Rubik’s Clock

https://commons.wikimedia.org/wiki/File:Rubiks-clock.jpg

Hungarian sculptor and architect Ernő Rubik presented this puzzle in 1988; it was originally created by Christopher C. Wiggs and Christopher J. Taylor. The puzzle has two sides, with nine clocks on each side, and the goal is to set all the clocks to 12 o’clock simultaneously.

There are two ways to adjust the clocks. Turning a wheel at any of the four corners will adjust the clock at that corner on both sides of the puzzle. And turning a wheel will also adjust the three clocks adjacent to that corner on one side of the puzzle or the other; which side is determined by the four buttons surrounding the central clock.

So, for example, pressing the northwest button “in” and then turning the northwest wheel will adjust the northwestern quartet of clocks and the corresponding corner clock on the other side of the puzzle. Pulling the northwest button “out” and turning the same wheel will adjust the northwestern clock on the front of the puzzle, its counterpart on the back, and the three clocks adjacent to it on that side.

This is more intuitive than it sounds. Here’s a simulator.

Since there are 14 independent clocks, with 12 settings each, there are a total of 1214 = 1,283,918,464,548,864 possible configurations. It turns out that no configuration requires more than 12 moves to solve; for comparison, in the “worst case” solving a Rubik’s cube can take 20 moves. The trouble, of course, is knowing how to go about it.

| Puzzles · Science & Math

The Drowning Wife

My wife and a stranger are both drowning. I can save only one of them. What should I do? In considering this question in 1981, Bernard Williams suggested that I’m having “one thought too many” if I stop to ponder what morality requires; I should save my wife simply because she’s my wife. Troy Jollimore argues that this should silence all other considerations — a husband must “perceive this consideration as possessing such overwhelming importance that it simply drives everything else from his mind.”

But “This sounds terrible,” writes Raja Halwani. “It is one thing to say that Sam should be motivated by the thought that his wife is drowning, but quite another that this thought should silence all others. The danger here is that even if love takes us out of self-absorption, it throws us into the absorption in another, and this does not sound moral.” Is love a moral emotion?

(Bernard Williams, Moral Luck, 1981; Troy Jollimore, Love’s Vision, 2011; Raja Halwani, Philosophy of Love, Sex, and Marriage, 2018.)

| Society

Open Questions

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The Mad Hatter poses a famous unanswered riddle in Alice’s Adventures in Wonderland: “Why is a raven like a writing desk?”

W.S. Gilbert poses another one in the Gilbert and Sullivan operetta The Yeomen of the Guard. The jester Jack Point asks, “Why is a cook’s brainpan like an overwound clock?” The Lieutenant impatiently says, “A truce to this fooling,” and Jack withdraws, saying, “Just my luck: my best conundrum wasted.”

“Like many in the audience, I have often wondered what the answer to that conundrum is, and one day I put a question about it to Gilbert,” wrote Henry A. Litton in The Secrets of a Savoyard (1922). “With a smile he said he couldn’t tell me then, but he would leave me the answer in his will.”

“I’m sorry to say that it was not found there — maybe because there was really no answer to the riddle, or perhaps because he had forgotten to bequeath to the world this interesting legacy.”

| Literature

Escalating Magic

Each number in this pandiagonal order-4 magic square is a three-digit prime:

277 197 631 431
661 401 307 167
137 337 491 571
461 601 107 367

Add 30 to each cell and you get a new magic square, also made up of 16 three-digit primes:

307 227 661 461
691 431 337 197
167 367 521 601
491 631 137 397

Add 1092 to each cell in that one and you get a magic square of four-digit primes:

1399 1319 1753 1553
1783 1523 1429 1289
1259 1459 1613 1693
1583 1723 1229 1489

(Allan William Johnson Jr., “Related Magic Squares,” Journal of Recreational Mathematics 20:1 [January 1988], 26-27, via Clifford A. Pickover, The Zen of Magic Squares, Circles, and Stars, 2011.)

| Science & Math

Wayward Pigeons

https://pxhere.com/en/photo/958529

In 1998, thousands of pigeons mysteriously went missing during two separate races in Virginia and Pennsylvania. More than 2,200 birds vanished, amounting to an 85 percent loss rate. The weather was calm, and it’s normal for a few birds to disappear, but the rate is usually closer to 5 percent.

