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

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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.

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Travel Broadens the Mind

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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.)

Problem Solved

In 1991, botanist John L. Strother was reviewing the classification of North American sunflowers when he identified a new genus. By this time his 100-page monograph was in the final stages of proofing, and adding a new entry in the middle would require troublesome changes in the layout.

The genera were listed alphabetically, and the last one was Zexmenia. So Strother named the new genus Zyzyxia. Since this placed the new entry near the end of the article, it minimized the necessary changes, and the editor accepted the addition.

Skylon

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Image: Peter Benton

A striking symbol of the 1951 Festival of Britain was this cigar-shaped sculpture, which seemed to float impossibly 15 meters above the ground.

Designed by Hidalgo Moya, Philip Powell, and Felix Samuely, the structure relied on the principle of tensegrity: The base rested at the junction of three tensioned cables, and three further cables held the body vertical. Together, these six well-positioned supports were enough to keep the 80-meter sculpture from toppling.

Britons joked that, like the national economy at the time, it had “no visible means of support.”

Fieldwork

On Oct. 24 [1947] two University of Chicago students rattled into Reno., Nev. in a Model-A Ford to try the gambling. Their total resources: $100. Wasting no time, they went to the Palace Club, where they studiously made a chart of the recurrence of numbers on the roulette wheel. Then they went into action. Playing number 9, which their records indicated as the best possibility, they parlayed their $100 into $5,000 in 40 hours. At this point the manager became uneasy, switched the wheel. So the students moved on to Harold’s Club.

There they used the same system. Sure enough, their $5,000 rose to $14,500. But then, unaccountably, their system went sour. They dropped from $14,500 to $10,000 and kept going down. That was when the young theoreticians made the smartest move of all. They pocketed their winnings, packed up the Model-A and went home, ahead by $6,500.

Life, Dec. 8, 1947

(The students were Albert Hibbs and Roy Walford. Accounts vary as to their total takings; Hibbs claimed $12,000 on You Bet Your Life in 1959. They spent a year sailing around the Caribbean and then returned to their studies. Hibbs went on to become a JPL physicist and Walford a UCLA pathologist.)