A problem submitted by the United States and shortlisted for the 16th International Mathematical Olympiad, Erfurt-Berlin, July 1974:
Alice, Betty, and Carol took the same series of examinations. There was one grade of A, one grade of B, and one grade of C for each examination, where A, B, C are different positive integers. The final test scores were
Alice: 20
Betty: 10
Carol: 9If Betty placed first in the arithmetic examination, who placed second in the spelling examination?
This is interesting: In 1585, Italian mathematician Giovanni Battista Benedetti devised a piece of music in which a precise application of the tuning mathematics causes the pitch to creep upward.
Avoiding this phenomenon requires an adjustment — a compromise to the dream of mathematically pure music.
A problem from the 1949 problems drive of the Archimedeans, the mathematical society of Cambridge University:
A farmer lives in a cottage 4/17 of a mile from a main road. There is a lane leading from his farm to the nearest point Q on the road. The road is straight running north and south, and there is a village two miles south of Q at which he keeps a bicycle. He wishes to go to a town on the road four miles north of Q. He can walk across the fields surrounding the roads at 1 1/2 miles per hour, but along the roads he can walk at 3 1/2 miles per hour. He can cycle at 14 miles per hour. Should he collect his bicycle in order to get to the town from his farm as quickly as possible?
The San Francisco earthquake of 1906 is remembered for its destructive intensity and terrible death toll. But the scale of the disaster can mask some remarkable personal stories. In this week’s episode of the Futility Closet podcast we’ll describe the experiences of some of the survivors, which ranged from the horrific to the surreal.
We’ll also consider a multilingual pun and puzzle over a deadly reptile.
Suppose that there’s no correlation between talent and attractiveness in the general population (left). A person who studies only celebrities might infer that the two traits are negatively correlated — that attractive people tend to lack talent and talented people tend to lack attractiveness (right). But this is deceiving: People who are neither attractive nor talented don’t typically become celebrities, and that large group of people aren’t represented in the sample. Celebrities tend to have one trait or the other but (unsurprisingly) rarely both.
The phenomenon was studied by Mayo Clinic statistician Joseph Berkson; this example is by CMG Lee.
In June 2006, Iowa paralegal Jane Wiggins looked out the window of her Cedar Rapids office and saw a cloud unlike any she’d seen before. “It looked like Armageddon,” she told the Associated Press. “The shadows of the clouds, the lights and the darks, and the greenish-yellow backdrop. They seemed to change.”
Wiggins sent a photo to the Cloud Appreciation Society, a weather-watching group founded by Gavin Pretor-Pinney, author of The Cloudspotter’s Guide. Other sightings were registered around the world (this one appeared over Tallinn, Estonia), and eventually Pretor-Pinney nominated it as an entirely new type.
The 2017 edition of the World Meteorological Organisation’s International Cloud Atlas included asperitas in a supplementary feature. The name is Latin for “roughen” or “agitate” — “not necessarily gentle or steady, but quite violent-looking, turbulent, almost twisted in its appearance,” Pretor-Pinney said.
It’s not new, really — such clouds have always been up there — but it’s the first formation added to the atlas since 1951. “We like to believe that just about everything that can be seen has been,” Society executive director Paul Hardaker said. “But you do get caught once in a while with the odd, new, interesting thing.”
On the morning of May 8, 1965, physicist Carl R. Disch departed the radio noise building of Antarctica’s Byrd Station to return to the main complex 7,000 feet away. He would be walking through a snowstorm with winds of 35 mph, but a hand-line had been installed connecting the two installations so that scientists wouldn’t lose their way.
When Disch didn’t arrive at the main station in a reasonable time, a search party was organized. This spotted his trail but had to return to the station to refuel, and by the time they returned the trail had been covered by drifting snow. The area was searched extensively and the station lighted to increase its visibility, but Disch was never found.
During the search, temperatures dropped to -79 degrees Fahrenheit. The search was called off on May 14. Disch is presumed dead, but his body has never been found.
1/3rd of an inch is a BARLEYCORN.
1/12th of an inch is a LINE.
1/72nd of an inch is a POINT.
1/100th of an inch is a GRY.
1/144th of an inch is a SECOND.
1/1000th of an inch is a THOU.
1/1440th of an inch is a TWIP.
Via Haggard Hawks. Pleasingly, you can interconvert most of these here.
Yale statistician Frank Anscombe devised this demonstration in 1973. Here are four datasets, each with 11 (x,y) points:
| I | II | III | IV | ||||
|---|---|---|---|---|---|---|---|
| x | y | x | y | x | y | x | y |
| 10.0 | 8.04 | 10.0 | 9.14 | 10.0 | 7.46 | 8.0 | 6.58 |
| 8.0 | 6.95 | 8.0 | 8.14 | 8.0 | 6.77 | 8.0 | 5.76 |
| 13.0 | 7.58 | 13.0 | 8.74 | 13.0 | 12.74 | 8.0 | 7.71 |
| 9.0 | 8.81 | 9.0 | 8.77 | 9.0 | 7.11 | 8.0 | 8.84 |
| 11.0 | 8.33 | 11.0 | 9.26 | 11.0 | 7.81 | 8.0 | 8.47 |
| 14.0 | 9.96 | 14.0 | 8.10 | 14.0 | 8.84 | 8.0 | 7.04 |
| 6.0 | 7.24 | 6.0 | 6.13 | 6.0 | 6.08 | 8.0 | 5.25 |
| 4.0 | 4.26 | 4.0 | 3.10 | 4.0 | 5.39 | 19.0 | 12.50 |
| 12.0 | 10.84 | 12.0 | 9.13 | 12.0 | 8.15 | 8.0 | 5.56 |
| 7.0 | 4.82 | 7.0 | 7.26 | 7.0 | 6.42 | 8.0 | 7.91 |
| 5.0 | 5.68 | 5.0 | 4.74 | 5.0 | 5.73 | 8.0 | 6.89 |
Each set produces the same summary statistics (mean, standard deviation, and correlation). But their graphs are strikingly different:
The lesson, Anscombe said, is to “make both calculations and graphs. Both sorts of output should be studied; each will contribute to understanding.”
Justin Matejka and George Fitzmaurice created a similar collection in 2017: the Datasaurus Dozen.
(Thanks, Rick.)
09/05/2021 UPDATE: Here’s an animation of the Datasaurus Dozen. (Thanks, Eric.)
In the 1960s, linguist Robert M.W. Dixon met Albert Bennett, one of the last native speakers of Mbabaram, a vanishing Australian Aboriginal language of north Queensland. “You know what we call ‘dog’?” Bennett said to him. “We call it dog.”
“My heart sank,” Dixon wrote. “He’d pronounced it just like the English word, except that the final g was forcefully released.” He worried that Bennett’s decades of using English had tainted his understanding of Mbabaram.
But Bennett’s assertion was accurate: The Mbabaram word for dog is dúg, which is pronounced nearly identically to the English word, “a one in a million accidental similarity of form and meaning in two unrelated languages,” Dixon wrote.
“It was because this was such an interesting coincidence, that Albert Bennett had thought of it as the first word to give me.”
(Robert M.W. Dixon, Searching for Aboriginal Languages: Memoirs of a Field Worker, 1984.)