It’s known that pigeons navigate by the sun and by sensing magnetic fields, but neither of those seems to be the culprit here. “Every year or so, you have one race like this where many disappear,” Cornell zoologist Charles Walcott told the Chicago Tribune. “But what is unusual is to lose so many birds from several races at the same time. What’s going on now is quite mysterious.”

Related: In 2010 a racing pigeon named Houdini disappeared during a 224-mile race in Britain and turned up five weeks later in Panama, 5,200 miles away.

“I was gobsmacked. I didn’t even know where Panama was,” owner Darren Cubberley told the Daily Mirror. “I’ve no idea how Houdini got there — I can only assume she hitched a lift on a ship across the Atlantic.”

The bird, reportedly in “perfect shape,” would have been too expensive to return, so she remained with Gustavo Ortiz, on whose roof she’d landed. At last report she was learning Spanish.

| Oddities

The Veiled Virgin

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Image: Wikimedia Commons

Sculptor Giovanni Strazza probably completed this bust of a veiled Virgin Mary in the early 1850s. It was transported to Newfoundland and placed in the Episcopal Palace next to St. John’s Basilica.

“To say that this representation surpasses in perfection of art, any piece of sculpture we have ever seen, conveys but weakly our impression of its exquisite beauty,” wrote a local newspaper. “The possibility of such a triumph of the chisel had not before entered into our conception. Ordinary language must ever fail to do justice to a subject like this — to the rare artistic skill, and to the emotions it produces in the beholder.”

| Art

The Sea Island Problem

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The Chinese mathematician Liu Hui offered this technique in a text composed about 500 years after Euclid. We’re on the mainland, and we want to find the height of a mountain on a distant island without crossing the sea.

Liu Hui showed that this can be accomplished by setting up two poles of a known height in a line with the mountain …

https://commons.wikimedia.org/wiki/File:Sea_Island_Measurement.jpg
Image: Wikimedia Commons

… and by appealing to a principle of complementary rectangles — here the red and the blue rectangles have the same area:

https://commons.wikimedia.org/wiki/File:Rectangle_in_triangle.jpg
Image: Wikimedia Commons

By using that principle it’s possible to recast the problem in terms of values that we can measure: the height of the poles (CD), the “offset” from which the top of the mountain can just be sighted from ground level over the top of each pole (DG and FH), and the distance between the poles (DF). Putting all that together we can find both the height of the mountain:

\displaystyle \frac{CD \times DF}{FH - DG} + CD

and the distance between the first pole and the mountain:

\displaystyle \frac{DG \times DF}{FH - DG}

without ever leaving the mainland. Penn State University mathematician Frank Swetz concluded that “in the endeavours of mathematical surveying, China’s accomplishments exceeded those realized in the West by about one thousand years.”

| Science & Math

Sorry

Rejection letter sent by the University of Portland’s Portland Magazine, devised by editor Brian Doyle:

Thank you for your lovely and thoughtful submission to the magazine, which we are afraid we are going to have to decline, for all sorts of reasons. The weather is dreary, our backs hurt, we have seen too many cats today and as you know cats are why God invented handguns, there is a sweet incoherence and self-absorption in your piece that we find alluring but we have published far too many of same in recent years mostly authored by the undersigned, did we mention the moist melancholy of the weather, our marriages are unkempt and disgruntled, our children surly and crammed to the gills with a sense of entitlement that you wonder how they will ever make their way in the world, we spent far too much money recently on silly graphic design and now must slash the storytelling budget, our insurance bills have gone up precipitously, the women’s basketball team has no rebounders, an aunt of ours needs a seventh new hip, the shimmer of hope that was the national zeitgeist looks to be nursing a whopper of a black eye, and someone left the toilet roll thing empty again, without the slightest consideration for who pays for things like that. And there were wet towels on the floor. And the parakeet has a goiter. And the dog barfed up crayons. Please feel free to send us anything you think would fit these pages, and thank you for considering our magazine for your work. It’s an honor.

From Letters of Note.

| Literature