Passing Tones

If you’re driving on the highway and pass a car traveling in the opposite direction, the frequency of its engine noise seems to drop. In 1980, Liverpool Polytechnic mathematician J.M.H. Peters realized that this pitch drop might be used to estimate the speed of the passing vehicle. Pleasingly, he discovered that each semitone in the interval corresponds to 21 miles per hour (to within 2 percent). If the other car’s engine seems to descend a whole tone in pitch as it passes you, then it’s traveling at approximately 43 mph; if it drops a minor third then it’s traveling at 64 mph; and so on.

“The reader should practise by humming a given note pianissimo increasing gradually to fortissimo at which point the hum is lowered by a chosen interval, … diminishing again to pianissimo, this being meant to imitate the effect of being suddenly passed on a quiet country lane by a fast moving high powered motor vehicle.”

(J.M.H. Peters, “64.8 Estimating the Speed of a Passing Vehicle,” Mathematical Gazette 64:428 [June 1980], 122-124.)

03/03/2025 UPDATE: My mistake — the observer is stationary, not moving. Thanks to readers Seth Cohen and Jon Jerome for pointing this out. The cited paper is behind a paywall, but the Physics Stack Exchange had a discussion on the same topic in 2017.

By the Book

The classic, of course, is the story that tells how Mrs. Webster once accidentally walked into a room and found her husband kissing the maid. ‘Noah!’ she exclaimed, ‘I’m surprised.’ Noah, ever the verbalist, was nonplussed. ‘No, my dear,’ he corrected. ‘It is I who am surprised. You are astonished.’

— Evan Esar, Humorous English, 1961

All Together Now

In March 1985, Science Digest published four pangrams composed by its readers — each 26-letter sentence uses every letter in the English alphabet:

Shiv cwm lynx, fjord qutb, zap keg. (Randall Kryn) “A powerful Islamic saint (qutb) who lives in a fjord is told first to knife a troublesome lynx that lives in a mountain hollow (cwm) and then to celebrate by awesomely attacking a keg of brew.”

Schwyz fjord map vext Qung bilk. (Brian Phillips) “A cheat (bilk) from the Qung tribe in southern Africa could not understand a map of fjords in Schwyz, a canton of Switzerland.”

Fly vext bird; zag cwm’s qoph junk! (Kent Teufel) “A blimp explodes, shattering a sign in Hebrew. Pieces of qoph, the nineteenth letter of the Hebrew alphabet, fall into a cwm. An annoyed, low-flying bird is told to zag in order to avoid the falling pieces.”

Qoph’s jag biz vext drunk cwm fly. (Falko Schilling) “The business of making the sharp notched edge on the nineteenth letter of the Hebrew alphabet irritated the inebriated fly from the mountain hollow.”

All the words appear in Webster’s Third New International Dictionary.

Last November, the National Security Agency published five pangram crosswords — in each completed grid, every letter of the alphabet must appear once.

Fair and Square

https://commons.wikimedia.org/wiki/File:Going_over_the_top_02.jpg

From Good-Bye to All That, poet Robert Graves’ 1929 account of his experiences in World War I:

Beaumont had been telling how he had won about five pounds’ worth of francs in the sweepstake after the Rue du Bois show: a sweepstake of the sort that leaves no bitterness behind it. Before a show, the platoon pools all its available cash and the survivors divide it up afterwards. Those who are killed can’t complain, the wounded would have given far more than that to escape as they have, and the unwounded regard the money as a consolation prize for still being here.

In 2003, the Journal of Political Economy reprinted this paragraph with the title “Optimal Risk Sharing in the Trenches.”

Going Places

https://archive.org/details/strand-1899-v-17/page/611/mode/2up?view=theater

From the Strand, May 1899:

Our next photograph is a facsimile of an address on a letter that found its way from Spain to the G.P.O., St. Martin’s-le-Grand. Remarkable as it may seem, this specimen of handwriting was deciphered by ‘the blind man of St. Martin’s,’ and the letter safely reached its destination. It is addressed to the ‘Spanish Ambassador (or Embassy), London.’

(The “blind men” were “the decipherers of illegible and imperfect addresses” in the returned letter office of the General Post Office. Further examples.)

Rapid Transit

https://archive.org/details/strand-1899-v-17/page/492/mode/2up?view=theater

A striking technology described in Strand, April 1899: The speck is a bundle of hay descending along a wire over a lake in Western Norway.

The Norwegians, who live for weeks and months in the summer on the great heights on either side of their beautiful valleys, send down milk, cheese, hay, etc. to the farms below by suspending them on inclined wires fastened at one end firmly to the ground and at the other to some point on the rocks above.

The snap-shot shows a bundle of hay on its way from a great height on one side of the lake to the farm on the other side. It sped along, the friction causing it to shed sparks in all directions, and was timed to take forty-four seconds.

The editors add: “If the bundle be closely examined the constriction caused by the cord holding it together is distinctly visible.”

Zeckendorf’s Theorem

https://commons.wikimedia.org/wiki/File:Zeckendorf_representations_89px.png

Every positive integer can be represented uniquely as the sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers.

Above, 51 = 34 + 13 + 3 + 1.

Discovered in 1952 by Dutch mathematician Gerrit Lekkerkerker (and remarked 20 years later by Edouard Zeckendorf).

Variations

https://commons.wikimedia.org/wiki/File:Mona_Lisa_face_hybrid_image.jpg

Illusion Diffusion uses Stable Diffusion to produce illusion artwork.

The image above was produced by uploading an image of the Mona Lisa and specifying the prompt “colour photograph of an Italian city in the Renaissance” (illusion strength 1 and seed 0).

Below is Vermeer’s Girl With a Pearl Earring modified with the prompt “Amsterdam canals in 17th century” (illusion strength 1.8 and seed 0).

https://commons.wikimedia.org/wiki/File:Girl_with_a_pearl_earring_hybrid_image.jpg#filelinks

In a Word

https://commons.wikimedia.org/wiki/File:William_Gaddis_1975.jpg

scribacious
adj. fond of writing

moiler
n. a toiler; a drudge

demiss
adj. downcast; humble; abject

guerdon
n. a reward, recompense, or requital

By the end of the 1960s, William Gaddis had secured an advance and an NEA grant that allowed him to work full-time on the novel J R.

“Even then, however, Gaddis would be so in need of money that he would ghostwrite articles for a dentist in exchange for root canals. His son recalls one day happening to find his checkbook, and noting the balance, meticulously calculated, of twelve cents. This was at the time when Gaddis had just won the 1976 National Book Award.”

From Joseph Tabbi’s introduction to Gaddis’ “Treatment for a Motion Picture on ‘Software'” in The Rush for Second Place: Essays and Occasional Writings, 2002.