Good Fortune

Letter from Albert Einstein to J.E. Switzer, April 23, 1953:

Dear Sir

Development of Western Science is based on two great achievements; the invention of the formal logical system (in Euclidean geometry) by the Greek philosophers, and the discovery of the possibility to find out causal relationship by systematic experiment (Renaissance). In my opinion one has not to be astonished that the Chinese sages have not made these steps. The astonishing thing is that these discoveries were made at all.

Sincerely yours,

A. Einstein

Magicker

walkington knight diagonals
Image: William Walkington (CC BY-NC-SA 4.0)

The “Lo Shu square” is the 3 × 3 square enclosed in dashed lines at the center of the diagram above. It’s “magic”: Each row, column, and long diagonal (marked in red) sums to 15. William Walkington has discovered a new magic property — imagine rolling the square into a tube (in either direction), and then bending the tube into a torus. And now imagine hopping from cell to cell around the torus with a “knight’s move” — two cells over and one up. (The extended diagram above helps with visualizing this — follow the blue lines.) It turns out that each such path touches three cells, and these cells always sum to 15. So the square is even more magic than we thought.

More info here. (Thanks, William.)

Podcast Episode 261: The Murder of Lord William Russell

https://curiosity.lib.harvard.edu/crime-broadsides/catalog/46-990080942200203941
Image: Harvard Digital Collections

In May 1840 London was scandalized by the murder of Lord William Russell, who’d been found in his bed with his throat cut. The evidence seemed to point to an intruder, but suspicion soon fell on Russell’s valet. In this week’s episode of the Futility Closet podcast we’ll follow the investigation and trial, and the late revelation that decided the case.

We’ll also marvel at Ireland’s greenery and puzzle over a foiled kidnapping.

See full show notes …

Revere’s Obelisk

revere's obelisk

To celebrate the repeal of the Stamp Act, Paul Revere designed an obelisk that was erected on Boston Common on the evening of May 22, 1776. Its four panels, painted on translucent waxed paper borne on a wooden frame, described the phases of the struggle against the act:

1. America in distress apprehending the total loss of Liberty.

2d. She implores the aid of her Patrons.

3d. She endures the Conflict for a short Season.

4. And has her Liberty restord by the Royal hand of George the Third.

At the bottom is the legend “To every Lover of Liberty, this Plate is humbly dedicated, by her true born Sons, in Boston New England.”

It was illuminated by 280 candles, and fireworks and Catherine wheels were launched from its sides. Unfortunately it “took Fire … and was consumed” a few hours a later. This is the only surviving copy of the engraving.

(Thanks, Charlie.)

A Flea’s Journey

https://commons.wikimedia.org/wiki/File:Euclid_Tetrahedron_4.svg
Image: Wikimedia Commons

A flea sits on one vertex of a regular tetrahedron. He hops continually from one vertex to another, resting for a minute between hops and choosing vertices without bias. Prove that, counting the first hop, we’d expect him to return to his starting point after four hops.

Click for Answer

“A Rabbit Tamed”

A notable detail from Alexander Morrison Stewart’s Camp, March and Battle-Field (1865): During the Battle of Malvern Hill, a terrified rabbit darted about the battlefield looking for safety until it came upon a Union regiment lying prone:

Ere the rabbit seemed aware, it had jumped into the midst of these men. It could go no farther, but presently nestled down beside a soldier, and tried to hide itself under his arm. As the man spread the skirt of his coat over the trembling fugitive, in order to insure it of all the protection in his power to bestow, he no doubt feelingly remembered how much himself then needed some higher protection, under the shadow of whose arm might be hidden his own defenceless head, from the fast-multiplying missiles of death, scattered in all directions.

It was not long, however, before the regiment was ordered up and forward. From the protection and safety granted, the timid creature had evidently acquired confidence in man — as the boys are wont to say, ‘Had been tamed.’ As the regiment moved forward to the front of the battle, it hopped along, tame, seemingly, as a kitten, close at the feet of the soldier who had bestowed the needed protection. Wherever the regiment afterwards went, during all the remaining part of that bloody day and terrible battle, the rabbit kept close beside its new friend.

