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:

https://commons.wikimedia.org/wiki/File:Anscombe%27s_quartet_3.svg
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

https://pixabay.com/photos/moon-full-moon-sky-night-sky-lunar-1859616/

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

https://commons.wikimedia.org/wiki/File:Reading_under_a_tree.png

“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

Meno’s Paradox

“[A] man cannot enquire either about that which he knows, or about that which he does not know; for if he knows, he has no need to enquire; and if not, he cannot; for he does not know the very subject about which he is to enquire.” — Socrates

| Oddities

The Billups Neon Crossing Signal

After numerous accidents where the Illinois Central Railroad crossed Highway 7 near Grenada, Mississippi, in the 1930s, inventor Alonzo Billups came up with a one-of-a-kind solution. When a train approached the crossing, motorists were confronted with a lighted skull and crossbones, the glowing words “Stop-DEATH-Stop,” flashing neon arrows indicating the train’s direction, and an air raid siren.

The video here is a simulation; the actual gantry was removed due to a scarcity of neon in the war years. But two photographs survive.

| Death · Oddities · Technology

Podcast Episode 356: A Strawberry’s Journey

https://commons.wikimedia.org/wiki/File:Strawberries_and_basket_LCCN2003664002.jpg

The modern strawberry has a surprisingly dramatic story, involving a French spy in Chile, a perilous ocean voyage, and the unlikely meeting of two botanical expatriates. In this week’s episode of the Futility Closet podcast we’ll describe the improbable origin of one of the world’s most popular fruits.

We’ll also discuss the answers to some of our queries and puzzle over a radioactive engineer.

See full show notes …

| History · Podcast · Science & Math

The Fortsas Hoax

https://commons.wikimedia.org/wiki/File:Cover_to_the_Fortsas_Catalogue.jpg

In 1840, librarians and booksellers throughout Europe received a catalog describing a unique collection of books to be auctioned: Jean Nepomucene Auguste Pichauld, Comte de Fortsas, had collected 52 unique books, books of which only a single copy was known to exist. The count had died the preceding September, the message said, and as his heirs had no interest in books, the collection would be auctioned off.

Bibliophiles converged on Binche, Belgium, that August for the event, only to discover that the appointed address did not exist. Notices declared that the town’s library had acquired the books — but Binche had no library. In time it became clear that the Comte de Fortsas himself had never existed.

The whole thing had been an elaborate hoax put on by an antiquarian and retired military officer named Renier Hubert Ghislain Chalon. Ironically, the catalog of nonexistent books itself in time became a collectors’ item.

What will happen if someone now writes those books?

| Hoaxes · Literature