Eodermdromes

A spelling net is the pattern made when one writes down one instance of each unique letter that appears in a word and then connects these letters with lines, spelling out the word. For instance, the spelling net for VIVID is made by writing down the letters V, I, and D and drawing a line from V to I, I to V, V to I, and I to D.

Different words produce different spelling nets, of course, but every spelling net is an example of a graph, a collection of points connected by lines. A graph is said to be non-planar if some of the lines must cross; in the case of the spelling net, this means that no matter how we arrange the letters on the page, when we connect them in order we find that at least two of the lines must cross.

A word with a non-planar spelling net is called an eodermdrome, an ungainly name that itself illustrates the idea. The unique letters in EODERMDROME are E, O, D, R, and M. Write these down and run a pen among them, spelling out the word. You’ll find that no matter how the letters are arranged, it’s never possible to complete the task without at least two of the lines crossing:

https://commons.wikimedia.org/wiki/File:Eodermdrome.png — Image: Wikimedia Commons

Ross Eckler sought all the eodermdromes in Webster’s second and third editions; another example he found is SUPERSATURATES:

https://commons.wikimedia.org/wiki/File:Supersaturates2.png — Image: Wikimedia Commons

Since spelling nets are graphs, they can be studied with the tools of graph theory, the mathematical study of such networks. One result from that discipline says that a graph is non-planar if and only if it can be reduced to one of the two patterns marked K₅ and K_{(3, 3)} above. Since both EODERMDROME and SUPERSATURATES contain these forbidden graphs, both are non-planar.

A good article describing recreational eodermdrome hunting, by computer scientists Gary S. Bloom, John W. Kennedy, and Peter J. Wexler, is here. One warning: They note that, with some linguistic flexibility, the word eodermdrome can be interpreted to mean “a course on which to go to be made miserable.”

August 24, 2016August 24, 2016 | Language · Science & Math

Oops

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

In 1726, the Swiss naturalist Johann Jakob Scheuchzer mistook the skull and vertebral column of a large salamander from the Miocene epoch for the “betrübten Beingerüst eines alten Sünders” (sad bony remains of an old human sinner) and dubbed it Homo diluvii testis, “the man who witnessed the Deluge.” The fossil lacked a tail or hind legs, so he thought it was the remains of a trampled human child:

It is certain that this [rock] contains the half, or nearly so, of the skeleton of a man; that the substance even of the bones, and, what is more, of the flesh and of parts still softer than the flesh, are there incorporated in the stone; in a word it is one of the rarest relics which we have of that accursed race which was buried under the waters. The figure shows us the contour of the frontal bone, the orbits with the openings which give passage to the great nerves of the fifth pair. We see there the remains of the brain, of the sphenoidal bone, of the roots of the nose, a notable fragment of the maxillary bone, and some vestiges of the liver.

The fossil made its way to Teylers Museum in the Netherlands, where in 1811 Georges Cuvier recognized it as a giant salamander. Ironically, Scheuchzer’s original belief is reflected in the fossil’s modern name, Andrias scheuchzeri — Andrias means “image of man.”

November 4, 2015November 3, 2015 | Science & Math

Number Squares

Howard W. Bergerson devised these:

number squares

As in a word square, the “columns” in each sum are identical with the “rows.”

12/07/2021 UPDATE: Reader James Foster finds that 20 such squares are possible. (Thanks, James.)

December 5, 2012December 7, 2021 | Science & Math

Footloose

A visitor’s description of William Kingston, a Somerset farmer born without arms, recounted in John Platts, Encyclopedia of Natural and Artificial Wonders and Curiosities, 1876:

He highly entertained us at breakfast, by putting his half-naked feet upon the table as he sat, and carrying his tea and toast between his great and second toe to his mouth, with as much facility as if his foot had been a hand, and his toes fingers. … He then shewed me how he shaves himself with the razor in his toes; and he can comb his own hair. He can dress and undress himself, except buttoning his clothes. He feeds himself, and can bring both his meat or his broth to his mouth, by holding the fork or spoon in his toes. He cleans his own shoes, lights the fire, and does almost any domestic business as well as any other man. … He can milk his cows with his toes, and cuts his own hay, binds it up in bundles, and carries it about the field for his cattle. Last winter he had eight heifers constantly to fodder. The last summer he made all his hay-ricks. He can do all the business of the hay-field (except mowing) as fast and as well with his feet as others can with rakes and forks. … In a word, he can nearly do as much without as others can with their arms.

