Words and Numbers


Strategies to memorize π sometimes rely on devising a sentence with words of representative lengths. Isaac Asimov offered this one:

How I want a drink, alcoholic, of course, after the heavy lectures involving quantum mechanics!

Count the letters in each word and you get 3.14159265358979. That’s not the best strategy, though: What shall we do about zero? And it’s hard to reel off the digits impressively for friends when you have to stop and count the letters in each word.

Arthur Benjamin, a mathematician at Harvey Mudd College, suggests using a phonetic code instead:

1 = t or th or d
2 = n
3 = m
4 = r
5 = l
6 = sh, ch, or j
7 = k or hard g
8 = f or v
9 = p or b
0 = s or z

Once we’ve memorized this list, we can turn a whole string of digits into a single word simply by inserting vowels between the consonants. So, for example, 314 could be represented by meter, motor, meteor, matter, mother, etc. The consonants h, w, and y, which don’t appear in the list, can be used like additional vowels.

Using this method, it takes only three sentences to encode the first 60 digits of π:

3. 1415 926 5 3 58 97 9 3 2 384 6264
My turtle Pancho will, my love, pick up my new mover Ginger.

3 38 327 950 2 8841 971
My movie monkey plays in a favorite bucket.

69 3 99 375 1 05820 97494
Ship my puppy Michael to Sullivan’s backrubber!

Now we just need a way to remember the sentences …

(Arthur T. Benjamin, “A Better Way to Memorize Pi: The Phonetic Code,” Math Horizons 7:3 [February 2000], 17.)

Romance Language


Samuel Pepys wrote his famous diary in shorthand, but he took a further precaution when writing about his amorous adventures — he adopted words based on Spanish, French, and Italian:

“I did come to sit avec [with] Betty Michell, and there had her main [hand], which elle [she] did give me very frankly now, and did hazer [make] whatever I voudrais avec l’ [would have with her], which did plaisir [pleasure] me grandement [greatly].”

“The garbled foreign phrases he often used for sexual incidents had something to do with concealment perhaps, much more with his pleasure in marking off sexual experiences through special words and so heightening the excitement of reliving them,” writes Claire Tomalin in Samuel Pepys: The Unequalled Self. “It is the clever schoolboy as lover, showing off to himself in two ways at once.”

In a Word

n. uncertain or doubtful meaning; ambiguity

adj. of a person: confused, fuddled

n. a third lapse

adj. defeated

When a twelfth-century youth fell in love he did not take three paces backward, gaze into her eyes, and tell her she was too beautiful to live. He said he would step outside and see about it. And if, when he got out, he met a man and broke his head — the other man’s head, I mean — then that proved that his — the first fellow’s — girl was a pretty girl. But if the other fellow broke his head — not his own, you know, but the other fellow’s — the other fellow to the second fellow, that is, because of course the other fellow would only be the other fellow to him, not the first fellow who — well, if he broke his head, then his girl — not the other fellow’s, but the fellow who was the — Look here, if A broke B’s head, then A’s girl was a pretty girl; but if B broke A’s head, then A’s girl wasn’t a pretty girl, but B’s girl was. That was their method of conducting art criticism.

— Jerome K. Jerome, Idle Thoughts of an Idle Fellow, 1886


The invention of logarithms came on the world as a bolt from the blue. No previous work had led up to it, foreshadowed it, or heralded its arrival. It stands isolated, breaking in upon human thought abruptly without borrowing from the work of other intellects or following known lines of mathematical thought.

— Lord Moulton on the 300th anniversary of John Napier’s 1614 book Description of the Wonderful Canon of Logarithms. E.W. Hobson called the invention “one of the very greatest scientific discoveries that the world has seen.”

A Forgotten Face

Conservators at the National Galleries of Scotland have discovered “what is almost certainly a previously unknown self-portrait by Vincent van Gogh.”

The image emerged in an x-ray of the artist’s 1885 painting Head of a Peasant Woman, taken in preparation for an upcoming exhibition. To save money, van Gogh sometimes used both sides of a canvas; in this case the reverse image had been hidden by layers of glue and cardboard that were applied before an exhibition in the early 20th century. It’s not yet clear whether these layers can be removed without harming Head of a Peasant Woman.

