The Trinity Hall Prime

On Thursday, Numberphile published this video, which features a startling wall hanging in the Senior Combination Room at Trinity Hall, Cambridge: Junior research fellow James McKee devised a 1350-digit prime number whose image forms a likeness of the college’s coat of arms. (The number of digits is significant, as it’s the year that Bishop William Bateman founded the college.)

https://math.stackexchange.com/q/2420510 — Image: Math Stack Exchange

It turns out that finding such “prime” images is easier than one might think. In the video description, McKee explains: “Most of the digits of p were fixed so that: (i) the top two thirds made the desired pattern; (ii) the bottom third ensured that p-1 had a nice large (composite) factor F with the factorisation of F known. Numbers of this shape can easily be checked for primality. A small number of digits (you can see which!) were looped over until p was found that was prime.'”

Indeed, on the following day, Cambridge math student Jack Hodkinson published his own prime number, this one presenting an image of Corpus Christi College and including his initials and date of birth:

Hodkinson explains that he knew he wanted a 2688-digit prime, and the prime number theorem tells us that approximately one in every 6200 2688-digit numbers is prime. And he wasn’t considering even numbers, which reduces the search time by half: He expected to find a candidate in 100 minutes, and in fact found eight overnight.

(Thanks, Danesh.)

September 10, 2017September 10, 2017 | Science & Math

Triangle

When blues singer Sally Osman filed for divorce from ventriloquist Herbert Dexter in 1934, she named his dummy, Charlie, as a co-respondent.

When she and Dexter had married two years earlier, she agreed that Dexter could take the puppet along on their honeymoon, as he had often complimented her through Charlie’s voice. But when they developed a new stage act, the dummy began to interrupt her songs with cruel ad libs and rob her of applause by making rude wisecracks. She asked Dexter to change the act so that she could sing without interruption, but he refused.

In I Can See Your Lips Moving, Valentine Vox writes, “She also accused the duo of physical cruelty, telling the court how she constantly received on-stage blows from the mechanical figure, which left her with severe bruises. One night in particular, Charlie had hit her so hard between the shoulder blades that he knocked the wind out of her.”

Osman further testified that Dexter would take the dummy everywhere they went and spent more time talking to it than to her. “I got to hate Charlie so deeply that homicidal thoughts began to haunt my mind,” she said. “Sometimes when I had Charlie alone and helpless, I fear that I would have thrown him out of the window, had I been able to unlock the coffin-like trunk in which he was kept.”

Dexter never contested the case, and Osman got her divorce. When the judge asked why she hadn’t requested alimony, she said, “I wouldn’t be able to collect it anyway; he spends all his money on Charlie.”

September 9, 2017 | Entertainment · Oddities

A Soaring Heart

From an advice column in Home Companion, March 4, 1899:

‘Sweet Briar’ (Swansea) writes in great trouble because her lover will persist in his intention to go up in a balloon. She urges him not to imperil his life in this foolhardy manner, but he only laughs at her fears.

I am sorry, ‘Sweet Briar’, that your lover occasions you anxiety in this manner, and I can only hope that he will ultimately see the wisdom of yielding to your wishes. What a pity it is that we have not a law like that which exists in Vienna! There no married man is allowed to go up in a balloon without the formal consent of his wife and children.

One solution: Go up with him, and marry him there.

September 8, 2017 | Society · Technology

Straight Business

In 2014 I described the Peaucellier–Lipkin linkage, a mechanism that transforms a rotary motion into a perfect straight-line motion:

https://commons.wikimedia.org/wiki/File:Peaucellier_linkage_animation.gif — Image: Wikimedia Commons

That linkage was invented in 1864 by French army engineer Charles-Nicolas Peaucellier. A decade later, Harry Hart invented two more. “Hart’s inversor” is a six-bar linkage — links of the same color are the same length. The fixed point on the left is at the midpoint of the red link, and the “input” and “output” are at the midpoints of the two blue links:

https://commons.wikimedia.org/wiki/File:Hart%27s_Inversor.gif — Image: Wikimedia Commons

In “Hart’s A-frame,” the short links are half the length of the long ones, and the center link is a quarter of the way down the long links:

https://commons.wikimedia.org/wiki/File:Hart%27s_A-frame.gif — Image: Wikimedia Commons

Pleasingly, the motion perpendicularly bisects a fixed link across the bottom, which is the same length as the long links.

September 8, 2017October 23, 2017 | Science & Math

The Victim

It goes against masculine pride to have a wife helping support the household, and once a man’s pride is shattered, anything can happen to him. …

There was a couple I once knew in Chicago. At the time of their marriage the husband was earning $5,000 a year. Two years after marriage the wife went to work, and presently was making more than her husband. His home became a desolate place, for his wife’s job required her to travel to other cities. Driven to seek companionship to escape from the loneliness of home the man became addicted to drink. Today they are divorced. The woman is a notable business woman, and the man is a drunken drifter.

But, the women will comment, the husband drank. What of it? No husband drinks to excess unless there’s a reason for it. If the truth were known there are many men who began drinking because their wives took to work.

— William Johnston, These Women, 1925

September 7, 2017 | Society

Prototype

In 2001, computer animator Wayne Lytle created “Pipe Dream,” a 3D music visualization in which falling balls trigger musical notes on vibraphones, tubular bells, bongos, and other instruments:

Entertainingly, in 2006 an email hoax claimed that the scene was not animated but real:

Amazingly, 97% of the machines components came from John Deere Industries and Irrigation Equipment of Bancroft Iowa, yes farm equipment!

