“The difficulty of ruling over a diverse nation,” a 1578 engraving by Antwerp-based artist Pieter van der Borcht the Elder.
James A. Garfield wrote, “All free governments are managed by the combined wisdom and folly of the people.”
From the Public Domain Review.
In 1951, Arthur B. Brown of Queens College noted that the number 3 can be expressed as the sum of one or more positive integers in four ways (taking the order of terms into account):
3
1 + 2
2 + 1
1 + 1 + 1
As it turns out, any positive integer n can be so expressed in 2n – 1 ways. Brown asked, how can this be proved?
William Moser of the University of Toronto offered this insightful solution:
Imagine the digit 1 written n times in a row. For example, if n = 4:
1 1 1 1
This is a picket fence, with n pickets and n – 1 spaces between them. At each space we can choose either to insert a plus sign or leave it blank. So that gives us n – 1 tasks to perform (i.e., making this choice for each space) and two options for each choice. Thus the total number of expressions for n as a sum is 2n – 1, or, in the case of n = 4, eight:
1 1 1 1 = 4
1 + 1 1 1 = 1 + 3
1 1 + 1 1 = 2 + 2
1 1 1 + 1 = 3 + 1
1 + 1 + 1 1 = 1 + 1 + 2
1 + 1 1 + 1 = 1 + 2 + 1
1 1 + 1 + 1 = 2 + 1 + 1
1 + 1 + 1 + 1 = 1 + 1 + 1 + 1
(Pi Mu Epsilon Journal 1:5 [November 1951], 186.)
Artist Akinori Goto created this 3D-printed zoetrope, a rotating design that produces an animation when illuminated with a slice of light.
It won both the Runner-up Grand Prix and the Audience Award at the 2016 Spiral Independent Creators Festival in Tokyo.
He followed it up with “Ballet”:
In 1944, a bizarre criminal assaulted the small town of Mattoon, Illinois. Victims reported smelling a sickly sweet odor in their bedrooms before being overcome with nausea and a feeling of paralysis. In this week’s episode of the Futility Closet podcast we’ll pursue the mad gasser of Mattoon, who vanished as quickly as he had struck, leaving residents to wonder whether he had ever existed at all.
We’ll also ponder the concept of identical cousins and puzzle over a midnight stabbing.
ubiety
n. the state of occupying a certain place or position; the place in which a person or thing is; “whereness”
After each of his victories as a matador, John Fulton would paint a portrait of the bull he had slain using its own blood, after the manner of the hunter-painters who had decorated the cave walls of Altamira.
Fulton grew up in a Philadelphia rowhouse but became captivated by the bullring after seeing the 1941 Tyrone Power film Blood and Sand. “The movie so stirred his sense of gallantry and romance that he decided on the spot to become a bullfighter,” reported the New York Times. “If a Rita Hayworth was the reward, he told friends years later, it was worth the effort and the risk.”
He spent a year at the Philadelphia Museum College of Art, won a scholarship to a Mexican art school, and began to study bullfighting. In 1956 he went to Spain, where he became the first American to qualify as a matador and spent 40 years fighting professionally in the ring.
The paintings were decidedly a sideline, as he regarded bullfighting itself as an art. “It is the most difficult art form in the world,” he once said. “You are required to create a work of art spontaneously with a semi-unknown medium, which can kill you, in front of one of the most critical audiences around. And it all leaves only a memory.”
Another conundrum from Henry Dudeney’s The Canterbury Puzzles:
A squire has drawn a portrait of King Edward III with a single continuous stroke of his pen. “‘Tis a riddle to find where the stroke doth begin and where it doth also end. To him who shall first show it unto me will I give the portraiture.” What is the answer?
Roman craftsmen made a remarkable coup around 300 A.D. — they produced a cup that is red when lit from behind and green when lit from the front. The effect occurs because the glass contains tiny proportions of gold and silver nanoparticles that reflect light of certain wavelengths. The workers themselves may have discovered the technique by accident, and may not have understood it fully; only a few pieces of 4th-century Roman glass display this “dichroic” property. Art historian Donald Harden called it “the most spectacular glass of the period, fittingly decorated, which we know to have existed.” It now resides in the British Museum.
In 1948, retired clock maker Lawrence Wahlstrom acquired a surplus World War II bomb sight bearing a complicated cluster of gears, restored it to operation, and began adding more gears to it over a period of 15 years. He resolved on adding 50 each year, and succeeded so well that today the total number isn’t known.
Popular Mechanics wrote in 1954, “We all know someone who works harder doing nothing than most of us work doing something, but we can’t possibly know anything that works harder at nothing that a machine built by a California hobbyist. The machine has over 700 working parts that rotate, twist, oscillate and reciprocate — all for no purpose except movement.”
In a review for the New Yorker in 1959, film critic Kenneth Tynan mistakenly referred to “the late Eric Blore,” and the magazine’s famously vigilant fact-checking department failed to note that the English comic actor was still alive.
Blore’s lawyer demanded a retraction, and a chastened Tynan prepared an apology, which was scheduled to appear in the following issue.
After that issue had been printed, though, the actor really did die … so while that day’s newspapers were reporting Blore’s death, the New Yorker was apologizing for saying he was no longer alive.
(Thanks, Johnny.)
