In a Word

hallucar
adj. pertaining to the big toe

In 1856, 10-year-old Ellen Terry was just about to give Puck’s final speech in A Midsummer Night’s Dream when a stagehand closed a trapdoor on her foot, breaking her toe. She screamed, but manager Ellen Kean offered to double her salary if she finished the play. So, supported by Kean on one side and her sister Kate on the other, she delivered the following soliloquy:

If we shadows have offended (Oh, Katie, Katie!)
Think but this, and all is mended, (Oh, my toe!)
That you have but slumbered here,
While these visions did appear. (I can’t, I can’t!)
And this weak and idle theme,
No more yielding but a dream, (Oh, dear! oh, dear!)
Gentles, do not reprehend; (A big sob)
If you pardon, we will mend. (Oh, Mrs. Kean!)

“How I got through it, I don’t know!” she wrote in her 1908 memoir. “But my salary was doubled — it had been fifteen shillings, and it was raised to thirty — and Mr. Skey, President of Bartholomew’s Hospital, who chanced to be in a stall that very evening, came round behind the scenes and put my toe right. He remained my friend for life.”

December 4, 2015December 3, 2015 | Literature

Breaking the News

In the December 2012 issue of 1 Across magazine, longtime crossword composer John Graham included a special instruction above one of his puzzles:

“I have 18dn of the 19; no 27, just 13 15; no 2 or 6 or 1dn 26 yet — plenty of 10, though I wouldn’t have chosen the timing.”

Solvers discovered that 18 down was CANCER and 19 across was OESOPHAGUS. The full message read:

“I have CANCER of the OESOPHAGUS; no CHEMOTHERAPY, just PALLIATIVE CARE; no NARCOTIC or STENT or MACMILLAN NURSE yet — plenty of MERRIMENT, though I wouldn’t have chosen the timing.”

The puzzle was reprinted as cryptic crossword No. 25,842 in the Guardian the following month.

“It seemed the natural thing to do somehow,” Graham said. “It just seemed right.” He died in November 2013, and the Guardian published a tribute crossword to remember him.

(Thanks, Anthony.)

December 3, 2015December 3, 2015 | Death · Puzzles

A Story Machine

Here’s a curious invention from 1916, in the early days of motion pictures: It’s a machine designed to suggest plot ideas by randomly juxtaposing ideas. Words, pictures, and even bars of music are printed on paper rollers, and the writer turns these to present six elements that form the basis of a story.

In the example above, the machine presents the words aged, aviator, bribes, cannibal, carousal, and escape. “These particular words readily suggest, for instance, that an aged aviator after flying through the air on a long trip, lands finally on a desolate island where he is met by a cannibal, whom he is forced to bribe to secure his safety. After an interim which is full of possibilities as a basis of a story, a carousal ensues following which the aviator escapes.”

Inventor Arthur Blanchard says that this technique can be used to inspire any fictional work, from a cartoon to a song, but he patented it specifically as a “movie writer.” Whether it inspired any movies I don’t know.

December 2, 2015December 2, 2015 | Entertainment · Technology

Three Sides

equilateral areas

If an equilateral triangle is inscribed in, and has a common vertex with, a rectangle, as shown above, then areas A + B = C.

If a triangle with angles α, β, γ is inscribed in, and has a common vertex with, a rectangle, as shown below, and if the right triangles opposite α, β, γ have areas A, B, C, respectively, then A cot α + B cot β = C cot γ.

cotangents

Somewhat related: A Curious Equality.

(Tom M. Apostol and Mamikon Mnatsakanian, “Triangles in Rectangles,” Math Horizons 5:3 [February 1998], 29-31.)

December 2, 2015December 3, 2015 | Science & Math

A Last Look

On Sept. 26, 1901, 13-year-old Fleetwood Lindley was attending school in Springfield, Ill., when his teacher handed him a note: His father wanted him urgently. He rode his bicycle to the Oak Ridge cemetery two miles out of town and found his father, Joseph, in the memorial hall of Abraham Lincoln’s tomb. The assassinated president, now 36 years dead, was being transferred to a new resting place, and a small group of caretakers had decided to open his coffin to confirm his identity.

The casket had been laid across a pair of sawhorses. A pair of workmen used a blowtorch to unseal the lead panel that covered Lincoln’s upper body, and the small group peered in.

Afterward the coffin was lowered into a hole 10 feet deep, encased in a cage of steel bars, and buried under tons of concrete. Over the years, as the other witnesses passed away, Lindley became the last living person to have looked on Lincoln’s body.

“His face was chalky white,” he remembered for a Life reporter in 1963, three days before his own death. “His clothes were mildewed. And I was allowed to hold one of the leather straps as we lowered the casket for the concrete to be poured.”

“I was not scared at the time, but I slept with Lincoln for the next six months.”

December 1, 2015November 30, 2015 | Death · History

Podcast Episode 83: Nuclear Close Calls

In 1983, Soviet satellites reported that the United States had launched a nuclear missile toward Moscow, and one officer had only minutes to decide whether to initiate a counterstrike. In today’s show we’ll learn about some nuclear near misses from the Cold War that came to light only decades after they occurred.

