The Wobbler

Here’s an odd little animal: Get two rigid disks, cut a notch in each one, fit them together as shown, and try to send them rolling across a table. If the notches are too deep, marrying the discs too closely together, then the object will pretty quickly slow to a stop with each disc standing at a 45° angle to the table. If the notches are too shallow, it will stop with one disc standing up at right angles to the table. But if the notches are about the right length, ideally 29.2893 percent of the radius, then the contraption will roll along quite happily for a surprisingly long distance.

The reason is that in that configuration the object’s center of mass remains level as it rolls along. (It does move from side to side, which is why it’s called the wobbler.)

Apparently this was originally discovered by A.T. Stewart, who dubbed his creation the “two-circle roller” in a 1966 note in the American Journal of Physics. I found it described in Matt Parker’s 2014 book Things to Make and Do in the Fourth Dimension, which includes a simple proof of the principle involved. There’s a more rigorous discussion here.

February 13, 2022February 12, 2022 | Science & Math

The Moses Illusion

How many animals of each kind did Moses take on the ark? If you’re like most people, you tend to answer two, even though you know it was Noah, not Moses, who took animals on the ark. People tend to have difficulty noticing when a term in a sentence or question is replaced with a semantically similar but incorrect term.

This isn’t really surprising on its face. What’s surprising is how robust the effect is. About 50 percent of people make the mistake even when asked to read the question aloud before answering it. The effect persists even when people are warned that a distortion might be present, and most people express confidence in their answer even when given unlimited time to think about it. Further examples:

What country was Margaret Thatcher president of?
What kind of tree did Lincoln chop down?
By flying a kite, what did Edison discover?
What did Goldilocks eat at the Three Little Pigs’ house?
Who found the glass slipper left at the ball by Snow White?
What is the name of the Mexican dip made with mashed-up artichokes?
In the biblical story, what was Joshua swallowed by?

One possible explanation is “partial matching” — the distorted question so closely resembles one that we recognize that we take the risk of jumping to the answer. “Everyday cognitive processing must be based on simple heuristics such as matching sets of features rather than exact matches, as very few tasks require exact matches,” suggest researchers Heekyeong Park and Lynne M. Reder. “Partial matching is immutable because it is the most efficient way for memory to operate, given the nature of the environment in which we live.”

(Heekyeong Park and Lynne M. Reder, “Moses Illusion,” in Rüdiger F. Pohl, ed., Cognitive Illusions, 2004.)

February 12, 2022February 11, 2022 | Science & Math

Handiwork

A team of volunteers have deciphered a message written by Charles Dickens in his own puzzling brand of shorthand, solving a riddle that had persisted for more than 150 years.

Apparently in 1859 the Times had mistakenly rejected an advertisement that Dickens had hoped to run during his delicate transition from the editorship of Household Words to All The Year Round. Dickens had written to the newspaper’s editor, J.T. Delane, asking him to intervene in the matter and had saved a cryptic copy of the message, possibly for legal reasons. With the passage of time the key to the author’s so-called Brachygraphy had been lost.

When scholars recently appealed for help in understanding the message, an international team of amateur solvers pooled their insights to decipher the “Tavistock Letter.” “Having the text of this letter at long last will allow scholars to learn more about Dickens’s shorthand method while gaining further insight into his life and work,” wrote Philip Palmer, curator and head of literary and historical manuscripts at Morgan Library & Museum. “We are thrilled that colleagues at the Dickens Code project have helped make this letter accessible in new ways to researchers.”

That’s not the end of it — a further puzzling page, this one from the notebooks of Dickens’ shorthand pupil Arthur Stone, still awaits solution.

(Thanks, Bill.)

February 11, 2022February 10, 2022 | Literature · Puzzles

Fair Enough

Engaged to give a talk at a university, logician Raymond Smullyan arrived half an hour early and wrote the following sentence on the blackboard, “to give the audience something to mull over”:

You have no reason to believe this sentence.