“When night came on, and the rage of battle had ceased, it finally, unmolested and quietly, hopped away, in order to find some one of its old and familiar haunts.”

Nose Harmony

https://commons.wikimedia.org/wiki/File:Philippe_Mercier_-_The_Sense_of_Smell_-_Google_Art_Project.jpg

English chemist Septimus Piesse likened scents to music:

Odors seem to affect the olfactory nerves in certain definite degrees, as sounds act on the auditory nerves. There is, so to speak, an octave of smells, as there is an octave of tones; some perfumes accord, like the notes of an instrument. Thus almond, vanilla, heliotrope, and clematis, harmonize perfectly, each of them producing almost the same impression in a different degree. On the other hand, we have citron, lemon, orange peel, and verbena, forming a similarly associated octave of odors, in a higher key. The analogy is completed by those odors which we call half-scents, such as the rose, with rose-geranium for its semitone; ‘petit-grain’ and neroli, followed by orange-flower. With the aid of flowers already known, by mixing them in fixed proportions, we can obtain the perfume of almost all flowers.

Using an “odaphone,” or scale, on which harmonies and discords of odors might be studied, his London perfumery Piesse and Lubin produced some of the most important scents of the Victorian era, such as Ambergris (1873), Hungary Water (1873), Kiss Me Quick (1873), The Flower of the Day (1875), White Rose (1875), and Frangipanni (1880).

It had been thought that none of these had survived, but in 2011 two unopened bottles were discovered in the bow of the Mary Celestia, a Civil War blockade runner that had foundered off Bermuda in 1864. The bottles contained Bouquet Opoponax, one of the company’s most popular fragrances, and after analysis with a gas chromatograph, Germany’s Drom Fragrances managed to reproduce the scent in 2014.

“I was shocked at how fresh and floral it was and by the amount of citrus in it,” senior perfumer Jean-Claude Delville told the Star-Ledger. “When the fragrance has been sitting at the bottom of the ocean and aging for so many years you expect something that is oxidized or damaged,” he told CTVNews. “But my first impression was ‘wow’.”

Character Study

https://commons.wikimedia.org/wiki/File:The_Wizard_of_Oz_Margaret_Hamilton_Judy_Garland_1939.jpg

Margaret Hamilton on the Wicked Witch of the West:

[There was] a feeling inside that you get. One word: skulduggery. She enjoyed every single minute of whatever she was doing, whether she was screaming or yelling about the fact that Dorothy had those slippers, or sending the monkeys after them all. And the other thing was her utter and complete frustration. She never got what she wanted. She didn’t want Dorothy and she didn’t want any of those other characters. She just wanted those slippers. And today, according to law, she probably would have had them. They were her sister’s, and she would have been in line to inherit them. But she didn’t get there fast enough.

(From Aljean Harmetz, The Making of The Wizard of Oz, 1977.)

Autopilot

https://www.flickr.com/photos/dennis/6174688
Image: Flickr

We often think of consciousness as fundamentally involving self-awareness. A conscious decision is one I’m aware of making; a conscious memory is one I’m aware of having. It would seem that most complex behaviors require this state. But philosopher David Malet Armstrong points out:

If you have driven for a very long distance without a break, you may have had experience of a curious state of automatism, which can occur in these conditions. One can suddenly ‘come to’ and realize that one has driven for long distances without being aware of what one was doing, or, indeed, without being aware of anything. One has kept the car on the road, used the brake and the clutch perhaps, yet all without any awareness of what one was doing.

What’s going on here? “The driver in a state of automatism perceives, or is aware of, the road. If he did not, the car would be in a ditch. But he is not currently aware of his awareness of the road. He perceives the road, but he does not perceive his perceiving, or anything else that is going on in his mind.” He is driving, it would seem, without conscious awareness of what he’s doing; we seem to be able to perform complex mental processes without conscious experience.

(From D.M. Armstrong, The Nature of Mind, 1981.)