This isn’t the first time a “lost” image has been discovered in a van Gogh painting. In 2008, x-rays revealed the portrait of a woman behind the artist’s 1887 painting Patch of Grass — apparently he had painted over an image he’d completed two years earlier.


Image: Wikimedia Commons

Usain Bolt is such a great sprinter that his distinctions may extend to other worlds.

In 2013, University of Leicester physics undergraduate Hannah Lerman and her colleagues determined that the Jamaican athlete was one of the few humans who could get aloft on Saturn’s moon Titan with wings strapped to his arms.

Factoring in Titan’s gravity and atmospheric density, Lerman found that a person could take flight in a normal-sized wingsuit only if they could run at 11 meters per second.

“This speed has been reached but only by the fastest human runners, for example, Usain Bolt, who ran almost 12 m/s,” Lerman wrote. “For an average human to take off with the standard wingsuit they would require some sort of propulsion device to give them enough speed to take off.”

(H. Lerman, B. Irwin, and P. Hicks, “P5_1 You Can Fly,” Journal of Physics Special Topics, University of Leicester, Oct. 22, 2013.)

Bad Seafood

In 1993, Greenland issued a 7.25-krone stamp depicting a locally fished crab that it labeled Chionoecetes oiliqo. The stamps were issued first in sheet form, but when they were reissued five months later in an eight-stamp booklet pane, collectors noticed something odd: The crabs’ Latin name had changed to Chionoecetes opilio.

What had happened? It turns out that the second name is correct; apparently during production the species name opilio had been mirror-reversed by accident. By a very unlikely coincidence, in the sans-serif typeface used all of its letters reversed into valid counterparts, producing a meaningless word that looked plausibly Latin and got past the inspectors.

The original stamps are now collectors’ items.

(Jim Puder, “OILIQO, The Looking-Glass Crab,” Word Ways 36:4 [November 2003], 243-246.)

Double Trouble

Arthur and Robert are identical twins. One always lies, and the other always tells the truth, but you don’t know which is the liar. One day you meet one of them and want to find out whether it’s Arthur or Robert. But you can ask only one yes/no question, and the question can’t contain more than three words. What question will do? Alternatively, suppose you want to find out whether it’s Arthur or Robert who’s truthful. What three-word yes/no question will reveal the answer?

Click for Answer



Argentina had a surprise on July 10, 1945: The German submarine U-530 turned up at Mar del Plata and surrendered. Commander Otto Wermuth said that he’d received orders on May 8 to cease hostilities and proceed to the nearest United Nations port for surrender. He’d thought this was an enemy trick and decided to intern his submarine and crew in a neutral country. He chose Argentina thinking that it had not declared war and turned up there two months after the German surrender.

That created a fertile field for speculation that the sub had been transporting Nazi gold or leaders to South America — Wermuth was blamed for sinking the Brazilian cruiser Bahia (later disproven), and one reporter even claimed that he’d seen a mysterious sub putting ashore an officer and a civilian who might have been Adolf Hitler and Eva Braun.

“In answer to questions, WERMUTH said that he did not know of any other submarines which were headed for Argentina, that he had been in touch with no other submarines,” read the intelligence report. “He added the somewhat enigmatic remark, however, that if any more were coming they would arrive within a week of his arrival. The reason for this statement was not given.”

Löb’s Paradox

A paradox by the German mathematician Martin Löb:

Let A be any sentence. Let B be the sentence: ‘If this sentence is true, then A.’ Then a contradiction arises.

Here’s the contradiction. B makes the assertion “If B is true, then A.” Now consider this argument. Assume B is true. Then, by B, since B is true, A is true. This argument shows that, if B is true, then A. But that’s exactly what B had asserted! So B is true. And therefore, by B, since B is true, A is true. And thus every sentence is true, which is impossible.

(Lan Wen, “Semantic Paradoxes as Equations,” Mathematical Intelligencer 23:1 [December 2001], 43-48.)