Ernest Thompson Seton called his father “the most selfish man I ever knew, or heard of, in history or in fiction.” In 1881, on Seton’s 21st birthday, his father called him into his study, took down an enormous cash book from a high shelf, and opened it at E.
In the book he had recorded every expense he had ever made on the boy, including the day and date of each outlay, all the way back to the doctor’s fee for his delivery. The total was $537.50.
“Hitherto,” he said, “I have charged no interest. But from now on I must add the reasonable amount of 6 per cent per annum. I shall be glad to have you reduce the amount at the earliest possible opportunity.”
Stunned, Seton staggered to his feet and left the room, refusing his father’s offer “to furnish without expense a full copy of the indebtedness.”
His father called after him, “God bless you, my son. In the natural course of events, you cannot much longer be an inmate of my house; but I must prayerfully trust that, wherever your lot is cast in the near future, you will never forget the debt you owe your father, who is to you on earth the next to God.”
In 1943 German submarines were devastating the merchant convoys carrying supplies to Britain. Unable to protect them with aircraft or conventional ships, the resource-strapped Royal Navy considered an outlandish solution: a 2-million-ton aircraft carrier made of ice.
In this episode of the Futility Closet podcast we’ll follow the strange history of the project, which Winston Churchill initially praised as dazzling but which ended in ignominy at the bottom of a Canadian lake. We’ll also discover a love pledge hidden for 200 years in the heart of a Yorkshire tree and puzzle over the deaths of two men in a remote cabin.
“The light in the world comes principally from two sources, — the sun, and the student’s lamp.” — Christian Nestell Bovee, Intuitions and Summaries of Thought, 1862
Create a strip of 19 triangles like the one above (printable version here) and fold the left portion back successively at each of the northeast-pointing lines to produce a spiral:
Then fold the resulting figure backward at cd. You should be left with one blank triangular tab that can be folded backward and pasted to another blank panel on the opposite side. The resulting hexagon should have six 1s on one side and six 2s on the other.
With some adroit pinching this hexagon produces some marvelous effects. Fold down two adjacent triangles so that they meet, and then press in the opposite corner to join them. Now the top of the figure can be prised open and folded down to produce a new hexagon — this one with 1s on one face and a surprising blank on the second. What has become of the 2s?
Exploring the properties of this “hexahexaflexagon” offers an intuitive lesson in geometric group theory:
When Martin Gardner wrote about these bemusing creatures in his first column for Scientific American in 1956, he received two letters. The first was from Neil Uptegrove of Allen B. Du Mont Laboratories in Clifton, N.J.:
Sirs:
I was quite taken with the article entitled ‘Flexagons’ in your December issue. It took us only six or seven hours to paste the hexahexaflexagon together in the proper configuration. Since then it has been a source of continuing wonder.
But we have a problem. This morning one of our fellows was sitting flexing the hexahexaflexagon idly when the tip of his necktie became caught in one of the folds. With each successive flex, more of his tie vanished into the flexagon. With the sixth flexing he disappeared entirely.
We have been flexing the thing madly, and can find no trace of him, but we have located a sixteenth configuration of the hexahexaflexagon.
Here is our question: Does his widow draw workmen’s compensation for the duration of his absence, or can we have him declared legally dead immediately? We await your advice.
The second was from Robert M. Hill of The Royal College of Science and Technology in Glasgow, Scotland:
Sirs:
The letter in the March issue of your magazine complaining of the disappearance of a fellow from the Allen B. Du Mont Laboratories ‘down’ a hexahexaflexagon, has solved a mystery for us.
One day, while idly flexing our latest hexahexaflexagon, we were confounded to find that it was producing a strip of multicolored material. Further flexing of the hexahexaflexagon finally disgorged a gum-chewing stranger.
Unfortunately he was in a weak state and, owing to an apparent loss of memory, unable to give any account of how he came to be with us. His health has now been restored on our national diet of porridge, haggis and whisky, and he has become quite a pet around the department, answering to the name of Eccles.
Our problem is, should we now return him and, if so, by what method? Unfortunately Eccles now cringes at the very sight of a hexahexaflexagon and absolutely refuses to ‘flex.’
When Wilhelm Kieft tried to outlaw smoking in New Amsterdam in the 1630s, he brought on a unique protest. Washington Irving writes:
A mob of factious citizens had … the hardihood to assemble before the governor’s house, where, setting themselves resolutely down, like a besieging army before a fortress, they one and all fell to smoking with a determined perseverance, that seemed as though it were their intention to smoke him into terms. The testy William issued out of his mansion like a wrathful spider, and demanded to know the cause of this seditious assemblage, and this lawless fumigation; to which these sturdy rioters made no other reply, than to loll back phlegmatically in their seats, and puff away with redoubled fury; whereby they raised such a murky cloud, that the governor was fain to take refuge in the interior of his castle.
Wilhelm finally gave in — people could smoke, he said, but they had to give up long pipes. “Thus ended this alarming insurrection, which was long known by the name of the pipe plot, and which, it has been somewhat quaintly observed, did end, like most other plots, seditions, and conspiracies, in mere smoke.”
Black’s pawns have made 14 captures altogether, which accounts for every one of the missing white pieces. So the missing piece cannot be white. Both kings are in check, which is illegal, so the missing black piece must be on a2, blocking the rook’s check. The missing piece cannot be a queen or rook, as this would put the white king in an illegal double check. So it’s a black knight or a black bishop. And it can’t be a bishop — Black’s light-squared bishop never left its home square (the pawns on b7 and d7 have not moved), and all his pawns are still on the board, so Black has made no promotions. So the missing piece is a black knight on a2.
“The Joker,” a picture-preserving geomagic square by Lee Sallows. The 16 pieces can be assembled in varying groups of 4 to produce the same picture in 16 different ways, without rotation or reflection.
The outline need not be a joker — it can take almost any shape.
n. “Name for a devil said to collect fragments of words dropped, skipped, or mumbled in the recitation of divine service, and to carry them to hell, to be registered against the offender.” [OED]
In 2008 L.A. Innes of Jamestown, Saint Helena, auctioned a collection of images taken during the Boer War. This one shows a prisoner standing next to a tortoise on the island. The tortoise was mature at the time of the photograph, which was taken in 1900, and investigators were surprised to find that he’s still alive — “Jonathan” lives on the grounds of the governor’s residence, blind in one eye but still active and mating with other tortoises.
If he was 70 at the time Innes’ photograph was taken, then he’s 184 today — the oldest living reptile on earth.
I don’t think this was ever built — in 1904 engineer Hiram Stevens Maxim designed an amusement with a rotating parabolic floor “for producing illusionary effects”:
With such a contrivance when persons enter the hollow sphere they will not be able to tell whether it is revolving or standing still and by reason of the parabolic floor, persons near the outer edge would, to the persons standing near the centre, appear to be walking with their heads directed inward. When the sphere revolves some curious phenomena will be obtained in walking outward and inward on such a floor, and the throwing of a ball from the centre outward and vice versa will move in an unexpected direction that will be very puzzling to the people in the sphere.
Fig. 3, below, shows the perspective from the edge of the floor as it rotates. If mirrors were positioned overhead, as in Fig. 4, “people could then be made to appear to be walking all over the inside of the sphere with their heads pointing inward and their feet pointing outward.”
