Pain and Possession

A stunning finding regarding the efficacy of placebos:

In 2017 Victoria Wai-lanYeung, a psychologist at Lingnan University in Hong Kong, and her colleagues gave a placebo painkilling cream at random to half their subjects, as a gift, and then put all the subjects to a moderately painful task (immersing a hand in ice water).

Participants who’d received the cream but hadn’t used it reported lower pain levels than those who hadn’t received it — merely owning a fake painkiller had reduced their pain.

Wagah-Attari Border Ceremony

Every evening since 1959, the security forces of India and Pakistan have performed a joint military ceremony at the Attari-Wagah border. Soldiers from both sides perform elaborate and highly choreographed maneuvers, including high leg raises, before the border gates are opened and the two flags are lowered simultaneously as the sun sets. The flags are folded, two soldiers shake hands, and the gates close again. For the spectators, the ceremony is a symbol of both the cooperation and the rivalry that exist between the two nations.

December 12, 2019December 11, 2019 | Society

A Hat Puzzle

Each of three people is wearing either a red hat or a blue hat. Each can see the color of the others’ hats but not her own. Each is told to raise her hand if she sees a red hat on another player. The first to guess the color of her own hat correctly wins.

All three raise their hands. A few minutes pass in which no guesses are made, and then one player says “Red” and wins. How did she know the color of her hat?

	Select Click for Answer
All three players raised their hands, so each can see at least one red hat. This means that at least two of the hats are red; if two or more were blue then there’d be at least one player who didn’t raise her hand. But any player who can see a blue hat can immediately infer that her own hat must be red, because she can see a red-wearing player whose hand is raised. In the puzzle this doesn’t happen: All three players raise their hands and yet none of them makes this inference. That allows one of the players to conclude that none of them is wearing a blue hat; all three hats must be red.

Click for Answer

December 11, 2019December 11, 2019 | Puzzles

A Match

Do there exist a right triangle and an isosceles triangle, each with sides of rational length, that have both the same perimeter and the same area?

Yes, there’s exactly one such pair!

The right triangle has sides of lengths (377, 135, 352) and the isosceles of lengths (366, 366, 132).

Via Robin Houston’s Twitter feed.

December 11, 2019December 10, 2019 | Science & Math

Reckoning

Mercyhurst College mathematician Charles Redmond used to get frantic phone calls at the end of each term from colleagues in other departments who’d written syllabi saying “Quiz 1 is 10% of your final grade” and now couldn’t figure out how to do the necessary calculation.

“There’s a good reason,” Redmond wrote. “They said something they didn’t mean to say, and they had only a vague notion of what they meant to say in the first place.”

He suggested that students might turn this confusion to their advantage. Suppose Quiz 1 is worth 10 or more points and your score is 9. If x is your final grade and “Quiz 1 is 10% of your final grade,” then 0.10x = 9 and suddenly your final grade is 90, an A.

“Not bad for about a week’s worth of work. Take the rest of the semester off.”

(Ed Barbeau, “Fallacies, Flaws, and Flimflam,” College Mathematics Journal 33:2 [March 2002], 137-139.)

December 10, 2019December 10, 2019 | Science & Math

Another Way

Carnegie-Mellon mathematician Po-Shen Loh has offered a new, simple proof of the quadratic formula that provides a natural, intuitive algorithm for solving general quadratic equations.

More here. “May this story encourage the reader to think afresh about old things; seeing as how new progress was made on this 4,000 year old topic, more surprises certainly await the light of discovery.”

(Thanks, Jason.)

December 10, 2019December 9, 2019 | Science & Math

Hidden Image

Matthew Scroggs has released this year’s Christmas card for Chalkdust magazine.

This year’s card contains nine mathematical puzzles. Finding the right answers will reveal a Christmas-themed picture in the image above.

You can download the card as a PDF or complete it online.

December 9, 2019 | Puzzles

Podcast Episode 276: An Unlikely Confederate Spy

As the Civil War fractured Washington D.C., socialite Rose O’Neal Greenhow coordinated a vital spy ring to funnel information to the Confederates. In this week’s episode of the Futility Closet podcast we’ll describe one of the war’s most unlikely spies, and her determination to aid the South.

We’ll also fragment the queen’s birthday and puzzle over a paid game of pinball.

See full show notes …

December 9, 2019December 19, 2019 | History · Podcast

First Friends

In 1978, archaeologists excavating a late Paleolithic tomb in northern Israel uncovered the skeletons of an elderly human and a 5-month-old puppy. They had lain there together for 12,000 years.

“The most striking thing about these remains was the fact that whoever presided over the original burial had carefully arranged the dead person’s left hand so that it rested, in a timeless and eloquent gesture of attachment, on the puppy’s shoulder,” writes James Serpell in In the Company of Animals (1996).

“The contents of this tomb not only provide us with some of the earliest solid evidence of animal domestication, they also strongly imply that man’s primordial relationship with this particular species was an affectionate one. In other words, prehistoric man may have loved his dogs and his other domestic animals as pets long before he made use of them for any other purpose.”

(Simon J.M. Davis and François R. Valla, “Evidence for Domestication of the Dog 12,000 Years Ago in the Natufian of Israel,” Nature 276:5688 [1978], 608.)

December 8, 2019 | Science & Math