fight. He ran to help you, but before he reached the spot your enemy had killed you with a great club.’

‘Oh, no,’ cried the husband across the room; ‘he killed you with a hatchet.’

“I remembered the remark of old Artaphernes,” Brown wrote, “that dreams are often the result of a train of thought started by conversation or reading, or the incidents of the working time, but I could recall nothing, nor could either of my friends cite any circumstance ‘that ever they had read, had ever heard by tale or history,’ in which they could trace the origin of this remarkable dream.”

The Friendship Theorem

https://en.wikipedia.org/wiki/File:Friendship_graphs.svg
Image: Wikimedia Commons

If every pair of people in a group have exactly one friend in common, then there’s always one person who is a friend to everyone.

This rather heartwarming fact was proven by Paul Erdös, Alfréd Rényi, and Vera T. Sós in 1966. It’s sometimes more cynically known as the paradox of the politician.

The Erdös proof uses combinatorics and linear algebra, but in 1972 Judith Longyear published a proof using elementary graph theory.

See The Elevator Problem.

Unquote

https://commons.wikimedia.org/wiki/File:4_The_Scientists.JPG

“The origin of science is in the desire to know causes; and the origin of all false science and imposture is in the desire to accept false causes rather than none; or, which is the same thing, in the unwillingness to acknowledge our own ignorance.” — William Hazlitt