Seems Right

SPRING SUMMER AUTUMN WINTER SUNDAY MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY JANUARY FEBRUARY MARCH APRIL MAY JUNE JULY AUGUST SEPTEMBER OCTOBER NOVEMBER DECEMBER ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE TEN ELEVEN TWELVE THIRTEEN FOURTEEN FIFTEEN SIXTEEN SEVENTEEN EIGHTEEN NINETEEN TWENTY TWENTY-ONE TWENTY-TWO TWENTY-THREE TWENTY-FOUR TWENTY-FIVE TWENTY-SIX TWENTY-SEVEN TWENTY-EIGHT TWENTY-NINE THIRTY THIRTY-ONE contains 365 letters.

(Dave Morice, “Kickshaws,” Word Ways 33:2 [May 2000], 133-145.)

03/06/2019 UPDATE: Reader Jean-Claude Georges finds that this works in French too if you label the categories (year, seasons, months, days, numbers):

seems right update

“And as in Dave Morice’s text, just add a ‘B’ (for bissextile = leap) after ‘AN’ to get 366 for leap years.” (Thanks, Jean-Claude.)

March 5, 2019July 13, 2019 | Trivia

In a Word

scrutator
n. a person who investigates

callid
adj. cunning or crafty

potpanion
n. a drinking companion

nocent
adj. guilty

In “The Adventure of the Abbey Grange,” a bottle of wine is two-thirds full and then half empty, without explanation.

In The New Annotated Sherlock Holmes, Leslie S. Klinger writes, “Perhaps Holmes poured some wine off to conduct an actual experiment, instead of simply imagining the result.” Or perhaps Holmes and Watson drank it themselves.

March 4, 2019 | Language · Literature

Podcast Episode 239: The Man-Eaters of Tsavo

In 1898, two lions descended on a company of railway workers in British East Africa. For nine months they terrorized the camp, carrying off a new victim every few days, as engineer John Patterson struggled to stop them. In this week’s episode of the Futility Closet podcast we’ll track the “man-eaters of Tsavo” and learn what modern science has discovered about their motivations.

We’ll also consider more uses for two cars and puzzle over some prolific penguins.

See full show notes …

March 4, 2019March 11, 2019 | History · Podcast

The Paradox of Forgiveness

I cannot forgive you unless you’re culpable — if you’re not culpable then there’s nothing to forgive.

But if you’re culpable, then what is the point of forgiving you? Either way, my forgiveness seems senseless.

Theologian Miroslav Volf writes, “Forgiveness … at its heart is both saying that justice has been violated and not letting that violation count against the offender.” And Jacques Derrida writes, “Forgiveness is thus mad. It must plunge, but lucidly, into the night of the unintelligible.”

March 3, 2019 | Society

For Pi Day

From the prolifically interesting Catriona Shearer: The red line is perpendicular to the bases of the three semicircles. What’s the total area shaded in yellow?

	Select Click for Answer
At first it appears there’s not enough information, but there is! No matter the relative sizes of the two smaller semicircles, the area of the shaded region is π. There are any number of ways of proving this; here’s a pretty “proof without words” that relies on the fact that the Pythagorean theorem works with similar figures of any shape (here, semicircles). (Thanks to Bill Bowser for the illustration.)

Click for Answer

March 2, 2019March 3, 2019 | Puzzles · Science & Math

A Thorough Anagram

This is incredible. In 2005, mathematician Mike Keith took a 717-word section from the essay on Mount Fuji in Lafcadio Hearn’s 1898 Exotics and Retrospective and anagrammed it into nine 81-word poems, each inspired by an image from Hokusai’s famous series of landscape woodcuts, the Views of Mount Fuji.

That’s not the most impressive part. Each anagrammed poem can be arranged into a 9 × 9 square, with one word in each cell. Stacking the nine grids produces a 9 × 9 × 9 cube. Make two of these cubes, and then:

In Cube “D” (for Divisibility), assign each cell the number “1” if the sum of the letter values in the corresponding word (using A=1, B=2, C=3 etc.) is exactly divisible by 9, or “0” if it is not.
In Cube “L” (for Length), assign each cell the number “1” if its word has exactly nine letters, or “0” if it does not.

Replace each “1” cell with solid wood and each “0” cell with transparent glass. Now suspend the two cubes in a room and shine beams of light from the top and right onto Cube D and from the front and right onto Cube L:

mike keith anagram cubes

The shadows they cast form reasonable renderings of four Japanese kanji characters relevant to the anagram:

The red shadow is the symbol for fire.
The green shadow is the symbol for mountain.
Put together, these make the compound Kanji symbol (“fire-mountain”) for volcano.

