Reverse Angle

Just a little detail that I thought was interesting: Famously the moon appears larger when it’s near the horizon, but you can defeat this illusion by bending over and viewing it between your legs.

Why this works isn’t clear — possibly it’s because the image is inverted on the retina, or it may be an effect of inverting the body’s orientation.

(Stanley Coren, “The Moon Illusion: A Different View Through the Legs,” Perceptual and Motor Skills 75:3 [1992], 827-831; Atsuki Higashiyama and Kohei Adachi, “Perceived Size and Perceived Distance of Targets Viewed From Between the Legs: Evidence for Proprioceptive Theory,” Vision Research 46:23 [2006], 3961-3976.)

“A Vignette”

Here’s a creepy fragment by English ghost story writer M.R. James, published shortly after his death in 1936 — he’s recalling a memory from his childhood, when, alone one day in his father’s Suffolk rectory, he had looked out upon a wooden gate in a grove of trees:

As was but right it was shut, and nobody was upon the path that led to it or from it. But as I said a while ago, there was in it a square hole giving access to the fastening; and through that hole, I could see — and it struck like a blow on the diaphragm — something white or partly white. Now this I could not bear, and with an access of something like courage — only it was more like desperation, like determining that I must know the worst — I did steal down and, quite uselessly, of course, taking cover behind bushes as I went, I made progress until I was within range of the gate and the hole. Things were, alas! worse than I had feared; through that hole a face was looking my way. It was not monstrous, not pale, fleshless, spectral. Malevolent I thought and think it was; at any rate the eyes were large and open and fixed. It was pink and, I thought, hot, and just above the eyes the border of a white linen drapery hung down from the brows.

There is something horrifying in the sight of a face looking at one out of a frame as this did; more particularly if its gaze is unmistakably fixed upon you. Nor does it make the matter any better if the expression gives no clue to what is to come next. I said just now that I took this face to be malevolent, and so I did, but not in regard of any positive dislike or fierceness which it expressed. It was, indeed, quite without emotion: I was only conscious that I could see the whites of the eyes all round the pupil, and that, we know, has a glamour of madness about it. The immovable face was enough for me. I fled, but at what I thought must be a safe distance inside my own precincts I could not but halt and look back. There was no white thing framed in the hole of the gate, but there was a draped form shambling away among the trees.

“Do not press me with questions as to how I bore myself when it became necessary to face my family again. That I was upset by something I had seen must have been pretty clear, but I am very sure that I fought off all attempts to describe it. Why I make a lame effort to do it now I cannot very well explain: it undoubtedly has had some formidable power of clinging through many years to my imagination. I feel that even now I should be circumspect in passing that Plantation gate; and every now and again the query haunts me: Are there here and there sequestered places which some curious creatures still frequent, whom once on a time anybody could see and speak to as they went about on their daily occasions, whereas now only at rare intervals in a series of years does one cross their paths and become aware of them; and perhaps that is just as well for the peace of mind of simple people.”


City A contains 20,000 people. One percent of these have one foot only and wear one shoe apiece. Half of the remaining people go barefoot, wearing no shoes at all, and the rest wear two shoes apiece.

In City B, 20 percent of the residents have one foot only and wear one shoe apiece. Of the remainder, half go barefoot and half wear two shoes apiece.

If 20,000 shoes are worn in City B, what is its population?

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The Kopp–Etchells Effect

In desert conditions, helicopter rotors are sometimes surrounded by sparkling rings. When flying sand strikes the abrasion strips on the leading edges of the blades, clouds of eroded titanium particles ignite as they’re exposed to oxygen.

The effect is most visible at night when the aircraft is near the ground, but it’s been observed as high as 1700 feet. It’s named after Benjamin Kopp and Joseph Etchells, two soldiers killed in combat in Afghanistan in July 2009.

The Einstellung Effect

Psychologist Abraham S. Luchins discovered a discouraging phenomenon in 1942: When people find a problem-solving strategy that works successfully in multiple trials, they’ll tend to adopt the same strategy even in situations when more efficient solutions are available.

