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Pat Ashforth and Steve Plummer make knitted illusions. When it’s viewed from the front, each piece presents only a series of unremarkable stripes, but when it’s viewed obliquely, an image emerges. Here’s an introduction to the technique, and here are some patterns.

Conventional stairs are somewhat extravagant: Because users alternate their steps (1), half of each tread goes unused. In close quarters, floor space can be conserved by omitting these unused portions (3), permitting a slope as high as 65 degrees without sacrificing the depth of the treads (2). Because each tread “overlaps” those that precede and follow it, an alternating staircase might require only half...

If nature be regarded as the teacher and we poor human beings as her pupils, the human race presents a very curious picture. We all sit together at a lecture and possess the necessary principles for understanding it, yet we always pay more attention to the chatter of our fellow students than to the lecturer’s discourse. Or, if our neighbor copies something down, we...

Raymond Smullyan presented this oddity in his Chess Mysteries of Sherlock Holmes in 1980. Suppose we come upon this abandoned chess game. Can White mate in two moves? The answer seems to be yes. If Black can’t castle, then White can play 1. Ke6 and then promote his g-pawn, giving mate. If Black can castle, that means that neither his king nor his rook...

This is beautifully well done — a humiliating list of all the ways your brain can deceive you (click to enlarge). Designed by John Manoogian III.

This is a picture of a cow. If you can’t see it (I couldn’t), there’s an explanatory image on page 66 of John McCrone’s 1991 book The Ape That Spoke. The experience illustrates how the brain is able to construct a picture from limited data by relying on patterns and experience.

Thomas Jefferson to the Rev. Isaac Story, Dec. 5, 1801, on the afterlife: When I was young I was fond of the speculations which seemed to promise some insight into that hidden country, but observing at length that they left me in the same ignorance in which they had found me, I have for very many years ceased to read or to think concerning...

These are the punts of Trinity College, Cambridge, moored on the River Cam. What is the significance of their names?

Steaming from New York to the Azores in 1867, Mark Twain noted a curious companion overhead: We had the phenomenon of a full moon located just in the same spot in the heavens at the same hour every night. The reason of this singular conduct on the part of the moon did not occur to us at first, but it did afterward when we...

Reader J. William Hook submitted this curiosity to the Strand in August 1899. Holding the page level with the eyes foreshortens the characters and reveals a love poem: Art thou not dear unto my heart? Oh, I search that heart and see And from my bosom tear the part That beats not true to thee. But to my bosom thou art dear, More dear...

(Until William Herschel’s advances in telescopes, stars seemed to have “rays” or “tails.”) At a dinner given by Mr Aubert in the year 1786, William Herschel was seated next to Mr Cavendish, who was reputed to be the most taciturn of men. Some time passed without his uttering a word, then he suddenly turned to his neighbour and said: ‘I am told that you...

An art gallery with n walls will always be safe with n/3 guards — the guards will always be able arrange themselves to observe the whole gallery. That’s Chvátal’s art gallery theorem, discovered in 1973 by mathematician Václav Chvátal. Interestingly, it’s true only of two-dimensional floor plans — a three-dimensional gallery may not be safe even if you post a guard at every corner....

For the past eighty years I have started each day in the same manner. It is not a mechanical routine but something essential to my daily life. I go to the piano, and I play two preludes and fugues of Bach. I cannot think of doing otherwise. It is a sort of benediction on the house. But that is not its only meaning for...

renitence n. unwillingness, resistance to persuasion subdolous adj. cunning, crafty, sly autoschediasm n. something done on the spur of the moment or without preparation legerity n. physical or mental quickness FDR’s secretary of state, Cordell Hull, was famously unforthcoming, concealing his plans and emotions with the skill of a poker player. When Hull was a legislator in Tennessee, one of his friends bet that...

Julius Caesar thought that elk have no knees. Duke Ellington’s first piano teacher was named Marietta Clinkscales. Orizabus subaziro, a rhinoceros beetle, has a palindromic species name. POSSESSIONLESSNESSES has 9 S’s. “Books are companions even if you don’t open them.” — Disraeli

From Martin Geldart’s Guide to Modern Greek, 1883: Here we are (arrived) at the station. What luggage have you, sir? I have two trunks, a travelling-bag, and a hat-box, for the luggage van. These I wish to register. My other luggage I will take with me. That is to say — a foot-wrapper, a stick, three or four parcels, a gun, a lap-dog, two...

In September 1931 the Weekend Review pointed out the “regrettable omission of any reference to tooth-brushing in the description of Adam and Eve retiring for the night” in Book IV of Paradise Lost. It challenged its readers to improve Milton’s text; polymath Edward Marsh inserted these lines: [… and eas’d the putting off These troublesome disguises which wee wear,] Yet pretermitted not the strait...

Who’s Who invites its contributors to list their recreations. Some responses are unusual: Charles Causley: “Playing the piano with expression.” John Faulkner: “Intricacies and wildernesses.” John Fowles: “Mainly Sabine.” Bevis Hillier: “Awarding marks out of ten for suburban front gardens.” James Kirkup: “Standing in shafts of sunlight.” (In old age he changed this to “Standing in shafts of moonlight.”) Edward Lucie-Smith: “Walking the dog;...

Gulliver’s Travels describes a device by which “the most ignorant person, at a reasonable charge, and with a little bodily labour, might write books in philosophy, poetry, politics, laws, mathematics, and theology, without the least assistance from genius or study”: He then led me to the frame, about the sides whereof all his pupils stood in ranks. It was twenty feet square, placed in...

In 1955, the editor of a Michigan high school newspaper wrote to E.E. Cummings, asking his advice for students who wanted to follow in his footsteps. He sent this reply: A Poet’s Advice to Students A poet is somebody who feels, and who expresses his feeling through words. This may sound easy. It isn’t. A lot of people think or believe or know they...

A problem from Cambridge mathematician J.E. Littlewood’s Miscellany (1953): Is it possible to pack a cube with a finite number of smaller cubes, no two of which are the same size?