Here are a penny and a quarter. Make a statement. If your statement is true, then I’ll give you one of these coins (not saying which). But if your statement is false, then I won’t give you either coin.
Raymond Smullyan says, “There is a statement you can make such that I would have no choice but to give you the quarter (assuming I keep my word).” What statement will accomplish that?
Lyudmila Pavlichenko was training for a career as a history teacher when Germany invaded the Soviet Union in 1941. She suspended her studies to enlist as a sniper in the Red Army, where she discovered a remarkable talent for shooting enemy soldiers. In this week’s episode of the Futility Closet podcast we’ll trace the career of “Lady Death,” the deadliest female sniper in history.
We’ll also learn where in the world futility.closet.podcast is and puzzle over Air Force One.
A puzzle by the Hungarian-Canadian mathematician George Grätzer:
I’m writing an article about a round-robin tennis tournament, in which each player plays each other player once. I decide to pick one player and ask her which players she defeated (in tennis there are no ties). Then I’ll ask each of those players which players they’ve defeated. Is it possible to pick a player so that everyone in the tournament is mentioned in my article?
For 50 years, Snoopy has been NASA’s official safety mascot. Every astronaut wears a sterling silver Snoopy pin into space and presents it personally afterward to an employee or contractor as a special commendation for outstanding achievements related to safety.
Each year, fewer than 1 percent of the aerospace program workforce receive the award; it’s the highest honour recognizing the people who work to keep astronauts safe.
I just thought this was interesting: In the 1970s a little spate of studies investigated why men and women carry books in stereotypically different ways. A 1976 study in Tennessee found that by junior high school males tended to carry books at their sides, with the arm relatively straight and the hand cupped under the book’s lower edge. Females cradled a book in the arm at the front side of the body, resting on the hip or pelvic bone.
A second study in the same year ruled out some theories: It found that men and women carried books of roughly equal weight, and that both had hand grips strong enough to carry their books in either position. (Also, carrying purses didn’t significantly alter the way women carried their books.)
A University of Washington study two years later replicated the earlier findings but suggested that “women with hips that extend past the comfortable fall line of the arm along the side of the body will not show the side carry typically seen in males.” (“In effect, the hip in females fills the side space that males fill with their books.”)
But a re-examination 15 years later found that the picture was changing: While 90 percent of the men still carried books at their sides, now so did 43-60 percent of the women. So perhaps it’s not correct to speak of these as intrinsically masculine and feminine styles. But that raises another question: “why … men’s carrying behavior is uniform and stable, whereas women’s behavior is more varied and changing.”
(Thomas P. Hanaway and Gordon M. Burghardt, “The Development of Sexually Dimorphic Book-Carrying Behavior,” Bulletin of the Psychonomic Society 7:3 [1976], 267-270; Philip J. Spottswood and Gordon M. Burghardt, “The Effects of Sex, Book Weight, and Grip Strength on Book-Carrying Styles,” Bulletin of the Psychonomic Society 8:2 (1976), 150-152; Judith D. Scheman, Joan S. Lockard, and Bruce L. Mehler, “Influences of Anatomical Differences on Gender-Specific Book-Carrying Behavior,” Bulletin of the Psychonomic Society 11:1 [1978], 17-20; Evelyne Thommen, Emiel Reith, and Christiane Steffen, “Gender-Related Book-Carrying Behavior: A Reexamination,” Perceptual and Motor Skills 76:2 [1993], 355-362.)
The crows like to insist a single crow is enough to destroy heaven. This is incontestably true, but it says nothing about heaven, because heaven is just another way of saying: the impossibility of crows.
— Kafka
Choose any four points on a circle and join them to form a quadrilateral. Drawing the diagonals of this quadrilateral produces four overlapping triangles (each diagonal creates two of them).
Draw the largest possible circle in each of these triangles, and the centers of these circles will always form a rectangle:
In his autobiography, Benjamin Franklin describes mollifying a rival legislator in the Pennsylvania statehouse:
Having heard that he had in his library a certain very scarce and curious book, I wrote a note to him, expressing my desire of perusing that book, and requesting he would do me the favour of lending it to me for a few days. He sent it immediately, and I return’d it in about a week with another note, expressing strongly my sense of the favour. When we next met in the House, he spoke to me (which he had never done before), and with great civility; and he ever after manifested a readiness to serve me on all occasions, so that we became great friends, and our friendship continued to his death.
This seems to be a real psychological phenomenon — you can sometimes more reliably make a friend by asking a favor than by doing one, or, as Franklin put it, “He that has once done you a kindness will be more ready to do you another, than he whom you yourself have obliged.”
In a 1969 study, subjects who had won money in a question-and-answer competition were asked to return it; those whom the researcher himself approached reported liking him more than those who’d been approached by a secretary. In another study, students were assigned a teaching task using two different methods, one in which they encouraged their students and one in which they insulted and criticized them. In a debriefing they rated the students they’d encouraged to be more likable and attractive than those they’d insulted. That may reveal a converse principle, that we devalue others in order to justify wronging them.
(Jon Jecker and David Landy, “Liking a Person as a Function of Doing Him a Favour,” Human Relations 22:4 [1969], 371-378; John Schopler and John S. Compere, “Effects of Being Kind or Harsh to Another on Liking,” Journal of Personality and Social Psychology 20:2 (1971), 155.)
“Evil is committed without effort, naturally, fatally; goodness is always the product of some art.” — Baudelaire
Northumberland’s Alnwick Garden contains a special section full of hemlock, belladonna, foxglove, deadly nightshade, Brugmansia, Laburnum, and the botanical ingredients of strychnine and ricin.
“If you’re building something, especially a visitor attraction, it needs to be something really unique,” Jane Percy, the Duchess of Northumberland, who designed the garden, told Smithsonian. “One of the things I hate in this day and age is the standardization of everything. I thought, ‘Let’s try and do something really different.'”
She collected more than 100 varieties, which visitors are forbidden to touch, taste, or smell. (Even so, in 2014 seven visitors reportedly fainted from inhaling the fumes alone.)
“I thought, ‘This is a way to interest children,'” the duchess said. “Children don’t care that aspirin comes from a bark of a tree. What’s really interesting is to know how a plant kills you, and how the patient dies, and what you feel like before you die.”
