When Glenn Seaborg appeared as a guest scientist on the children’s radio show Quiz Kids in 1945, one of the children asked whether any new elements, other than plutonium and neptunium, had been discovered at the Metallurgical Laboratory in Chicago during the war.
In fact two had — Seaborg announced for the first time anywhere that two new elements, with atomic numbers 95 and 96 (americium and curium), had been discovered. He said, “So now you’ll have to tell your teachers to change the 92 elements in your schoolbook to 96 elements.”
In his 1979 Priestley Medal address, Seaborg recalled that many students apparently did bring this knowledge to school. And “judging from some of the letters I received from such youngsters, they were not entirely successful in convincing their teachers.”
When British forces plundered the palace of Indian prince Tipu Sultan in May 1799, they found an infuriating trophy:
In a room appropriated for musical instruments was found an article which merits particular notice, as another proof of the deep hate, and extreme loathing of Tippoo Saib towards the English. This piece of mechanism represents a royal Tyger in the act of devouring a prostrate European. There are some barrels in imitation of an Organ, within the body of the Tyger. The sounds produced by the Organ are intended to resemble the cries of a person in distress intermixed with the roar of a Tyger. The machinery is so contrived that while the Organ is playing, the hand of the European is often lifted up, to express his helpless and deplorable condition.
Tipu had allied himself with France against the encroaching East India Company, and the Fourth Mysore War brought his downfall. The tiger, it appears, had symbolized his defiance of British colonialism. The instrument was removed to London, where it became a centerpiece in the Company’s Leadenhall Street gallery; John Keats saw it there and immortalized it in The Cap and Bells, his satirical verse of 1819:
Replied the Page: “that little buzzing noise,
Whate’er your palmistry may make of it,
Comes from a play-thing of the Emperor’s choice,
From a Man-Tiger-Organ, prettiest of his toys.”
“Indeed, the horrific image of a wild beast attacking a helpless fellow Briton must have stirred strong reactions in the British audience so few years after the brutal Mysore campaigns,” write Jane Kromm and Susan Benforado Bakewell in A History of Visual Culture (2010). “Contained within one wondrous work of art was an illustration of the intensity of resentment toward European imperialism, the ferocious power of the enemy prince, and the moral justification for colonization.”
A pretty new theorem by Lee Sallows: Connect each vertex of a triangle to the midpoint of the opposite side, and place a hinge at that point. Now rotate the smaller triangles about these hinges and you’ll produce three congruent triangles.
If the original triangle is isosceles (or equilateral), then the three resulting triangles will be too.
The theorem appears in the December 2014 issue of Mathematics Magazine.
Louisiana State University law professor Christine Alice Corcos points out that Ghostbusters, apart from being an entertaining comedy, also offers “a thoughtful introduction to environmental law and policy, suitable for discussion in a law school class.” For example, the team has no license for the containment unit in the basement of their firehouse:
The LLRWA sets forth extremely specific terms under which sites must be proposed, evaluated, and chosen. It also mandates environmental impact statements, which the Ghostbusters could not have prepared since they did not notify any agency of their activities. Additionally, the LLRWA guidelines require that the waste being stored, and the disposal site, be structurally stable. Apparently the psychic waste being stored does not meet Class B or C waste guidelines, nor does it seem to have the minimum stability required by any other class. As we see on Peck’s second visit to the facility, it is neither liquid nor solid, and if released will likely ignite or emit toxic vapors. Furthermore, storage is likely to be advisable not for 100 years, as with Class A and B wastes, but forever. However, under RCRA, the government need only show that the waste is hazardous within the statutory definition. The EPA might prefer to exercise this option for this particular case.
