Bookmarks (202)

Is every integer the sum of four perfect cubes? Interestingly, no one knows. It’s conjectured that the answer is yes, but no one yet has been able to prove this.

“Good tests kill flawed theories; we remain alive to guess again.” — Karl Popper “There are two possible outcomes: if the result confirms the hypothesis, then you’ve made a measurement. If the result is contrary to the hypothesis, then you’ve made a discovery.” — Enrico Fermi “This particular thesis was addressed to me a quarter of a century ago by John Campbell, who …...

In 2020, three researchers from UT Austin and Lancaster University examined 40,000 fictional narratives and discovered a consistent linguistic pattern. Articles and prepositions such as a and the are common at the start of a story, where they set the stage by providing information about people, places, and things. As the plot progresses, auxiliary verbs, adverbs, and pronouns become more common — words that...

A tail behind, a trunk in front, Complete the usual elephant. The tail in front, the trunk behind, Is what you very seldom find; If you for specimens should hunt With trunks behind and tails in front, That hunt would occupy you long; The force of habit is so strong. — A.E. Housman

“One of the strangest things about life is that the poor, who need the money most, are the very ones that never have it.” — Finley Peter Dunne

By Wikimedia user Cmglee, a visual proof that 33 + 43 + 53 = 63: This value, 216, is sometimes called Plato’s number because it seems to correspond to this enigmatic passage in the Republic: Now for divine begettings there is a period comprehended by a perfect number, and for mortal by the first in which augmentations dominating and dominated when they have attained...

I don’t know anything about this; it just popped up on the subreddit r/funny: “Someone in the Netherlands has a sense of humor.”

In the December 2024 issue of Recreational Mathematics Magazine, Illinois State University mathematician Sunil Chebolu demonstrates that the digits of π can be generated using the positions of stars. The probability P(x, y) that two randomly chosen positive integers, x and y, are relatively prime is 6/π2. The stars in the night sky appear to be distributed randomly on the celestial sphere, and this...

postation n. the placing of one thing after another consectaneous adj. succeeding, following as by consequence resiliating adj. that resumes or causes to resume a former shape or position finifugal adj. shunning the end of something Jason Allemann built this infinite LEGO domino ring in 2023. Sixty-four dominoes fall in a continuous loop, with a robot circulating perpetually opposite the cascade to restore the...

In his 1957 book A Testament, Frank Lloyd Wright described a skyscraper a mile high that he hoped to build in Chicago. Atomic-powered elevators would serve a net rentable area of more than 13 million square feet, with covered parking for 15,000 cars and landing decks for 150 helicopters. Wright imaged it would be “more permanent than the pyramids,” but the plan was never...

In discussing the paintings, [Jackson Pollock] would ask, ‘Does it work?’ Or in looking at mine, he would comment, ‘It works’ or ‘It doesn’t work.’ He may have been the first artist to have used the word ‘work’ in that sense. — Lee Krasner, quoted in B.H. Friedman, Jackson Pollock: Energy Made Visible, 1972

In 1937 a Sabena Junkers Ju 52 crashed in Ostend — the plane struck a factory chimney while attempting to land in thick fog. Everyone aboard was killed, including Princess Cecilie, the older sister of Prince Philip, later Duke of Edinburgh. She had been eight months pregnant, and a newborn infant was discovered in the wreckage. It’s speculated that she had given birth during...

In his later years Joseph Conrad became obsessed with the opening scene of an unwritten novel that he planned to set in an Eastern European state. “So vividly used he to describe this scene to me,” wrote his friend Richard Curle, “that at last it was as though I had been a witness to it myself”: “In the courtyard of a royal palace, brilliantly...

C.W. Hooper of Keswick sent this creation to the Strand in August 1901: “It contains all the letters of the alphabet, twenty-six in all. They can be traced with patience. The letter N is the smallest (in the centre), and is the only indistinct one.”

This poem, by Lewis Carroll, can be read line by line in the conventional way, but the same text results when it’s scanned “downward” in columns, reading the first word of each of the six lines, then the second, and so on: I often wondered when I cursed Often feared where I would be -- Wondered where she'd yield her love, When I yield,...

Obscure words from the personal collection of Eric Albert, from a Word Ways article in November 1988: agroof: face downward amphoric: resembling the sound produced by blowing into a bottle benedict: an apparently confirmed bachelor who marries bort: the fragments removed from diamonds in cutting callipygian: having shapely buttocks charette: a period of intense group work to meet a deadline clishmaclaver: gossip crepitaculum: the...

In 1940, George Gamow published Mr Tompkins in Wonderland, in which a bank clerk attends a lecture on relativity and then finds that Einstein’s principles have become apparent in the ordinary street scenes before him: A single cyclist was coming slowly down the street and, as he approached, Mr Tompkins’s eyes opened wide with astonishment. For the bicycle and the young man on it...

