https://www.youtube.com/watch?v=TlLxUYKldHk
For about two weeks each February, the last rays of the setting sun set Yosemite’s Horsetail Fall glowing orange and red.
The effect is best seen from a clearing close to the picnic area on the north road leading out of the valley east of El Capitan.
Shanghai’s Urban Planning Exhibition Center contains a 1:500 scale model of the city, showing all existing and approved buildings according to the city’s master plan for 2020.
The model measures about 5,200 square feet, or 480 square meters, but even at that size it covers only the central part of the city, within the Inner Ring Road, an area about 9 miles by 5 miles. The full city is about 58 miles by 55 miles, with three more expressway rings beyond the inner ring.
Because the exhibition center is itself located within the central district, the model contains a miniature replica of its own building. Ideally that replica would contain its own, doubly tiny scale model of the city, but I guess there’s no way to check.
(Thanks, Jim.)
A mouse wants to eat his way through a 3 × 3 × 3 cube of cheese, starting in one of the corners and tunneling through all 27 1 × 1 × 1 sub-cubes, visiting each once. Can he arrange his route so that he finishes at the center of the cube? Assume that he always moves between orthogonally adjacent cubes, traveling through walls but not through edges or corners.
Edgar Allan Poe’s “The Murders in the Rue Morgue” is credited with being the first modern detective story — biographer Jeffrey Meyers says it “changed the history of world literature.” The story established the convention of the brilliant investigator who unveils a climactic revelation before explaining the reasoning that led him to it. The lead character, C. Auguste Dupin, served as a prototype for fictional detectives from Sherlock Holmes to Hercule Poirot.
But Poe himself thought the praise was overblown. “These tales of ratiocination owe most of their popularity to being something in a new key,” he wrote. “People think them more ingenious than they are — on account of their method and air of method. In the ‘Murders in the Rue Morgue,’ for instance, where is the ingenuity in unraveling a web which you yourself … have woven for the express purpose of unraveling?” The brilliance of a detective story is transparently contrived, he said: “The reader is made to confound the ingenuity of the suppositious Dupin with that of the writer of the story.”
In May 1861, Union troops occupied Arlington House, Robert E. Lee’s mansion overlooking the capital. When Lee’s wife Mary Custis Lee wrote to the army expressing her concern about the house’s safety, she received this reply:
Mrs. R.E. Lee:
MADAM: Having been ordered by the Government to relieve Major-General Sandford in command of this department, I had the honor to receive this morning your letter of to-day, addressed to him at this place.
With respect to the occupation of Arlington by the United States troops, I beg to say it has been done by my predecessor with every regard to the preservation of the place. I am here temporarily in camp on the grounds, preferring this to sleeping in the house, under the circumstances which the painful state of the country places me with respect to its proprietors.
I assure you it has been and will be my earnest endeavor to have all things so ordered that on your return you will find things as little disturbed as possible. In this I have the hearty concurrence of the courteous, kind-hearted gentleman in the immediate command of the troops quartered here, and who lives in the lower part of the house to insure its being respected.
Everything has been done as you desired with respect to your servants, and your wishes, as far as they are known or could be anticipated, have been complied with. When you desire to return, every facility will be given you for so doing.
I trust, madam, you will not consider it an intrusion if I say I have the most sincere sympathy for your distress, and that, as far as is compatible with my duty, I shall always be ready to do whatever may alleviate it.
I have the honor to be, very respectfully, your most obedient servant,
Irvin McDowell
P.S. — I am informed it was the order of the General-in-Chief, if the troops on coming here found the family in the house, that no one should enter it, but that a guard should be placed for its protection.
The Union troops erected tents, dug latrines, and felled trees on the 1,100-acre plantation, but they left the house relatively untouched.
Introduced in the early 1800s, the “separate system” of prison architecture kept prisoners isolated from one another, to make them easier to control and to destroy the criminal subculture that could otherwise arise in dense populations. Prisoners were reduced to numbers, without names or histories, and the guards were forbidden to speak to them; in the exercise yard they tramped silently in rows, their faces hidden by brown cloth masks.