It took the team a combined 13,029 hours of set-up, alignment, Calibration, and tuning before filming this video but as you can see it was WELL worth the effort.

The hoax was entertaining because it was preposterous — who could build such a thing in real life?

You can guess where this is going — in 2011 Intel created a real version in which 2300 paintballs trigger 120 unique notes on replicas of Lytle’s animated instruments:

That’s just 10 years after Lytle made the original animation.

(Thanks, Jacob.)

September 7, 2017September 16, 2017 | Technology

Unquote

Excerpts from the notebooks of English belletrist Geoffrey Madan (1895-1947):

“Work shapes the mind; leisure colors it.” — Revd. James Dolbear (1861)

“In language, the ignorant have prescribed laws to the learned.” — Richard Duppa

“To speak highly of one with whom we are intimate is a form of egotism.” — Hazlitt

“Who loves, will not be adored.” — Revd. J.C. Lavater

“While philosophers were looking for a characteristic to distinguish man from other animals, inconsistency ought not to have been forgotten.” — Richard Duppe

“Never be afraid to think yourself fit for anything for which your friends think you fit.” — Dr. Johnson

“What passes in the world for enterprise is often only a want of moral principle.” — Hazlitt

“I see no reason to suppose that these machines will ever force themselves into general use.” — Duke of Wellington on Steam Locomotives, 1827

“The room smelt of not having been smoked in.” — R.A. Knox

“Never make a god of your religion.” — Sir Arthur Helps

Treachery is the very essence of snobbery.

Alive, in the sense that he can’t legally be buried.

To forget your own good sayings is the mark of intellectual aristocracy.

Conservative ideal of freedom and progress: everyone to have an unfettered opportunity of remaining exactly where they are.

“Perhaps the most lasting pleasure in life is the pleasure of not going to church.” — Dean Inge

September 6, 2017 | Quotations

Unto the Breach

In 2004, engineers Richard Clements and Roger Hughes put their study of crowd dynamics to an unusual application: the medieval Battle of Agincourt, which pitted Henry V’s English army against a numerically superior French army representing Charles VI. In their model, an instability arises on the front between the contending forces, which may account for the relatively large proportion of captured soldiers:

[P]ockets of French men-at-arms are predicted to push into the English lines and with hindsight be surrounded and either taken prisoner or killed. … Such an instability might explain the victory by the weaker English army by surrounding groups of the stronger army.

This description is consistent with the three large mounds of fallen soldiers that are reported in contemporary accounts of the battle. If the model is accurate then perhaps French men-at-arms succeeded in pushing back the English in certain locations, only to be surrounded and slaughtered, rallying around their leaders. By contrast, modern accounts perhaps incorrectly describe a “wall” of dead running the length of the field.

“Interestingly, the study suggests that the battle was lost by the greater army, because of its excessive zeal for combat leading to sections of it pushing through the ranks of the weaker army only to be surrounded and isolated.” The whole paper is here.

(Richard R. Clements and Roger L. Hughes. “Mathematical Modelling of a Mediaeval Battle: The Battle of Agincourt, 1415,” Mathematics and Computers in Simulation 64:2 [2004], 259-269.)

September 6, 2017September 5, 2017 | History · Science & Math

Moving Spirits

Vaudeville ventriloquist Harry Lester made his reputation with feats of vocal dexterity — he would walk among the audience while his dummy whistled a tune, or place telephone calls to heaven and hell, altering his voice to simulate a remote character on the line. Most famously he could drink water and smoke while his dummies talked.

In 1925, during a performance at the Balaban and Katz Theatre in Chicago, Lester’s drinking feat was unexpectedly modified when straight whisky replaced the usual coloured water in his decanter. The orchestra had switched drinks as a joke, trying to catch him off guard. When Lester innocently drank the liquid, not a muscle moved in his face, but the figure exploded into a storm of coughing. This piece of showmanship was so much appreciated by the orchestra that they rose from their seats and applauded; the audience, sensing something unusual, joined in.

(From Valentine Vox, I Can See Your Lips Moving, 1981.)

September 5, 2017September 5, 2017 | Entertainment

Sitting In

In 1915, American artist John Singer Sargent donated a blank canvas for auction at a Red Cross benefit, promising to paint a portrait of the donor who purchased it. Sir Hugh Lane bought it for £10,000 but died in the sinking of the Lusitania. He left his art collection to the National Gallery of Ireland, which didn’t know what to do with the blank canvas, so the executors finally held a referendum to ask whose portrait Sargent should paint. The popular choice, to Sargent’s surprise, was Woodrow Wilson.

At the White House Sargent confided his nerves to first lady Edith Wilson, who tried to amuse him at the easel. Still, she didn’t care for the result. “I think it lacks virility and makes Mr. Wilson look older than he did at the time,” she said later. Advisor Edward M. House said he thought it too austere, but then “I think I never knew a man whose general appearance changed so much from hour to hour.” Wilson’s opinion is not recorded.

Bonus blank canvas story: In 1951 Robert Rauschenberg painted a series of “white paintings” with the explicit intention that they appear untouched by human hands. Some patrons considered this an outright swindle when the paintings were first exhibited in 1953, but Rauschenberg wasn’t kidding: In 1962, when curator Pontus Hulten wanted to show them at Stockholm’s Moderna Museet, the paintings had been lost, so Rauschenberg simply sent him the measurements and samples of the paint and the canvas, and Hulten remade them from scratch.

September 5, 2017September 5, 2017 | Art