“A Dimensional Howler”

The 1961 GCE O-level exam included this question:

If one square yard of material costs 18 pence, what is the price of one square foot?

One student considered:

1 square yard costs 18 pence.

Therefore 1 yard costs \sqrt{18} , or 4.243, pence.

Therefore 1 foot costs 4.243 ÷ 3 = 1.414 pence.

Therefore 1 square foot costs 1.4142 = 2 pence.

(Via Eureka.)

05/26/2026 UPDATE: Reader Catalin Voinescu adds:

For more dimensional fun, check out ‘ohms per square’ (symbol: capital omega divided by a literal square). The resistance of sheet material depends only on the shape of the object, not on the scale (assuming the thickness of the sheet stays the same). Any square of a given material, of any size, has the same resistance when measured between opposite edges. Longer, narrower shapes have higher resistance, and shorter, wider ones have lower resistance, but only the aspect ratio matters, not the actual dimensions. So the resistivity of conductive sheet is expressed as the resistance of a square piece of that material: ohms per square. This unit is used in electrical engineering, where thin conductive layers and foils are common, most obviously in PCB manufacturing, but also in the manufacturing of resistors, capacitors, semiconductors, batteries and solar panels.

(Thanks, Catalin.)

| Science & Math

Riding Along

https://www.flickr.com/photos/vanamonde81/15628715671/
Image: Flickr

A striking observation in Far From the Madding Crowd:

To persons standing alone on a hill during a clear midnight such as this, the roll of the world eastward is almost a palpable movement. The sensation may be caused by the panoramic glide of the stars past earthly objects, which is perceptible in a few minutes of stillness, or by the better outlook upon space that a hill affords, or by the wind, or by the solitude; but whatever be its origin, the impression of riding along is vivid and abiding. The poetry of motion is a phrase much in use, and to enjoy the epic form of that gratification it is necessary to stand on a hill at a small hour of the night, and, having first expanded with a sense of difference from the mass of civilised mankind, who are dreamwrapt and disregardful of all such proceedings at this time, long and quietly watch your stately progress through the stars.

“After such a nocturnal reconnoitre it is hard to get back to earth, and to believe that the consciousness of such majestic speeding is derived from a tiny human frame.”

| Literature · Oddities

Milestones

“In the beginning God created the heaven and the earth. This beginning of time, according to our chronology, happened at the start of the evening preceding the 23rd day of October in the year of the Julian Calendar, 710 [4004 B.C.].” — James Ussher, The Annals of the World, 1658

“The Middle Ages ended on July 16, 1453, at 12 o’clock meridian, and the Reformation was not launched by Martin Luther until October 31, 1517, at 10:15 a.m.” — H.L. Mencken, “The Collapse of Protestantism,” American Mercury, March 1925

“On or about December 1910 human character changed.” — Virginia Woolf, “Mr. Bennett and Mrs. Brown,” 1924

| History

New Leaves

https://commons.wikimedia.org/wiki/File:John_Constable_-_Wivenhoe_Park,_Essex,_1816.jpg

Constable said that the superiority of the green he uses for his meadows derives from the fact that it is composed of a multitude of different greens. What causes the lack of intensity and of life in verdure as it is painted by the common run of landscapists is that they ordinarily do it with a uniform tint. What he said about the green of the meadows can be applied to all the other tones.

— Eugène Delacroix, Journal

| Art

Dark Matter

Merriam-Webster points out something I’d never noticed: In many languages, the word for night consists of the word for eight preceded by the letter N:

English: N + eight = Night
German: N + acht = Nacht
French: N + huit = Nuit
Spanish: N + ocho = Noche
Italian: N + otto = Notte
Portuguese: N + oito = Noite

It’s a coincidence. Romance languages derive their words for eight and night from the Latin octo and noctem, and the Germanic languages get them from the Old High German ahto and the Germanic naht. In each case the similarity of the sounds is just happenstance.

(Thanks, Sharon.)

| Language

Snunkoople

In each of these pairs of nonsense words, which is funnier?

  • quingel vs. heashes
  • prousup vs. mestins
  • finglam vs. cortsio
  • witypro vs. octeste
  • rembrob vs. sectori
  • pranomp vs. anotain
  • fityrud vs. tessina

If you’re like most people, you’ll find the first word in each pair funnier than the second. In a 2015 study, University of Alberta psychologist Chris Westbury found that the difference is explained surprisingly well by Shannon entropy, which here measures the unlikelihood of each combination of letters: Outlandish specimens such as yuzz-a-ma-tuzz, oobleck, truffula, and sneetch, all from Dr. Seuss, seem funnier than, say, clester, which might plausibly be a real word. (Schopenhauer had argued that humor results from the violation of expectations.)

“The results show that the bigger the difference in the entropy between the two words, the more likely the subjects were to choose the way we expected them to,” Westbury said. Indeed, the most accurate subject chose correctly 92 percent of the time. “To be able to predict with that level of accuracy is amazing. You hardly ever get that in psychology, where you get to predict what someone will choose 92 percent of the time.”

Interestingly, Westbury had to omit vulgar-sounding nonwords (whong, dongl, shart, focky, clunt) before he even got started — these were so consistently considered funny that they would have interfered with the rest of the examination.

(Chris Westbury, et al., “Telling the World’s Least Funny Jokes: On the Quantification of Humor as Entropy,” Journal of Memory and Language 86 [2016]: 141-156.)

| Language