This, he reasoned, was a paradox. If you have no reason to believe the sentence, then what it states is really the case, which is certainly a good reason to believe it. But if you have a good reason to believe it, then it must be true … which means that you have no reason to believe it.

Half an hour later he came down the stairs to a packed audience. Spotting a bright-looking boy in the front row, he pointed to the sentence and asked him, “Do you believe that sentence?”

“Yes,” said the boy.

“What is your reason?”

“I don’t have any.”

Smullyan asked, “Then why do you believe it?”

The boy said, “Intuition.”

(Raymond Smullyan, “Self-Reference in All Its Glory!” conference “Self-Reference,” Copenhagen, Oct. 31-Nov. 2, 2002.)

February 11, 2022February 10, 2022 | Science & Math

Second Life

https://commons.wikimedia.org/wiki/File:Heikegani.jpg — Image: Wikimedia Commons

The samurai crab, Heikea japonica, earns its nickname well: Its shell bears a startling resemblance to the face of an angry warrior. Some Japanese believe that these crabs are reincarnated samurai who, defeated at the Battle of Dan-no-ura, threw themselves into the sea, as described in the epic Tale of the Heike.

Biologist Julian Huxley put forward the idea that the “faces” were an example of artificial selection. He suggested that fishermen who caught crabs with particularly face-shaped carapaces, believing them to be reincarnated spirits, threw them back into the sea, permitting them to reproduce while their brothers were eaten.

But humans don’t eat these crabs, and in any case the “warrior” crabs exist even far from sites of human fishing. Really the crabs are an example of another, equally compelling phenomenon — pareidolia, our tendency to see significant patterns where none exist.

February 10, 2022February 9, 2022 | Science & Math

Short Notice

Having lost both his legs at the Second Battle of Bull Run, James Tanner had settled into life as a government stenographer in the Ordnance Department in Washington, D.C., when on April 14, 1865, he was suddenly summoned to the building next to his boarding house, where Abraham Lincoln lay dying. Between midnight and 1:30 a.m., using shorthand, he recorded the accounts of those who had witnessed the assassination, and, he said later, “in fifteen minutes I had testimony enough to hang Wilkes Booth, the assassin, higher than ever Haman hung.” Here’s a sample, the statement of actor William Henry Hawk, who had been performing at Ford’s Theatre that night:

I was on the stage at the time of the firing & heard the report of the pistol. My back was towards the Presidents box at the time. I heard something tear & somebody fell & as I looked towards him he came in the direction in which I was standing & I believe to the best of my knowledge that it was John Wilkes Booth. Still I am not positive that it was him. I only had one glance at him as he was rushing towards me with a dagger & I turned and run & after I run up a flight of stairs I turned and exclaimed ‘My God that’s John Booth.’ I am acquainted with Booth. I met him the first time a year ago. I saw him today about one o’clock. Said I ‘how do you do Mr. Booth’ and he says ‘how are you Hawk.’ He was sitting on the steps of Fords Theatre reading a letter. He had the appearance of being sober at the time. I was never intimate with him. He had no hat on when I saw him on the stage. In my own mind I do not have any doubt but that it was Booth. He made some expression when he came on the stage but I did not understand what.

Tanner’s notes are known as the Tanner Manuscript — you can read them at the Internet Archive.

February 10, 2022February 9, 2022 | History

A Company of Soldiers

During World War II, British thespian Maurice Evans toured the Central Pacific with a stripped-down version of Hamlet in which all the male actors were G.I.s. He cut down and sped up the text so that the play ran in 2 hours and 45 minutes, so that the men could return to their quarters on time.

“As I remember, on opening night, Hamlet seemed like a flop,” recalled one participant. “There was barely a murmur of response from the house and a fair amount of gloom backstage. We were later told that the audience had been reminded that this was not some cheap skin show but a classic, and that they were to show respect for Shakespeare and for Hamlet, who happened to be, by God, an officer in the United States Army. With this misunderstanding cleared up, future audiences were much more enthusiastic.”