“A Lowlands Holiday Ends in Enjoyable Inactivity,” a poem by Miles Kington: In Ayrshire hill areas, a cruise, eh, lass? Inertia, hilarious, accrues, hélas! In certain British dialects, the two lines sound the same.

An invertible word made of impossible letters, by Basile Morin: An emphatic assertion by Douglas Hofstadter: In 1908, after observing that chump in cursive reads largely the same upside down, the Strand asked for similar specimens and received this:

Writing in the New Yorker in 1949, John Davenport documented a rising language he’d observed among his countrymen. He called it Slurvian. “When Slurvians travel abroad, they go to visit farn (or forn) countries to see what the farners do that’s different from the way we Murcans do things. While in farn countries, they refer to themselves as Murcan tersts, and usually say they...

Charles Craik of Weston-super-Mare received this enigmatic postcard from a friend in 1901 and sent it on to the Strand: I think it rather cleverly done, and it took me some time before I could understand its meaning. The principal message is on the big island in the centre of the map — an invitation to meet the sender at a café, with the...

But despite the gaiety of his song, Balso did not feel sure of himself. He thought of the Phoenix Excrementi, a race of men he had invented one Sunday afternoon while in bed, and trembled, thinking he might well meet one in this place. And he had good cause to tremble, for the Phoenix Excrementi eat themselves, digest themselves, and give birth to themselves...

While at Eton, Winston Churchill’s son Randolph was “immensely impressed” to hear his friend Freddie Furneaux recite the following passage without notes. Ostensibly it’s about Henry VIII: “This monarch was sincere, open, gallant, liberal, intrepid, inflexible and courageous; but with these virtues he combined the vices of violence, cruelty, profusion, rapacity, obstinacy, injustice, arrogance, presumption and conceit.” When Churchill asked the source of the...

An odd detail from the autobiography of Bertrand Russell: “The summers of 1903 and 1904 we spent at Churt and Tilford. I made a practice of wandering about the common every night from eleven till one, by which means I came to know the three different noises made by night-jars.” He adds, “(Most people only know one.)” He says nothing more.

In a set of weights, no weight exceeds 10 kg. If the set is divided arbitrarily into two groups, the combined mass of one of these groups also will not exceed 10 kg. What’s the greatest possible mass of the full set of weights?

“A red rose absorbs all colours but red; red is therefore the one colour that it is not.” — Aleister Crowley, of all people

Some personal names used in the land moiety of the Miwok people of Northern California, listed in Brian Bibby’s Deeper Than Gold: Indian Life in the Sierra Foothills, 2005: akaino: bear holding its head up engeto: bear bending its foot in a particular manner while walking esege: bear showing its teeth when cross etumu: bear warming itself in the sun sutuluye: bear making noise...

Paris newspapers once carried an ad offering a cheap and pleasant way of travelling for the price of 25 centimes. Several simpletons mailed this sum. Each received a letter of the following content: ‘Sir, rest at peace in bed and remember that the earth turns. At the 49th parallel — that of Paris — you travel more than 25,000 km a day. Should you...

There was a fence with spaces you Could look through if you wanted to. An architect who saw this thing Stood there one summer evening, Took out the spaces with great care And built a castle in the air. The fence was utterly dumbfounded: Each post stood there with nothing round it. A sight most terrible to see. (They charged it with indecency.) The...

“Marriage is the only legal contract which abrogates as between the parties all the laws that safeguard the particular relation to which it refers.” — Shaw

Kevin Purbhoo invented this vivid puzzle while a student at Northern Secondary School in Toronto: On a remote Norwegian mountain top, there is a huge checkerboard, 1000 squares wide and 1000 squares long, surrounded by steep cliffs to the north, south, east, and west. Each square is marked with an arrow pointing in one of the eight compass directions, so (with the possible exception...

A remarkable number of apparently intelligent people are baffled by the fact that a different group of apparently intelligent people profess to a knowledge of God when common sense tells them — the first group of apparently intelligent people — that knowledge is only a possibility in matters that can be demonstrated to be true or false, such as that the Bristol train leaves...

Occasionally, by coincidence, the gaps between words on a page of printed text will become aligned, producing “rivers” of white space that descend across multiple lines. These occur most commonly when the font is monospaced and justification is full. Because they’re distracting, these artifacts are generally discouraged; typographers sometimes view a printed page upside down in order to spot them. In ordinary text long...

Memorable passages from the pulp detective stories of Robert Leslie Bellem (1902-1968): “There were tears brimming on her azure peepers, and tremulous grief twisted her kisser.” (“Forgery’s Foil”) “She wrapped her arms around my neck; glued her crimson kisser to my lips. She fed me an osculation that sent seven thousand volts of electricity past my tonsils.” (“Design for Dying”) “And then, from the...

