To Town

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?

Click for Answer
| Puzzles

Podcast Episode 357: Scenes From an Earthquake

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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.

See full show notes …

| History · Podcast

Berkson’s Paradox

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Image: Wikimedia Commons

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.

| Science & Math

Something New

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Image: Wikimedia Commons

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.”

| Science & Math

An Antarctic Disappearance

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.

| Death

Anscombe’s Quartet

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:

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Image: Wikimedia Commons

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.)

| Science & Math

Coincidence

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.)

| Language

Growing Room

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On April 6, 1966, to celebrate 100 years of the city’s incorporation, 35 citizens of Geneva, Ohio, signed a “Declaration of Lunar Ownership”:

When in the course of human events and space-age accomplishments, the destiny of mankind becomes influenced … [by] the presence of a particular controversial Celestial Body unclaimed and unregulated … it should be advisable and honorable … to lay definitive and prior claim to the entire physical mass and any and all aura, aspect, imaginative or otherwise, of … the Moon.

Geneva assumed “full possession and complete responsibility” of the Moon, yielding “to no man or State in its sovereign right so to do.” The declaration asserted the city’s claim as “positive, supreme, permanent and sovereign,” transcending and voiding “all other claims both real and fancied … previously made for the possession of all or any part of the Moon.” It permitted all humans “to enjoy and to behold and bask” in moonlight but disclaimed responsibility for “any mental, physical, or spiritual influences … [or] for any advantages or disadvantages from tidal phenomena.” Space explorers would be charged per hour for “landings and close fly bys of the visible acreage of the Moon,” and any activities on the far side required “the express consent of the official Councils of the City of Geneva.” And the declaration provided for the sale, rent, or lease of the visible lunar face “to desirable applicants upon a two-thirds vote of the entire population of Geneva,” granting the United States government “prior option to this privilege.”

For the year 1966, the document allowed the sale of 100 deeds “for the sum of $100 describing 100 acres from Mare Imbrium”; “the possessor of this deed shall have it to hold, his heirs and assigns forever and unencumbered.” Whether any were sold I can’t tell.

(From Virgiliu Pop, Who Owns the Moon?: Extraterrestrial Aspects of Land and Mineral Resources Ownership, 2008.)

| Oddities

Choosing

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“Study hard what interests you the most in the most undisciplined, irreverent and original manner possible.” — Richard Feynman

“A man ought to read just as inclination leads him; for what he reads as a task will do him little good.” — Samuel Johnson

“Read what interests you. If Scott does not interest you and Dickens does, drop Scott and read Dickens. You need not be any one’s enemy; but you need not be a friend with everybody. This is as true of books as of persons. For friendship some agreement in temperament is quite essential.” — Lyman Abbott

| Literature · Quotations