The white shadow is the symbol for wealth, pronounced FU
The blue shadow is the symbol for samurai, pronounced JI
Put together, these make the compound word Fuji, the name of the mountain.

See Keith’s other anagrams, including a 211,000-word recasting of Moby-Dick.

March 1, 2019 | Language · Science & Math

Second Thoughts

There was once a very successful architect who made a great name for himself. At length he built a magnificent temple, to which he devoted more time and thought than to any of the other buildings he had erected; and the world pronounced it his masterpiece. Shortly afterward he died, and when he came before the judgment angel he was not asked how many sins he had committed, but how many houses he had built.

He hung his head and said, more than he could count.

The judgment angel asked what they were like, and the architect said that he was afraid they were pretty bad.

‘And are you sorry?’ asked the angel.

‘Very sorry,’ said the architect, with honest contrition.

‘And how about that famous temple that you built just before you died?’ the angel continued. ‘Are you satisfied with that?’

‘Oh, no,’ the architect exclaimed. ‘I really think it has some good points about it, — I did try my best, you know, — but there’s one dreadful mistake that I’d give my soul to go back and rectify.’

‘Well,’ said the angel, ‘you can’t go back and rectify it, but you can take your choice of the following alternatives: either we can let the world go on thinking your temple a masterpiece and you the greatest architect that ever lived, or we can send to earth a young fellow we’ve got here who will discover your mistake at a glance, and point it out so clearly to posterity that you’ll be the laughing-stock of all succeeding generations of architects. Which do you choose?’

‘Oh, well,’ said the architect, ‘if it comes to that, you know — as long as it suits my clients as it is, I really don’t see the use of making such a fuss.’

— Edith Wharton, The Valley of Childish Things, and Other Emblems, 1896

March 1, 2019 | Society

Signposts

The “tombstone” (∎) used to denote the end of a proof was suggested by mathematician Paul Halmos. “The symbol is definitely not my invention,” he wrote. “It appeared in popular magazines (not mathematical ones) before I adopted it, but, once again, I seem to have introduced it into mathematics. It is the symbol that sometimes looks like ∎, and is used to indicate an end, usually the end of a proof. It is most frequently called the ‘tombstone’, but at least one generous author referred to it as the ‘halmos’.”

https://commons.wikimedia.org/wiki/File:Knuth%27s_dangerous_bend_symbol.svg — Image: Wikimedia Commons

The group of mathematicians who wrote under the name Nicolas Bourbaki would include a “dangerous bend” symbol in the margin next to tricky or difficult passages, “to forewarn the reader against serious errors, where he risks falling.” Other writers have adopted the symbol, including computer scientist Donald Knuth, who included American-style road signs in his Metafont and TeX typesetting systems.

https://commons.wikimedia.org/wiki/File:Krul.svg — Image: Wikimedia Commons

And teachers in the Netherlands use a distinctive “flourish of approval” when grading schoolwork to show that they have seen and agreed with a paragraph. The mark, which may have evolved from a hastily written g (for “good” [goed] or “seen” [gezien]), rarely appears outside the Netherlands and its former colonies.

February 28, 2019February 28, 2019 | Language

Bootstraps

However, there is one thing that cannot be the result of God’s will: the fact that his will is effective. For if God’s will is not effective, then nothing he wills could come about. It would follow that he could not will that his will become effective and, as a result, have it become effective. Unless God’s will is already effective, he could not will it to become effective and have it in fact become effective. If God’s will is not effective, God could not make it effective. Thus, if God’s will is effective, God did not make it effective. So there is at least one state of affairs that cannot be dependent on God’s will: namely, that his will is effective.

— B.C. Johnson, The Atheist Debater’s Handbook, 1983

February 28, 2019February 27, 2019 | Religion

E Pluribus Unum

Replace each * with a different digit 1-9 to make this equation true:

$\displaystyle \frac{*}{**} + \frac{*}{**} + \frac{*}{**} = 1$

	Select Click for Answer
$\displaystyle \frac{9}{12} + \frac{5}{34} + \frac{7}{68} = 1$ It’s easy to solve this by writing a program to try all possibilities, but reasoning it out is tricky. Donald Aucamp gives one solution in MIT Technology Review, March 2002. 03/18/2019 UPDATE: I should have explained that the double asterisks in the denominators are two-digit numbers. Interestingly, there are two other interpretations that both yield answers! Reader Nick Berry sent this: $\displaystyle \frac{1}{6 \times 3} + \frac{7}{4 \times 2} + \frac{5}{9 \times 8} = 1$ And Paul Wagner sent: $\displaystyle \frac{6}{3 + 9} + \frac{5}{7 + 8} + \frac{1}{2 + 4} = 1$ Thanks to both of them.

Click for Answer

February 27, 2019March 18, 2019 | Puzzles