Side-Eye

jealousy glass

This is sneaky: Operagoers in the 18th century could spy on their neighbors using a “jealousy glass” — you’d appear to be watching the stage but a mirror would direct your view to the side, like a horizontal periscope. Marc Thomin, optician to the queen of France, wrote in 1749:

It is sufficient to turn this opening in the direction of whatever one wishes to observe and the curiosity is immediately satisfied. Its usefulness is confined to letting us see surreptitiously a person we seem not to be observing. This lorgnette may have been called a decorum glass because there is nothing more rude than to use an ordinary opera glass for looking at some one face to face.

Hanneke Grootenboer writes in Treasuring the Gaze, “Apparently, it was very convenient in allowing one to keep track of latecomers entering the opera without having to turn one’s head.”

(From J. William Rosenthal, From Spectacles and Other Vision Aids: A History and Guide to Collecting, 1996.)

| Society · Technology

Lost Voices

In 2009 three historians engaged forensic lip reader Jessica Rees to analyze silent film shot at the Battle of the Somme in 1916.

Soldiers of the Essex Regiment washing at a pool shout “Hi Mum!” and “Hello Mum, it’s me.” A soldier with a wounded foot repeats, “Jesus, Jesus, Jesus, Jesus.” And another soldier tells the crew, “Stop filming, this is awful.”

“What struck me the most was the optimism of the soldiers and their bravery,” Rees said. “They all seemed very positive, full of team spirit and jocular. Yet, as I was stunned to learn, many of them did not even survive the day of filming. I came away feeling a bit humble.”

| History

The Nimm0 Property

In the 17th century the French mathematician Bernard Frénicle de Bessy described all 880 possible order-4 magic squares — that is, all the ways in which the numbers 1 to 16 can be arranged in a 4 × 4 array so that the long diagonals and all the rows and columns have the same sum.

These squares share a curious property: If we subtract 1 from each cell, to get a square of the numbers 0-15, then each of the rows and columns has a nim sum of 0. A nim sum is a binary sum in which 1 + 1 is evaluated as 0 rather than “0, carry 1.” For example, here’s one of Frénicle’s squares:

\displaystyle \begin{matrix} 0 & 5 & 10 & 15\\ 14 & 11 & 4 & 1\\ 13 & 8 & 7 & 2\\ 3 & 6 & 9 & 12 \end{matrix}

Translating each of these numbers into binary we get

\displaystyle \begin{bmatrix} 0000 & 0101 & 1010 & 1111\\ 1110 & 1011 & 0100 & 0001\\ 1101 & 1000 & 0111 & 0010\\ 0011 & 0110 & 1001 & 1100 \end{bmatrix}

And the binary sums of the four rows, evaluated without carry, are

0000 + 0101 + 1010 + 1111 = 0000
1110 + 1011 + 0100 + 0001 = 0000
1101 + 1000 + 0111 + 0010 = 0000
0011 + 0110 + 1001 + 1100 = 0000

The same is true of the columns. (The diagonals won’t necessarily sum to zero, but they will equal one another. And note that the property described above won’t necessarily work in a “submagic” square in which the diagonals don’t add to the magic constant … but it does work in all 880 of Frénicle’s “true” 4 × 4 squares.)

(John Conway, Simon Norton, and Alex Ryba, “Frenicle’s 880 Magic Squares,” in Jennifer Beineke and Jason Rosenhouse, eds., The Mathematics of Various Entertaining Subjects, Vol. 2, 2017.)

| Science & Math

Needs Analysis

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I do not believe in freedom of will. Schopenhauer’s words, ‘Man can indeed do what he wants, but he cannot want what he wants,’ accompany me in all life situations and console me in my dealings with people, even those that are really painful to me. This recognition of the unfreedom of the will protects me from taking myself and my fellow men too seriously as acting and judging individuals and losing good humor.

— Albert Einstein, Mein Glaubensbekenntnis, August 1932

| Society

Absent Friends

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If existence is taken as betokening thisness and thereness, then nonexistence is going to have, speaking informally, this problem: It obliges us to speak of a nothing. If a nonexistent object were always like a footprint in the sand, we might refer to it by its mold, its negative place. But usually the world closes up without much trace around things that have passed their time and ceased to exist, and often there is not even a world left to hold the mold — think of extinct dodos and never existent unicorns; there is no empty niche left in our ‘real’ world for the former and there never was — some say — one for the latter. What kind of focus allows us then to speak of things that are definitely and determinately nowhere and not now and not ever? What, if anything, is it we are referring to when we say: This does not exist?

— Eva Brann, The Ways of Naysaying, 2001

| Oddities

False or True?

A Russian coin-weighing puzzle:

You have 101 coins, and you know that 50 of them are counterfeit. Every true coin has the same weight, an unknown integer, and every false coin has the same weight, which differs from that of a true coin by 1 gram. You also have a two-pan pointer scale that will show you the difference in weight between the contents of each pan. You choose one coin. Can you tell in a single weighing whether it’s true or false?

Click for Answer
| Puzzles

Making Cases

https://commons.wikimedia.org/wiki/File:Vinci,_Leonardo_da_-_Crossbow_sketch_-_1500.jpg

Testimony is like an arrow shot from a longbow; the force of it depends on the strength of the hand that draws it.

Argument is like an arrow from a crossbow, which has equal force though shot by a child.

— Robert Boyle, paraphrased by Samuel Johnson

| Quotations

Podcast Episode 204: Mary Anning’s Fossils

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In 1804, when she was 5 years old, Mary Anning began to dig in the cliffs that flanked her English seaside town. What she found amazed the scientists of her time and challenged the established view of world history. In this week’s episode of the Futility Closet podcast we’ll tell the story of “the greatest fossilist the world ever knew.”

We’ll also try to identify a Norwegian commando and puzzle over some further string pulling.

See full show notes …

| History · Podcast · Science & Math

In a Word

mampus
n. a great number, a crowd

onde
n. strong feeling against a person

siffilate
v. to whisper

fremescent
adj. murmuring, growing noisy

Gladys Cooper’s sister, Cissie, was equally misled by an audience when she went on stage for the first time, after acting as her sister’s dresser for many years. Although she only had a small part, the audience apparently started to hiss almost as soon as she had come on stage. This happened every night and in the end she came into the wings in tears. Gladys Cooper could not understand what was going wrong and she asked the House Manager to see if he could find out what was the matter. So he slipped into the back of the stalls just as her sister was making her entrance and from where he was standing he heard the audience whispering:

‘It’s Cissie Cooper, Gladys Cooper’s sister … It’s Cissie Cooper, Gladys Cooper’s sister …’

— Kenneth Williams, The Complete Acid Drops, 1999

| Language