In fact the “G.I. Hamlet” proved so successful that when the war was over Evans moved it to New York and then toured the country. He didn’t mean to be typed as a Shakespearean actor, he said; he just wanted audiences to enjoy the plays as “rattling good shows.”

February 9, 2022February 8, 2022 | Art

An Idea Grows

This is Charles Darwin’s first diagram of an evolutionary tree, from his First Notebook on Transmutation of Species. He drew it around July 1837, barely a month after he’d opened his first full transmutation notebook.

“Case must be that one generation should have as many living as now,” he wrote. “To do this and to have as many species in same genus (as is) requires extinction. Thus between A + B the immense gap of relation. C + B the finest gradation. B + D rather greater distinction. Thus genera would be formed. Bearing relation to ancient types with several extinct forms.”

At the top he’s written “I think.”

February 9, 2022February 8, 2022 | Science & Math

Noted

In a Midlands pub in October 1888, a Londoner named Alfred Blanchard told the landlord that he was the Whitechapel murderer. He repeated the statement to several people and was taken to the Duke Street police station, where he quickly recanted his confession. He had been in the pub for nine hours and drunk about five and a half pints of beer. From the Birmingham Press Gazette:

About half-past twelve o’clock he asked witness what kind of detectives they had in Birmingham. Witness told him he believed them to be very clever men. Prisoner said that it would be a funny thing if the Whitechapel murderer were to give himself up in Birmingham. Witness acquiesced, and prisoner continued, ‘I am the Whitechapel murderer.’ Turning round to an elderly gentleman sitting in the bar, prisoner said, ‘Look here, old gentleman; perhaps you would not think there was a murderer in the house.’ ‘I don’t know about that,’ replied the customer; ‘you might not look unlike one.’ Prisoner said, ‘I am one, then.’ Later on the old gentleman asked prisoner had he got the knife with him, and he answered that he had left a long knife behind him. Someone asked prisoner how he did the murders without making the victims scream. He explained that this was done ‘simply by placing the thumb and finger on the windpipe and cutting the throat with the right hand.’ He said he had ‘done six of them in London.’ He was sober when he made this statement. Turning round to witness prisoner said, ‘You are a fool if you don’t get the thousand pounds reward offered for me; you may as well have it as anyone else.’

He told the magistrate’s clerk that he had been drinking for two or three days before this and hoped that the press would be kind enough not to mention his case. He was dismissed with the admonition, “What a foolish man you have been.”

February 8, 2022February 7, 2022 | Crime

The Telharmonium

Inventor Thaddeus Cahill offered a startling advance in 1895: An electronic keyboard instrument that could distribute music over the nation’s telephone networks. By combining sine waves according to Hermann Helmholtz’s new theories, the device could approximate the tone of any given instrument using electrical dynamos.

After hearing a demonstration at the Hotel Hamilton, Ray Stannard Baker wrote in McClure’s, “The first impression the music makes upon the listener is its singular difference from any music ever heard before: in the fullness, roundness, completeness, of its tones.”

Unfortunately, the device required an enormous amount of electricity, it disrupted the New York telephone network, and it was rapidly overtaken by other inventions in an immensely fruitful period. Cahill had hoped to fund it through subscriptions, and this quickly became impossible. But it had its adherents — Mark Twain’s friend Albert Bigelow Paine recalled a social gathering at the Clemens home at which the author demonstrated the instrument:

“Clemens was filled with enthusiasm over the idea. He made a speech a little before midnight, in which he told how he had generally been enthusiastic about inventions which had turned out more or less well in about equal proportions. He did not dwell on the failures, but he told how he had been the first to use a typewriter for manuscript work; how he had been one of the earliest users of the fountain-pen; how he had installed the first telephone ever used in a private house, and how the audience now would have a demonstration of the first telharmonium music so employed. It was just about the stroke of midnight when he finished, and a moment later the horns began to play chimes and ‘Auld Lang Syne’ and ‘America.'”

February 8, 2022February 7, 2022 | Art · Technology