In a Word

n. a person who investigates

adj. cunning or crafty

n. a drinking companion

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.

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.


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’.”
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.
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.


The roots of the word helicopter are not heli and copter but helico and pter, from the Greek “helix” (spiral) and “pteron” (wing).

G.L.M. de Ponton’s 1861 British patent says, “The required ascensional motion is given to my aerostatical apparatus (which I intend denominating aeronef or helicoptere,) by means of two or more superposed horizontal helixes combined together.”

Scattered Stars

When I heard the learn’d astronomer,
When the proofs, the figures, were ranged in columns before me,
When I was shown the charts and diagrams, to add, divide, and measure them,
When I sitting heard the astronomer where he lectured with much applause in the lecture-room,
How soon unaccountable I became tired and sick,
Till rising and gliding out I wander’d off by myself,
In the mystical moist night-air, and from time to time,
Look’d up in perfect silence at the stars.

That’s Walt Whitman. In 2000, mathematician Mike Keith noted a similar idea in Psalm 19:1-6:

The heavens declare the glory of God;
And the firmament sheweth his handywork.
Day unto day uttereth speech,
And night unto night sheweth knowledge.
There is no speech nor language,
Where their voice is not heard.
Their line is gone out through all the earth,
And their words to the end of the world.
In them hath he set a tabernacle for the sun,
Which is as a bridegroom coming out of his chamber,
And rejoiceth as a strong man to run a race.
His going forth is from the end of the heaven,
And his circuit unto the ends of it:
And there is nothing hid from the heat thereof.

So he married them by rearranging the psalm’s letters:

When I had listened to the erudite astronomer,
When his high thoughts were arranged and charted before me,
When I was shown the length and breadth and height of it,
The Earth, the horned Moon, the chariot of fire,
The hundredth flight of the shuttle through heavyish air,
How soon, mysteriously, I became sad and sick,
Had to wander out, ousted, charging through the forest,
Joining the sure chaos here in a foreign heath,
Having forgotten the vocation of the learned man,
And in the mystic clearing, once more looked up
In perfect silence at the sermon in the stars.

(Michael Keith, “Anagramming the Bible,” Word Ways 33:3 [August 2000], 180-185.)


  • The negative space in the eight of diamonds forms an 8.
  • William Brewster, leader of the Plymouth Colony, named his children Jonathan, Patience, Fear, Love, and Wrestling.
  • Wilfred Owen’s mother received the news of his death on Armistice Day.
  • “I never had any philosophic instruction, the first lecture on psychology I ever heard being the first I ever gave.” — William James

The Vowel Triangle

Chris McManus discovered this oddity. If W and Y are accepted as vowels, that gives us AEIOUWY. Starting with O, number these according to their positions on a circular alphabet without starting the count over for A (that is, O is the 15th letter of the alphabet, so it’s assigned number 15; beyond Z we’d reach A as the “27th” letter; and so on). Now write these numbers into a triangle, again starting with O:

   O                15
 U W Y           21 23 25
A  E  I         27  31  35

Each of the five lines in the figure gives a different arithmetic progression:

UWY: difference of 2
AEI: difference of 4
OUA: difference of 6
OWE: difference of 8
OYI: difference of 10

(David Morice, “Kickshaws,” Word Ways 34:4 [November 2001], 292-305.)

Fortuitous Numbers

In American usage, 84,672 is said EIGHTY FOUR THOUSAND SIX HUNDRED SEVENTY TWO. Count the letters in each of those words, multiply the counts, and you get 6 × 4 × 8 × 3 × 7 × 7 × 3 = 84,672.

Brandeis University mathematician Michael Kleber calls such a number fortuitous. The next few are 1,852,200, 829,785,600, 20,910,597,120, and 92,215,733,299,200.

If you normally say “and” after “hundred” when speaking number names, then the first few fortuitous numbers are 333,396,000 (THREE HUNDRED AND THIRTY THREE MILLION, THREE HUNDRED AND NINETY SIX THOUSAND), 23,337,720,000, 19,516,557,312,000, 56,458,612,224,000, and 98,802,571,392,000.

And 54 works in both French and Russian.

(Michael Kleber, “Four, Twenty-Four, … ?,” Mathematical Intelligencer 24:2 [March 2002], 13-14.)