For the Record

When a tornado struck Mayfield, Ohio, in 1842, Western Reserve College mathematician Elias Loomis noticed that several fowl had been picked almost clean of their feathers. To find out what wind velocity could accomplish this, he charged a cannon with 5 ounces of gunpowder and inserted a freshly killed chicken in place of a ball:

As the gun was small, it was necessary to press down the chicken with considerable force, by which means it was probably somewhat bruised. The gun was pointed vertically upwards and fired; the feathers rose twenty or thirty feet, and were scattered by the wind. On examination they were found to be pulled out clean, the skin seldom adhering to them. The body was torn into small fragments, only a part of which could be found. The velocity is computed at five hundred feet per second, or three hundred and forty one miles per hour. A fowl, then, forced through the air with this velocity, is torn entirely to pieces; with a less velocity, it is probable most of the feathers might be pulled out without mutilating the body.

“If I could have the use of a suitable gun I would determine this velocity by experiment,” he ended. “It is presumed to be not far from a hundred miles per hour.”

(Elias Loomis, “On a Tornado Which Passed Over Mayfield, Ohio, February 4th, 1842,” American Journal of Science 43:2 [July-September 1842], 278-301.)

Shared Birthdays

Famously, in a group of 23 randomly chosen people, the chance is slightly higher than 50 percent that two will share a birthday.

In 2014, James Fletcher considered the birth dates of players in the World Cup, who were conveniently organized into squads of 23 people each. He found that 16 of the 32 squads had at least one shared birthday. If data from 2010 World Cup was included, 31 of 64 squads had shared birthdays, still quite close to 50 percent.

If a group numbers 366 people, the probability of a shared birthday is 100 percent (neglecting leap years). But to reach 99 percent certainty we need only 55 people. “It is almost unbelievable that such a small difference between the probabilities 99% and 100% can lead to such a big difference between the numbers of people,” writes Gabor Szekely in Paradoxes in Probability Theory and Mathematical Statistics (1986). “This paradoxical phenomenon is one of the main reasons why probability theory is so wide-ranging in its application.”

Digit Work

In Mathematics in Fun and in Earnest (2006), Nathan Altshiller-Court describes an ancient method of finger arithmetic to compute the product of two numbers in the range 6-10. Each number is assigned to a finger (on both hands):

6: little finger
7: ring finger
8: middle finger
9: index finger
10: thumb

Now, to multiply 7 by 9, hold your hands before you with the thumbs up and touch the ring finger of one hand to the index finger of the other. These two fingers and all the others physically below them number six and count for 60 toward the final result. Above the joined fingers are three fingers on one hand and one on the other — multiply those two values, add the result (3) to the existing 60, and you get the final answer: 7 × 9 = (6 × 10) + (3 × 1) = 63.

“Besides its arithmetical uses, this clever trick may also serve, with telling effect, to enhance the prestige of an ambitious grandfather in the eyes of a bright fourth-grade grandson,” Altshiller-Court observes. “Competent observers report that it is still resorted to by the Wallachian peasants of southern Rumania.”

Simple Enough

https://commons.wikimedia.org/wiki/File:Churchane-2D-skeletal-bold.png

These compounds are named housane, churchane, basketane, and penguinone.

Below: To celebrate the 2012 London Olympics, chemists Graham Richards and Antony Williams offered a molecule of five rings. They called it olympicene.

https://commons.wikimedia.org/wiki/File:Olympicene.svg

Travel Broadens the Mind

https://en.wikipedia.org/wiki/File:Hafele%E2%80%93Keating_experiment.jpg

In 1971, physicist Joseph C. Hafele and astronomer Richard E. Keating bought airline tickets for a party of four to circle the world twice on commercial airliners. Each party consisted of Hafele, Keating, and two passengers named “Mr. Clock.”

The guests were cesium-beam atomic clocks. The researchers chaperoned the timepieces once eastward around the world and once westward. Then they compared the traveling clocks with one that had remained at the United States Naval Observatory.

The results were published in Science the following year. The clocks had been found to disagree, demonstrating the effects of kinematic and gravitational time dilation.

The total cost of the effort was $8,000. It’s been called one of the most inexpensive tests ever conducted of Einstein’s relativity.

It Begins

Cockatoos in Sydney have mastered a five-step process for opening the lids of trash bins to reach the food inside.

“It was so exciting to observe such an ingenious and innovative way to access a food resource, we knew immediately that we had to systematically study this unique foraging behavior,” wrote behavioral ecologist Barbara Klump.

The birds learn the technique from one another, and cockatoos in different regions have worked out different techniques. Before 2018, the behavior had been reported in only three suburbs, but by the end of 2019 the number had reached 44.

“These results show the animals really learned the behavior from other cockatoos in their vicinity,” Klump wrote.

(Barbara C. Klump et al. “Innovation and Geographic Spread of a Complex Foraging Culture in an Urban Parrot,” Science 373:6553 [2021], 456-460.) (Thanks, Sharon.)