Buried Treasure

Cecil B. DeMille’s 1959 autobiography contains an odd passage: “If a thousand years from now, archaeologists happen to dig beneath the sands of Guadalupe, I hope they will not rush into print with the amazing news that Egyptian civilization, far from being confined to the valley of the Nile, extended all the way to the Pacific coast of North America. The sphinxes they will find were buried when we had finished with them and dismantled our huge set of the gates of Pharaoh’s city.”

He was referring to his 1923 silent film The Ten Commandments — after shooting was finished, he’d had the massive sets buried where they’d been built, in California’s Guadalupe-Nipomo Dunes. It’s not clear why — possibly he lacked the funds to remove them and didn’t want other filmmakers to use them. The sets included four Pharaoh statues 35 feet tall, 21 sphinxes, and gates 110 feet high, forming an ersatz Egyptian civilization for modern archaeologists to uncover.

Their time is limited. “It was like working with a hollow chocolate rabbit,” Doug Jenzen, executive director of the Guadalupe-Nipomo Dunes Center, told the Los Angeles Times of one dig in 2014. “These were built to last two months during filming in 1923, and these statues have been sitting out in the elements since then.”

Reversing Relations

The Book of Common Prayer includes a Table of Kindred and Affinity that lists prohibited degrees of marriage in the Church of England. For example, a man may not marry his daughter’s son’s wife, and a woman may not marry her husband’s mother’s father. In this case, the two proscriptions correspond — they describe the same relationship “from both sides,” so this union is prohibited to both parties in the relationship. But is this always the case? Is each union that’s denied to a man also denied to the woman? (The table lists only heterosexual unions.) It’s not immediately clear; 25 prohibited degrees are listed for each sex, and our language makes it hard to “reverse” the description of a relationship mentally.

In 1989 Manchester Polytechnic mathematician M.D. Stern worked out a notation that makes this easy. Use 1 to denote a male and 0 a female, and use this code to denote relationships between individuals:

00 spouse
01 parent
10 child
11 sibling

Now, to show the relationship between one person and another, write one digit for the first person followed by a sequence of three more digits — two to represent the relationship and one to represent the sex of the second person. So, taking the example above, a man’s daughter’s son’s wife would be denoted:

1 100 101 000

To interpret the same relationship from the woman’s point of view, we just reverse the order of the digits:

0 001 010 011

He is her husband’s mother’s father.

Applying this to the prohibited degrees in the table, Stern found that every prohibition for a man corresponds to an inverse prohibition for a woman — there are no prospective marriages that would be prohibited to one party but not the other.

(M.D. Stern, “A Notational Device for Analysing Relationships,” Mathematical Gazette 73:463 [March 1989], 37-40.)

Lost in Translation

A dry footnote from Walter Scott’s The Heart of Midlothian, regarding the Porteous Riots of 1736, in which a guard captain was lynched in Edinburgh:

The Magistrates were closely interrogated before the House of Peers, concerning the particulars of the Mob, and the patois in which these functionaries made their answers, sounded strange in the ears of the Southern nobles. The Duke of Newcastle having demanded to know with what kind of shot the guard which Porteous commanded had loaded their muskets, was answered naively, ‘Ow, just sic as ane shoots dukes and fools with.’ This reply was considered as a contempt of the House of Lords, and the Provost would have suffered accordingly, but that the Duke of Argyle explained, that the expression, properly rendered into English, meant ducks and waterfowl.

(Thanks, Fred.)

Podcast Episode 280: Leaving St. Kilda

Image: Wikimedia Commons

1930 saw the quiet conclusion of a remarkable era. The tiny population of St. Kilda, an isolated Scottish archipelago, decided to end their thousand-year tenure as the most remote community in Britain and move to the mainland. In this week’s episode of the Futility Closet podcast we’ll describe the remarkable life they’d shared on the island and the reasons they chose to leave.

We’ll also track a stork to Sudan and puzzle over the uses of tea trays.

See full show notes …

More Prime Images

Inspired by James McKee’s Trinity Hall prime, physics researcher Gilles Esposito-Farese (of the self-descriptive pangram) has worked out that this 2,258-digit prime number:


renders these 7,500 digits in binary:

Esposito-Farese map

This is a 30,000-digit prime:

Esposito-Farese Gioconda

And this is self-explanatory:

Esposito-Farese prime declaration

More here.

(Thanks, Gilles.)

Nine Lives

Image: Wikimedia Commons
Image: Wikimedia Commons

In the 1960s, Soviet mathematician Vladimir Arnold mapped the square image of a cat to a torus, “stretched” (sheared) it as shown on that surface, then sliced the resulting image into pieces and recomposed them into a square.

As the process is repeated, any two points in the image quickly become separated, but, surprisingly, after sufficient repetitions the original image reappears.

A discrete analogue is at right. As the transformation is repeated, the image appears increasingly random or disordered, but the underlying cat can be glimpsed making occasional appearances, sometimes as a ghostly suggestion, sometimes in multiple smaller images, and occasionally (yowling, one imagines) even upside down.

It reappears again, unhurt, at the 300th iteration.

It’s called Arnold’s cat map. You can try it yourself here.

False Fronts

Numbers 23 and 24 Leinster Gardens, London, are not the terraced houses they appear to be. Their façades match their neighbors’, with columned porches and windows and balustraded balconies, but the doors have no knobs or letter boxes.

In fact the whole expanse is false, only a façade 5 feet thick. Behind it is a section of uncovered railway track. When a tube line was built through the neighborhood in 1863, the steam engines that hauled the trains needed a section of uncovered track to let off smoke and steam. To preserve appearances for the surrounding residents, the railway company built these frontages, and they remain to this day.

Writes Stuart Barton in Monumental Follies, “It is unfortunate that more sham facades like this are not built to conceal some of the eye-sores that scar our cities today.”