At London’s Pentonville prison this separation extended even to the chapel, where the assembled prisoners could see the chaplain but not each other. “Every man, as he enters, knows the precise row and seat that he has to occupy, and though some few pass in together at the same moment, these go to opposite quarters of the gallery,” observed journalist Henry Mayhew. “Each convict is able to get to his seat, and to close the partition-door of his stall after him, before the one following his steps has time to enter the same row.”
After the service, their exit was managed by a curious mechanical device that displayed each stall number in succession. “Thus the chapel is entirely emptied, not only with considerable rapidity, but without any disturbance or confusion.”
Pentonville was considered a model British prison of its time, and some 300 prisons worldwide were eventually built on the separate system. But an official report acknowledged that “for every sixty thousand persons imprisoned in Pentonville there were 220 cases of insanity, 210 cases of delusion, and forty suicides.”
(Henry Mayhew, The Criminal Prisons of London, 1862.)
In a 1946 essay, Warner Brothers animator Chuck Jones presented two shapes:
These represent two nonsense words, tackety and goloomb. Which is which? Most people decide immediately that the shape on the left is tackety — even though that word has no meaning.
Similarly, one of these shapes is a bassoon, and one is a harp:
Here again, the correspondence seems obvious. “These are static examples of what are mostly static sounds,” Jones wrote. “The art of animation brings them to life, brings them fluidity and power; endows them, in short, with the qualities of music. The field of graphic symbols is a great but highly unexplored field. It will, I believe, prove an important one to the musician, and to any audience that is interested in satisfying the visual appetite, side by side with the auditory appetite.”
German-American psychologist Wolfgang Köhler had considered the same question in 1929. It’s been documented as “the bouba/kiki effect.”
(Chuck Jones, “Music and the Animated Cartoon,” Hollywood Quarterly 1:4 [1946], 364-370.)
During the 1974 English Amateur stroke play championship at the Moortown Golf Club in Leeds, businessman Nigel Denham’s approach shot on the 18th fairway struck a path in front of the clubhouse and bounced up the steps, through the open door, off a wall, and into the bar.
Denham was allowed inside, having first removed his golf shoes as required by the club. Local rules showed that the clubhouse was not out of bounds, so it followed that the ball lay within an obstruction from which no relief was available. He could move a chair or a table, but once this was done there was no interference with his stance or the intended area of his swing. He reasoned that he must play the ball as it lay.
So he opened the window and shot the ball neatly through it. It traveled 20 yards and finished 12 feet from the hole, to an ovation from the bar patrons. He even completed the subsequent putt for par.
“In the fulness of time the details of this daring stroke were conveyed to the Rules of Golf Committee at St Andrews for adjudication,” writes Peter Dobereiner in The Book of Golf Disasters. “The commitee ruled that Denham should have been penalized two strokes for opening the window. Chairs, tables, beer mats and sundry impediments could be cleared aside with impunity as movable obstructions but the window, as an integral part of the immovable obstruction of a clubhouse, should not have been moved.”
The clubhouse has since been declared out of bounds.
In May 2017, brothers Ollie and Harry Ferguson launched a plastic pirate ship, the Adventure, into the North Sea at Peterhead, Scotland. It carried a message asking anyone who found it to record their location and return it to the sea. After the ship had visited Denmark, Sweden, and Norway, the crew of a Norwegian ship volunteered to launch the Adventure in new waters, and on Nov. 8 released it 100 miles off the coast of Mauritania, hoping that it would cross the Atlantic westward to the Americas.
It nearly ran aground in the Cape Verde Islands but had made it past Barbados by mid-May. You can track its progress here.
(Via MetaFilter.)
Take any two rational numbers whose product is 2, and add 2 to each. The results are the legs of a right triangle with rational sides.
For example, 13/17 × 34/13 = 2. If we add 2 to each of these we get 47/17 and 60/13 or, clearing fractions, 611 and 1020. The hypotenuse is 1189.
Because (z + 2)2 + [(2/z) + 2]2 = [z + 2 + (2/z)]2, if z is rational, so are all three sides.
(R.S. Williamson, “A Formula for Rational Right-Angle Triangles,” Mathematical Gazette 37:322 [December 1953], 289-290, via Claudi Alsina and Roger B. Nelsen, Icons of Mathematics, 2011.)
