In any language, the most frequently used word occurs about twice as often as the second most frequent word, three times as often as the third most frequent word, and so on.
In American English text, the word the occurs most frequently, accounting for nearly 7% of all word occurrences. The second most frequent word, of, accounts for slightly over 3.5% of words, and so on.
This pattern obtains even in non-natural languages like Esperanto. It’s named for American linguist George Kingsley Zipf, who popularized it.
12/24/2021 UPDATE: Apart from languages, the law is observed in measurements of the citations of scientific papers, web hits, copies of books sold, telephone calls, the magnitude of earthquakes, the diameter of moon craters, the intensity of solar flares, the intensity of wars, and the populations of cities. See this paper. (Thanks, Snehal.)
Thomas More’s Utopia gives us not only a description of that imaginary land but the actual alphabet used there: More’s friend Peter Giles wrote an addendum to the book that presents the letters and gives an example of the Utopian writing system:
Vtopos ha Boccas peu la chama polta chamaan.
Bargol he maglomi Baccan foma gymno sophaon.
Agrama gymnosophon labarembacha bodamilomin.
Voluala barchin heman la lauoluola dramme pagloni.
This is translated into Latin as
Utopus me dux ex non insula fecit insulam.
Una ego terrarum omnium absque philosophia
Civitatem philosophicam expressi mortalibus
Libenter impartio mea, non gravatim accipio meliora.
And in English this becomes
The commander Utopus made me into an island out of a non-island.
I alone of all nations, without philosophy,
Have portrayed for mortals the philosophical city.
Freely I impart my benefits; not unwillingly I accept whatever is better.
Working backward, this makes it possible to divine the meaning of a few Utopian words: boccas is commander, chama is island, voluala is willingly, and gymnosophaon is philosophy. You couldn’t really talk about much beyond perfect societies, but maybe that’s the point.
Just a charming little anecdote: When German chemist Adolf von Baeyer achieved a long-sought result, he tipped his hat to it:
Eventually, however, even Baeyer was supersaturated with these hydrogenations, and the sorely tried assistants hailed with deep relief the transference of his interest to succinylsuccinic ester and diketocyclohexane. By means of a dodge (‘Kunstgriff’) of which Baeyer was very proud (treatment with sodium amalgam in presence of sodium bicarbonate), the diketone was reduced to quinitol. At the first glimpse of the crystals of the new substance Baeyer ceremoniously raised his hat!
It must be explained here that the Master’s famous greenish-black hat plays the part of a perpetual epithet in Prof. Rupe’s narrative. As the celebrated sword-pommel to Paracelsus, so this romantic hard-hitter or ‘alte Melone’ to Baeyer: the former was said to contain the vital mercury of the mediaeval philosophers; the latter certainly enshrined one of the keenest chemical intellects of the modern world. … Baeyer’s head was normally covered. Only in moments of unusual excitement or elation did the Chef remove his hat: apart from such occasions his shiny pate remained in permanent eclipse.
(From his colleague John Read’s 1947 book Humour and Humanism in Chemistry.)
“Some of us wish to send you a word at this sad Christmastide,” it ran. “The Christmas message sounds like mockery to a world at war, but those of us who wished, and still wish, for peace may surely offer a solemn greeting to such of you who feel as we do.”
Though our sons are sent to slay each other, and our hearts are torn by the cruelty of this fate, yet through pain supreme we will be true to our common womanhood. We will let not bitterness enter into this tragedy, made sacred by the life-blood of our best, nor mar with hate the heroism of their sacrifice. Though much has been done on all sides you will, as deeply as ourselves, deplore — shall we not steadily refuse to give credence to those false tales so free told us, each of the other?
We hope it may lessen your anxiety to learn we are doing our utmost to soften the lot of your civilians and war prisoners within our shores, even as we rely on your goodness of heart to do the same for ours in Germany and Austria.
The following spring they received a reply:
If English women alleviated misery and distress at this time, relieved anxiety, and gave help irrespective of nationality, let them accept the warmest thanks of German women and the true assurance that they are and were prepared to do likewise. In war time we are united by the same unspeakable suffering of all nations taking part in the war. Women of all nations have the same love of justice, civilization and beauty, which are all destroyed by war. Women of all nations have the same hatred for barbarity, cruelty and destruction, which accompany every war.
Women, creators and guardians of life, must loathe war, which destroys life. Through the smoke of battle and thunder of cannon of hostile peoples, through death, terror, destruction, and unending pain and anxiety, there glows like the dawn of a coming better day the deep community of feeling of many women of all nations.
It was signed by 155 women of Germany and Austria.
In the “language of flowers,” a meaning is assigned to every flower in a bouquet, so that it’s possible to send a message to your beloved without saying a word. The trouble is that different dictionaries give different meanings. In Collier’s Cyclopedia of 1882, they get very specific:
American starwort: Cheerfulness in old age.
Apple (blossom): Fame speaks him great and good.
Balsam, red: Touch me not.
Bay leaf: I change but in death.
Bud of white rose: Heart ignorant of love.
Butterfly weed: Let me go.
Camellia japonica, red: Unpretending excellence.
Camomile: Energy in adversity.
Cape jasmine: I’m too happy.
Carnation, deep red: Alas! for my poor heart.
Chinese chrysanthemum: Cheerfulness under adversity.
Cistus, gum: I shall die tomorrow.
Citron: Ill-natured beauty.
Convolvulus: Worth sustained by judicious and tender affection.
Corchorus: Impatient of absence.
Damask rose: Brilliant complexion.
Geranium, lemon: Unexpected meeting.
