In the 19th century, photographic subjects had to hold still during an exposure of 30 seconds or more. That’s hard enough for an adult, but it’s practically impossible for an infant. So mothers would sometimes hide in the scene, impersonating a chair or a pair of curtains, in order to hold the baby still while the photographer did his work:
More in this Flickr group.
What’s the shortest string of letters that contains the words ONE, TWO, and THREE, each spelled out in order but not necessarily using adjacent letters? It can be done in eight letters — THRWONEE is one example — and it turns out that no shorter solution is possible.
In 2001, A. Ross Eckler set out to do the same thing with the names of the planets, from MERCURY through PLUTO. He got down as far as 26 letters, MNVESARCPJLUPITHOURYANUSER, and to my knowledge no one has found a shorter solution.
Dana Richards offered a discussion of the problem from a computing perspective later that year. He found that Eckler’s task is related to a problem in Garey and Johnson’s 1979 Computers and Intractability.
“Why would planet packing be found in a serious computer science book?” he writes. “It turns out to be an important problem with applications to data compression, DNA sequencing, and job scheduling. … The first practical thing is to abandon all hope of solving the problem with a fast algorithm that always gets the optimal answer.”
(A. Ross Eckler, “Planet Packing,” Word Ways 34:2 [May 2001], 157.)
09/23/2017 UPDATE: Reader Mikko Ratala has found a 25-letter solution: JVSMEURANEPLICTUERNTYESOH. “The string is not unique solution as you can, for example, change the order of the first four letters as you wish.”
What’s the shortest distance between the points in the lower left and upper right? In our familiar Euclidean geometry, it’s the green line. But in taxicab geometry, an intriguing variant devised by Hermann Minkowski in the 19th century, distance is reckoned as the sum of the absolute differences of Cartesian coordinates — basically the distance that a taxicab would drive if this were a city grid. In that case, the shortest distance between the two points is 12, and it’s shown equally well by the red, blue, and yellow lines. Any of these routes will cover the same “distance” in taking you from one point to the other.
This way of considering things is intriguing in the abstract, but it has some practical value as well. “Taxicab geometry is a more useful model of urban geography than is Euclidean geometry,” writes Eugene F. Krause in Taxicab Geometry. “Only a pigeon would benefit from the knowledge that the Euclidean distance from the Post Office to the Museum [below] is 
To earn some money during college, Raymond Smullyan applied for a job as a salesman. He had to take an examination, and one of the questions asked whether he had any objection to telling a small lie now and then. Smullyan did object, but he was afraid that he wouldn’t get the job if he said so. So he lied and said no.
“Later on, I realized I was in a kind of paradox!” Smullyan wrote later. “Did I object to the lie I told the sales company? I realized that I did not! Then since I didn’t object to that particular lie, it therefore followed that I don’t object to all lies, hence my answer ‘No’ was not a lie, but the truth! So was I lying or not?”
(From his book A Mixed Bag, 2016.)
The vortex tube is a bit of a magic trick: When a stream of compressed gas is injected into the chamber, it accelerates to a high rate of rotation and moves toward the nozzle on the right. Because of the nozzle’s shape, though, only the quickly rotating outer shell of this gas can escape; the rest moves back through the center of the vortex and escapes through the opening on the left.
The result, perplexingly, is that even though the tube has no moving parts, it emits hot air (up to 200°C) on the right and cold air (down to -50° C) on the left.
Could this principle be used to air-condition a home or vehicle? “That’s what everyone thinks when they first hear about it,” engineer Leslie Inglis told Popular Science in 1976. “I always tell them that they wouldn’t buy a toaster for the kitchen if they had to buy the generator to produce the electricity. You’ve got to think of this as a compressed-air appliance.”
Dear God,
I wrote you before do you remember? Well I did what I promised. But you did not send me the horse yet. What about it?
Lewis
— Children’s Letters to God, 1967
Ships need a reliable way to know their exact location at sea — and for centuries, the lack of a dependable method caused shipwrecks and economic havoc for every seafaring nation. In this week’s episode of the Futility Closet podcast we’ll meet John Harrison, the self-taught English clockmaker who dedicated his life to crafting a reliable solution to this crucial problem.
We’ll also admire a dentist and puzzle over a magic bus stop.
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.)
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.)
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.”
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.