Unusual personal names collected by the Society for the Verification and Enjoyment of Fascinating Names of Actual Persons, listed by curator Allan Fotheringham in 1991: Procter R. Hug Polly Wanda Crocker Sexious Boonjug Philander Philpott Pettibone Zilpher Spittle Petrus J.G. Prink Burke Uzzle Pansy Reamsbottom Dunwoody Zook Bastion Hello Fang W. Wang Montague Tyrwhitt-Drake Nimrod Spong Dulcie Pillage Jake Moak Sir Tufton Beamish Sir...

What do you call a person from Connecticut? Today we’d call them a Connecticuter or a Connecticutian (or, colloquially, a Nutmegger), but in a 1987 address etymologist Allen Walker Read announced that he’d also found these options: Connecticotian, used in 1702 by Cotton Mather Connecticutensian, used in 1781 by historian Samuel Peters Connectican, used in 1942 in a letter to the Baltimore Evening Sun...

Sydney Smith wrote a recipe for salad dressing: Two boiled potatoes, strained through a kitchen sieve, Softness and smoothness to the salad give; Of mordant mustard take a single spoon — Distrust the condiment that bites too soon; Yet deem it not, thou man of taste, a fault, To add a double quantity of salt. Four times the spoon with oil of Lucca crown,...

Draw an arbitrary quadrilateral and divide each of its sides into three equal parts. Draw a line through adjacent points of trisection on either side of each vertex and you’ll have a parallelogram. Discovered by Austrian engineer Ferdinand Wittenbauer.

Titles of paintings by Salvador Dalí: Debris of an Automobile Giving Birth to a Blind Horse Biting a Telephone Bed and Two Bedside Tables Ferociously Attacking a Cello Premature Ossification of a Railroad Station Rock and Infuriated Horse Sleeping Under the Sea Fifty Abstract Paintings Which as Seen From Two Yards Change Into Three Lenins Masquerading as Chinese and as Seen From Six Yards...

In 1897, German mathematician August Leopold Crelle published a book listing all the products of pairs of 3-digit numbers. He offered it as a useful aid in the multiplication of large numbers. Suppose we want to multiply 26457081 by 247183. Divide each factor into 3-digit “chunks”: 026 457 081 and 247 183. Now think of each full chunk as a digit — instead of...

The September 1981 University Computing Center Newsletter at the University of Southern California included this recipe for “Famous Rum Cake,” written in Assembler by a systems programmer for the IBM 360: RUMCAKE CSECT * THIS INTRODUCES SOME NEW MNEMONICS * MX MIX * MXL MIX UNTIL LIGHT * BSOP BEAT UNTIL SOFT PEAKS * BSTP BEAT UNTIL STIFF PEAKS * BKE BAKE (SECOND OPERAND...

An interesting query by Bob High, posed in the May-June 1994 issue of MIT Technology Review: Suppose a billiard ball with a small black dot precisely on its top is rolled around the full circumference of a circle of the same radius. Assuming no slippage or twisting, where is the dot when the ball returns to its starting point?

A very efficient poem by Leigh Hunt: Here, without any more ado, we have the whole history of a couple of successful rural lovers comparing notes. They issue forth in the morning; fall into the proper place and dialogue; record the charms and kindness of their respective mistresses; do justice at the same time to the fields and shades; and conclude by telling their...

From an appreciation of Ernest Rutherford by C.P. Snow in the November 1958 issue of The Atlantic: Worldly success? He loved every minute of it: flattery, titles, the company of the high official world. He said in a speech: ‘As I was standing in the drawing room at Trinity, a clergyman came in. And I said to him: “I’m Lord Rutherford.” And he said...

In the 1950s, mathematician C. Dudley Langford was watching his son play with blocks, two of each color, when he noticed that they formed a curious pattern: one block lay between the red blocks, two between the blue blocks, and three between the yellow blocks. Langford found that by rearranging the blocks he could add a green pair with four blocks between them. This...

In a 1901 parody edition, the journal Mind! offered £1,000 to any philosopher who could produce adequate documentary evidence that he: Knows what he means. Knows what anyone else means. Knows what everyone means. Knows what anything means. Knows what everything else means. Means what he says. Means what he means. Means what everyone else means. Means what everyone else says that he means....

A man of the State of Chêng was one day gathering fuel, when he came across a startled deer, which he pursued and killed. Fearing lest any one should see him, he hastily concealed the carcass in a ditch and covered it with plantain leaves, rejoicing excessively at his good fortune. By and by, he forgot the place where he had put it, and,...