On the other hand, it’s EPA lawyer Walter Peck who orders the unit to be shut down, over the team’s protests. “Peck’s unilateral action may leave the EPA liable for suit by New York City residents under the Federal Tort Claims Act,” Corcos writes. “A successful suit would have to fall outside one of two exceptions to the federal government’s waiver of immunity. The discretionary function exception, exempts the acts and omissions of a government employee ‘exercising due care in the execution of a statute or regulation,’ or specific intentional torts, such as assault, battery and false imprisonment. Peck’s behavior in forcing the release of the psychic waste arguably falls within the battery exception, as would Venkman’s claim of malicious prosecution.”
“All the business of war, and indeed all the business of life, is to endeavour to find out what you don’t know by what you do; that’s what I called ‘guessing what was at the other side of the hill.'” — Duke of Wellington
Three players enter a room, and a maroon or orange hat is placed on each one’s head. The color of each hat is determined by a coin toss, and the outcome of one toss has no effect on the others. Each player can see the other players’ hats but not his own.
The players can discuss strategy before the game begins, but after this they may not communicate. Each player considers the colors of the other players’ hats, and then simultaneously each player must either guess the color of his own hat or pass.
The group shares a $3 million prize if at least one player guesses correctly and no player guesses incorrectly. What strategy will raise their chance of winning above 50 percent?
A player who sees two hats of the same color (say, orange) guesses the opposite color (maroon). A player who sees hats of two different colors passes. There are 8 possible arrangements of hats:
OOO
OOM
OMM
MOO
MMO
MMM
MOM
OMO
In six of these, two of the players see hats of different colors and so will pass, and the third player sees two hats of the same color and guesses the opposite color, winning. In the other two cases, all three players are wearing hats of the same color, so all guess the wrong color and lose. This strategy produces a win in six of the eight cases, so the players will win 3/4 of the time.
From “Applications of Recursive Operators to Randomness and Complexity,” the 1998 UCSB doctoral thesis of computer scientist Todd Ebert.
In 1925, Nome, Alaska, was struck by an outbreak of diphtheria, and only a relay of dogsleds could deliver the life-saving serum in time. In this week’s episode of the Futility Closet podcast we’ll follow the dogs’ desperate race through arctic blizzards to save the town from epidemic.
We’ll also hear a song about S.A. Andree’s balloon expedition to the North Pole and puzzle over a lost accomplishment of ancient civilizations.
Achilles overtakes the tortoise and runs on into the sunset, exulting. As he does so, a fly leaves the tortoise’s back, flies to Achilles, then returns to the tortoise, and continues to oscillate between the two as the distance between them grows, changing direction instantaneously each time. Suppose the tortoise travels at 1 mph, Achilles at 5 mph, and the fly at 10 mph. An hour later, where is the fly, and which way is it facing?
Strangely, the fly can be anywhere between the two, facing in either direction. We can find the answer by running the scenario backward, letting the three participants reverse their motions until all three are again abreast. The right answer is the one that returns the fly to the tortoise’s back just as Achilles passes it. But all solutions do this: Place the fly anywhere between Achilles and the tortoise, run the race backward, and the fly will arrive satisfactorily on the tortoise’s back at just the right moment.
This is puzzling. The conditions of the problem allow us to predict exactly where Achilles and the tortoise will be after an hour’s running. But the fly’s position admits of an infinite number of solutions. Why?
(From University of Arizona philosopher Wesley Salmon’s Space, Time, and Motion, after an idea by A.K. Austin.)
I propose a card game. I’ll shuffle an ordinary deck of cards and turn up the cards in pairs. If both cards in a given pair are black, I’ll give them to you. If both are red, I’ll take them. And if one is black and one red, then we’ll put them aside, belonging to no one.
You pay a dollar for the privilege of playing the game, and then we’ll go through the whole deck. When the game is over, if you have no more cards than I do, you pay nothing. But for every card that you have more than I, I’ll pay you 3 dollars. Should you play this game?
No. Because the cards that are put aside are paired by color, the remaining cards must be divided equally between red and black. So at the end of the game you and I will always have the same number of cards. You’ll lose a dollar every time you play.
From Edward Barbeau, Murray Klamkin, and William Moser, Five Hundred Mathematical Challenges, 1995.