Geranium, nutmeg: Expected meeting.
Helmet-flower: Knight-errantry.
Hemlock: You will be my death. [!]
Hundred-leaved rose: Dignity of mind.
Japan rose: Beauty is your only attraction.
Laurestina: I die if neglected.
Locust tree (green): Affection beyond the grave. [!]
Meadow saffron: My best days are past.
Mistletoe: I surmount difficulties.
Mourning bride: Unfortunate attachment. I have lost all.
Mulberry tree (black): I shall not survive you.
Persimmon: Bury me amid nature’s beauties.
Poppy, scarlet: Fantastic extravagance.
Rose, Christmas: Tranquilize my anxiety.
Rose, daily: Thy smile I aspire to.
Scarlet lychnis: Sunbeaming eyes.
Sorrel, wild: Wit ill-timed.
Spindle tree: Your charms are engraven on my heart.
Straw, broken: Rupture of a contract.
Tiger flower: For once may pride befriend me.
Virginian spiderwort: Momentary happiness.
Zinnia: Thoughts of absent friends.
“How charmingly a young gentleman can speak to a young lady, and with what eloquent silence in this delightful language. How delicately she can respond, the beautiful little flowers telling her tale in perfumed words; what a delicate story the myrtle or the rose tells!” But I think only florists could do this articulately.
Conductor and musical lexicographer Nicolas Slonimsky composed a “Möbius Strip Tease” in 1965, while he was teaching at UCLA. The text reads:
Ach! Professor Möbius, glörious Möbius
Ach, we love your topological,
And, ach, so logical strip!
One-sided inside and two-sided outside!
Ach! euphörius, glörius Möbius Strip-Tease!
Slonimsky described the piece as “a unilateral perpetual rondo in a linearly dodecaphonic vertically consonant counterpoint.” The instructions on the score read: “Copy the music for each performer on a strip of 110-b card stock, 68″ by 6″. Give the strip a half twist to turn it into a Möbius strip.” In performance the endless score rotates perpetually around each musician’s head. (That’s Slonimsky above, trying it out with John Cage.)
The score is here if you’d like to try it yourself. Be careful.
Here’s an oddity: In 1882 Lewis Carroll collaborated on a song with the dreaming imagination of his friend the Rev. C.E. Hutchinson of Chichester. Hutchinson had told Carroll of a strange dream he’d had:
I found myself seated, with many others, in darkness, in a large amphitheatre. Deep stillness prevailed. A kind of hushed expectancy was upon us. We sat awaiting I know not what. Before us hung a vast and dark curtain, and between it and us was a kind of stage. Suddenly an intense wish seized me to look upon the forms of some of the heroes of past days. I cannot say whom in particular I longed to behold, but, even as I wished, a faint light flickered over the stage, and I was aware of a silent procession of figures moving from right to left across the platform in front of me. As each figure approached the left-hand corner it turned and gazed at me, and I knew (by what means I cannot say) its name. One only I recall — Saint George; the light shone with a peculiar blueish lustre on his shield and helmet as he turned and slowly faced me. The figures were shadowy, and floated like mist before me; as each one disappeared an invisible choir behind the curtain sang the ‘Dream music.’ I awoke with the melody ringing in my ears, and the words of the last line complete — ‘I see the shadows falling, and slowly pass away.’ The rest I could not recall.
He played the melody for Carroll, who wrote a suitable lyric of five verses. Hutchinson disclaimed writing the music, but if he didn’t … who did?
In 1891, a mysterious figure appeared on the streets of London, dispensing pills to poor young women who then died in agony. Suspicion came to center on a Scottish-Canadian doctor with a dark past in North America. In this week’s episode of the Futility Closet podcast we’ll describe the career of the Lambeth Poisoner, whose victims remain uncounted.
We’ll also consider a Hungarian Jules Verne and puzzle over an ambiguous sentence.
In 1984, a diver was working in the beluga whale enclosure at San Diego’s National Marine Mammal Foundation when someone shouted “Out, out, out!” On emerging, the diver asked who had told him to exit the tank, and it turned out that the speaker was the whale itself, Noc, who had lived at the facility since his capture in 1977.
Noc’s keepers had previously heard strange sounds coming from the whale and dolphin enclosure that seemed to resemble people talking in the distance, their words just beyond the limit of comprehension. “We were sceptical at first,” neurobiologist Sam Ridgway told New Scientist. “They were definitely unlike usual sounds for a [beluga], and similar to human voices in rhythm and acoustic spectrum.”
The researchers concluded that he was indeed mimicking human speech, though Noc used his nasal tract to produce sounds, rather than a larynx, as humans do. They had only a short window in which to study the behavior: After four years Noc stopped, either because he’d reached maturity or because he’d lost interest.
Suppose we have a group of n men and n women. Each of the women can find some subset of the men whom she would be happy to marry. And each of the men would be happy with any woman who will have him. Is it always possible to pair everyone off into happy marriages?
Clearly this won’t work if, for example, two of the women have their hearts set on the same man and won’t be happy with anyone else. In general, for any subset of the women, we need to be sure that they can reconcile their preferences so that each of them finds a mate.
Surprisingly, though, that’s all that’s required. So long as every subset of women can collectively express interest in a group of men at least as numerous as their own, it will always be possible to marry off the whole group into happy couples.
The theorem was proved by English mathematician Philip Hall in 1935. Another application of the same principle: Shuffle an ordinary deck of 52 playing cards and deal it into 13 piles of 4 cards each. Now it’s always possible to assemble a run of 13 cards, ace through king, by drawing one card from each pile.
