“There is nothing at McDonald’s that makes it necessary to have teeth.” — Harvard nutritionist Jean Mayer, Time, 1973
Observation
Outside the Box
An old puzzle asks: Without lifting your pencil from the paper, can you draw a series of four straight lines that passes through all nine points in this grid?
The trick is to realize that the lines can extend beyond the grid’s area:
In 1970 Solomon Golomb and John Selfridge found a way to draw a closed path of eight segments that passes through all 25 points in this grid:
Can you?
Full Circle
Before they departed on Apollo 16 in April 1972, lunar module pilot Charles Duke told commander John Young about an eerie dream he’d had. The two of them were driving the lunar rover toward the North Ray crater when they crossed a ridge and discovered a set of tire tracks. They followed them, and after an hour they came upon another lunar rover that had been standing on the moon’s surface for thousands of years. In it were two dead astronauts who looked like Duke and Young.
In folklore seeing one’s double can be an omen of imminent death, but Duke didn’t take it that way. “I felt kind of comfortable,” he said later. “I took parts from this other vehicle, to show to the people down at Houston.”
But the impression remained with him as the mission departed for the moon. “The dream was so vivid that when we were landing I looked out of the window to the north to see if there were any tracks on the surface of the moon,” he said. “The landscape was very similar to what I [had] seen in my dream.”
On April 23, he found himself driving the rover with Young toward the North Ray crater and couldn’t resist looking for a second set of tracks. There was none, of course, but while he was distracted the rover began to slide backward down the slope and he had to fight to keep it from overturning. When they came to a stop the rover’s tracks extended ahead of them up the slope.
Young said, “Charlie, you said you were going to see some other tracks on the Moon.”
Unquote
“None think the great unhappy but the great.” — Edward Young
Fair Play
Any two lines drawn between opposite sides of a square and intersecting at right angles are equal.
Podcast Episode 233: Flight to Freedom
In 1978 two families hatched a daring plan to escape East Germany: They would build a hot-air balloon and sail it by night across the border. In this week’s episode of the Futility Closet podcast we’ll follow their struggles to evade the authorities and realize their dream of a new life in the West.
We’ll also shuffle some vehicles and puzzle over a perplexing worker.
Doorstops
I do not like books. I believe I have the smallest library of any literary man in London, and I have no wish to increase it. I keep my books at the British Museum and at Mudie’s, and it makes me very angry if any one gives me one for my private library. I once heard two ladies disputing in a railway carriage as to whether one of them had or had not been wasting money. ‘I spent it in books,’ said the accused, ‘and it’s not wasting money to buy books.’ ‘Indeed, my dear, I think it is,’ was the rejoinder, and in practice I agree with it.
— Samuel Butler, Ramblings in Cheapside, 1890
Thinking Big
This is fantastic — in 2017, 56 enthusiasts built an O-gauge model railway 71 miles long, connecting Fort William and the City of Inverness in the Scottish Highlands. At a scale of 46:1, that’s half the length of the Trans-Siberian Railway.
Only one journey was made on the completed railway. The locomotive Silver Lady departed Corpach Double Lock on June 23, 2017, and arrived, on time, at Inverness Castle on July 1.
Volunteer team leader Lawrence Robbins told the Daily Record, “Just because it’s bonkers doesn’t mean it’s a bad idea.”
Threes and Fours
A problem from the Tenth International Mathematical Olympiad, 1968:
Prove that in every tetrahedron there is a vertex such that the three edges meeting there have lengths which are the sides of a triangle.
Misc
- The negative space in the eight of diamonds forms an 8.
- William Brewster, leader of the Plymouth Colony, named his children Jonathan, Patience, Fear, Love, and Wrestling.
- Wilfred Owen’s mother received the news of his death on Armistice Day.
- SCHOOLMASTER = SMOTE SCHOLAR
- “I never had any philosophic instruction, the first lecture on psychology I ever heard being the first I ever gave.” — William James