Suppose you’re given water jugs with capacities of 21 units (A), 127 units (B), and 3 units (C) of water. Then you’re asked to use these to measure out 100 units of water. You find that you can do this by filling jug B and using that to fill jug A once and jug C twice, leaving 100 units in jug B. In several similar problems you find that this strategy, B – A – 2C, works.

But then you’re given an “extinction problem” in which this strategy doesn’t work. And in the next problem you’re given jugs of capacity 15, 39, and 3 and asked to measure 18 units of water. The old strategy, B – A – 2C, works here, but there’s a simpler solution: A + C.

In Luchins’ experiments, a control group that had not been primed with the early B – A – 2C successes hit immediately on the A + C solution in the last test. But subjects who did have those early successes tended to revert to the original strategy, reflecting a “mechanized” state of mind that prevented them from seeking more efficient solutions. When Luchins told them “Don’t be blind,” more than half of them found the A + C solution.

The reasons for this are still being studied in different populations and with different types of tasks. Luchins acknowledges that habit can be useful, but notes that when, “instead of the individual mastering the habit, the habit masters the individual — then mechanization is indeed a dangerous thing.”

(Abraham S. Luchins, “Mechanization in Problem Solving: The Effect of Einstellung,” Psychological Monographs 54:6 [1942]: i.)

The Golden Arrowhead

The flag of Guyana was designed by a college student. In 1960, as that country was emerging from British colonial rule, Whitney Smith, then a 20-year-old undergraduate at Harvard, wrote to independence leader Cheddi Jagan and asked what flag the new country had chosen. Jagan told him no decision had been made and asked him for ideas. Smith designed a flag, got his mother to sew it, and sent it in, and Guyana adopted it, with some slight modifications.

Smith went on to create the journal Flag Bulletin; found the Flag Research Center; design flags for the Saudi Navy, Bonaire, and Aruba; organize the First International Congress of Vexillology (and coin that term); help to found the North American Vexillological Association and the Flag Heritage Association; and write The Flag Book of the United States, Flag Lore of All Nations, and more than 250 flag histories for the Encyclopaedia Britannica.

“I’m a monomaniac, that’s clear,” he told People magazine. “But I’m more fortunate than most people because I have something that infuses my whole life. I relate flags to everything.”


Lime juice is phototoxic — on contact it sensitizes the skin to ultraviolet light, so that exposure to sunlight can then produce redness, itching, burning, and even blisters.

The reaction is called phytophotodermatitis, or margarita photodermatitis. It can also be caused by celery, parsnips, parsley, and figs.

Image: Wikimedia Commons

The dome in Vienna’s Jesuit Church isn’t there — artist Andrea Pozzo painted the ceiling of the nave in 1703 to create a convincing illusion when viewed from the right angle.

A stone slab in the floor indicates the ideal spot from which to view it.

In a Word

n. an introduction to some branch of learning

In Umberto Eco’s Foucault’s Pendulum (1988), two publishers propose a School of Comparative Irrelevance that teaches “useless or impossible courses,” such as Urban Planning for Gypsies, Aztec Equitation, and Potio-section.

‘Potio-section, as everybody knows, of course, is the art of slicing soup. No, no,’ he said to Diotallevi. ‘It’s not a department, it’s a subject, like Mechanical Avunculogratulation or Pylocatabasis. They all fall under the heading of Tetrapyloctomy.’

‘What’s tetra …?’ I asked.

‘The art of splitting a hair four ways. This is the department of useless techniques. Mechanical Avunculogratulation, for example, is how to build machines for greeting uncles. We’re not sure, though, if Pylocatabasis belongs, since it’s the art of being saved by a hair. Somehow that doesn’t seem completely useless.’

Overall, the school’s aim is “to turn out scholars capable of endlessly increasing the number of unnecessary subjects.” “The Tetrapyloctomy department has a preparatory function; its purpose is to inculcate a sense of irrelevance. Another important department is Adynata, or Impossibilia. Like Urban Planning for Gypsies. The essence of the discipline is the comprehension of the underlying reasons for a thing’s absurdity. We have courses in Morse syntax, the history of antarctic agriculture, the history of Easter Island painting, contemporary Sumerian literature, Montessori grading, Assyrio-Babylonian philately, the technology of the wheel in pre-Columbian empires, and the phonetics of the silent film.”

(Thanks, Macari.)