We’ll also hear listeners’ input about crescent moons and newcomers to India, and puzzle over the fatal consequences of a man’s departure from his job.

See full show notes …

November 30, 2015October 23, 2017 | History · Podcast

In a Word

chrystal identity

operose
adj. involving great labor

(Thanks, Trevor.)

November 30, 2015November 30, 2015 | Language · Science & Math

Heel!

In walking through a park and observing the signs, ‘All dogs found on these grounds without their owners, will be shot,’ a friend of mine exclaimed, ‘That’s a hard case for dogs that can’t read.’

— Irving Browne, Humorous Phases of the Law, 1876

November 29, 2015November 28, 2015 | Humor

Chernoff’s Faces

Humans are bad at evaluating complex data, but we’re good at reading faces. So in 1973 Stanford statistician Herman Chernoff proposed using cartoon faces to encode information. He found that up to 18 different data dimensions can be represented in a computer-drawn face, mapping one variable to the length of the nose, another to the space between the eyes or the position of the mouth, and so on. This produces an array of faces that we can assess quickly using the brain’s natural talent for reading features. (The example above shows lawyers’ ratings of state judges in U.S. Superior Court.)

“This approach is an amusing reversal of a common one in artificial intelligence,” Chernoff noted. “Instead of using machines to discriminate between human faces by reducing them to numbers, we discriminate between numbers by using the machine to do the brute labor of drawing faces and leaving the intelligence to the humans, who are still more flexible and clever.”

(Herman Chernoff, “The Use of Faces to Represent Points in K-Dimensional Space Graphically,” Journal of the American Statistical Association 68:342 [June 1973], 361-368.)

November 29, 2015November 28, 2015 | Science & Math

DIY

Nepal’s constitution contains complete instructions for drawing its flag:

(A) Method of Making the Shape Inside the Border

(1) On the lower portion of a crimson cloth draw a line AB of the required length from left to right.
(2) From A draw a line AC perpendicular to AB making AC equal to AB plus one third AB. From AC mark off D making line AD equal to line AB. Join BD.
(3) From BD mark off E making BE equal to AB.
(4) Touching E draw a line FG, starting from the point F on line AC, parallel to AB to the right hand-side. Mark off FG equal to AB.
(5) Join CG.

(B) Method of Making the Moon

(6) From AB mark off AH making AH equal to one-fourth of line AB and starting from H draw a line HI parallel to line AC touching line CG at point I.
(7) Bisect CF at J and draw a line JK parallel to AB touching CG at point K.
(8) Let L be the point where lines JK and HI cut one another.
(9) Join JG.
(10) Let M be the point where line JG and HI cut one another.
(11) With centre M and with a distance shortest from M to BD mark off N on the lower portion of line HI.
(12) Touching M and starting from O, a point on AC, draw a line from left to right parallel to AB.
(13) With centre L and radius LN draw a semi-circle on the lower portion and let P and Q be the points where it touches the line OM respectively.
(14) With centre M and radius MQ draw a semi-circle on the lower portion touching P and Q.
(15) With centre N and radius NM draw an arc touching PNQ [sic] at R and S. Join RS. Let T be the point where RS and HI cut one another.
(16) With Centre T and radius TS draw a semi-circle on the upper portion of PNQ touching it at two points.
(17) With centre T and radius TM draw an arc on the upper portion of PNQ touching at two points.
(18) Eight equal and similar triangles of the moon are to be made in the space lying inside the semi-circle of No. (16) and outside the arc of No. (17) of this Schedule.

(C) Method of Making the Sun

(19) Bisect line AF at U and draw a line UV parallel to line AB touching line BE at V.
(20) With centre W, the point where HI and UV cut one another and radius MN draw a circle.
(21) With centre W and radius LN draw a circle
(22) Twelve equal and similar triangles of the sun are to be made in the space enclosed by the circles of No. (20) and of No. (21) with the two apexes of two triangles touching line HI.

(D) Method of Making the Border

(23) The width of the border will be equal to the width TN. This will be of deep blue colour and will be provided on all the sides of the flag. However, on the five angles of the flag the external angles will be equal to the internal angles.
(24) The above mentioned border will be provided if the flag is to be used with a rope. On the other hand, if it is to be hoisted on a pole, the hole on the border on the side AC can be extended according to requirements.

Explanation: The lines HI, RS, FE, ED, JG, OQ, JK and UV are imaginary. Similarly, the external and internal circles of the sun and the other arcs except the crescent moon are also imaginary. These are not shown on the flag.

That’s a good thing — it’s the only national flag that’s not a quadrilateral. The two pennants represent different branches of a ruling dynasty in the 19th century. The nation signaled its pride in the new design last February by setting a world record for the largest human flag — 35,000 Nepalese gathered in Kathmandu to break Pakistan’s record and to demonstrate their own national unity. I wonder how they worked out the geometry:

https://commons.wikimedia.org/wiki/File:Human_Made_National_Flag_of_Nepal.JPG — Image: Wikimedia Commons

November 28, 2015November 27, 2015 | Science & Math