January 30, 2008January 26, 2008 | Oddities

The Silver Rule

“When asked by a disciple if there were one single word which could serve as a principle of conduct for life, Confucius replied, ‘Perhaps the word reciprocity will do. Never impose on others what you would not choose for yourself.'” — Analects

May 13, 2026May 12, 2026 | Society

“To a Lost Sweetheart”

When Whistler’s Mother’s Picture’s frame
Split, that sad morn, in two,
Your tense words scorched me like a flame —
You shrieked, “Ah, glue! Get glue!”

O Glue! O God! there was not glue
Enough in all the feet
Of all the kine the wide world through
To hold you to me, Sweet!

— Don Marquis

May 11, 2026May 10, 2026 | Poems

A Union Cipher

This baffling message illustrates a cipher adopted by the Union Army in 1862:

TO GEORGE C. MAYNARD, Washington

Regulars ordered of my to public out suspending received 1862 spoiled thirty I dispatch command of continue of best otherwise worst Arabia my command discharge duty of my last for Lincoln September period your from sense shall duties the until Seward ability to the I a removal evening Adam herald tribune.

PHILIP BRUNER

The address and signature are “covers” that don’t enter into the cipher. The first word, Regulars, is a code indicating that the original message had been written in five columns of nine words each. Tribune, herald, spoiled, Seward, for, and worst are null words; Lincoln is code for Louisville, Kentucky; Adam means General Henry Wager Halleck; and Arabia is code for Major General Don Carlos Buell. The word Period indicates a full stop. This had been the original message:

Louisville, Kentucky
September thirty 1862

General Halleck:

(Adam)   (period)   I           received     last
evening  your       dispatch    suspending   my
removal  from       command.    Out          of
a        sense      of          public       duty,
I        shall      continue    to           discharge
the      duties     of          my           command
to       the        best        of           my
ability  until      otherwise   ordered.

D.C. Buell,
Major General

This message had been enciphered by reading up the fourth column, down the third, up the fifth, down the second, and up the first; inserting the null words; and encoding the most sensitive particulars. The system worked well until July 1864, when Union cipher operator Stephen L. Robinson was captured by Confederate guerrillas and the key seized.

(John Laffin, Codes and Ciphers Secret Writing Through the Ages, 1964.)

May 11, 2026May 10, 2026 | History · Puzzles · Science & Math

Training

Suppose it were perfectly certain that the life and fortune of every one of us would, one day or other, depend upon his winning or losing a game at chess. …

The chess-board is the world, the pieces are the phenomena of the universe, the rules of the game are what we call the laws of Nature. The player on the other side is hidden from us. We know that his play is always fair, just, and patient. But also we know, to our cost, that he never overlooks a mistake, or makes the smallest allowance for ignorance. …

My metaphor will remind some of you of the famous picture in which Retzsch has depicted Satan playing at chess with man for his soul. Substitute for the mocking fiend in that picture, a calm, strong angel who is playing for love, as we say, and would rather lose than win — and I should accept it as an image of human life.

Well, what I mean by Education is learning the rules of this mighty game. In other words, education is the instruction of the intellect in the laws of Nature, under which name I include not merely things and their forces, but men and their ways; and the fashioning of the affections and of the will into an earnest and loving desire to move in harmony with those laws. For me, education means neither more nor less than this. Anything which professes to call itself education must be tried by this standard, and if it fails to stand the test, I will not call it education, whatever may be the force of authority, or of numbers, upon the other side.

— Thomas Huxley, “A Liberal Education and Where to Find It,” 1868

May 6, 2026May 5, 2026 | Society